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Denver Montessori Junior/Senior High School

Innovation Plan

Respectfully submitted by:

Katy Myers Principal

Denver Montessori Junior/Senior High School (303) 431-2385

[email protected]

mailto:[email protected]

Denver Montessori Junior/Senior High School Co-located with Gilpin Montessori Public School 2949 California St.

Denver, CO 80205

(720) 424-2600 dmhs.dpsk12.org

December 19, 2012

Board of Education 900 Grant St. Denver, CO 80203

Dear Board of Education,

Thank you for the opportunity to submit this Innovation plan on behalf of Denver Montessori Junior/Senior High School. Please find enclosed the plan, requested waivers, and the finalized budget. I have also included the original school design as presented in the Performance School Application. This school design was thought out and presented to the Board of Education during the 2012 Call for Quality Schools and was unanimously approved in June, 2012.

This submission builds on the Performance School Application by providing a list of waiver requests and detailed replacement policy language regarding State, District and DCTA agreements. These waivers and replacement policies will allow DMHS to run the school consistent with the vision and mission as outlined in the school’s Performance Plan Application.

I look forward to your questions and ideas as we move forward through the Innovation approval process.

Sincerely,

Katy Myers Principal Denver Montessori Junior/Senior High School

Table of Contents:

Part I: Innovation Plan Statements

Mission Statement: Page 2

Succession Plan and School Governance: Page 4

Efficiencies, Cost Savings, NCLB Page 8

Part II: Requested Waivers and Replacement Policies

District Policies Page 10

DCTA Policies Page 34

State Policies Page 40

Part III: Evidence of Support Page 47

Part IV: Curriculum Components

DMHS Alignment to DPS Graduation Standards 5

DMHS Evidence of Math Curricular Alignments Page 65

Part V: Performance School Application Page 103

Part I: Innovation Plan Statements

Innovation Plan Denver Montessori Junior/Senior HS

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Mission Statement

Denver Montessori Junior/Senior High School (DMHS) will combine Montessori best practices with current research on adolescent brain development to provide a learning environment that promotes high achievement for each student while also supporting them socially and emotionally. Graduates, regardless of ethnicity or income status, will be prepared for college or a career as well as demonstrate ingenuity, adaptability, creativity, initiative and excellent communication and problem solving skills.

1. How will innovation status help you more fully realize your mission?

DMHS is requesting Innovation Status through the DPS Innovation School Application. For a school to achieve excellence, it must hold on to its vision and implement the vision as clearly and effectively as possible. DMHS will require the innovative school status to maintain fidelity to its mission and vision.

Montessori secondary education focuses on the whole child, self- construction,

valorization and preparation for adult life. By creating a high quality 7th through 12 grade program on these principles, students will graduate with the academic skills necessary to thrive in both post secondary education or career options, while at the same time have well developed communication and problem solving abilities along with strong interpersonal relationship skills. Finally, they will have developed creativity, ingenuity, adaptability and initiative through the many problem solving, community building and real world experiences they will encounter at DMHS.

During year one and possibly year two, DMHS will also have 6th grade in order to

provide continuity to Gilpin students as that program ends after 5th grade. Both DMHS and Gilpin would like to see 6th grade eventually remain with Gilpin, as that is fundamentally how Montessori grade orientations are configured. In Montessori, 4th, 5th

and 6th grade students work together within an “upper elementary” classroom. Sandoval and Denison currently have this upper elementary configuration, and Lincoln will also retain its sixth grade students in their upper elementary classrooms starting next year (2013).

Montessori secondary schools are divided into two “sub-planes”. The 7th - 9th

grade program is a land based program with real life problems solving scenarios. Students combine didactic, academic lessons with real world scenarios. They are daily working with both their head and their hands to deeply internalize academic concepts. The 10th - 12th grade program is a highly academic program preparing students for university. Having come through the Montessori program to this point, students are well able and ready to handle the most rigorous content. The high school remains centered on core Montessori values. This includes Montessori trained teachers, long periods of uninterrupted work time, key lessons, and a variety of methods whereby a student can


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demonstrate mastery of knowledge. Assessments will include rubrics, portfolios, presentations, quizzes on vocabulary and skills, end of unit knowledge assessments plus all Federal and Colorado State mandated testing.

The 6th grade through 12th grade Montessori curriculum that DMHS will

implement is rigorous, innovative, interesting and is designed to engage students to produce optimal academic achievement as well as social and emotional maturity and well-being. Montessori adolescent curriculum has been designed and tested over the last fifteen years at both private and public Montessori schools. This curriculum, referenced throughout this application as Montessori National Curriculum, has been collected, refined and reported through The NAMTA Journal, A Montessori National Curriculum Report, The NAMTA Journal, Volume 37, No. 1, Winter 2012. DMHS will design its program using this curriculum. Recently, the Montessori National Curriculum for the Adolescent Program from Twelve to Fifteen/Sixteen Years was reviewed by the Australian Curriculum Assessment and Reporting Authority. Their findings, as reported in A National Montessori Curriculum Report, are as follows: ACARA (Australian Curriculum Assessment and Reporting Authority) established an extremely rigorous recognition process to determine the extent to which a well-established alternative national curriculum can deliver comparable educational outcomes for students to those based on the Australian National Curriculum. ACARA have advised that (the National Montessori Curriculum) aligns with the Melbourne Declaration on Educational Goals for Young Australians, meets the particular principles and guidelines in relation to the Shape of the Australian Curriculum v3 paper, and allows for broadly comparable educational outcomes in English, mathematics, science and history by the end of year 10.

In order to effectively implement the curriculum, DMHS will need to adopt its own

schedule, its own standards for hiring teachers, its own school calendar and professional development plan, its own assessments, and, of course the National Montessori Curriculum.

DMHS will be using the National Montessori Curriculum for grades 7-9 for

science, history and language arts. The 7,8,9 Spanish curriculum will be the TPRS curriculum. TPRS matches the meaningful, relative approach that defines Montessori education.

DMHS will use a math curriculum that is individualized for each student

combined with small group lessons. For grades 7 and 8, this math curriculum will be a combination of Khan Academy, Montessori Math materials, project based math, and small group lessons by a highly qualified math teacher. The small group lessons will be designed to meet each student at the particular benchmark the student is currently working, and the teacher will use a variety of instructional methods, including Montessori math materials, to assist the student in mastering that benchmark and preparing to work on the next on-line unit. Students will also be expected to apply math towards a variety of hands-on projects utilizing the farm, the culinary arts program and micro-economy. For grades 9 – 12, the project based math curriculum will be replaced


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with Exeter Math. Exeter math is the math curriculum used by Philips Exeter Academy, and is widely recognized as an innovative college preparatory math curriculum. This 6th grade through 12th grade math curricular approach has been fully aligned to the Common Core State Standards and has been submitted to DPS’ Office of School Reform and Innovation (OSRI).

The high school, grades 10, 11 and 12, will create an integrated college

preparatory curriculum using DPS approved curriculum, with the exception of math as noted above. Compass Montessori High School uses a similar curriculum and curriculum delivery method. Their three year SPF results for this curriculum are a median growth percentile of 58 for reading, 54 for mathematics and 66 for writing, and an academic achievement score for science of 59%. The academic growth gaps achieved a level of exceeds for reading and writing and meets for math. The three year ACT composite is 21.7.

Although the most of the curriculum for high school will be similar to DPS’s

conventional schools, there will still be innovative differences. First, the curriculum will be integrated so that literature studied in Language Arts will, at the same time, support the history curriculum for an overall integrated humanities curriculum. The math and science teacher will work together to insure students are obtaining the mathematical skills needed to work out currently studied complex scientific equations. Linkages between science, math and history will be explored. Throughout all areas of study, there will be in-depth reading and writing instruction.

The schedules for both the junior high and the senior high will support the

Montessori approach. There will be minimal required transition times. Instead, students will be called to small group lesson as those lessons are needed to support the next level of study. This schedule is currently in place at Compass Montessori high school. During the morning, students are independently working on a variety of assignments and further exploration of their current units of study. At the same time, teachers are giving small group lessons to students in math, science, language arts and history. The culture of respect and hard work is resolutely held by both the staff and the students. One hundred percent of the students are on task and engaged because they are enjoying their academic studies. This on task and engaged behavior is the hallmark of Montessori education, and this is what we intend to create at DMHS.

Succession Plan and School Governance

A. Succession Plan

If not addressed in the school’s performance application, please provide specifics of a succession plan (or process) that will ensure consistency and stability in implementing the innovation plan in the school in the case that there are leadership changes.

DMHS will work with the “Self-Governance” leadership model as outlined in

Appendix G of the Performance School Application. During year one and two, the school will have up to 80 students. In order to be economically sustainable, the school


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leader will also work half time in the classroom. During that time, she will work with the other advisors to create a culture of shared leadership. Key leadership roles and responsibilities will be reviewed with staff to insure reasonable redundancies can be created. In year two, a junior high program director will be identified and that person will start attending professional leadership and administration development as offered through DPS. In year three, the school principal will no longer be teaching in order to focus on the well being of DMHS students, data analysis, and professional development for staff. She will also conduct curriculum and programmatic review to insure that 9th grade is successfully meeting DPS high school standards and that DMHS is ready to move forward with adding the high school program. Also In year three, a high school program director will be identified and will start attending professional leadership and administration development as offered through DPS. In year four, the leadership team will consist of the principal, the junior high and the senior high program directors. At that point, the principal will insure that both program directors have the knowledge base needed to assume the principal role of the school should that event be necessary.

The principal’s roles and responsibilities include creating and maintaining the school’s mission and vision, hiring and evaluating staff, maintaining a culture of high expectation regarding behavior and academic achievement, creating and reviewing measurable data systems to insure the students are obtaining a rich and rigorous education, creating and linking staff to professional development, visiting classrooms every day and conducting monthly, longer staff observations, creating and maintaining a welcoming environment for all community members, high level student discipline and attendance.

The program director’s roles and responsibilities include maintaining a culture of high expectations regarding student behavior and academic achievement, daily check in with fellow staff, weekly staff meetings to insure that the school is holding to its mission and vision, ground level parent communication, and resolving low level student conflict and discipline. Program Directors will also be advisors / teachers.

Program directors must be highly qualified teachers who are Montessori trained in both elementary and adolescent education. They need to have completed or be willing to complete a Master’s level leadership program. They must demonstrate either in their DMHS position or in past positions they can create a culture of respect, inclusivity, shared decision-making, recursive learning, and empowering staff to work at their highest level.

Should a leadership change be necessary, both the junior high and senior high program directors will be qualified to become the school leaders. The school staff will work with its School Accountability Committee to interview both candidates along with any other DMHS teachers who are qualified and any outside candidates who are qualified. The staff and School Accountability Committee will interview candidates and determine two finalists through a majority vote conducted by secret ballot in order to maintain confidentiality. The Chairman of the SAC along with one community member shall be in charge of the voting process. The final decision for hiring the new school principal from the two qualified finalists will be made by the School District Superintendant.


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B. School Governance: If not addressed in the school’s performance application, what plans are

being made to ensure that a robust and participatory school governance structure will provide accountability and support to the school?

DMHS will create a vibrant School Accountability Committee (SAC) that will include no less then one staff member along with the principal, three parents and two community members. The SAC will assess school performance based on agreed upon outcomes that include academic goals, student well-being and community involvement. The SAC will meet once per month to discuss school progress and make recommendations to the principal.

Each year, the chairperson of the school accountability committee will insure that the DPS parent satisfaction survey measuring parent satisfaction regarding the school achieving established outcomes is delivered to all parents and guardians. All surveys will be delivered in English and the parent’s native language. Surveys will be anonymous but the SAC chairperson will assess percentage of surveys returned based on school population. If that percentage is less than 75%, the SAC committee will assess the current population and find solutions on how to bring that percentage up to 75%. Should parent satisfaction not meet the standard on the SPF rubric, DMHS will take the following steps:

1. Hold community meetings to determine the root of parent dissatisfaction

2. Increase parent education to insure that parents are comfortable with the Montessori Method and how it is being implemented at DMHS.

3. Create a strategic plan that includes both tactical and strategic steps to resolve parent concerns.

DMHS will use a variety of data points and observation to determine the school leader’s need for coaching and professional development. First, the SAC team will review monthly achievement data and the annual SPF to see if the school has met set targets. Second, the SAC will review annual parent, staff and student surveys to determine the overall health of the school and community opinions of the school. Third, the SAC will meet with a Montessori consultant who will be hired in year 1, 2, 3 and year 5 to observe the school and provide feedback to the SAC, school leadership and staff.

The SAC will use the DPS Framework for Effective School Leadership as their evaluative tool. The principal will also welcome designated DPS leadership to observe the school and provide feedback using the DPS Framework. Every month, the principal will meet with the SAC to discuss the school’s successes and challenges based on data and observation. During those meetings, the principal will seek out feedback regarding current leadership effectiveness. The principal will also solicit feedback from staff and community members during informal meetings. At all times, the DMHS principal will model the value of recursive learning, seeking and accepting feedback, and inclusive problem solving in order to continue to evolve towards distinguished leadership.


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Should the SAC and/or DPS leadership determine that the principal require additional coaching and professional development, the principal, SAC and DPS Leadership will create a professional development plan along with benchmarks to measure progress. Progress will be reviewed monthly. If, after six months, the principal has not made satisfactory improvement, DPS will replace him or her with a program director and begin the search for a new principal.


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Efficiencies, Cost Savings and NCLB

A. What cost savings and/or efficiencies that are projected through attainment of innovation status?

DMHS projects that it will obtain cost efficiencies by using primary source

materials and free on-line programs, such as Khan Academy, versus using conventional textbooks. DMHS also intends to use free resources such as Edmodo and Google Apps for Education.

DMHS will meet or exceed the salary schedule set forth by DPS for teacher and

staff salaries. However, DMHS will use the actual salaries for teachers versus the cost averaging model. This will result in demonstrating the true cost of running a Montessori Junior/Senior high school. DMHS has incorporated into the annual teacher salary, versus as additional costs, time spent on overnight trips, professional development and after school events. This will allow DMHS to offer these very important Montessori elements without making the cost of the school program prohibitive.

By having innovation status, DMHS will be able to complete the hiring process on

a schedule that more closely aligns with the hiring window for high quality Montessori teachers.

B. Will the school continue to comply with the Highly Qualified Teacher requirement of No Child Left Behind?

DMHS will work closely with Denver Public Schools’ Human Resources

Department to insure that the school is in compliance with the Highly Qualified Teacher requirement of No Child Left Behind.1

1 Clarification to CDE: All teachers who teach core content classes will meet the Highly Qualified requirements by holding a

Colorado teaching license and demonstrating subject matter competency.

Part II: Requested Waivers and Replacement Policies

Denver Montessori Junior/Senior High School Request for Innovation Status December 19,

2012

Waivers Requests and Replacement Policies DPS, DCTA, and Colorado State Statutes

School Proposal

CFBA: Evaluation of Evaluators

Human Resource Management: Teacher Evaluation

Policy

Provision shall be made for periodic evaluation of evaluators…All persons who evaluate professional staff members shall possess an administrative certificate issued by the Colorado Department of Education and shall have received education and training in evaluation skills approved by the department. Evaluation instruments for all professional staff administrators shall include a section dealing with their evaluation skills. The superintendent or his/her designee shall review all evaluations done by professional staff administrators and when necessary shall discuss with them procedure and form…the district…shall seek evidence that evaluators are implementing the process in a fair, professional and credible

Replacement Policy

Only the following individuals may serve as evaluators for DMHS: The school principal, the school's program directors at the permission of the school principal, other professional teacher evaluators through the LEAP Peer Observer program. The school principal, as hired by the district, shall be allowed to evaluate professional staff members regardless of whether the administrator has an active administrative certificate. No other individual will have de facto authorization to evaluate staff without the explicit designation by the school principal with the following exceptions: the school principal will continue to be evaluated by the superintendent or his/her designee and will receive feedback on the quality of evaluations being given at the school. The school principal will be responsible for evaluation of other evaluators on campus, but may discuss evaluations with district staff as well to ensure meaningful calibration of scores. P. 43 of PSA

School

Proposal

DF: Revenue from Non Tax Sources/DF-R: Revenue from Non Tax Sources Procedures for School-Based Sponsorships

Budget

Policy

No agreements for sponsorship shall be made with commercial entities that promote products or services that are inconsistent with the mission and image of Denver Public Schools School-Based Sponsorships…These sponsorships include the following components: *involve local commercial entities, *do not conflict with exclusivity agreements within the district, *have district approval for any visibility components involved, *offer a minimum of $10,000 in benefits to the school with ongoing annual visibility for the sponsor, *offer less than $10,000 in benefits to the school but are limited to single season/event visibility., *can be negotiated by the principal with the approval of the superintendent or his/her designee. DF-R: Process: 1. Obtain a Sponsorship Proposal form from the Community Partnership Office, complete, and submit 2. Community Partnership Office will review the proposal 3. The Community Partnership Office will refer the proposal to the Superintendent for review. If appropriate, the Superintendent will present the proposal to the Board of Education for approval. 4. Following approval, the Superintendent will direct that a "Memorandum of Agreement" be developed 5. The appropriate district staff will review and, if appropriate, execute the Agreement. 6. The school(s) will be provided with a copy of the Memorandum of Understanding. Evaluation: Within thirty days of the end of the contract stipulation sponsorship, the Community Partnership Office will provide a Sponsorship Evaluation form to be completed by the principal.

Replacement Policy

School will have the ability to request and secure school-based sponsorships independent of the district according to the following policies: -The sponsorship must not compromise or show inconsistency with the beliefs/values of the district and school. - The sponsorship will not alter any district owned resources unless permission is granted by the district - The sponsorship does not create a real or perceived conflict of interest with school administrators or staff - The sponsorship agreement will be reported to the district budget office at least 30 days before an agreement is to take effect. The budget office will have the ability to refuse the agreement only in situations where said agreement will adversely impact funding arrangements for other schools in the district more than it would benefit Denver Montessori or because it would be in conflict with existing fund regulations (such as federal grants).

School Proposal

EEAA – Walkers and Riders

Student Transportation

Policy

Generally, students eligible to receive transportation provided by the school district if they attend the school serving their residential area and are enrolled in 1. Elementary schools more than one mile walking distance from their home 2. Middle schools more than two and one-half miles walking distance from their home 3. High schools more than three and one-half miles walking distance from their home 4. Magnet and other special educational programs may also have trans-portation provided as approved by the Board. Such transportation will be reviewed annually

Replacement Policy

The School may request that students find alternative methods for transportation to and from school. The principal will work with district budget staff on an annual basis to establish a transportation budget for the school. Based on the budget, the school principal will develop a transportation plan that maximizes the availability of transportation services to students to and from school. Should the school develop a plan that applies a different policy from the one specified in EEAA, the plan will be shared with and approved by the district transportation department and then published and made available to parents no later than 6 weeks prior to the school year. The DMHS 2013 transportation plan will be located on the school's website at dmhs.dpsk12.org.

School Proposal

GBEBA: Staff Dress, Accessories and Grooming for Certificated Staff (Teachers)

Human Resource Management:

Policy

Certificated staff must exercise good judgment in their choice of professional appearance for work or work-related activities by always appearing in a manner: * that is appropriate to the situation, * that will invoke a positive impression from the community, * that provides appropriate role modeling for students, * that promotes a working and learning environment that is free from unnecessary disruption, and * that is conducive to high student and staff performance.

Replacement Policy

The professional appearance of school staff members includes dress, accessories, body adornments, and grooming. Appropriate professional appearance reinforces a shared- vision of the school. Therefore, all staff must exercise appropriate judgment in their choice of professional appearance for work or work-related activities by always appearing in a manner:

* that is appropriate to the situation, * that promotes ideals of respecting others, respecting self and respecting the environment * that demonstrates a readiness to work in all of the school's environments * that promotes a working and learning environment that is free from unnecessary disruption, and * that is conducive to high student and staff performance.

During the work day and any time employees attend work-related activities, employees shall appear in appropriate dress. Items that are not acceptable in the workplace shall be

identified in an annual school dress code by the school principal. The principal is delegated the authority and bears the responsibility for ensuring compliance with the school dress policy and is expected to counsel employees upon initial infractions and implement further disciplinary procedures when violations continue to persist

School Proposal

GBEBA-R: Staff Dress, Accessories and Grooming for Certificated Staff (Teachers)


Policy

Examples of professional attire include, but are not limited to, collared shirts, dress slacks, dress coordinates, suits, dresses, ties, and sport coats. Items that are not acceptable in the workplace include the following: * attire that is prohibited in the student dress code, * shorts or other similar article of clothing shorter than mid-thigh… Principals are delegated the authority and bear the responsibility for ensuring compliance with this policy and are expected to counsel employees and discipline any violators

Replacement Policy

See replacement language for GBEBA (above)

School Proposal

GBEBB: Dress Code for Non-Teaching Staff


Policy

Employees of the District project an image to the community and to students about the professionalism of the District. Therefore, the Board of Education hereby adopts this Dress Code Policy for all non-teaching staff… employees covered by this policy shall adhere to a standard of dress appropriate to their position…Uniformed workers shall continue to wear the approved uniform… Unacceptable items 1. Shorts, dresses, skirts or other similar clothing shorter than mid-thigh length…

Replacement Policy

See replacement language for GBEBA (above)

School

Proposal

GCB: Professional Staff Contracts and Compensation

Human Resource Management: Hiring, Compensation, Job Descriptions

Policy

It is the Board's intent to review all compensation plans annually with representatives of the district's teaching staff. Administrator's salaries shall be determined by Board action with consideration given to the assigned responsibilities and specialized training. Salaries shall be reviewed annually at the regular Board meeting in June, and contracts as appropriate. The school district shall adhere strictly to the employment contract procedures established by Colorado statutes.

Replacement Policy

The school will adhere to district salary schedules for all staff but requires autonomy in determining the years of experience for educators and administrators in order to account for private and other school experience. For exempt employees, the School reserves the right to not provide additional compensation for additional time that occurs during overnight and extended trips, after school meetings, after school activities, school performances, events, or games, evening meetings and professional development. If the school does give compensation for such additional time, the compensation will be provided evenly to all teachers and staff working such additional time. Relative to employment

contracts, the school will have the ability to require teachers obtain specified levels of Montessori training, minimum licensure, and meet requirements for Highly Qualified Teacher status. The school will be able to develop the contract in a way to monitor employee progress toward accomplishing these requirements and terminate the contract when progress is not being met. P. 45-46 PSA.

School Proposal

GCCBB – Administrative & Non-Licensed Leave

Human Resource Management, Personal Leave

Policy

Personal leave -Personal leave is not restricted to reasons of hardship or other pressing business or emergency needs. Personal leave also may be used to extend a period of school intermission or used in conjunction with the observance of a district holiday…Must be pre- approved …Shall not accumulate from year to year. A … form shall be completed. Administrative Staff - An administrator has ...leave annually. Four are paid; …Unused paid personal leave will be automatically converted to sick leave Non-Licensed Support Staff - Employees who work a minimum of 20 hours per week and are not covered by a collective bargaining agreement … shall be granted up to a total of five days Jury Leave- Employees shall be granted leaves of absence for jury service …Full wages and salaries shall be granted … All fees received for such service …shall be turned in to the Disbursing Office …In the event that an employee reporting to the court for jury duty is excused for the day, he shall report to his school or unit for duty within a reasonable time

Replacement Policy

Personal leave is not restricted to reasons of hardship or other pressing business or emergency needs. Personal leave also may be used to extend a period of school intermission or used in conjunction with the observance of a district holiday with specific permission of the principal, or, in the case of the principal, by the principal supervisor. All personal leave must be pre-approved by the supervisor. Unused portions of such leave for personal reasons shall not accumulate from year to year. A "Request for Short Leave of Absence for Personal Reasons" form shall be completed in sufficient time for approval before the time of the requested leave.

An administrator has up to four days of personal leave annually. All other personnel have up to four days of personal leave annually, all paid. Unused paid personal leave will be refunded to staff at the end of every year at the rate of $75 per day. The minimum time allowed per personal day shall be one-half day.

The superintendent may approve short leaves of absence for the Principal without pay for no more than 10 days if such a leave does not interfere with the programs of the school. No short leaves without pay shall be granted during the first or last three weeks of the school year, the last two weeks of the fall semester or the first two weeks of the spring semester. The Principal may approve short leaves of absence for the staff without pay for no more than 10 days if such a leave does not interfere with the programs of the schools. No short leaves without pay shall be granted during the first or last three weeks of the school year, the last two weeks of the fall semester or the first two weeks of the spring semester.

Jury Leave

Employees shall be granted leaves of absence for jury service and when the employee is the subject of a properly issued subpoena. Full wages and salaries shall be granted during such period of jury service. All fees received for such service during regular working days shall be turned in to the Disbursing Office of the school district. Unless otherwise agreed by the supervisor, employees shall take personal leave or vacation if available or leave without pay for leaves attributable to subpoenas.

Other Legal Leaves

Jury or witness fees earned during holidays or vacations may be retained by the employee.

In the event that an employee reporting to the court for jury duty is excused for the day, he shall report to his school or unit for duty within a reasonable time.

School Proposal

GCBC- Professional Staff Supplementary Pay Plans / Overtime (Coaches)

Human Resources, Compensation, Job Descriptions

Policy

Coaches shall not receive any pay, gift or other remuneration for teaching or coaching other than the stipulated contract salary or pay scale agreed upon by the Board of Education. Athletic coaches may be selected and assigned coaching duties for one or more three- month period, i.e., September through November, December through February, and/or March through May. Remuneration shall be on a monthly basis. All coaches shall report for duty on the opening practice dates of their respective sports as set by the Colorado High School Activities Association. In addition, coaches shall attend required meetings and meet all terms and conditions established by the athletic board of control.

Replacement Policy

Should the school elect to hire and pay for coaching duties, then extra duty pay for coaches for the school will be set at an hourly rate for the year by the school principal. The school principal will consult with the school's leadership team to evaluate various proposals for hourly compensation but will eventually make a determination that follows a clear policy for the year that will be equally followed for any school coaches.

School Proposal

GCF: Professional Staff Hiring Human Resource Management: Hiring

Policy

From the list of available candidates for teaching positions in the Denver Public Schools, the superintendent shall recommend those persons best fitted to serve…Applicants for probationary appointments shall be required to have a bachelor's degree…Teachers in the Denver Public Schools shall hold a…teacher certificate…Exceptions to this certification requirement may be made by the superintendent in cases of teachers of adult vocational education and in other unusual cases…Prior to hiring any person, in accordance with state law the district shall conduct background checks Reappointment after resignation: Teachers reappointed to teaching positions after resignation shall be employed on probationary appointments. A teacher who has been absent five years or less may be considered for reappointment at the salary to which he was entitled at the time of resignation. Reappointment of probationary teachers: Reappointment of probationary teachers shall by considered annually at a meeting of the Board prior to June 1.

Replacement Policy

Teachers in the Denver Public Schools shall hold a Type A general teacher certificate, Type B professional teaching certificate, Type C vocational teaching certificate, Type D administrative certificate or Type E special service certificate issued by the Colorado Department of Education. Provisional certificates also shall be accepted. Exceptions to this certification requirement may be made by the superintendent in cases of teachers of adult vocational education and in other unusual cases.

DMHS will work with the district HR office to post teaching positions through the district website. From this posting, DMHS will engage in independent outreach efforts to recruit candidates outside of the centralized recruitment channels.

Teachers shall be hired based on the following criteria: DMHS will create a rubric that values Montessori training, NAMTA or other Montessori Adolescent training, Highly qualified, teacher licensure, demonstrated ability to team teach, experience with

Montessori adolescent programs, and demonstrated understanding and ability to implement a Montessori adolescent program. Initial hiring decisions will be made by the school principal. Subsequent hiring decisions will be made as the school’s “personnel committee”, with final determination to be made by the school principal. The personnel committee shall consist of volunteer representatives from all staffing areas that will be affected by the new hire, such as the teaching team, the program director, special education and support staff. All candidates must pass a DPS background check, which will be conducted through the district HR process.

The school will adhere to district salary schedules for all teachers but requires autonomy in determining the years of experience in order to account for private and other school experience.

School Proposal

GCF-2: Professional Staff Hiring (Athletic Coaches)


Policy

Priority shall be given to hiring qualified athletic coaches from among the regularly certificated teachers employed by the district. Effort shall be made to assign qualified coaches from the existing school faculty. When a program is in jeopardy or a coaching position cannot be filled within the high schools, other certificated teachers or individuals holding a Coaching Registration from the Colorado High School Activities Association who are qualified to coach may be assigned.

Replacement Policy

Should the school elect to hire and pay for coaching duties, the school will hire athletic coaches from its current teaching staff based on a position announcement and establishment of minimum qualifications for the position. If the school is unable to secure a qualified candidate through this the process, the school shall attempt to recruit a coach from a list of parents or other adults who meet the minimum qualifications for the position. Any person hired will need to pass a DPS background check.

School

Proposal

GCID: Professional Staff Training, Workshops and Conferences

Human Resource Management: Professional Development

Policy

Attendance by school personnel at professional meetings shall be justified by meaningful guidelines or rationale for such attendance. Such guidelines or rationale may differ by department but shall be well-defined and understood by appropriate personnel. An understanding of reasonable expenses should be developed prior to travel. The budgetary allocation of departmental travel accounts shall not be construed as automatic approval for expenditure. Travel outside the continental United States shall be considered only as an exception.

Replacement

Policy

Staff professional development will be determined in accordance with the plan proposed in the Performance School Application as also specified below. The school will determine the value of all Staff Training, Workshops and Conferences as it relates to the school's mission and vision. All out of school professional development will need to be approved by the school principal or program director. Any staff that attends an out of school professional development opportunity will need to then disseminate that information to staff. Ability to attend an out of state conference will be based on budget ability and rotated among staff unless a particular staff person is presenting at that conference and therefore has their expenses covered by other means. In-school professional development will be determined based on how well it furthers the school's ability to meet its mission and vision. All

professional development will be surveyed for relevance, quality and ability to implement lessons learned.

From the school innovation plan:

The principal at DMHS will ultimately be responsible for managing and evaluating professional development. There will be several areas of professional development. The first area will be DPS sponsored. This will include RtI, ELA-T and ELA-E, Positive behavior support, and any other DPS professional development that will insure our staff is well educated in providing an optimal education to a diverse student body.

The second area of professional development will be on Montessori education and adolescent brain development. All teaching staff will be required to attend training on Montessori adolescent education such as the AMI Montessori Orientation to Adolescent Education. This five week intensive course of study includes all aspects of adolescent Montessori education.During the school year, each member of the teaching staff and leadership team will lead a seminar based on Montessori literature. The North American Montessori Teachers Association has given DMHS a $3,000 grant and an additional $5,000 in-kind for professional development. The principal will create a professional development plan to utilize this grant throughout the first three years.

The third area of professional development will be led by the principal and will be on data collection and evaluation. The principal, working with DPS, will work with staff to create appropriate data collection tools and methods whereby the data is frequently reviewed.

The fourth area of professional development will be led by the special education provider and/or the psychologist social worker. This area will cover adolescent brain development, differentiated learning, implementing effective teaching strategies with students who have special needs, and ongoing professional development on RtI. The Special Education teacher and/or school psychologist/social worker will attend professional development on these topics at DPS and review materials and/or attend workshops by professionals such as Dr. Steve Hughes and the Gurian Institute. Prior to the first day of the first school year, DMHS will have ten professional development (PD) days in order to insure that we are fully prepared for the very first day of school. During this time staff will attend DPS professional development for ELA and RtI. Because staff will already be trained in Montessori at both the elementary and adolescent levels, a majority of the planning time will allow for staff to prepare their environments and review curriculum for the first series of Occupations. The Occupations curriculum requires a deep understanding of the land, the local area, public transportation, and local community resources. Staff will work with the principal to make sure that all necessary materials to run successful Occupations are readily available so that the school year can start as smoothly as possible. There will also be professional development around positive behavior support and Discipline through Love and Logic offered by the Love and Logic Institute. The principal will review with staff the DMHS farm school portfolio, rubrics, record keeping, assessment and all other tools necessary to frequently and accurately obtain data regarding student achievement.

After the first year, DMHS will have five PD days prior to the first day of school. During the school year, DMHS will have an additional five professional development days. The topics for the professional development days during the first school year will be as follows: Record keeping and assessment, RtI and meeting the individual learning needs for all of students, review of and creating best practices for writing and implementing Occupations curriculum, further work regarding RtI and meeting the individual learning needs for all students, and understanding the Urban Farm and how it applies to Montessori adolescent education. In addition, on Wednesday afternoons from 1:30 - 3:30, staff will attend staff integration meetings. These meetings will include data review, discussion on recent observations, curriculum review and student discussion.

DMHS will have monthly ninety minute staff meetings on where the primary focus is Montessori theory and understanding adolescent brain development. These staff meetings will support the recursive learning environment. The meetings will allow for reflective conversation to evaluate and improve practice. Staff will improve Montessori practice by examining the principles of Montessori theory and how it applies to adolescent education. Colleagues will share their acquired knowledge and skills with one another resulting in the knowledge being reinforced for the “teacher” and spread exponentially among the other staff members.

School

Proposal

GCP – Professional Staff Promotion & Reclassification

Human Resource Management: Promotion and Reclassification

Policy

A change of assignment from one occupational classification to another may be requested by the affected employee, may be recommended by the employee's administrator or supervisor, or may be initiated by the superintendent and his staff. Approval of the promotion by the superintendent and the Board shall be required. Qualifications for promotion of certificated personnel shall be: 1. Master's degree, or master's degree and other professional preparation 2. Good scholarship3. Satisfactory recommendations and appraisals of service 4. Good working relations 5. Satisfactory experiences in certificated assignments 6. Reasonable length of time in service in the Denver Public Schools 7. Professional growth and demonstrated potential 8. Ability to direct other employees Responsibility of the employee An employee may initiate a request for change of assignment ... Principals and department heads periodically should submit to the executive director for personnel services letters of commendation for persons who ought to be considered for change of assignment. ...include references to scholastic background, professional growth, parent and student relationships, and general fitness for assuming other and additional responsibilities.

Replacement Policy

A change of assignment from one occupational classification to another may be requested by the affected employee, or may be recommended by the employee's administrator or supervisor. Approval of the promotion by the school principal shall be required.

Candidates for promotion at or above the level of a program director shall meet the

following qualifications:

1. Must be highly qualified teachers who are Montessori trained in both elementary and adolescent education.

2. Need to have completed or be willing to complete a Master’s level leadership program.

3. Must demonstrate either in their DMHS position or in past positions they can create a culture of respect, inclusivity, shared decision making, recursive learning, and empowering staff to work at their highest level.

When assignment change decisions have been made, the principal shall submit notice to the executive director for personnel services or the appropriate Human Resource official to process the change in status.

School Proposal

GDA – Support Staff Positions

Human Resource Management: Hiring of Support Staff

Policy

All support staff positions in the school system shall be established initially by the Board. Support staff members shall be employed for such time as the district is in need of or desirous of the services of such employees... The Board shall approve a statement of job requirements as presented by the superintendent. This shall be in the form of a job description setting forth the qualifications for the job, a detailed list of performance responsibilities and any required physical capabilities. Only the Board may abolish a position that it has created.

Replacement Policy

The school will use the same support staff positions as identified by the Board. Should these positions prove to not properly reflect the need for support staff, the school principal will identify additional support staff roles. Once these roles are identified, job descriptions will be created. The school leader or her designee will then provide the job description to the Office of Human Resources for the district so that the school leader can then move forward with staffing the position. Further, should the board abolish a position that it has created, DMHS retains the right to continue staffing the position in the historic way unless it would be in conflict with state or federal laws that supersede innovation autonomies.

School Proposal

GDD: Support Staff Vacations

Calendar and Schedule

Policy

Professional technical and nonaffiliated staff: Vacations and holidays for professional technical and nonaffiliated staff members shall be those determined by the officially adopted school calendar.

Facility managers: Facility managers shall be granted 15 days of paid vacation per year. Those who have completed 15 years of continuous service…shall be granted an five additional days of vacation for a total of 20 days. Holidays for facility managers shall be those determined by the officially adopted school calendar for 245-day classified employees.

Replacement Policy

GDD will be followed with the following exception: Vacations and holidays for professional technical and nonaffiliated staff members shall be those determined by the DMHS school calendar.

School Proposal

GDF-R: Selection, Appointment, and Reappointment of Full-time Classified Employees – Procedures

Human Resource Management: Hiring,

Policy

The term "classified employee" …shall be deemed to include, each DPS employee assigned to a full-time position listed in the salary and classification schedules for classified employees as maintained by the Department of Human Resources. No position requiring Department of Education certification or license shall be considered a classified position. Employees on the administrative and managerial salary schedules are not subject to the provisions of this policy.

Replacement Policy

DMHS will follow the district hiring process for Classified employees and select candidates through the district recruitment and application processes; however, final hiring determinations will be reserved by the school principal. Should the school principal determine that the candidates for a position as provided through the district recruitment and staffing process do not meet the expectations of the principal, the principal will have the ability to not hire the position and re-post the position for new applicants, and pursue additional recruitment activities as deemed necessary to fill the position appropriately.

If DMHS identifies a need for a position that does not exist in the district's current list of classified positions, DMHS will create a profile for this position, provide the information to the district's HR office, and use district systems to post the position and hire a candidate for the position.

School Proposal

GDI: Support Staff Probation, Tenure and Seniority Human Resources: Hiring and Dismissal

Policy

A full-time classified employee shall serve a probationary period of two years on a full-time basis…before attaining the status of continuing service. Any classified employee having served as an employee in active service…for two complete years…and who has been notified in writing shall have continuing service as a classified employee during efficient performance of duties, good behavior and continuous service without the need for recurring annual appointment…A classified employee who has resigned and who is reappointed after the expiration of five years or more shall be reappointed on the conditions applying to a classified employee employed for the first time.

Replacement

Policy

All employees will be employed according to an annual contract.

Annual contracts for the following academic year will generally be provided to all staff who receive a rating on their end-of-year performance evaluation of "meets or exceeds expectations" (or whatever the equivalent will be in any future evaluation system) except for staff positions that may need to be restructured to meet the needs of the school in the following year. The school principal also reserves the right to offer a new annual contract to a staff member before a final evaluation is completed in a situation where the staff member has communicated a need to confirm employment for the following year due to extenuating circumstances (such as another job offer or a potential move). In such situations, the school principal will base the decision on information collected throughout the current year and whether the staff member's performance at that time warrants a rating of meets or exceeds expectations.

School Proposal

GDO: Evaluation of Support Staff

Human Resource Management: Staff Evaluation

Policy

All classified employees in the Denver Public Schools shall be appraised throughout the first two years of employment and at least annually thereafter. Transportation personnel shall be appraised each six months during the first two years and each year during continued employment. Buildings and grounds personnel shall receive an appraisal each six months during the first year and annually thereafter. Operations employees, helpers and assistant custodians shall be appraised after the first 30 and on a six-month sequence during the first two years and then semi-annually throughout employment. Head custodians shall be appraised once each year. Nonaffiliated and professional technical employees shall follow the pattern of six months for appraisal during the first two years and annually thereafter. Food services personnel shall be appraised once each year throughout continued employment. Classified office personnel shall receive an evaluation each six months during the first two years of employment and for two years after a change of job status. Appraisal of facility managers shall be the responsibility of the principal or immediate supervisor with input from area supervisors in accordance with Board-approved procedures. Review The principal… shall review …and provide the employee with a copy Signatures Classified employees' signatures on appraisal reports shall indicate only that they are acquainted with the contents of the reports.

Replacement

Policy:

All classified employees that report directly to the school shall receive an annual appraisal from the Principal or Principal's designee. The principal or her designee shall review the results of the appraisal with each employee and provide the employee with a copy. Classified employees' signatures on appraisal reports shall indicate only that they are acquainted with the contents of the reports. If an employee wishes to make comments, they may do so on the reverse side of the form or by attaching an additional sheet to the form. For performance review appraisals, the reports shall include a designation of whether or not the employee is meeting expectations. P. 43 and 44 of the PSA.

School Proposal

IC/ICA: School Year/School Calendar

Calendar & Schedule

Policy

Prior to the end of the school year, the Board of Education shall determine the length of time during which district schools shall be in session during the next school year…All calendars shall include the dates for all staff in-service programs scheduled for the coming school year…Any change in the calendar except for emergency closings or other unforeseen circumstances shall be preceded by adequate and timely notice of no less than 30 days.

Replacement Policy:

Prior to the end of the school year, the school principal shall determine the following year's school calendar that meets or exceeds the Board of Education's determination of the length of time during which district schools shall be in session during the next school year. All calendars shall include the dates for all staff in-service programs scheduled for the coming school year. Any change in the calendar except for emergency closings or other unforeseen circumstances shall be preceded by adequate and timely notice of no less than 30 days. The school's calendar will be placed on its website prior to February 1 of the previous year. A calendar for school year 2013/14 is posted on the school's website at dmhs.dpsk12.org.

School Proposal

IE: Organization of Instruction

Education Program

Policy

The schools of the district shall be organized to present a unified program of instruction and shall be operated as a single system under the direction of the superintendent. The grouping and housing of instructional levels in school facilities shall be in accordance with the P5-3-4 plan. Under this plan, preschool through the first five grades shall be the elementary schools; middle schools shall contain grades 6, 7 and 8, and high schools shall contain grades 9, 10, 11 and 12.

Replacement Policy:

The organization of instruction for DMHS will be separate and distinct from the district's organization. The model will be designed in accordance with the organization of instruction appropriate for a secondary Montessori school. Section III: Education Program of the DMHS performance application specifies the organization of instruction for the school including specifics on grade levels and configuration.

School Proposal

IEA: Alternative Grade Level Organization in Neighborhood Schools (K-8 Policies)

Education Program

Policy

All students may attend the neighborhood school serving their residence area or another neighborhood school consistent with Policy JC and Policy Procedures JC-R or as otherwise provided in district policy… The Board recognizes that neighborhood schools with different (alternative) grade level configurations and educational programs may be established through School Design (Policy IF) and Policy Waiver Procedures (BGR-R… Resolution 2529 which states:… increased parental and community support is fostered and enhanced by parents having the opportunity …to select from among the numerous educational offerings of the district and to participate in site-based governance. 1. .. enrollment in alternative grades is a choice…may not duplicate or be as extensive as the educational program in neighborhood schools serving those grades. The affected schools are responsible for maintaining a viable educational program for students in alternative grades consistent with this policy. …Schools with alternative grades that wish to participate in extra-curricular activities are responsible for developing alternatives ...If an extra-curricular activity is not offered at the school with alternative grade levels, students may participate in the extra-curricular activity at another district … 3. Schools serving students in alternative grades are responsible for ensuring that students in these grades are provided with the opportunity to achieve all district content…If a school with an alternative grade level organization intends to grant diplomas, the high school courses necessary to meet graduation requirements must be offered. In addition, such schools must meet North Central Association accreditation requirements…5. Teachers assigned to an alternative grade level must meet district and state education, certification, and endorsement requirements for that grade level… Neighborhood school students in grades identified in Policy IE have a priority for enrollment …9. Board of Education policies that apply to students in a particular grade also apply to students in that grade in a neighborhood school with an alternative grade level organization…10. Transportation is not provided for students in alternative grades…12. The Board of Education may review fund- raising

Replacement Policy:

The organization of instruction for DMHS will be separate and distinct from the district's organization. The model will be designed in accordance with the organization of instruction appropriate for a secondary Montessori school. Section III: Education Program of the DMHS performance application specifies the organization of instruction for the school including specifics on grade levels and configuration. DMHS agrees that:

1. An understanding that enrollment in alternative grades is a choice. As such, the educational program, including extra-curricular activities, may not duplicate or be as extensive as the educational program in neighborhood schools serving those grades. The affected schools are responsible for maintaining a viable educational program for students in alternative grades consistent with this policy.

2. Participation in the Nuggets Prep League, the Denver Prep League, and athletic competitions are offered at schools with alternative grades to the extent practicable. Considerations for determining the offerings include incremental costs, facility characteristics, the nature of the program, and the nature of the extra-curricular offerings.

Schools with alternative grades that wish to participate in extra-curricular activities are responsible for developing alternatives that make such participation viable and are subject to the same conditions as other participating schools.

If an extra-curricular activity is not offered at the school with alternative grade levels, students may participate in the extra-curricular activity at another district school consistent with Department of Athletics rules.

3. Schools serving students in alternative grades are responsible for ensuring that students in these grades are provided with the opportunity to achieve all district content standards (e.g., first and second tier). Resources allocated through the district's resource allocation methodology may be used for this purpose. Additional resources may not be provided by the district.

If a school with an alternative grade level organization intends to grant diplomas, the high school courses necessary to meet graduation requirements must be offered. In addition, such schools must meet North Central Association accreditation requirements.

Other curricular offerings for students in alternative grade levels are based on the school's educational program, facility considerations, and available resources.

4. District assessment requirements apply to all district students in affected grades including those with alternative grade levels.

5. Teachers assigned to an alternative grade level must meet district and state education, certification, and endorsement requirements for that grade level.

6. Opportunities to participate in district-organized staff development and activities related to alternative grade levels will be based on the nature of the school's educational program.

7. Neighborhood school students in grades identified in Policy IE have a priority for enrollment within the parameters agreed upon at the time of approval of the performance school application. This priority is specified in the replacement language for policy JC-R.

8. Resources for a school with alternative grades will be allocated according to the formulas for the grades identified in Policy IE (e.g., elementary schools serving grades 6, 7, or 8 are allocated resources for these grades based on the elementary school formulas; a middle school serving fifth graders would be allocated resources for this grade based on the middle school formulas). The district does not provide additional resources for operating expenses that are the result of establishing an alternative grade level organization.

9. Transportation is not provided for students in alternative grades unless otherwise approved by the Board of Education.

10. Schools serving alternative grades are responsible for making necessary adjustments as the district's educational program changes. Resources allocated through the district's resource allocation methodology may be used for this purpose. Additional resources may not be provided by the district for this purpose.

11. The Board of Education may review fund-raising efforts to support educational programming or extra-curricular activities for alternative grades. Such review will include consideration of the extent to which the proposed fund-raising is consistent with Resolution 2529 and whether or not the proposed fund-raising disadvantages other students.

Principals of affected schools are responsible for reviewing this policy and its implications with their supervisors. Principals, in turn, are responsible for distributing this policy and explaining its implications to the parents of students considering enrollment in an alternate grade level.

School Proposal

IGA: Curriculum Development

Educational Program

Policy

Constant adaptation and development of the curriculum is necessary if the district is to meet the needs of the students in its schools. As standards for student outcomes and performance are adopted, the curriculum shall provide a program of instruction based on and designed to enable students to meet the Board-adopted standards, which meet or exceed state adopted standards. The Board expects its faculty and administration to regularly evaluate the education program and to recommend modifications of practice and changes in curriculum content as well as the addition of new courses to the instructional program.

Replacement Policy:

Denver Montessori will be using the Montessori curriculum for the instruction of students in grades 6-12. This curriculum will be aligned to the Common Core State Standards and the Colorado Academic Standards. The curricular framework is described in the Performance School Application, Appendix C. The mapping is targeted for completion in January 2013.

The curricular design approach will use the following schedule: 1. Unit plans for all subjects and grades mapped to the “at a glance” level of CAS and CCSS standards = end of December. 2. Development of all classes aligned to the course units = mid-January. 3. Individual classes mapped back to CCSS and CAS = end of January 2013. Complete gap analysis on any standards not mapped to individual lessons and develop new lessons that map to these missing standards = mid-to-late February.

School Proposal

IGD: Curriculum Adoption

Educational Program

Policy

The Board of Education is required by state statutes to determine the educational programs to be carried on in the schools of the district and to prescribe the textbooks for any course of instruction or study in such programs

Replacement Policy:

The DPS Board recognizes the distinctiveness of the DMHS educational model and therefore delegates curricular and educational material adoption/modification to the local level with feedback and support to be provided by the DPS Departments of Elementary and Secondary Education and School Reform and Innovation. DMHS will be authorized to use a Montessori curriculum for the instruction of students in grades 6-12. This curriculum must be aligned to the Common Core State Standards and the Colorado Academic Standards. The curricular framework is described in the Performance School Application, Appendix C. The mapping is targeted for completion in January 2013.

The curricular design approach will use the following schedule: 1. Unit plans for all subjects and grades = end of November. 2. Development of all classes aligned to the course units = early January. 3. Individual classes mapped back to CCSS and CAS = end of January 2013. Complete gap analysis on any standards not mapped to individual lessons and develop new lessons that map to these missing standards = mid-to-late February.

The school principal will select the instructional materials used by the school after careful consideration of Montessori best practices and recommendations of the school-based instructional materials committee. The school principal will respond to any District concerns regarding selected instructional materials by demonstrating the Montessori pedagogical need and alignment to CAS and CCSS. For grades 10 – 12 Science, History and

Language Arts, 9th grade Earth Science, and 9th grade Civics, DMHS will use DPS curriculum and DPS approved textbooks unless as otherwise adopted through a separate curriculum waiver process.

School Proposal

IIA: Instructional Materials (Textbooks or their Equivalent Learning Materials)

Educational Program

Policy

I. Identification Phase A. Establishment of Curriculum Committees, B. Textbook Fair, C. Identification of Textbooks for Evaluation II. Evaluation Phase, A. Textbook Analysis, B. Selections for Review III. Review Phase: A. Parent Advisory Committee Review, B. Community Review, C. Board of Education Review, D. Preparation of Textbook Evaluation Matrix and Documentation , E. Board of Education Consideration for Adoption IV. Purchase of Textbooks: A. All schools use adopted textbooks for the core subject areas of mathematics, social studies, science, foreign language and language arts; B. Following subject area adoption, schools purchase new textbooks for the next school year using procedures developed by staff; and C. The Board of Education grants waivers for purchase and use of non-adopted textbooks in core subject areas, except that non-adopted textbooks may be purchased subject to approval of the Superintendent or his/her designess, prior to the dates below. IV. Purchase and Use of Supplemental Instructional Materials and Textbooks in Non-core Subject Areas.

Replacement Policy

Following approval of the DMHS curriculum, a school-based instructional materials committee will be formed to manage the selection process for choosing instructional materials that align to the Montessori educational model. The selection process will be conducted in a transparent manner that follows purchasing best practices. As materials are integrated into the DMHS curriculum, the school principal will evaluate the effectiveness of instructional materials and seek feedback from teachers. Highlights of findings will be communicated to OSRI to further district awareness of how materials are driving education.



School Proposal

IIA-R: Instructional Materials

Education Program

Policy

I. Planning and Acquisition A. In cooperation with their Collaborative Decision Making (CDM) committee, each school will determine needs and prepare a three-year plan …C. assure that the school meets or exceeds the district's course and grade level standards D. The departments of Elementary and Secondary Education will review…Each school will maintain a current inventory of textbooks III. Each school…will enact measures to ensure that teachers return textbooks A. Students are required to pay for or replace damaged or lost books. C. Until payment is made, the student's grades, transcript, and diploma will be withheld

Replacement Policy



Language Arts, 9th grade Earth Science, and 9th grade Civics, DMHS will use DPS curriculum and DPS approved textbooks unless otherwise adopted through a separate curriculum waiver process.

School Proposal

IJJ: Instructional Materials (Textbooks) Selection or Adoption

Educational Program

Policy

Instructional materials will be adopted by the Board of Education based upon their effectiveness in implementing the instructional program for which they are intended and according to the following criteria: 1. The extent to which they are aligned with Denver Public Schools Standards for Success, district goals, and adopted curricula; 2. The extent to which they meet a wide range of needs, interests, and student performance levels; 3. The extent to which they support teaching practices known to positively impact student learning; and 4. The extent to which they reflect diversity in such areas as ethnicity, gender, national origin and handicapping conditions. Spanish and English language materials shall be adopted at the same time, if practicable. Schools shall use the current adopted instructional materials in each subject area, except as otherwise provided by superintendent and/or designee. Supplementary materials generally do not require adoption by the Board of Education. Definitions: The following definitions apply to the terms as used in this policy: Instructional materials are the basic set of materials teachers use to guide the instructional activities of a course of study and, thereby, reach their objectives. The basic set of instructional materials for a course of study may be a single textbook or multiple books and include such materials as workbooks, visual aids, videos, software, literature and resource supplements, classroom libraries, and activity kits. Supplementary materials are most often used for short term instruction to provide extended or enriched learning opportunities to motivate individual and/or small groups of students. Procedures The Superintendent or designee shall promulgate such procedures as may be needed for the implementation of this policy.

Replacement Policy




School Proposal

IJJ-R: Instructional Materials (Textbooks) Selection or Adoption Procedures

Educational Program

Policy

New textbooks in each subject area are considered for adoption on a rotating schedule. Textbooks suggested for consideration are evaluated, rated and reviewed by curriculum committees, teachers, parents and community before formal review and adoption by the Board of Education. Spanish language textbooks are considered for adoption along with English language textbooks in each subject area. Under special circumstances, textbooks may be considered for adoption outside of the established cycle. The textbook selection process is outlined below.I. Identification PhaseA. Establishment of Curriculum Committees…B. Textbook Fair…C. Identification of Textbooks for Evaluation…II. Evaluation PhaseA. Textbook AnalysisThe curriculum committees review and evaluate the textbooks using a numerical ranking system to determine the extent to which they meet the criteria below……B. Selections for ReviewDesignated administrative staff select textbooks for the review phase based on the results of the evaluation phase.III. Review PhaseThe review phase allows for additional input from Parent Advisory Committees, the community and the Board of Education. Opportunities are provided for each group to examine recommended textbooks and their evaluations as well as any other supporting documentation.A. Parent Advisory Committee Review…B. Community Review…C. Board of Education Review…D. Preparation of Textbook Evaluation Matrix and Documentation…E. Board of Education Consideration for AdoptionThe Board of Education reviews the textbooks and their attached evaluative materials, including:…IV. Purchase of TextbooksA. All schools use adopted textbooks…B. Schools purchase new textbooks using procedures developed by staff; andC. The Board of Education grants waivers for purchase and use of non-adopted textbooks in core subject areas, except that non-adopted textbooks may be purchased subject to approval of the Superintendent or his/her designess, prior to the dates below.IV. Purchase and Use of Supplemental Instructional Materials and Textbooks in Non-core Subject Areas.A. Supplemental instructional materials and non-adopted textbooks for subject areas not defined as "core" may be purchased subject to the approval of the principal. The principal considers such requests based on the extent to which the textbook:1. Aligns with Denver Public Schools Standards for Success, Curriculum Matrix, and District Goals;2. Provides assessment skills practice;…8. Makes available ancillary materials to support instruction…B. Principals are encouraged to display…all adopted, non- adopted, and supplemental materials so that they may be perused by the school community.

Replacement Policy




School Proposal

IJOA: Field Trips / IJOA-R: Field Trips (Guidelines for Extended Excursions)

Educational Program

Policy

Most educational excursions shall be carried out on school time to approved destinations listed in the catalog for approved excursions. Excursions to destinations not listed in the catalog may be arranged by following the accompanying procedures for field trips. Sometimes these experiences in the field will last overnight or for even longer periods. The accompanying procedures for extended excursions give guidance to teachers and principals so that judicious decisions may be made at the local level concerning most such excursions. When the proposed experience involves long, extended periods of time...principals shall seek counsel, direction and approval from their lead principal who in turn may secure approval from the superintendent or designee. School buses shall be provided for teachers to take their classes on educational excursions insofar as possible using bus allocations established for that school. When school buses are not available, arrangements may be made to use public transportation or private transportation. For all excursions requiring students transportation in school buses, arrangements should be made through the department of transportation.

Replacement Policy

DMHS will follow the district field trip policies and procedures with two exceptions: The school will design field trips that match the Montessori curriculum and therefore may be outside of the district catalog. In such situations, DMHS will have autonomy in determining the appropriateness of field trips, and the school principal will be responsible for approving all school field trips. Second, if a situation exists where the school must pay the district for transportation services, the school may choose to contract with another school transportation provider if the cost estimate from the district is significantly higher that the other school district's cost estimate.

School Proposal

IK- Student Academic Achievement

Education Program

Policy

The Board’s vision is…In order to achieve this vision the board adopts the following core beliefs which will govern district policy decisions… The Board adopts an instructional reform theory for Denver that has the following essential elements that will positively impact student achievement.. This is an integrated reform strategy that addresses three of DPS's greatest challenges-a high mobility rate among our students and teachers, low academic preparedness of our students, and lack of consistent and timely data… Each student is expected to meet or exceed the District's academic content standards before they transition from level to level and before they are eligible to graduate…The school staff and students are directly responsible for student learning... The District content standards are to be the focal point of classroom instruction…To fulfill this expectation, all students will be provided challenging instructional programs. Student learning and performance will be continuously monitored against the standards through the use of valid and reliable measures...The Superintendent is directed to comply, modify and implement the core belief and action plan as necessary.

Replacement Policy

Student progression in their mastery of curricular content will be monitored and documented through a detailed junior and senior high portfolio. All record keeping will be

School Proposal

Policy

Replacement Policy

School Proposal

Policy

Replacement Policy

maintained in a Student Electronic Portfolio, which will contain documentation of lessons attended, student submitted work, teacher feedback, mastery level quizzes, cumulative project, and overall unit assessment. The Performance School Application, Appendix C, Sections B and C specify the alternative benchmark assessment program and the graduation and promotion standards for the school. In addition, DMHS has provided further policy definition in the attachment, DMHS Alignment with Graduation Standards, and the relevant mapping to each of the core subject standards.

IKB: Homework Educational Program

Parents should expect their children to have regular homework assignments and should question the lack of such assignments. Elementary school: The amount, length and type of homework at the elementary school level may vary…but the minimum amount assigned shall be as follows: Kindergarten and grade 1- 10-15 minutes, one or two days per week Grade 2- 10-20 minutes, two days per week Grade 3- 15-25 minutes, two days per week Grade 4- 15-30 minutes, two to three days per week Grade 5- 20-30 minutes, three to four days per week Middle school: A minimum of five hours of homework per week High school: The expected minimum amount of homework shall be 10 hours per week in grades 9 through 12.

The school will implement a Montessori homework policy that is in alignment with the Montessori educational philosophy. Homework will only be assigned as deemed necessary at the school level. Students are given independent work time during the school day that usually allows them to accomplish a majority of the school's work requirements. In instances when work is not completed at school, students are expected to complete their work by a specified deadline set by the teacher. As the students progress to higher grades, the homework load will increase in order to appropriately prepare students for post- academic success.

IKE - Promotion, Retention, and Acceleration of Students

General Considerations Grade retention or acceleration will be based on the best interests of the student and

his/her educational success. Elementary and Middle School: Students will be retained or accelerated, if the following criteria are met: 1. The parents and the school principal agree that grade retention or acceleration is in the best interests of the student based on the general considerations above and is consistent with Policy Procedures IKE-R. 2. The student does not comply with requirements for promotion that are established by the Superintendent High School Grade levels will be determined based on credits earned as defined below: Grade 9 (Freshman) Less than 60 credits Grade 10 (Sophomore) 60 to 120 credits Grade 11 (Junior) 121 to 170 credits Grade 12 (Senior) 171 to 240 credits

Student progression in their mastery of curricular content will be monitored and documented through a detailed junior and senior high portfolio. The Performance School Application, Appendix C, Sections B and C specify the alternative benchmark assessment program and the graduation and promotion standards for the school. In addition, DMHS has provided further policy definition in the attachment, DMHS Alignment with Graduation Standards, and the relevant mapping to each of the core subject standards.

DMHS is designed to respect stages of adolescent development, and promotion and retention criteria will reflect this value. Students will be expected to be promoted within their established class. A key time for evaluation will occur towards the end of the ninth grade year. If a student is demonstrating significant gaps in academic achievement, social and/or emotional growth to the level that they may not thrive in the high school environment, a conference will be called between the student, their family, the principal and the student’s advisor to determine if the student should spend an additional year in the junior high. In high school, if a student is not on track to meet all DMHS graduation requirements, the student, their family, the principal and the student’s advisor will meet to create a plan in order for the student to graduate. One possible outcome of that plan may be for the student to spend an additional semester or year at DMHS until all graduation requirements are met. If a student has exceeded graduation requirements before the end of their 12th grade year, that student will have the option to graduate early or dually enroll in UCD, Metropolitan State, or another college that offers dual enrollment. Again, a meeting will be called between the student, their family, the principal and the student’s advisor to determine the best course of action for that student.

School Proposal

IKF: Graduation

Graduation and Promotion

Policy Highly detailed. Specifies credit for general ed, etc.

Replacement Policy

Alternative graduation requirements are specified in the document, DMHS Alignment with Graduation Standards.

School Proposal

JC-R: Pupil Assignment

Enrollment

Policy Highly detailed. Specifies choice process for parents.

Replacement

Policy

DMHS will participate in the School Choice process with the exception that enrollment priority will be given according to the following schema:

1) Students who are currently attending Sandoval, Gilpin, Denison, or Lincoln 2) Students who have a sibling currently attending DMHS 3) Students who are the children of DMHS staff members 4) Denver residents who have attended Montessori elementary school 5) Non-Denver residents who have attended Montessori elementary school 6) Denver residents who have not attended Montessori elementary school 7) Non-Denver residents who have not attended Montessori elementary school

Additionally, for all priorities stated above, neighborhood students will be granted seat priority over non-neighborhood students. For example, if after applying priority 1, there are more students than seats, then priority will be given to students who reside in the school neighborhood area over students from other areas in the district.

NOTE: “Family Link” will be in effect at DMHS. This means that siblings who apply together will be systematically linked, maximizing their opportunity to stay together.

DMHS will continue to reach out to the Montessori community in an equitable manner to create a diverse student body that is reflective of the DPS and the neighborhood student body. If a situation arises where a noticeable demographic difference exists between the school and the neighborhood, the school principal will work with the district in implementing a plan that recruits more students from the neighborhood area while also ensuring for their success in a Montessori program.

School Proposal

DCTA: Article 1-7 Definition of “School Year”

Calendar & Schedule

Policy The term "school year" as used in these Articles shall mean the officially adopted school calendar.

Replacement Policy

The term "school year" as used in these Articles shall mean the officially adopted DMHS school calendar.

School Proposal

Article 5-1-4: Teamwork among Teachers

Curriculum

Policy

Teamwork among teachers and with the principals is an important component for improving achievement. Teachers shall have a significant role in identifying and developing the instructional program.

Replacement

Policy

Teamwork among teachers and with the principals is an important component for improving achievement. Teachers shall have a significant role in identifying and developing the instructional program as long as the primary focus is in alignment with the mission of the school as stated in the Performance School Application.

School Proposal

Article 5-4: School Leadership Team

Management

Policy

Each school will have a School Leadership Team (SLT) consisting of the principal, the association representative, a teacher appointed by the principal, and a minimum of 3 teacher representatives … elected annually by a majority of the faculty voting by secret ballot The SLT will make decisions by consensus. A consensus is either a unanimous decision or a majority decision that the entire SLT, including the dissenters, will support. Their responsibilities shall include: a. Collaborate in the development of the School Improvement Plans; b. Review and collaborate on the design of and schedule for the professional development c. Review and collaborate on the implementation of the District’s instructional program …including prioritizing and sequencing activities within the work week;…f. Collaborate to implement best instructional practices

Replacement Policy

Teachers will be active participants in the management of the school through the School Accountability Committee as it is outlined in district policy BDFH and in the Performance School Application.

School Proposal

Professional Standards (Article 8): Sets Teacher Calendar, Work Year, Work Week, Work Day, Class Size and Teaching Load

· Calendar & Schedule

Policy

6 pages. Sections include: School leadership team, contract year, evening meetings, 40 hour work week, lunch periods, planning time, multi-school assignments, teaching loads, funding specialized service providers, non-teaching duties, lesson plans, class coverage, emergency school closings, and teacher-in-charge status.

Replacement Provisions specified in Article 8 will not apply to the school. The school will create and

Policy publish an annual calendar that shall be used for defining the contract year for teachers. The teacher schedule is highlighted in pages 25 and 26 of the Performance School Application.

School Proposal

Article 7 Grievance Policy Human Resource Management

Policy

6 pages. Sections include: 1. Definitions, Purpose, Procedure (Level 1, Level 2, Level 3,

Mediation/arbitration), Rights of teachers to representation, Miscellaneous

Replacement Policy

The school shall maintain the following Grievance Policy: 7-1 Definitions.

7-1-1 A "grievance" shall mean a written complaint by a school staff member that there has

been a violation, a misinterpretation, or inequitable application of any of the provisions of

the School’s Employment Contract or the School’s Employee Handbook.

7-1-2 Unless provided otherwise in this Agreement, all administrative procedures, practices

and written personnel policies that affect staff are grievable.

7-1-3 The term "grievance" shall not apply to any matter as to which (1) the method of

review is prescribed by law, (2) the Board is without authority to act, or (3) a grievance is

specifically prohibited or limited by the terms of the Employment Contract or School

Handbook.

7-1-4 An "aggrieved person" is a school staff member asserting a grievance.

7-2 Purpose. The purpose of this grievance procedure is to secure equitable solutions at the

lowest possible administrative level to problems that may arise. To this end, grievance

proceedings will be kept informal and confidential and both parties will work toward a

resolution to avoid litigation.

7-3 Procedure. Since it is important that grievances be processed as rapidly as possible, the

number of days indicated at each level is a maximum, and every effort should be made to

expedite the process. The time limits specified may, however, be extended by mutual

agreement.

Information. The School agrees to make available to the aggrieved person and the aggrieved

person’s representative, all pertinent information not privileged under law, in its possession

or control, and which is relevant to the issues raised by the grievance. The grievant agrees to

make available to the School and its representatives, all pertinent information not privileged

under law in its possession or control, and which is relevant to the issue raised by the

grievant.

Timing. No grievance shall be recognized by the District or the School unless it is presented

at the appropriate level within fifteen (15) school days after the aggrieved person knew, or

should have known, of the act or condition on which the grievance is based. No grievance

shall be recognized at Level Two unless it is filed with the Department of Human Resources

within at least twenty (20) school days after the act or condition upon which it is based

occurred. Grievances not timely presented will be considered as waived. 7-3-1 Level One. A grievance first will be discussed with the aggrieved person's principal to

attempt to resolve the matter informally, at which time the aggrieved person (1) may discuss

the grievance personally, (2) may be accompanied by a District Human Resource

Representative, or (3) may request that the District Human Resource Representative act on

behalf of the aggrieved person. No written documentation of the grievance or administrative

response will be required if the grievance is settled at Level One.

7-3-2 If the aggrieved person is not satisfied with the results of the informal conference, the

aggrieved person may then file a grievance in writing on the proper form with the principal

or supervisor within seven (7) school days. The grievance must refer to the specific Articles

of the Employment Contract and/or School Handbook and explain how they were violated

and indicate the reason why the Level One decision is unsatisfactory. The principal shall

also have the opportunity to provide comment related to the Level One in writing. The

grievant shall send a copy of the written grievance and the principal response to the

Department of Human Resources. All known documentation related to the grievance must

be provided prior to the Level Two meeting.

7-3-3 Level Two. The Human Resources Director or Instructional Superintendent will go to

the school and meet with the teacher and principal to facilitate a resolution. Such meeting

will take place within seven (7) school days after receipt of the written grievance by the

Department of Human Resources. Any resolution determined by the Human Resources

Director or Instructional Superintendent will be considered final.

7-4 Miscellaneous. If the time limits for processing a grievance are not met by the

administrator responding to the grievance, the grievance may be moved to the next level at

the request of the aggrieved. The Department of Human Resources may take appropriate

action on whether to grant the grievant’s requested remedy based on its review of the

situation.

School Proposal

Article 10 Teacher Evaluation: Describes the Evaluation Process for Teachers

Human Resource Management: Teacher Evaluation

Policy

12 page process, which includes: defining evaluators, documentation, records of teaching, observations, interview data, written communication, sequence of evaluation, pre and post observation conferences, evaluation data review conferences, performance ratings, completion of evaluation, remediation, conducting a remediation plan, PD plans, special evaluations, personnel performance evaluation council.

Replacement Policy

All teachers will receive annual performance evaluations. DMHS will use the LEAP framework. The evaluation and feedback process is specified in pages 42-44 of the Performance School Application.

School Proposal

Committees (Articles 5, 13, 29): Development Committee (5-4-1) and Personnel Committee (13-8)

Governance & Human Resource Management: Leadership Structure

Policy

Committees identified in these sections include: - Instructional Issues Council - IS Advisory Committee - School Leadership Team - Personnel Committee - Task Force on School and District Climate

Replacement

Policy

The school will be lead by a School Accountability Committee and will operate as the Collaborative School Committee as established in district policy BDFH. Ad-hoc committees created to address specific needs or concerns within the school will be created when appropriate either at the direction of the school principal or the SAC.

School Proposal

Article 11: Complaints Against Teachers/Administrative Leave/Corrective Action

Human Resource Management

Policy

11-2 Administrative Leave. If a principal decides to place a teacher on administrative leave for…the principal or designee shall meet with the teacher to give specific allegation(s) and the basic reason why the administrative leave for investigation is necessary, when possible. 11-2-1 The meeting shall take place at the end of the school day or whenever it is appropriate.11-2-2 The principal shall provide the teacher a copy of the administrative leave checklist and review it with the teacher. The teacher shall sign the form only as acknowledgement of receipt..11-2-3 At the teacher’s request a meeting will be held within three (3) school days...to give the teacher an opportunity to respond. The teacher may have Association representation at the meeting. 11-2-4…If an investigation must extend beyond seven (7) calendar days…the teacher and the Association will be notified by phone calls…[with]…the reasons for the extension and the expected date of completion…11-2-5 During the investigation, the teacher…will… receive full pay. 11-2-6 Following completion…the principal or designee shall…share the results…and give the teacher an opportunity to respond…11-2-7 Administrative leave should be considered as an option to be used only when necessary to protect the students or staff or to conduct an appropriate investigation…There will be no record of the leave in a teacher's personnel file…11-2-8 The Agreement Review Committee (ARC) will review on an annual basis administrative leaves for the prior year to ensure that the above procedures have been implemented appropriately. 11-3 Corrective Action. Before taking a corrective action against a teacher, the principal shall investigate the situation, meet with the teacher and give the teacher an opportunity to respond.

Replacement Policy

Complaints: When a person makes a written or verbal complaint against a teacher, the principal or designee shall promptly notify the teacher of the complaint and the teacher shall be given the opportunity to respond. The principal or designee shall investigate the complaint and attempt to resolve the complaint informally if appropriate.

If any record of the complaint, or its formal or informal resolution, is placed in the teacher's files, the teacher shall have the right to file a written response within twenty (20) school days.

Administrative Leave: If a principal decides to place a teacher on administrative leave for the purpose of further investigation, the principal or designee shall meet with the teacher

to give specific allegation(s) and the basic reason why the administrative leave for investigation is necessary, when possible.

At the teacher’s request a meeting will be held within three (3) school days. The purpose of the meeting is to give the teacher an opportunity to respond. The teacher may have his or her own representation at the meeting.

Administrative leave should be considered as an option to be used only when necessary to protect the students or staff or to conduct an appropriate investigation.

Corrective action: If a principal or designee determines it may be necessary to take a corrective action, the principal shall inform the teacher of his/her intent to consider potential corrective action measures and allow the teacher the opportunity to have a representative of their choosing present at the meeting.

School Proposal

Assignments, Schedules and Transfer (Article 13): Describes District and School Procedures for Transfer and Reassignment of Teachers

Human Resource Management: Hiring & Staff Assignments

Policy

10 Pages. Sections include: Timelines with the HR process, Hiring through Personnel Committee, Reduction in Building Staff (RIBS), Voluntary Transfers, In-Building Bidding, Posting Vacancies, Applications, Selection Procedure, Assignments/Placements.

Replacement

Policy

DMHS will work with the district HR office to post teaching positions through the district website. From this posting, DMHS will engage in independent outreach efforts to recruit candidates outside of the centralized recruitment channels.

Teachers shall be hired based on the following criteria: DMHS will create a rubric that values Montessori training, NAMTA or other Montessori Adolescent training, Highly qualified, teacher licensure, demonstrated ability to team teach, experience with Montessori adolescent programs, and demonstrated understanding and ability to implement a Montessori adolescent program. Initial hiring decisions will be made by the school principal. Subsequent hiring decisions will be made as the school’s “personnel committee”, with final determination to be made by the school principal. The personnel committee shall consist of volunteer representatives from all staffing areas that will be affected by the new hire, such as the teaching team, the program director, special education and support staff. All candidates must pass a DPS background check, which will be conducted through the district HR process.

The school will adhere to district salary schedules for all teachers but requires autonomy in determining the years of experience in order to account for private and other school experience.

School Proposal

Article 14-1: Summer school teaching positions Human Resource Management: Hiring & Staff Assignments

Policy

Summer School and Evening School. Summer and evening school programs shall be provided flexibility of design and implementation following the guidelines set forth below. 14-1-1 Staffing. The purpose of all staffing procedures is to find the most suitable candidates for the teaching positions needed to run the summer school. 14-1-1-1 Summer school teaching positions shall be posted. 14-1-1-2 Postings shall include the following basic components: descriptions of any

teaching position that may be included in the summer school, and an explanation of the selection process. 14-1-1-3 All teaching positions in summer school programs will be filled first by teachers currently in the District.

Replacement

Policy

In the event that Denver Montessori offers summer school classes, the school principal will first work with a district HR representative to specify job descriptions and compensation for the positions to be hired for. Summer school positions will first be shared internally and staff will be encouraged to apply by a specified deadline. The school leaders will then interview all internal candidates for the position and make offers to candidates that there is mutual consent for the position. After this internal hiring has been completed, the school leader will work with a district HR representative to post an open position for the summer school term. The school leader will be provided with all applications received and will have the ability to offer positions to any qualified applicant that they deem would be the best fit for the position.

School Proposal

Reduction in Force (RIF) (Article 20): Procedures for Conducting Reduction in Force

Human Resource Management: Staffing

Policy

20-1 Reduction in Force…shall be done in compliance with federal and state statutes, any existing court orders upon the District, and in a manner that will maintain the best educational program for the District. 20-1-1 If the District anticipates a reduction in staff, the Executive Director of Human Resources…shall consult with the Association…20-1-2 Normal attrition shall precede any reduction in force of regularly assigned teachers…20-1-3 Required staff reductions should be done by endorsement area in reverse order of being hired as a teacher…20-1-5 Whenever possible, Reductions in Force will be limited to the end of the semester or school year. Affected teachers shall receive thirty (30) days written notice. 20-1-6 Upon the written request of the teacher identified for job reduction, the administration shall investigate all possible assignments for which the teacher is eligible.

Replacement

Policy

In the event that the school is required to implement a reduction in force process, it shall be done in compliance with federal and state statutes, any existing court orders upon the District, and in a manner that will maintain the DMHS educational program. RIF determinations will be made by the school principal as deemed appropriate to minimize the impact to the delivery of high quality educational services to students. Determinations will be made in consultation with district staff to ensure compliance with state and federal statutes.

School Proposal

Job Sharing and Half-Time (Article 25): Procedures for Arranging Job-Sharing Assignments and Half Time

Human Resource Management: Staff Assignments

Policy

25-1 Job sharing,…may be requested by…full-time equivalent non-probationary teachers who wish to work only half-time…25-1-2 Teachers wishing to job share must find another teacher who also wishes to job share…25-1-3…assignments, when possible, shall be for one (1) year at a time. 25-1-4 Salary, benefits, accrued service and other employment entitlements shall be half their usual value... 25-1-5…the job sharing or half-time assignments must be approved by the CSC

Replacement Policy

Job-Sharing: Job sharing, or converting from a full-time employee to a half-time employee, may be requested by regularly assigned full-time equivalent teachers who wish to work only half time. Procedures for assignment to a job sharing or half-time position will be

available upon request from the Department of Human Resources. -Application for a job sharing or half-time position must be made in writing to the

Department of Human Resources by the published date. -Teachers wishing to job share must find another teacher who also wishes to job share. -Job share and half-time assignments, when possible, shall be for one (1) year at a time. -Salary, benefits, accrued service and other employment entitlements shall be half their usual value, as applicable. -Job sharing or half-time assignment must be approved by the school leader

School Proposal

Article 32: Extra Duty Comp: Sets Rates for Extra Duty Compensation

Human Resource Management: Compensation

Policy Various tables that specify compensation levels for activities that include: Substitute pay, Hourly rates, Activity salaries with steps and schedules

Replacement Policy

The School reserves the right to not provide additional compensation to exempt employees for additional time that occurs during overnight and extended trips, after school meetings, parent/teacher conferences, after school activities, school performances, events, or games, evening meetings and professional development. If the school does give compensation for such additional time, the compensation will be provided consistently to all teachers and staff working such additional time.

School Proposal

Colorado State Statutes: Section 22-9-106: Local Board Duties Concerning Performance Evaluations for Licensed Personnel

Human Resource Management: Teacher Evaluations

Policy

All of the teacher and principal effectiveness legislation.

Replacement

Policy

The school will have the authority to adapt LEAP or adopt an alternative evaluation system, provided such system meets the standards of SENATE BILL 10-191 and is approved by the District HR office. An alternative proposal will be provided prior to use in formally evaluating staff.

Only the following individuals may serve as evaluators for DPMS: The school principal, the school's program directors at the permission of the school principal, other professional teacher evaluators through the LEAP Peer Observer program. The school principal, as hired by the district, shall be allowed to evaluate professional staff members regardless of whether the administrator has an active administrative certificate. No other individual will have de facto authorization to evaluate staff without the explicit designation by the school principal. The school principal will continue to be evaluated by the superintendent or his/her designee and will receive feedback on the quality of evaluations being given at the school. The school principal will be responsible for evaluation of other evaluators on campus, but may discuss evaluations with district staff as well to ensure meaningful calibration of scores.

The policy will apply evenly to all teachers in the school. All teachers will receive at least one formal evaluation each year. P. 43 of PSA.

School

Proposal

Section 22-32-109(1)(f): Local Board Duties Concerning Selection of Personnel and Pay

Human Resource Management: Staff Hiring, Compensation

Policy

22-32-109. Board of education - specific duties. (1) …each board of education shall have and perform the following specific duties:

(f) (I) To employ all personnel required to maintain the operations and carry out the educational program of the district and to fix and order paid their compensation...A board of a district of innovation…may delegate the duty specified in this paragraph (f) to an innovation school,

Replacement Policy

The principal, in consultation with the school leadership team, will select teaching staff directly and rates of pay will be based on the district schedule.

School Proposal

Section 22-32-109(1)(cc):


Policy


(cc) To adopt a dress code policy for teachers and other school employees;

Replacement Policy

The principal, in consultation with the school leadership team, will adopt a dress code policy for teachers and other school employees.

School Proposal

Section 22-32-109(1)(n)(I): Schedule and Calendar


Policy


(n) (I) To determine, prior to the end of a school year, the length of time which the schools of the district shall be in session during the next following school year, but in no event shall said schools be scheduled to have fewer than [varies by grade level] hours of planned teacher-pupil instruction

Replacement

Policy

The principal, in consultation with the school leadership team, will determine prior to the end of a school year, the length of time which the school shall be in session during the next following school year, but in no event shall DMHS have fewer than the minimum hours set by the district and state for public instruction.

School Proposal

Section 22-32-109 (1)(n)(II)(A): Actual Hours of Teacher-Pupil Instruction and Contact


Policy


(II) (A) The actual hours of teacher-pupil instruction and teacher-pupil contact specified in subparagraph (I) of this paragraph (n) may be reduced to no fewer than one thousand fifty- six hours for secondary school pupils, no fewer than nine hundred sixtyeight hours for elementary school pupils, no fewer than four hundred thirty-five hours for half-day kindergarten pupils, or no fewer than eight hundred seventy hours for full-day kindergarten pupils, for parent-teacher conferences, staff in-service programs, and closing deemed by the board to be necessary for the health, safety, or welfare of students.

Replacement Policy

The school leader, in consultation with the school leadership team, will determine prior to the end of a school year, the length of time which the school shall be in session during the

next following school year, but in no event shall DMHS have fewer than the minimum hours set by the district and state for public instruction.

School Proposal

Section 22-32-109 (1)(n)(II)(B): School Calendar


Policy


(B) Prior to the beginning of the school year, each district shall provide for the adoption of a district calendar which is applicable to all schools within the district…A copy of the calendar shall be provided to the parents or guardians of all children enrolled…Such calendar shall include the dates for all staff in-service programs…[The] school administration shall allow for public input from parents and teachers prior to scheduling …staff in-service programs. Any change in the calendar…shall be preceded by adequate and timely…of not less than thirty days.

Replacement Policy

The principal, in consultation with the school leadership team, will determine prior to the end of a school year, the length of time which the school shall be in session during the next following school year, but in no event shall DMHS have fewer than the minimum hours set by the district and state for public instruction.

The school calendar will replace the school’s need to follow the district calendar.

School Proposal

Section22-32-109 (1)(aa): Adopt Content Standards and Plan for Implementation of Content Standards

Educational Program

Policy


(aa) To adopt content standards and a plan for implementation of such content standards pursuant to the provisions of section 22-7-407;

Replacement Policy

The DPS Board delegates to DMHS the authority to develop a local plan for implementation of the CCSS and the CAS in a way that aligns to the mission and vision of the school. All substantial material changes to the district educational program must be communicated to the district offices of Elementary and Secondary Education and School Reform and Innovation for review. These offices are provided with final authority for determining whether the changes will be approved by the district.

School Proposal

Section 22-32-109(1)(t): Determine Educational Program and Prescribe Textbooks

Education Program

Policy


(t) To determine the educational programs to be carried on in the schools of the district and to prescribe the textbooks for any course of instruction or study in such programs;

Replacement Policy

The DPS Board delegates to DMHS the authority to develop a local plan for implementation of the CCSS and the CAS in a way that aligns to the mission and vision of the school. All substantial material changes to the district educational program must be communicated to the district offices of Elementary and Secondary Education and School Reform and Innovation for review. These offices are provided with final authority for determining whether the changes will be approved by the district.

School Section 22-32-109(1)(jj): Identify Areas in which the Human Resource Management:

Proposal Principal/s Require Training or Development Professional Development

Policy


(jj) To identify any areas in which one or more of the principals of the schools of the school district require further training or development. The board of education shall contract for or otherwise assist the identified principals in participating in professional development programs to assist the identified principals in improving their skills in the identified areas.

Replacement

Policy

District will establish a supervisory role with the school principal and as part of this role, will jointly develop a professional development plan that will be followed by the school principal. This relationship, through the waiver, will be such that a personalized PD plan that can be developed to allow for greater autonomy of the school leader.

School Proposal

Section 22-32-110(1)(h), C.R.S.: Local Board Powers Concerning Employment Termination of School Personnel

Human Resource Management: Staff Dismissals

Policy

22-32-110. Board of education - specific powers. (1) In addition to any other power granted … each board of education of a school district shall have the following specific powers, to be exercised in its judgment:

(h) To discharge or otherwise terminate the employment of any personnel. A board of a district of innovation…may delegate the power specified in this paragraph (h) to an innovation school

Replacement Policy

The principal will have the authority to discharge or otherwise terminate the employment of any personnel in accordance with dismissal policies outlined in the innovation plan (see GDQD waiver language).

School

Proposal

Teacher Employment, Compensation and Dismissal Act of 1990 Section 22-63- 201: Employment-License Required-Exception

Human Resource Management: Hiring and Teacher Qualifications

Policy Paraphrasing - Must hire a teacher with a license. An alternative license is okay. Districts are not required to hire administrators with the requisite license.

Replacement Policy

Policy will remain, but with recognition that the principal does the hiring. Additionally, refer to replacement policy for CFBA for replacement language that exempts the school from needing to be licensed.

School Proposal

Teacher Employment, Compensation and Dismissal Act of 1990 Section 22-63-202, C.R.S.: Contracts in Writing Duration Damage Provision

Human Resource Management: Hiring, Contracts and Employment Offer Letters

Policy

Contracts shall be in writing, amount of notice required by a teacher/principal who intends to resign, when a position can be re-opened, penalties for resigning outside of the window, no direct placement requirement, priority hiring preference for effective/satisfactory teachers, management of displaced teachers, disclosure of why contracts were terminated.

Replacement Policy

All contracts will be in writing. DMHS will provide contract language to the district for feedback before any employment contracts are offered. Mutual terminations will be negotiated between the teacher and the school principal and teachers must give notice at

least 30 days prior to the date of termination (unless mutually agreed upon that the termination date could be sooner). Teachers will be at-will employees of the school, but will also receive an annual contract outlining the terms of employment. Contract renewals for the following school year must be finalized no later than 60 days before the end of the current school year.

The school principal has the authority to make employment offers to qualified candidates. Termination of all staff will follow the dismissal procedures outline in GDQD. DMHS will not provide first opportunity to interview rights to priority hiring pool candidates, but will still consider them for employment. The school has the right to refuse direct assignment of teachers from the district.

School

Proposal

Teacher Employment, Compensation and Dismissal Act of 1990 Section 22-63-203, C.R.S.: Probationary Teachers – Renewal and Nonrenewal of Employment Contract

Human Resource Management: Dismissals

Policy Non-probationary status - how established, treatment of probationary teachers, time, ability to not renew contracts,

Replacement Policy

DMHS will hire teachers with terms specified in an annual contract.

School

Proposal

Teacher Employment, Compensation and Dismissal Act of 1990 Section 22-63-206, C.R.S.: Transfer of Teachers – Compensation

Human Resource Management: Direct Placement of Teachers

Policy Specifies that schools are not required to accept transfers from the Chief Admin Officer of a district, but if they do, specifies the manner in which compensation should be handled.

Replacement

Policy

School will have the authority to decide whether to accept transfers of any staff from the district on a case-by-case basis. In such situations where transfers occur, the school principal has the authority to determine the appropriate years of experience on the salary schedule.

School Proposal

Teacher Employment, Compensation and Dismissal Act of 1990 Section 22-63- 301: Grounds for Dismissal


Policy Specifies reasons for why a teacher could be dismissed.

Replacement Policy

All teachers will be employed using an annual contract. This contract can be non-renewed at the end of the contract term for any reason.

In all situations related to teacher dismissal except for non-renewal of annual contracts, a teacher may only be dismissed for cause in accordance with the dismissal policies outlined in the replacement policy for 22-63-302.

School

Proposal

Teacher Employment, Compensation and Dismissal Act of 1990 Section 22-63- 302: Procedures for Dismissal of Teachers and Judicial Review


Policy

Process for terminating a teacher through judicial review. Teacher can appeal for an impartial hearing, appeal to court of appeals, appeal to supreme court. Instances when a district can dismiss a teacher without cause is specified. Criminal convictions.

Replacement

Policy

School will administer dismissal policies as specified below: I. Dismissal Procedures For Teachers

-These procedures do not apply to non-renewal of annual contracts.

A. No teacher will be dismissed until he/she has been notified by one of his/her

supervisors of the supervisor's intent to recommend dismissal to the

Superintendent or his/her designee. The supervisor will inform the teacher of the

grounds for the recommended dismissal and will give the teacher a reasonable

opportunity to respond.

B. If the supervisor decides to proceed with the dismissal recommendation, the

supervisor will provide the teacher with written notice of the ground(s) for the

dismissal recommendation and the teacher may request a post-termination hearing

before an administrator (designated by the Superintendent or his/her designee) in

the Human Resources Department. The teacher must request the post-termination

hearing within three (3) scheduled working days of the last day of work.

1. If the teacher does not request the post-termination hearing within three (3)

scheduled working days, the termination will be considered final. The

recommendation for dismissal of teachers who do not request a post-termination

hearing will be forwarded to the Superintendent or his/her designee for final

action. If the Superintendent or his/her designee does not uphold the supervisor's

recommendation for dismissal, then the teacher shall be entitled to back pay.

2. If the teacher makes a timely request for a post-termination hearing, then the

Human Resources administrator shall conduct the hearing within ten (10)

scheduled working days of the receipt of the request for hearing, unless

extraordinary circumstances require additional time.

i. The Human Resources administrator shall review the supervisor's decision in

order to determine if there are facts that demonstrate that any of the ground(s)

specified in the notice of dismissal recommendation provided the teacher are

present. The Human Resources administrator shall issue a decision in writing

affirming, modifying, or reversing the dismissal recommendation. The decision shall

be rendered within five (5) working days of the hearing, unless extraordinary

circumstances require additional time.

ii. If the Human Resources administrator affirms the dismissal recommendation,

the recommendation will be forwarded to the Superintendent or his / her designee

for final action. If the Superintendent or his/her designee does not uphold the

recommendation for dismissal, the teacher shall be entitled to back pay.

School

Proposal

Teacher Employment, Compensation and Dismissal Act of 1990 Section 22-63- 401: Teachers Subject to Adopted Salary Schedule

Human Resource Management: Compensation

Policy

Districts are required to pay teachers according to a schedule or according to a performance policy. Salaries are not to be changed until the end of the year. Individual teachers cannot have their salaries cut unless all teachers have salaries cut.

Replacement Policy

The school will use the district salary schedule for determining pay for teachers and staff; however, they will have discretion on how the budget is impacted for paying staff (actuals vs. averages). The school principal reserves the right to develop a supplemental compensation system to reimburse employees for extra duty pay as it may arise for activities that may include, but not necessarily be limited to coaching, tutoring, external professional development or for performance incentive pay.

Part III: Evidence of Support

Evidence of Community Support for Innovation Status

As the founders of Denver Montessori Junior/Senior High School (DMHS) wrote and compiled the School Performance Application, they sought out both the national and local Montessori community to review and comment on every section. This community expressed its support of the Application as noted in Appendix F, Evidence of Support

For this application for Innovation Status, the majority of the application is the Performance School Application. All additional sections of the Request for Innovation Status have been presented to this same group of community supporters. Please find below the evidence of their support for Denver Montessori Junior/Senior High School’s application for innovation Status. Also included is a letter of support from DMHS employee Carol Delong. Principal Katy Myer’s evidence of support is evidenced by the cover letter she wrote for this application for innovation status. Katy and Carol are currently the only two employees of DMHS.

From: "Delong, Carol" <[email protected]> Subject: request for innovation status Date: December 19, 2012 11:38:59 AM MST To: "'Katy Myers' ([email protected])" <[email protected]>

I, Carol Delong, Office Support for the Denver Montessori Junior/Senior High, support the request for DMHS to have innovation status. I have worked at Gilpin Montessori Public School for four years now and have seen such positive growth in our students as a result of their Montessori education. It is very exciting that our students in Denver Public Schools will now have an option to continue their Montessori education through high school.

Sincerely, Carol Delong



From: Vincent, Frank Sent: Wednesday, December 19, 2012 1:59 PM To: Katy Myers ([email protected]); Myers, Katy Subject: Support for the Denver Montessori Junior/Senior High School

Katy,

I strongly support the Denver Montessori Junior/Senior High School’s request for Innovation Status. I think it will allow this school to move forward in the fastest possible manner to ensure the continuation of the Montessori program for our students in Denver Montessori programs, whether public, charter, or private. I look forward to working with this school to develop this groundbreaking model for school innovation that has been shown to be exactly what students need in their middle and high school years.

Frank Vincent Principal Gilpin Montessori Public School

On Dec 19, 2012, at 3:41 PM, [email protected] wrote:

Dear Denver Public Schools and Katy Myers,

I strongly endorse and support the Denver Montessori Junior/Senior High School's request for Innovation Status.

The Denver Public Schools has strongly supported Montessori Education for over twenty years.

It is exciting to provide parents and students with an opportunity to continue and complete their public school education in a Montessori setting and the innovation status approach will ensure successful completion.

Denver Public Schools is truly a national leader in the quest for innovative school design. We have an amazing opportunity to demonstrate that adolescent Montessori programs can work within the confines of District run schools.

Sincerely,

Dr. Martha M. Urioste Former Mitchell Montessori Elementary Citywide Magnet School Principal Former Denison Montessori Elementary Citywide Magnet School Principal Montessori Consultant for Sandoval, Lincoln, and Gilpin Montessori Elementary Schools Co-founder, President, and Board Member of Family Star 0-3 Montessori Education; two sites


On Dec 19, 2012, at 11:33 AM, Hannah Ewert-Krocker <[email protected]> wrote: Dear Katy,

I wanted to send you a quick email to let you know that as a graduate of the Hershey Montessori Adolescent Farm Program in Huntsburg, Ohio, a resident of the City and County of Denver, and the former High School Intern at Compass Montessori School in Golden, CO, support Denver Montessori Junior/Senior High School’s request for Innovation Status.

Good luck!

Hannah Ewert-Krocker

1346 Downing St. Apt. 2 Denver, CO, 80218 440.313.5882

On Dec 19, 2012, at 10:51 AM, Kathryn Ross <[email protected]> wrote: To Whom It May Concern:

I am writing to express strong support of the Denver Montessori Junior/High School's request for Innovation Status within DPS. As president of the Colorado Montessori Association, I know I speak for all our members when I say that we are excited to have the opportunity for a Montessori junior/senior high school option in Colorado. Support for and understanding of the Montessori education approach continues to grow in Colorado. Approving DMHS as a school with Innovation Status will be a valuable step in this process.

Sincerely,

Kathryn Ross

-- Kathryn Ross President, Colorado Montessori Association 2500 Curtis St. Denver, CO 80205



On Dec 19, 2012, at 10:21 AM, Greg MacDonald <[email protected]> wrote: Dear Katy,

As a Director of Elementary Teacher Training in the Montessori movement, I am very pleased to support Denver Montessori Junior/Senior High School’s request for Innovation Status.

Please let me know if there is anything else that I can do to support your work – This is a wonderful project that will impact generations to come!

Greg MacDonald Director of Elementary Training Hershey Montessori Training Institute 10924 Magnolia Drive Cleveland OH 44106 Telephone: 216-231-2651, ext. 306 (Office) 240-304-0275 (Cell) e-mail: [email protected]

On Dec 19, 2012, at 10:16 AM, JUDITH ORION <[email protected]> wrote:

I, Judith Orion, Director of Training, The Montessori Institute, Denver, support Denver Montessori Junior/Senior High School’s request for Innovation Status.

On Dec 19, 2012, at 1:46 PM, Laurie Ewert-Krocker <[email protected]> wrote:

Dear Katy,

Please make it known that as a National Consultant to Montessori Adolescent programs and Co-Director of the AMI-NAMTA Orientation to Adolescent Studies Course, I fully support the Denver Montessori Junior/Senior High School’s request for Innovation Status.

Please let me know how else I can help or support this endeavor.

Sincerely,

Laurie Ewert-Krocker North American Montessori Teachers Association and Montessori Development Partnerships -- Laurie Ewert-Krocker Hershey Montessori School Adolescent Program on the Farm 11530 Madison Rd. Huntsburg, OH 44046





From: Kristy Cash - HS Program Director [[email protected]] Sent: Saturday, December 29, 2012 9:25 AM To: Myers, Katy Subject: Support Statement

As the program director of Compass Montessori School's secondary school program for the past 13 years, I am absolutely thrilled with the enormous possibilities of Denver Montessori Junior/Senior High School to be a powerful leader in the national movement for educational innovation and change. Therefore, I would fully support Denver Montessori Junior/Senior High School's request for Innovation Status.

Please feel free to contact me anytime with any questions. Thank you for your kind and encouraging consideration.

-- Kristy Cash, Program Director Compass Montessori Secondary School Website: www.compassmontessori.org Phone: (303) 271-1977 x242 Fax: (303) 271-1984

Statement Regarding Other Evidence of Support

The proposed innovation school is a new school, and thus, currently employs no teachers or other staff members. All employees will have access to the innovation school’s plan prior to being hired. Prior to being hired and upon acceptance of employment at the school, each employee shall make a commitment that s/he supports and consents to the designation as an innovation school.

Similarly, as a new school, the school has no school accountability committee (“SAC”). Included in this plan, is a letter from the current administrators at the school, which outlines administrative support and consent to the designation as an innovation school.


http://www.compassmontessori.org/

http://www.compassmontessori.org/

Part IV: Curriculum Components

DMHS Alignment with DPS Graduation Standards October 2012

Denver Montessori Junior/Senior High School (DMHS) is an approved DPS performance school that will open in August 2013. As part of the approval process, DMHS agreed to provide evidence as to how they will meet or exceed DPS Graduation Requirements. DMHS will meet all graduation requirements as stated in the DPS Board Policy IKF. Explanation of how DMHS will meet these requirements is included below.

Nearly all of DMHS classes will be taught through an integrated approach with mastery level requirements for each subject area. For example, in the 6th, 7th , 8th

and 9th grade, Language Arts and History will be taught together as a Humanities Class. Art will be integrated into this unit as well as music. Each unit will have stated objectives for each subject area along with related required evidence of mastery for each objective. All record keeping will be maintained in a Student Electronic Portfolio, which will contain documentation of lessons attended, student submitted work, teacher feedback, mastery level quizzes, cumulative project, and overall unit assessment.

Because of this integrated approach and focus on mastery, DMHS will refer to units in the graduation requirements versus semester hours. Each unit will equate to one year’s instructional content, and a .5 unit will equal one semester of instructional content.

In addition to DMHS classes, high school juniors and seniors will also have the option to obtain dual credit through either attendance at a local college or university or through vetted and approved accredited on-line university level course work. Students will be responsible for fees associated with college credit. DMHS will assist students in the application process, navigating the college or university and applying for scholarships and financial aid.

In addition to the DPS high school graduation requirements, DMHS will require community service / service learning versus allowing it to be optional. DMHS will also strongly encourage all students to apply to three colleges / universities / technical college or other similar post secondary options.

Following are requirements as outlined by DPS Board Policy IKF and the DMHS response to each requirement.

REQUIRED UNITS OF STUDY Requirement:

THE PERSONAL EDUCATION PLAN Each student who enters a Denver Public Schools high school will develop a personal education plan (P.E.P.). This plan will set his/her intended course of study as he/she begins his/her journey toward graduation. The student and an academic adviser (this may be a teacher, counselor, dean administrator or other professional school staff member) will review and amend the P.E.P. each semester, prior to the development of a new class schedule (for students attending the 8th grade in the Denver Public Schools, the P.E.P. will be initiated during the spring semester of the 8th grade year). Schools may opt for an "advisement" class to provide for the P.E.P. This process will not only provide clear information and a focus on the future for the student, but also bring a new purpose to the important articulation between middle school and high school staff members.

Response:

Every student at DMHS will have a personal education plan (P.E.P). Beginning in 8th

grade, students will design their plan with assistance from their academic advisor. The P.E.P will be reviewed at every student/advisor/family conference and amended as agreed by that team.

Requirement:

General Course of Study Twenty-four (24) units of study (240 semester hours) shall be required in grades 9, 10, 11, and 12 for students to graduate from high school and receive a high school diploma.

Response:

DMHS students will receive a minimum of twenty-four (24) units of study. Completion of a unit of study will be determined by assessments that demonstrate mastery of that particular course of study.

Requirement:

1. Language Arts A minimum of forty semester hours (4 units) shall be earned including ten semester hours (1 unit) of Introduction to Literature and Composition 1 & 2 (9th Grade), ten semester hours (1 unit) of American Literature 1 & 2 (10th Grade), ten semester hours (1 unit) of upper division writing academic elective or world literature, and ten semester hours (1 unit) of other language arts.

Response:

9th Grade:

Ninth grade students will receive 1 unit of Literature and Composition1&2 that will be integrated as part of the thematic humanities course of study.

10th, 11th and 12th:

Over a three-year cycle, students will be required to take 1 unit of American Literature 1 & 2, 1 unit of upper division writing academic elective or world literature, and 1 unit of other Language Arts.

American Literature will be offered every other year to insure that students meet this requirement. American Literature will be integrated with U.S. History.

Each year, an AP component will be offered in Language Arts.

Requirement:

2. Social Studies

Thirty semester hours (3 units) shall be earned: ten semester hours (1 unit) in U.S. History, five semester hours (.5 units) in Civics, and fifteen semester hours (1.5 units) of other Social Studies are required.

Response:

9th Grade: Ninth grade students at DMHS will receive .5 units of Civics. Ninth grade students will also receive .5 units of Social Studies. Social Studies will be integrated with Language Arts and delivered as an overall thematic humanities course of study.

10th, 11th and 12th. Over a three-year cycle, student will be required to take 1 unit of U.S. History and a minimum 1 unit of other Social Studies.

U.S. history will be offered every other year to insure that students meet this requirement. U.S. History will be integrated with American Literature. During these years, DMHS will also offer A.P. U.S. History.

On the alternate years, DMHS will offer 1 unit of World History.

Requirement:

3. Science

Thirty semester hours (3 units) shall be earned: Students will be required to complete 30 semester hours of science credit, 20 semester hours (2 units) must come from Earth Science, Biology, Chemistry, or Physics.

Response:

9th Grade: Ninth grade students will receive .5 units of Earth Science. Ninth grade students will also receive .5 units of Health and Human Development.

10th, 11th and 12th

During a three-year cycle, students will be required to take a total of 1. 5 units of Biology and Chemistry. DMHS will offer Biology (1 unit), Chemistry (1 unit) and Environmental Science (1 unit). DMHS will offer A.P. Environmental Science as well as A.P. Biology.

Requirement:

4. Mathematics Forty semester hours (4 units) shall be earned. Ten semester hours (1 unit) of Algebra I or its integrated equivalent (9th Grade), ten semester hours (1 unit) of Geometry or its integrated equivalent (10th Grade), ten semester hours (1 unit) of Algebra II or the integrated equivalent, and ten semester hours (1 unit) of higher math from an approved course list are required. Except that the high school Algebra requirement will be waived for a student who successfully completes one year of algebra in middle school. However, such students will still be required to complete forty semester hours (4 units) of mathematics in high school, including ten semester hours (1 unit) of Geometry and 10 semester hours of Algebra II (1 unit). In no case, will students receive high school credit for courses completed in middle school.

Response:

9th Grade: Students will earn 1 unit of math based on the individual student’s Math placement. Students will work at the level of Algebra I unless they have already demonstrated mastery in Algebra I.

The DMHS High School Math Curriculum is composed of three elements. The first element is subject lessons through Khan Academy. Khan Academy is an on-line program that provides detailed lessons starting with addition and proceeding through Calculus. Each subject area has extensive on-line lessons that fully cover the identified subject. The second element is Exeter Math, which is the curriculum delivered at Phillips Exeter Academy. Exeter Math is delivered via real-world problem solving, seminar and group work. The third element is a highly qualified

secondary Math teacher who will provide individualized assistance to students as they progress through the Khan curricular map. The math teacher will also participate in the Exeter groups providing group instruction as needed.

Credit will be awarded based on the following criteria: Students have completed a full unit of study such as Algebra I. Students will have participated in an Exeter study group for and average of no less than one hour per week. Students have turned in a completed math album that shows evidence of work for each Khan unit of study and their weekly Exeter group problem solving exercises.

Most students will already be placed on the Khan curriculum map from their DMHS work in 8th grade. Students new to DMHS will take an on-line evaluative math assessment (currently identified as the STAR Assessment but subject to change as on-line assessments continue to evolve and improve) to determine placement on the curriculum map. Students will work individually through the Khan curriculum map, and they will have the opportunity to accelerate or remediate based on their success level with placement.

10th, 11th and 12th

Over the three-year cycle, students will complete 3 units of math. Unless they have already demonstrated mastery, studies will include Algebra II and Geometry and continue through pre-calculus and calculus.

The DMHS High School Math Curriculum is composed of three elements. The first element is subject lessons through Khan Academy. Khan Academy is an on-line program that provides detailed lessons starting with addition and proceeding through Calculus. Each subject area has extensive on-line lessons that fully cover the identified subject. The second element is Exeter Math, which is the curriculum delivered at Phillips Exeter Academy. Exeter Math is delivered via real-world problem solving, seminar and group work. The third element is a highly qualified secondary Math teacher who will provide individualized assistance to students as they progress through the Khan curricular map. The math teacher will also participate in the Exeter groups providing group instruction as needed.

Credit will be awarded based on the following criteria: Students have completed a full unit of study such as Geometry. Students will have participated in an Exeter study group for and average of no less than one hour per week. Students have turned in a completed math album that shows evidence of work for each Khan unit of study and their weekly Exeter group problem solving exercises.

Most students will already be placed on the Khan curriculum map from their previous DMHS work. Students new to DMHS will take an on-line evaluative math assessment (currently identified as the STAR Assessment but subject to change as on-line assessments continue to evolve and improve) to determine placement on the curriculum map. Students will have the opportunity to accelerate or remediate based on their success level with placement. Advanced students will have the

opportunity to take advanced trigonometry or calculus via on-line college or university curriculum or through Metropolitan State University.

Requirement:

5. Physical Education/Dance, Citywide Marching Band, ROTC, or DPS Athletics Ten semester hours (1 unit) of Physical Education or Dance shall be earned or an equivalent shall exempt the student from this requirement. Equivalents shall include: Citywide Marching Band, ROTC, DPS Athletics. Athletic sports that are sanctioned by the Denver Public Schools Board of Education and meet the criteria below may exempt a student from the physical education graduation requirement. No grade or credit will be given for athletic participation and such exemptions will not reduce the total number of hours required to earn a diploma. Both semesters of the physical education requirement may be exempted by athletic participation. Criteria governing physical education exemptions: a. The student must maintain academic eligibility for the entire season. b. One full sport season is required to exempt a student from five semester hours (5 units) of P.E. requirement, c. A student must be a high school freshman, sophomore, or junior to qualify for the exemption. Seniors who have not yet met the physical education requirement are not allowed to take this exemption and must enroll in a physical education course. d. The waiver must be requested in the same semester that the sport s played. (Rationale: this aligns the criteria of the Board policy and with the guidelines provided on the Criteria for Athletic Exemption form that is located on page 23 of the High School Procedures Guide. Provides clarification.) d. The waiver must be requested in the same semester that the sport is played.

Response:

9th – 12th grade

DMHS students will be required to complete 1 unit of Physical Education / Dance, Citywide Marching Band, ROTC, or DPS Athletics in compliance with requirement. DMHS will have a competitive Ultimate Frisbee team that will include after-school practices and games.

Requirement: 6. Electives: Ninety semester hours (9 units) shall be earned.

Academic Electives Forty semester hours (4 units) shall be earned. Ten semester hours (1 unit) shall be earned from an approved electives list. Another ten semester hours (1 unit) of fine arts (Music, Art, Drama) or Career Technical Education (CTE) must be earned.

Response:

9th Grade: Ninth grade students will be required to take 1 unit of Spanish. Spanish will be delivered via a highly qualified Spanish Teacher using the TPRS curriculum. Students will also complete .5 units of art, drama or music.

10th, 11th, 12th

Students will be required to complete 1 unit of Spanish. Spanish will be delivered via a highly qualified Spanish Teacher using the TPRS curriculum. Students will also complete a minimum of .5 units of art, drama or music.

If a student elects not to continue foreign language instruction, they will be required to complete 1 more unit of an academic elective in order to meet the 4 unit requirement for academic electives.

Requirement:

Other Electives Student must earn 50 semester hours of electives, of which 20 semester hours may be community service and service learning.

Response:

DMHS will offer a variety of electives to insure students have the opportunity to meet this graduation requirement. Electives will include drama, art, music, Ultimate Frisbee, Social Justice, cooking, craft work, and Micro-economy.

Requirement:

Community-Based experience- Within the 240 semester hours (24 units) required for a diploma, a minimum of 220 semester hours (22 units) shall be earned in classroom-based instruction. Students may, therefore, earn and apply a maximum of twenty semester hours (2 units) of community service and/or service learning experience, approved by the school, toward graduation requirements. These experiences may include, but are not limited to, field or service experiences, work experiences, volunteering with community organizations, and internships.

Response:

9th Grade: Students may have the opportunity to apply for a community service opportunity. Credit will be awarded based on the number of semester hours worked. Twenty completed hours worked will be equal to a .5 unit of Community Service.

10th, 11th and 12th Grade: Students will be required to participate in either a Community Service or Service Learning experience for a minimum of two hours per academic week. The schedule is designed to allow students to complete this requirement on Wednesday afternoons. Students may elect to complete their service during other hours in the week with advisor approval.

Requirement:

General Course of Study Additional Information At least four years (eight semesters) of attendance is required for students to complete grades 9, 10, 11, and 12 except that: * students with a 3.0 GPA who have completed all core curriculum/elective requirements and 240 credit hours (24 units) and all required assessments may graduate in seven semesters * students with a 3.5 GPA who have completed all core curriculum/elective requirements and 240 credit hours (24 units) and all required assessments may graduate in six semesters. * students with an Individual Education Program who are working towards a general course of study may earn up to 40 semester hours (4 units) in Special Education modified classes in only one core subject area. In addition, they may earn up to twenty semester hours (2 units) of Special Education modified credit in world language classes.

Achieving Personal Excellence (APEX) Requirements COURSE OF STUDY Provided that the high school has approval by the Superintendent or his designee, students will be awarded an ASCENT diploma if they meet all of the requirements in one through five in the general course of study, earn 35 hours of elective credit, and meet the requirements to earn an Associate of Arts (A.A.), Associate of Science (A.S.), or Associate of Applied Science (A.A.S.) Degree from a community college or a certificate of career and technical education.

Combined General Course of Study The combined General Course of Study requirements are the same as those for the General Course of Study, except that students with an Individual Education Program may earn up to 140 semester hours (14 units) in Special Education modified courses in the core subject areas and world language classes.

Two hundred and forty semester hours (24 units) will be required in grades 9, 10, 11, and 12, and/or through the first semester in which the student's twenty-first (21st) birthday falls, from courses approved by the school principal and determined by the staffing team. Transcripts will reflect differences in program content. The content areas and work study requirements are as listed below. Numbers of units are stated as minimums: 1. Language Arts 3.0 Units

2. Social Studies 2.0 Units 3. Science 1.0 Unit 4. Mathematics 2.0 Units 5. Physical Education/ Dance, Citywide Marching Band, or ROTC 1.0 Unit (unless otherwise specified by IEP) 6. Electives 1.0 Unit in vocations and/or Transition Classes - Required 8.0 Units (may include work experience) 7. Work Experience and Study 6.0 Units of work experience earned in Special Education-coordinated work experience. Vocations/Transitions course must be taken and passed as a prerequisite or in conjunction with work experience/study 1. Language Arts 3.0 Units 2. Social Studies 2.0 Units 3. Science 1.0 Unit 4. Mathematics 2.0 Units 5. Physical Education/ Dance, Citywide Marching Band, or ROTC 1.0 Unit (unless otherwise specified by IEP) 6. Electives 1.0 Unit in vocations and/or Transition Classes - Required 8.0 Units (may include work experience) 7. Work Experience and Study 6.0 Units of work experience earned in Special Education-coordinated work experience. Vocations/Transitions course must be taken and passed as a prerequisite or in conjunction with work experience/study

Designated Course of Study Requirements: The designated course of study will substitute for the curriculum/content standard approved by the Board of Education. In making determinations for earning a diploma, assessment instruments will be selected and administered so as to best ensure that when an assessment is administered to a student with impaired sensory, manual, or speaking skills, the test results accurately reflect the student's aptitude or achievement level rather than reflecting the student's impaired sensory, manual, or speaking skills. 1. Students with severe and profound disabling conditions that interfere with their ability to meet the requirements for either of the above courses of study and have satisfied the requirements of an Individualized Education Program shall graduate with a high school diploma. 2. Students may attend school in grades 9, 10, 11, and 12, and/or through the semester in which the student's twenty-first (21st) birthday falls, as determined by the IEP.

Transfer Students A transfer student from outside the Denver Public Schools must meet the requirements to receive a diploma from the Denver Public Schools. All graduation requirements must be met prior to graduation, including attendance in the Denver Public Schools for at least two semesters, with a minimum of 50 semester hours (5 units) of credit earned.

Certificate of Attendance Students who attend school regularly but do not meet the course of study requirements in any of the three courses of study areas may be awarded a Certificate of Attendance.

Response:

DMHS agrees with these requirements.

Credit

CCSS

CCSS Category

CCSS Sub-Category

Khan Academy Work - Videos:

Khan Academy Work - Exercises:

Occupations Work: 6,7,8 /

Montessori Materials

6th Grade Math

Denver Montessori Junior/Senior High School: Grades 6 - 8 Math Curriculum Alignment to the Common Core State Standards

6.EE.1 Expressions and

Equations

6th Grade Math 6.EE.2 Expressions and

Equations

Write and evaluate numerical expressions

involving whole-number exponents.

Write, read, and evaluate expressions in

which letters stand for numbers.

• Dividing Monomials • Exponent rules

• Dividing polynomials 1 • Positive and zero exponents

• Dividing polynomials with remainders • Dividing Monomials

• Evaluating exponential expressions

• Evaluating exponential expressions 2

• Exponent Properties 1



• ...and 16 more ...

• Dividing real numbers with different signs • Evaluating expressions in 2 variables

• Equation Special Cases • Evaluating expressions in one variable

• Evaluating an expression with multiple variables • Writing expressions

• Evaluating exponential expressions 2

• Multi-step equations 1


• Multiplying real number application

• Simplifying Expressions with Exponents

• ...and 5 more ...

MM: Algebra, Bead Chains, Base work

(e.g. Base 2, Base 9), Binomial/Trinomial

Cubes, Command Cards

MM: Algebra, Fact Families, Algebraic

Decanomial, Story of the Kings, Cubing

Materials, Colored Counting Bars,

Binomial Squares and Trinomial Squares,

Bead Cabinet, Bead Bars

6th Grade Math 6.EE.2.a Expressions and

Equations

6th Grade Math 6.EE.2.b Expressions and

Equations

Apply and extend previous understandings

of arithmetic to algebraic expressions

Identify parts of an expression using

mathematical terms (sum, term, product,

factor, quotient, coefficient); view one or

more parts of an expression as a single

entity. For example, describe the expression

2 (8 + 7) as a product of two factors; view

(8 + 7) as both a single entity and a sum of

two terms.

• • Writing expressions MM: Algebra

• Terms coefficients and exponents in a polynomial • Writing expressions MM: Algebra, Fact Families, Algebraic




Bead Cabinet, Bead Bars.

• Application problems with equation in one

variable

• Evaluating expressions in 2 variables MM: Algebra, Fact Families, Algebraic


6th Grade Math 6.EE.2.c Expressions and

Equations

Evaluate expressions at specific values of

their variables. Include expressions that

arise from formulas used in real-world

problems. Perform arithmetic operations,

including those involving whole-number

exponents, in the conventional order when

there are no parentheses to specify a

particular order (Order of Operations). For

• Applying Radical Equations 2 • Evaluating expressions in one variable • Direct Variation Application • Properties of numbers 2 • Dividing Monomials • Solving equations in terms of a variable • Dividing polynomials 1 • Writing expressions • Dividing polynomials with remainders • Writing expressions 2




example, use the formulas V = s3 and A = 6 • Dividing real numbers with different signs

s2 to find the volume and surface area of a

cube with sides of length s = 1/2. • Evaluate a formula using substitution • ...and 43 more ...

Apply the properties of operations to

• Equation Special Cases • Combining like terms with distribution

• Fractional Exponent Expressions 1 • Distributive property

MM: Algebra, Fact Families, Algebraic




Equations

6th Grade Math 6.EE.4

Expressions and Equations

generate equivalent expressions. For

example, apply the distributive property to

the expression 3 (2 + x) to produce the

equivalent expression 6 + 3x; apply the

distributive property to the expression 24x

+ 18y to produce the equivalent expression

6 (4x + 3y); apply properties of operations

to y + y + y to produce the equivalent

expression 3y.

Identify when two expressions are

equivalent (i.e., when the two expressions

name the same number regardless of which

value is substituted into them). For

example, the expressions y + y + y and 3y

are equivalent because they name the same

number regardless of which number y

stands for.

Understand solving an equation or

inequality as a process of answering a

• Fractional Exponent Expressions 2 • Distributive property with variables

• Fractional Exponent Expressions 3 • Expressions with unknown variables

• Inductive Reasoning 3 • Writing expressions 2


• Solving Equations with the Distributive Property

• The Distributive Property

• ...and 1 more ...

• Algebra: Solving Inequalities

• Algebraic Word Problem

• Equation Special Cases



Constructive Triangles, Geometric Insets

Cabinet, Pattern Blocks, Bead Bars,

Golden Beads, Decanomial

Occupations Unit 1 and 2

question: which values from a specified set, • Equations of Sequence Patterns


Equations if any, make the equation or inequality • Graphing Inequalities

true? Use substitution to determine whether • Graphing Inequalities 2

a given number in a specified set makes an

equation or inequality true.

• Simple Equations

• Solving systems by substitution 1

• ...and 3 more ...

• Algebraic Word Problem • Midpoint of a segment


Use variables to represent numbers and


variable

• Writing expressions


Equations

write expressions when solving a real-world • Averages

or mathematical problem; understand that a • Equations of Sequence Patterns

variable can represent an unknown number, • Evaluate a formula using substitution

or, depending on the purpose at hand, any

number in a specified set.

Solve real-world and mathematical

problems by writing and solving equations

• Example of Solving for a Variable

• Extraneous Solutions to Rational Equations


• ...and 6 more ...

• Multiplying and Dividing Monomials 1 • Addition and subtraction word problems

MM: Word Problems, Occupations Unit 1

and 2

6th Grade Math 6.EE.7 Expressions and of the form x + p = q and px = q for cases in • Multiplying and Dividing Monomials 2 • Multiplication and division word

Equations which p, q and x are all nonnegative

rational numbers. • Multiplying and Dividing Monomials 3

• Absolute Inequalities 2

problems 2

• Inequalities on a number line Occupations Unit 1 and 2

Write an inequality of the form x > c or x < • Absolute Value Inequalities



c to represent a constraint or condition in a

real-world or mathematical problem.

Recognize that inequalities of the form x >

c or x < c have infinitely many solutions;

represent solutions of such inequalities on

number line diagrams.

Use variables to represent two quantities in

• Absolute value inequalities example 3

• Algebra: Solving Inequalities

• Compound Inequalities 3


• Compund Inequalities

• Compund Inequalities 2

• ...and 14 more ...

• Deductive Reasoning 1 • Identifying linear relationships


a real-world problem that change in

relationship to one another; write an

• Direct Inverse and Joint Variation • Reading line charts 1

equation to express one quantity, thought of • Direct Variation Application • Reading tables 1

as the dependent variable, in terms of the



other quantity, thought of as the

independent variable. Analyze the

relationship between the dependent and

independent variables using graphs and

tables, and relate these to the equation. For

example, in a problem involving motion at

constant speed, list and graph ordered pairs

of distances and times, and write the

equation d = 65t to represent the

relationship between distance and time.

Find the area of right triangles, other

• Evaluate a formula using substitution • Reading tables 2

• Inverse Variation Application


• Proportionality Constant for Direct Variation

• Solving systems by graphing

• ...and 1 more ...

• Area and Perimeter • Area of parallelograms

Occupations Unit 1/ MM: Geometry:

triangles, special quadrilaterals, and

polygons by composing into rectangles or

• Area of Diagonal Generated Triangles of

Rectangle are Equal

• Area of squares and rectangles Geometric Insets, Yellow Area Materials,

Stick Box

6th Grade Math 6.G.1 Geometry




decomposing into triangles and other

shapes; apply these techniques in the

context of solving real-world and

mathematical problems.

Find the volume of a right rectangular prism

with fractional edge lengths by packing it

with unit cubes of the appropriate unit

fraction edge lengths, and show that

the volume is the same as would be found

by multiplying the edge lengths of the

prism. Apply the formulas V = l w h and V

= b h to find volumes of right rectangular

prisms with fractional edge lengths in the



Draw polygons in the coordinate plane given

coordinates for the vertices; use coordinates

to find the length of a side joining points

with the same first coordinate or the same

second coordinate. Apply these techniques

in the context of solving real- world and


Represent three-dimensional figures using

nets made up of rectangles and triangles,

and use the nets to find the surface area of

these figures. Apply these techniques in the



• Heron's Formula • Area of trapezoids, rhombi, and kites

• Rearrange formulas to isolate specific variables • Geometry 1

• Rhombus Diagonals • Heron's formula

• Perimeter of squares and rectangles

• Solid geometry MM: Geometry: Volume Cubes, Volume

Containers, Five Yellow Prisms

• The Coordinate Plane Occupations Unit 1

• Applying Radical Equations 2 MM: Geometry: Geometric Solids,

Volume Boxes.

6th Grade Math 6.RP.1 Ratios and Proportional Understand ratio concepts and use ratio

• Introduction to Ratios (new HD version)

• Ratios as Fractions in Simplest Form MM: Ratio and Proportion

Relationships reasoning to solve problems • Simplifying Rates and Ratios

• Finding Unit Prices • Expressing ratios as fractions MM: Ratio and Proportion. Occupations

6th Grade Math 6.RP.2 Ratios and Proportional Understand ratio concepts and use ratio

• Finding Unit Rates Unit 2 Relationships reasoning to solve problems

• Introduction to Ratios (new HD version)

• Another Take on the Rate Problem MM: Ratio and Proportion. Occupations

Use ratio and rate reasoning to solve real-

world and mathematical problems, e.g., by

6th Grade Math 6.RP.3 Ratios and Proportional

reasoning about tables of equivalent ratios, Relationships

• Finding Unit Prices

• Finding Unit Rates

• Introduction to Ratios

• Rate Problem Involving Rational Equations

Unit 2

tape diagrams, double number line

diagrams, or equations.

Make tables of equivalent ratios relating

quantities with whole-number

6th Grade Math 6.RP.3.a Ratios and Proportional measurements, find missing values in the

• Ratio and Proportion

• Scale and Indirect Measurement

• Systems and rate problems

• ...and 1 more ...

MM: Ratio and Proportion. Occupations

Unit 2

Relationships tables, and plot the pairs of values on the

coordinate plane. Use tables to compare

ratios.

Solve unit rate problems including those

involving unit pricing and constant speed.

• Another Take on the Rate Problem • Rate problems 0.5

• Rate Problem Involving Rational Equations • Rate problems 1

MM: Word Problems, Ratio and

Proportion. Occupations Unit 2

6th Grade Math 6.RP.3.b Ratios and Proportional For example, if it took 7 hours to mow 4 • Systems and rate problems • Ratio word problems

Relationships lawns, then at that rate, how many lawns

could be mowed in 35 hours? At what rate

were lawns being mowed?

Find a percent of a quantity as a rate per

100 (e.g., 30% of a quantity means 30/100

• Systems and rate problems 2


• Describing the Meaning of Percent • Converting decimals to percents

• Describing the Meaning of Percent 2 • Converting percents to decimals

• Percent and decimals • Discount tax and tip word problems

MM: Centesimal Protractor, Fraction

Circles, Geometric Cabinet, Word

Problems. Occupations Unit 2.

6th Grade Math 6.RP.3.c Ratios and Proportional

times the quantity); solve problems • Percent Problems • Markup and commission word problems

Relationships involving finding the whole, given a part

and the percent.

• Solving Percent Problems 2

• Solving Percent Problems 3

• Taking percentages

• Adding different units for weight

• Application problems involving units of weight

• Comparing Celsius and Farenheit temperature

MM: Ratio and Proportion, Word

Problems. Occupations Unit 2

Use ratio reasoning to convert measurement scales

6th Grade Math 6.RP.3.d Ratios and Proportional units; manipulate and transform units • Conversion between metric units

Relationships

6th Grade Math 6.SP.1 Statistics and Probability

appropriately when multiplying or dividing

quantities.

Develop understanding of statistical

variability

• Converting Farenheit to Celsius

• Converting Gallons to quarts pints and cups

• Converting pounds to ounces

• Converting units of length

• ...and 4 more ...

• Statistics: The Average Integrated Humanities: Population Study

• Average or Central Tendency: Arithmetic Mean, • Exploring standard deviation 1 Integrated Humanities: Population Study,


Understand that a set of data collected to

answer a statistical question has a

distribution which can be described by its

center, spread, and overall shape.

Median, and Mode

• Central Limit Theorem

• Sampling Distribution of the Sample Mean

• Sampling Distribution of the Sample Mean 2

• Standard Error of the Mean

• Statistics: The Average

Occupations Unit 2: Yield

• Average or Central Tendency: Arithmetic Mean, • Mean median and mode Integrated Humanities: Population Study,


Recognize that a measure of center for a

numerical data set summarizes all of its

values with a single number, while a

measure of variation describes how its

Median, and Mode

• Statistics: Alternate Variance Formulas

• Statistics: Sample Variance

• Statistics: Sample vs. Population Mean

Occupations Unit 2: Yield


values vary with a single number.

Display numerical data in plots on a

number line, including dot plots,

histograms, and box plots.


• Statistics: Variance of a Population

• Box-and-whisker Plot • Creating bar charts 1

• Central Limit Theorem • Reading bar charts 1

• Histograms • Reading bar charts 2

• Sampling Distribution of the Sample Mean • Reading bar charts 3

• Sampling Distribution of the Sample Mean 2 • Reading stem and leaf plots


• Statistics: Alternate Variance Formulas


• ...and 1 more ...

Integrated Humanities: Population Study,

Occupations Unit 2: Yield, MM: Graphs

and Charts


Summarize numerical data sets in relation

to their context, such as by:

• • Mean median and mode •

6th Grade Math 6.SP.5.a Statistics and Probability

Reporting the number of observations.



• Statistics: Standard Deviation

• Mean median and mode Occupations Unit 2: Yield

6th Grade Math 6.SP.5.b Statistics and Probability

Describing the nature of the attribute under

investigation, including how it was

measured and its units of measurement.

• • Mean median and mode Occupations Unit 2: Yield

• Average or Central Tendency: Arithmetic Mean, • Mean median and mode Integrated Humanities: Population Study,

Giving quantitative measures of center

(median and/or mean) and variability

(interquartile range and/or mean absolute

Median, and Mode


• ck12.org Exercise: Standard Normal Distribution

and the Empirical Rule

• ck12.org Normal Distribution Problems:

Empirical Rule


and Charts

6th Grade Math 6.SP.5.c Statistics and Probability

deviation), as well as describing any overall • ck12.org Normal Distribution Problems:

pattern and any striking deviations from the Qualitative sense of normal distributions

overall pattern with reference to the context • ck12.org Normal Distribution Problems: z-score

in which the data were gathered.

6th Grade Math 6.SP.5.d Statistics and Probability

Relating the choice of measures of center

and variability to the shape of the data

distribution and the context in which the

data were gathered.

• ck12.org: More Empirical Rule and Z-score

practice

• Law of Large Numbers

• ...and 8 more ...


• ck12.org Exercise: Standard Normal Distribution

and the Empirical Rule


Empirical Rule


Qualitative sense of normal distributions

• ck12.org Normal Distribution Problems: z-score

• Mean median and mode Integrated Humanities: Population Study,


and Charts

6th Grade Math 6.NS.1 The Number System


of multiplication and division to divide

fractions by fractions

• Introduction to the Normal Distribution

• Normal Distribution Excel Exercise


• ...and 2 more ...

• Dividing fractions • Dividing fractions

• Dividing Mixed Numbers • Dividing fractions 0.5

• Dividing Mixed Numbers and Fractions • Dividing fractions word problems

• Reciprocal of a Mixed Number

MM: Fraction Circles, Fraction Operation

Boards, Fraction Skittles

6th Grade Math 6.NS.2 The Number System Fluently divide multi-digit numbers using

the standard algorithm

• Level 4 division • Addition and subtraction word problems MM: Racks and Tubes, Division Boards


Fluently add, subtract, multiply, and divide

multi-digit decimals using the standard

algorithm for each operation.

• Multi-digit division

• Adding Decimals • 4-digit addition with carrying

• Dividing decimal • 4-digit subtraction with borrowing

• Dividing Decimals • Adding decimals 2

• Dividing Decimals 2.1 • Dividing decimals

• Dividing real numbers with different signs • Multi-digit division

• Dividing Whole Numbers and Applications 1 • Multi-digit multiplication

• Dividing Whole Numbers and Applications 2 • Multiplying decimals

• Dividing Whole Numbers and Applications 3 • Subtracting decimals

• ...and 11 more ...

• Comparing Fractions • Divisibility

• Comparing Fractions 2 • Divisibility 0.5

• Finding Factors of a Number • Divisibility tests

MM: Yellow Decimal Board, Decimal

Checkerboard, Decimal Checkerboard

Squares, Centesimal Protractor

MM: Peg Board, Sieve of Erathostenes,

Factor Trees.

6th Grade Math 6.NS.4 The Number System Compute fluently with multi-digit numbers

and find common factors and multiples

Understand that positive and negative

numbers are used together to describe

quantities having opposite directions or

• Fractions in lowest terms • Greatest common divisor

• Greatest Common Divisor • LCM and GCD word problems

• Least Common Multiple • Least common multiple

• The Distributive Property • Prime numbers

• The Distributive Property 2 • The fundamental theorem of arithmetic

• Negative Numbers Introduction • Adding and subtracting negative

numbers

MM: Positive/Negative Snake Game,

Number Line, Temperature Measurement


values (e.g., temperature above/below zero, • Opposite of a given number • Adding negative numbers elevation above/below sea level,

credits/debits, positive/negative electric

charge); use positive and negative numbers

to represent quantities in real-world

contexts, explaining the mean of 0 in each

situation.

• Negative number word problems

Understand a rational number as a point on

the number line. Extend number line

• Integers and Rational Numbers • Number line 2

• Number Sets • Points lines and planes

• Number Sets 1

MM: Negative Snake Game, World

Problems, Graphing

6th Grade Math 6.NS.6 The Number System diagrams and coordinate axes familiar from

• Number Sets 2 previous grades to represent points on the

line and in the plane with negative number

coordinates.

• Number Sets 3

• Points on a number line

• Quadrants of Coordinate Plane Apply and extend previous understandings

6th Grade Math 6.NS.6.a The Number System of numbers to the system of rational • Integers and Rational Numbers • Ordering negative numbers MM: Number Lines, Graphing

nUunmdebresrtsand signs of numbers in ordered • Opposite of a given number

6th Grade Math 6.NS.6.b The Number System pairs as indicating locations in quadrants of • Quadrants of Coordinate Plane • Graphing points MM: Graphing

the coordinate plane; recognize that when • Points on the coordinate plane

6th Grade Math 6.NS.6.c The Number System

Find and position integers and other

rational numbers on a horizontal or vertical

number line diagram; find and position

• Absolute Value Inequalities





• Ordering negative numbers MM: Graphing

pairs of integers and other rational numbers • Inequalities on a number line

on a coordinate plane.

6th Grade Math 6.NS.7 The Number System Understand ordering and absolute value of

rational numbers.

• Integers and Rational Numbers

• Locate integers on a number line

• ...and 11 more ...

• Absolute Value 1 • Comparing absolute values

• Absolute Value and Number Lines • Finding absolute values

• Absolute Value of Integers • Ordering numbers

• Application of addition of real numbers

MM: Number Line, Graphing

• Ordering Numeric Expressions

• Absolute Inequalities 2 • Comparing absolute values MM: Number Line, Graphing

• Absolute Value and Number Lines • Finding absolute values • Absolute Value Inequalities • Inequalities on a number line Apply and extend previous understandings • Absolute value inequalities example 3

6th Grade Math 6.NS.7.a The Number System of numbers to the system of rational • Compound Inequalities 3 numbers • Compound Inequalities 4 • Compund Inequalities • Compund Inequalities 2 • ...and 7 more ... Apply and extend previous understandings • Absolute Value and Number Lines • Comparing absolute values MM: Number Line, Graphing. Occupations

6th Grade Math 6.NS.7.b The Number System of numbers to the system of rational • Negative Numbers Introduction • Finding absolute values 1: GIS Mapping.

numbers • Ordering Numeric Expressions • Ordering numbers • Absolute Inequalities 2 • Comparing absolute values MM: Number Line, Graphing. Occupations

• Absolute Value 1 • Finding absolute values 1: GIS Mapping.

• Absolute Value and Number Lines • Ordering negative numbers Apply and extend previous understandings • Absolute Value Equation Example 2 • Ordering numbers 6th Grade Math 6.NS.7.c The Number System of numbers to the system of rational • Absolute Value Equations numbers • Absolute Value Equations 1 • Absolute Value Inequalities • Absolute value inequalities example 3 • ...and 3 more ... Apply and extend previous understandings • Absolute Value Inequalities • Comparing absolute values MM: Number Line, Graphing. Occupations

6th Grade Math 6.NS.7.d The Number System of numbers to the system of rational • Finding absolute values 1: GIS Mapping.

numbers • Ordering numbers Solve real-world and mathematical

problems by graphing points in all four

quadrants of the coordinate plane. Include

• Graphing points Occupations 1: GIS Mapping, Occupations

2: Yield, Integrated Humanities 1:

Population Study

6th Grade Math 6.NS.8 The Number System use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Credit

CCSS

CCSS Category

CCSS Sub-Category





7th Grade Math

• Algebra: Linear Equations 4 • Combining like terms MM: Algebra, Fact Families, Algebraic

• Equations 2 • Expressions with unknown variables Decanomial, Story of the Kings, Cubing

• Equations 3 • One step equations Materials, Colored Counting Bars,

Apply properties of operations as strategies • Multiplying Monomials • One step equations 0.5 Binomial Squares and Trinomial Squares,

7.EE.1 Expressions and

to add, subtract, factor, and expand linear • Multiplying Monomials by Polynomials • One-step equations with mult Bead Cabinet, Bead Bars, Equations

expressions with rational coefficients. • Opposite of a Polynomial

• Simple Equations

• The Distributive Property

• ...and 1 more ...


Equations

Use properties of operations to generate

equivalent expressions

• Growing by a percentage • Writing expressions 2 MM: Algebra

Solve multi-step real-life and mathematical • Basic Rate Problem • MM: Word Problems, Occupations Unit 1


Equations

problems posed with positive and negative

rational numbers in any form (whole

numbers fractions and decimals) using

• Representing a number as a decimal, percent, and

fraction

and 2

tools strategically. Apply properties of

• Representing a number as a decimal, percent, and

operations to calculate with numbers in any fraction 2 • Absolute Value Inequalities


variable

• MM: Word Problems, Occupations Unit 1

and 2



Use variables to represent quantities in a

real-world or mathematical problem, and

construct simple equations and inequalities

to solve problems by reasoning about the

quantities.

Solve word problems leading to equations





• Equations and Inequalities

• Evaluate a formula using substitution

• ...and 18 more ...

• Algebraic Word Problem • Age word problems

MM: Algebra, Word Problems,


Equations

of the form px + q = r and p(x + q) = r,

where p, q, and r are specific rational

numbers. Solve equations of these forms

fluently. Compare an algebraic solution to

an arithmetic solution, identifying the

sequence of the operations used in each

approach. For example, the perimeter of a

rectangle is 54 cm. Its length is 6 cm. What

is its width?


variable

• Converting within the metric system

• Equations 2

• Equations 3


• Extraneous Solutions to Rational Equations

• Multiplying and Dividing Monomials 1

• ...and 7 more ...

• Reading tables 2 Occupations Unit 1 and 2


Solve word problems leading to inequalities • Algebra: Solving Inequalities

of the form px + q > r or px + q < r, where

• MM: Algebra, Word Problems,


p, q, and r are specific rational numbers.

Graph the solution set of the inequality and

interpret it in the context of the problem.




Equations For example: As a salesperson, you are paid • Compund Inequalities

Geometry

$50 per week plus $3 per sale. This week

you want your pay to be at least $100.

Write an inequality for the number of sales

you need to make, and describe the

solutions.


• Graphing linear inequalities in two variables 2

• Inequalities

• ...and 6 more ...

Solve problems involving scale drawings of • Polynomials1 • MM: Geometry, Solids, Area of Plane


geometric figures, including computing

actual lengths and areas from a scale

drawing and reproducing a scale drawing at

a different scale.

Figures, Geometric Construction.

Occupations Unit 1.

Draw (freehand, with ruler and protractor, • • Congruency postulates MM: Geometry, Solids, Area of Plane

and with technology) geometric shapes with Figures, Geometric Construction,

given conditions. Focus on constructing Constructive Triangles, Occupations Unit

7th Grade Math 7.G.2 Geometry triangles from three measures of angles or

sides, noticing when the conditions

determine a unique triangle, more than one

triangle, or no triangle.

1.


Describe the two-dimensional figures that

result from slicing three-dimensional

figures, as in plane sections of right

rectangular prisms and right rectangular

pyramids.

• Applying Radical Equations 3 • MM: Geometry, Solids, Area of Plane

Figures, Geometric Construction,

Know the formulas for the area and

circumference of a circle and use them to

• Area of a circle • Area of a circle

• Circles: Radius, Diameter and Circumference • Areas of circles and sectors

MM: Geometry, The Circle, Area of a

Circle, Circumference of a Circle.

7th Grade Math 7.G.4 Geometry solve problems; give an informal derivation • Polynomials1 • Circles and arcs


of the relationship between the

circumference and area of a circle.

Use facts about supplementary,

complementary, vertical, and adjacent

angles in a multi-step problem to write and

solve simple equations for an unknown

angle in a figure.

• Geometry 1

• Radius diameter and circumference

• Shaded areas

• Angle Game (part 2) • Alternate exterior angles 2

• Angles (part 2) • Alternate interior angles

• Similar triangles • Alternate interior angles 2

• Similar triangles (part 2) • Angle addition postulate

• The Angle Game • Angles 1

• Angles of a polygon

• Complementary and supplementary

angles

• Complementary angles

• Congruent angles

• Corresponding angles 2

• Exploring angle pairs

• Parallel lines 2

• Supplementary angles

• Vertical angles 2

MM: Geometry, Angles, Variety of

Angles, Measurement of an Angle, Adding

and Subtracting Angles using the

Montessori Protractor.



problems involving area, volume and

surface area of two- and three-dimensional

objects composed of triangles,

quadrilaterals, polygons, cubes, and right

prisms.

Compute unit rates associated with ratios of

• 2003 AIME II Problem 7

• Heron's Formula

• Performing arithmetic calculations on units of

volume

• Polynomials1

• Simplifying Expressions with Exponents 3

• Solid Geometry Volume

• Solving application problems involving units of

volume

• Solving Quadratic Equations by Factoring 3

• Heron's formula MM: Geometry: Solids, Volume, Volume

Cubes, Triangles, Constructive Triangles,

Geometric Plates. Occupations Unit 1 and

2.

7th Grade Math 7.RP.1 Ratios and Proportional

fractions, including ratios of lengths, areas • Basic Rate Problem • Units MM: Ratio and Proportion, Word

Relationships and other quantities measured in like or


• Find an Unknown in a Proportion • Proportions 1

• Find an Unknown in a Proportion 2 • Proportions 2

• Mixture problems 1

Problems. Occupations Unit 1 and 2.

MM: Ratio and Proportion, Word

Problems, Occupations Unit 1 and 2.

7th Grade Math 7.RP.2 Ratios and Proportional Recognize and represent proportional

• Mixture problems 2 Relationships relationships between quantities.

Decide whether two quantities are in a

proportional relationship, e.g., by testing for


• Proportionality

• Understanding Proportions

• Understanding Proportions

• Graphing points and naming quadrants

• Proportions 1

MM: Ratio and Proportion. Graphing.

7th Grade Math 7.RP.2.a Ratios and Proportional

equivalent ratios in a table or graphing on a Relationships

coordinate plane and observing whether the

graph is a straight line through the origin.

• Proportions 2

• Finding Unit Rates Identify the constant of proportionality (unit

• Mixture problems 1 • MM: Ratio and Proportion. Graphing.

7th Grade Math 7.RP.2.b Ratios and Proportional rate) in tables, graphs, equations, diagrams,

• Mixture problems 2 Relationships and verbal descriptions of proportional

relationships. Represent proportional relationships by

equations. For example, if total cost t is


• Proportionality

• Age word problems 1

• Age word problems 2

• MM: Ratio and Proportion. Occupations

Unit 2.

7th Grade Math 7.RP.2.c Ratios and Proportional proportional to the number n of items • Age word problems 3

Relationships purchased at a constant price p, the

relationship between the total cost and the



number of items can be expressed as t = pn. • Mixture problems 3

Explain what a point (x, y) on the graph of

a proportional relationship means in terms

7th Grade Math 7.RP.2.d Ratios and Proportional

of the situation, with special attention to the

• • MM: Ratio and Proportion. Occupations

Unit 2.

Relationships points (0, 0) and (1, r) where r is the unit

rate.

• Advanced ratio problems • Percentage word problems 1

MM: Ratio and Proportion. Word

Use proportional relationships to solve

multistep ratio and percent problems.

• Alternate Solution to Ratio Problem (HD

Version)

• Another Percent Word Problem

• Percentage word problems 2 Problems. Occupations Unit 2.

7th Grade Math 7.RP.3 Ratios and Proportional Examples: simple interest, tax, markups and • Growing by a percentage

Relationships markdowns, gratuities and commissions, • Introduction to interest

fees, percent increase and decrease, percent • Mixture problems 1

error. • Mixture problems 2


• ...and 5 more ...


Understand that statistics can be used to

gain information about a population by

examining a sample of the population;

generalizations about a population from a

sample are valid only if the sample is

representative of that population.

Understand that random sampling tends to


• Confidence Interval Example


• Margin of Error 1




• Variance Integrated Thematics: Population Study.

produce representative samples and support • Statistics: Sample Variance

valid inferences.

Use data from a random sample to draw

inferences about a population with an

• ...and 3 more ...



Qualitative sense of normal distributions

• MM: Word Problems. Occupations Unit 1

and 2.

unknown characteristic of interest. Generate • ck12.org Normal Distribution Problems: z-score

multiple samples (or simulated samples) of


the same size to gauge the variation in

estimates or predictions. For example,

estimate the mean word length in a book by

randomly sampling words from the book;

predict the winner of a school election

based on randomly sampled survey data.

Gauge how far off the estimate or

prediction might be.

Informally assess the degree of visual

overlap of two numerical data distributions

with similar variabilities, measuring the

difference between the centers by

• ck12.org: More Empirical Rule and Z-score

practice

• Clarification of Confidence Interval of Difference

of Means


• Confidence Interval of Difference of Means


• ...and 7 more ...

• ANOVA 1 - Calculating SST (Total Sum of

Squares)

• ANOVA 2 - Calculating SSW and SSB (Total

Sum of Squares Within and Between).avi

• Integrated Thematic Units 1 and 2:

Compare and Contrast.

expressing it as a multiple of a measure of • ANOVA 3 -Hypothesis Test with F-Statistic

Statistics and variability. For example, the mean height of • Clarification of Confidence Interval of Difference 7th Grade Math 7.SP.3

7th Grade Math 7.SP.4

Probability

Statistics and

Probability

players on the basketball team is 10 cm

greater than the mean height of players on

the soccer team, about twice the variability

(mean absolute deviation) on either team;

on a dot plot, the separation between the

two distributions of heights is noticeable.

Use measures of center and measures of

variability for numerical data from random

samples to draw informal comparative

inferences about two populations. For

example, decide whether the words in a

of Means

• Comparing Population Proportions 1



• Hypothesis Test Comparing Population

Proportions

• ANOVA 1 - Calculating SST (Total Sum of

Squares)

• ANOVA 2 - Calculating SSW and SSB (Total

Sum of Squares Within and Between).avi

• ANOVA 3 -Hypothesis Test with F-Statistic

• Clarification of Confidence Interval of Difference

of Means

• Integrated Thematic Units 1 and 2:


chapter of a seventh-grade science book are • Comparing Population Proportions 1

generally longer than the words in a chapter • Comparing Population Proportions 2

of a fourth-grade science book.

Understand that the probability of a chance

event is a number between 0 and 1 that

expresses the likelihood of the event

occurring. Larger numbers indicate greater


• Hypothesis Test Comparing Population

Proportions

• Dependent Probability Example 2

• Events and Outcomes 1



• Probability 1 MM: Yellow Decimal Board, Occupations

Unit 1.

7th Grade Math 7.SP.5 Statistics and Probability likelihood. A probability near 0 indicates an • Probability (part 2)

unlikely event, a probability around 1/2

indicates an event that is neither unlikely

• Probability (part 3)


nor likely, and a probability near 1 indicates • Probability (part 5)

a likely event.

Approximate the probability of a chance

event by collecting data on the chance

process that produces it and observing its

• ...and 2 more ...




• Probability 1 •

long-run relative frequency, and predict the • Events and Outcomes 3


approximate relative frequency given the

probability. For example, when rolling a

• Independent Events 3


number cube 600 times, predict that a 3 or 6 • Probability (part 3)


Statistics and Probability

would be rolled roughly 200 times, but

probably not exactly 200 times.

Develop a probability model and use it to

find probabilities of events. Compare

probabilities from a model to observed

frequencies; if the agreement is not good,


• ...and 4 more ...







• Probability 1 Occupations Unit 1.

explain possible sources of the discrepancy. • Probability (part 4)


• ...and 4 more ... Develop a uniform probability model by

• Events and Outcomes 1 assigning equal probability to all outcomes,


• Probability 1 •


and use the model to determine

probabilities of events. For example, if a

student is selected at random from a class,

find the probability that Jane will be

selected and the probability that a girl will





be selected • Probability 1 Module Examples

Develop a probability model (which may • Dependent Probability Example 2 • Probability 1 •

not be uniform) by observing frequencies in • Events and Outcomes 1

7th Grade Math 7.SP.7.b



data generated from a chance process. For

example, find the approximate probability

that a spinning penny will land heads up or

that a tossed paper cup will land open-end

down. Do the outcomes for the spinning

penny appear to be equally likely based on

the observed frequencies?

Find probabilities of compound events

using organized lists, tables, tree diagrams,

and simulation.







• ...and 4 more ...









• ...and 1 more ...




• Occupations Unit 1 and 2.

• Occupations Unit 1 and 2.

Understand that, just as with simple events, • Probability (part 3)


7th Grade Math 7.SP.8.b Statistics and Probability

the probability of a compound event is the

fraction of outcomes in the sample space

for which the compound event occurs.

Investigate chance processes and develop,

use, and evaluate probability models





• ...and 1 more ...

• Dependent Probability Example 2 • •








• ...and 1 more ... Design and use a simulation to generate

• Independent Events 2 • Occupations 1 and 2

7th Grade Math 7.SP.8.c Statistics and Probability

frequencies for compound events. For

example, use random digits as a simulation

tool to approximate the answer to the

question: If 40% of donors have type A

• Introduction to Random Variables



blood what is the probability that it will • Sampling Distribution Example Problem



of addition and subtraction to add and

subtract rational numbers; represent

addition and subtraction on a horizontal or

vertical number line diagram.

• Absolute Inequalities 2



• Adding and subtracting fractions

• Addition of Rational Numbers

• Subraction of Rational Numbers

• MM: Positive/Negative Snake Game,

Number Line, Decimal Fractions, Yellow

Decimal Board, Decimal Chequer Board,

Centesimal Frame, Graphing.

7th Grade Math 7.NS.1.a The Number System

Describe situations in which opposite

quantities combine to make 0. For example,

a hydrogen atom has 0 charge because its

two constituents are oppositely charged.

• • MM: Number Line, Signed Numbers.

Understand p + q as the number located a • Adding and subtracting real numbers

• MM: Number Line, Signed Numbers.

7th Grade Math 7.NS.1.b The Number System

distance |q| from p, in the positive or

negative direction depending on whether q

is positive or negative. Show that a number

and its opposite have a sum of 0 (are

additive inverses). Interpret sums of

• Adding and subtracting real numbers application

• Adding integers with different signs

• Adding real numbers with different signs

• Application of addition of real numbers

rational numbers by describing real-world • Subtracting Real Numbers • Absolute Value Equations

• Absolute Value Equations 2


• MM: Number Line, Signed Numbers,

Decimal Fractions, Yellow Decimal Board,

Decimal Chequer Board, Centesimal

Apply and extend previous understandings • Adding and subtracting real numbers Frame, Graphing.

7th Grade Math 7.NS.1.c The Number System of operations with fractions to add, subtract, • Adding and subtracting real numbers application

multiply, and divide rational numbers

7th Grade Math 7.NS.1.d The Number System Apply properties of operations as strategies

to add and subtract rational numbers.

• Adding integers with different signs

• Adding real numbers with different signs

• Adding/Subtracting negative numbers

• ...and 3 more ...

• Adding and subtracting fractions • MM: Adding and Subtracting Fractions,

Signed Numbers, Decimal Fractions,

Yellow Decimal Board, Decimal Chequer

Board, Centesimal Frame



of multiplication and division and of

fractions to multiply and divide rational

numbers.


• Dividing fractions

• Dividing real numbers with different signs

• Division of Rational Numbers

• Fractional Exponent Expressions 1



• Multiplication of Rational Numbers

• Multiplying Fractions

• ...and 2 more ...



• Multiplying and dividing negative

numbers


numbers

MM: Signed Numbers, Fraction Circles,

Fraction Operation Boards, Fraction

Skittles

MM: Signed Numbers

7th Grade Math 7.NS.2.a The Number System of operations with fractions to add, subtract, • Fractional Exponent Expressions 3

multiply, and divide rational numbers • Multiplying and dividing negative numbers

• Multiplying negative real numbers

• Multiplying real number application Apply and extend previous understandings

7th Grade Math 7.NS.2.b The Number System of operations with fractions to add, subtract, • Dividing real numbers with different signs • Multiplying and dividing negative MM: Signed Numbers

multiply and divide rational numbers • Multiplying and dividing negative numbers • Dividing fractions

• Dividing real numbers with different signs


numbers


numbers

MM: Signed Numbers

7th Grade Math 7.NS.2.c The Number System Apply properties of operations as strategies

to multiply and divide rational numbers.

Convert a rational number to a decimal



• Multiplying Fractions

• Multiplying negative real numbers


• Representing a number as a decimal, percent, and • Multiplying and dividing negative

Group Division with Stamp Game.

7th Grade Math 7.NS.2.d The Number System using long division; know that the decimal

form of a rational number terminates in 0s

or eventually repeats.

fraction 2 numbers

Credit

CCSS

CCSS Category

CCSS Sub-Category





8th Grade Math

8.EE.1

Solve real-world and mathematical • Fractional Exponent Expressions 1 • Average word problems MM: Word Problems, Occupations Unit 1

7th Grade Math 7.NS.3 The Number System problems involving the four operations with • Fractional Exponent Expressions 2 and 2

rational numbers.1 • Fractional Exponent Expressions 3

Expressions and

Equations

Work with radicals and integer exponents

Use square root and cube root symbols to

• Dividing Monomials • Exponent rules

• Evaluating exponential expressions • Fractional exponents

• Evaluating exponential expressions 2 • Negative fractional exponents






• ...and 13 more ...

• Applying Radical Equations 2 • Cube roots

MM: Squaring and Cubing. Powers of

Numbers

MM: Cube Root, Square Root.

represent solutions to equations of the form • Simplifying Expressions with Exponents • Estimating square roots


Equations


Expressions and

x2 = p and x3 = p, where p is a positive

rational number. Evaluate square roots of

small perfect squares and cube roots of

small perfect cubes. Know that _2 is

irrational.

• Simplifying Expressions with Exponents 2 • Square roots

• Simplifying Expressions with Exponents 3

• Solving Radical Equations 3

• Square Roots and Real Numbers

• Understanding Square Roots

• Scientific Notation • Multiplying and dividing scientific

notation

• Scientific notation 1 • Scientific notation

MM: Powers of Numbers

Equations Work with radicals and integer exponents

• Scientific notation 2 • Scientific notation intuition

• Scientific notation 3

• Scientific Notation Examples Perform operations with numbers expressed

• Scientific Notation • Multiplying and dividing scientific MM: Powers of Numbers in scientific notation, including problems

where both decimal and scientific notation • Scientific notation 1 notation

8th Grade Math 8.EE.4 Expressions and are used. Use scientific notation and choose

• Scientific notation 2 Equations

units of appropriate size for measurements

of very large or very small quantities (e.g.,

• Scientific notation 3

• Scientific Notation Examples

use millimeters per year for seafloor • Scientific Notation I


Equations

Graph proportional relationships,

interpreting the unit rate as the slope of the

graph. Compare two different proportional

relationships represented in different ways.

For example, compare a distance-time

graph to a distance-time equation to

• Calculus: Derivatives 1 (new HD version)


• Converting to slope-intercept form

• Graphical Slope of a Line

• Slope Example

• Slope of a line

• MM: Graphing. Occupations Unit 1 and 2.

Integrated Humanities Units 1 and 2:


determine which of two moving objects has • Slope of a Line 2

greater speed. • Slope of a Line 3


Expressions and

Equations

Use similar triangles to explain why the

slope m is the same between any two

distinct points on a non-vertical line in the

coordinate plane; derive the equation y =

mx for a line through the origin and the

equation y = mx + b for a line intercepting

the vertical axis at b.

• Algebra: Equation of a line • Converting between point-slope and

slope-intercept

• Algebra: graphing lines 1 • Converting between slope-intercept and

standard form

• Algebra: Slope • Equations of parallel and perpendicular

lines

• Algebra: Slope 2 • Finding the equation of a line

• Algebra: Slope 3 • Identifying slope of a line

• Algebra: Slope and Y-intercept intuition • Line graph intuition

• Equation of a line 1 • Solving for the y-intercept

• Equation of a line 3

• ...and 6 more ...

MM: Algebra, Graphing.



Solve linear equations in one variable.

• Absolute Value Equation Example 2

• Absolute Value Equations 1

• Application problem with graph


• Graphing using X and Y intercepts

• Plotting (x,y) relationships

• Solving Equations 1


• ...and 2 more ...

• 2-step equations MM: Algebra, Graphing

8th Grade Math 8.EE.7.a


Give examples of linear equations in one

variable with one solution, infinitely many

solutions, or no solutions. Show which of

these possibilities is the case by

successively transforming the given

equation into simpler forms, until an

• Absolute Value Equation Example 2 • 2-step equations

• Absolute Value Equations 1 • One-step equations with mult



variable


MM: Algebra, Graphing

equivalent equation of the form x = a, a = a, • Graphing using X and Y intercepts

or a = b results (where a and b are different

numbers). • Multiplying real number application

• Solving systems by graphing 3

• Algebra: Linear Equations 4 • 2-step equations

• Algebraic Word Problem • Expressions with unknown variables 2

MM: Distributive Laws, Introduction to

Algebra, Word Problems, Binomial Cube,

Solve linear equations with rational number • Example of Solving for a Variable • One-step equations with mult Trinomial Cube.


Equations

coefficients, including equations whose

solutions require expanding expressions

using the distributive property and

collecting like terms.

• Factoring and the Distributive Property • Solving equations in terms of a variable

• Factoring and the Distributive Property 2




• ...and 2 more ...


Equations


Equations

Analyze and solve pairs of simultaneous

linear equations.

Understand that solutions to a system of

two linear equations in two variables

correspond to points of intersection of their

graphs, because points of intersection

satisfy both equations simultaneously.

Solve systems of two linear equations in

• Addition Elimination Method 3


• systems of equations



• Consistent and Inconsistent Systems

• Graphical Systems Application Problem

• Independent and Dependent Systems

• Solving Linear Systems by Graphing

• Solving systems by graphing

• Solving systems by graphing 2

• ...and 6 more ...



• Systems of equations MM: Algebra, Graphing

• Systems of equations MM: Algebra, Graphing

• Systems of equations MM: Algebra, Graphing.

two variables algebraically, and estimate

solutions by graphing the equations. Solve




Equations simple cases by inspection. For example, 3x • Consistent and Inconsistent Systems

+ 2y = 5 and 3x + 2y = 6 have no solution • Converting to slope-intercept form

because 3x + 2y cannot simultaneously be 5 • Graphical Systems Application Problem

8th Grade Math 8.EE.8.c


and 6.


problems leading to two linear equations in

two variables. For example, given

coordinates for two pairs of points,

• Independent and Dependent Systems

• ...and 15 more ...


• Point-slope and standard form

• Solving systems by elimination

• Solving systems by elimination 2

• Solving systems by elimination 3

• Systems of equations Occupations Unit 1.

determine whether the line through the first • Solving systems by graphing

pair of points intersects the line through the • Solving systems by graphing 2

second pair. • Solving systems by graphing 3

• ...and 4 more ...

• Application problem with graph • Ordered pair solutions to linear equations MM: Algebra

Understand that a function is a rule that

assigns to each input exactly one output.

• Direct Variation 1 • Understanding function notation

•

• Domain and Range 2

8th Grade Math 8.F.1 Functions The graph of a function is the set of ordered • Functional Relationships 1

8th Grade Math 8.F.2 Functions

pairs consisting of an input and the

corresponding output.1

Compare properties of two functions each

represented in a different way

(algebraically, graphically, numerically in

tables, or by verbal descriptions). For

example, given a linear function

represented by a table of values and a linear

function represented by an algebraic

expression, determine which function has

the greater rate of change.

• Functions as Graphs

• Introduction to functions

• Slope of a Line 3

• Testing if a relationship is a function

• ...and 1 more ...

• • Evaluating expressions with function

notation

MM: Algebra

Interpret the equation y = mx + b as

defining a linear function, whose graph is a

straight line; give examples of functions

that are not linear. For example, the

• Basic Linear Function




• Ordered pair solutions to linear equations MM: Algebra

8th Grade Math 8.F.3 Functions function A = s^2 giving the area of a square • Equation of a line 3

as a function of its side length is not linear

because its graph contains the points (1,1),

(2,4) and (3,9), which are not on a straight

line.

Construct a function to model a linear

relationship between two quantities.

Determine the rate of change and initial

• Exploring linear relationships

• Graphing a line in slope intercept form


• ...and 5 more ...

• Application problem with graph

• Basic Linear Function

• Ordered pair solutions to linear equations MM: Algebra, Occupation Unit 1

8th Grade Math 8.F.4 Functions value of the function from a description of a • Calculus BC 2008 2 a

relationship or from two (x, y) values, • Direct Variation 1

including reading these from a table or from • Exploring linear relationships

a graph Interpret the rate of change and • Linear Equations in Slope Intercept Form • Application problem with graph

• MM: Algebra, Graphing, Occupations Unit


8th Grade Math 8.G.1.a Geometry

8th Grade Math 8.G.1.b Geometry

8th Grade Math 8.F.5 Functions

Describe qualitatively the functional

relationship between two quantities by

analyzing a graph (e.g., where the function

is increasing or decreasing, linear or

nonlinear). Sketch a graph that exhibits the

qualitative features of a function that has

been described verbally.



• Direct Variation 1


• Exploring linear relationships

• Exploring nonlinear relationships

• Functional Relationships 1

• ...and 7 more ...

1 and 2.

Verify experimentally the properties of

rotations, reflections, and translations:

Lines are taken to lines, and line segments

to line segments of the same length.

Angles are taken to angles of the same

measure.

• • •

• • •

• • •

8th Grade Math 8.G.1.c Geometry Parallel lines are taken to parallel lines. • • Parallel lines 1 • Understand that a two-dimensional figure is

8th Grade Math 8.G.2 Geometry congruent to another if the second can be • • Congruent triangles 1 MM: Constructive Triangles, Geometric

obtained from the first by a sequence of • Congruent triangles 2 Cabinet, Blue Triangles.


Describe the effect of dilations, translations, • • Shifting and reflecting functions •

rotations, and reflections on two-

dimensional figures using coordinates. Understand that a two-dimensional figure is

• Similar triangles similar to another if the second can be

• Similar triangles 1

• Similar triangles 2 MM: Constructive Triangles, Geometric

Cabinet, Blue Triangles



obtained from the first by a sequence of

rotations, reflections, translations, and

dilations; given two similar two-

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about the angle sum and exterior angle of

triangles, about the angles created when

parallel lines are cut by a transversal, and

the angle-angle criterion for similarity of

triangles. For example, arrange three copies

of the same triangle so that the sum of the

• Similar triangles review

• Solving similar triangles 1


• Angle Game (part 2) • Angles 2

• Angles (part 3) • Congruent triangles 1

• Angles formed between transversals and parallel • Congruent triangles 2

lines

• Angles of parallel lines 2

• Similar triangles

MM: Angles, Constructive Triangles,

Geometric Cabinet, Blue Triangles.

three angles appears to form a line, and give • Similar triangles (part 2)

an argument in terms of transversals why • The Angle Game

this is so. • Triangle Medians and Centroids • Pythagorean Theorem II

• Pythagorean theorem MM: Theorems, Pythagoras Geometric

8th Grade Math 8.G.6 Geometry Explain a proof of the Pythagorean Theorem and its converse.

Apply the Pythagorean Theorem to

• The Pythagorean Theorem

• Visual Pythagorean Theorem Proof

• 30-60-90 Triangles II

• Basic Trigonometry

• Pythagorean Theorem

Plates I, II and III.

• Special right triangles MM: Theorems, Pythagoras Geometric

Plates I, II, and III. Occupations (Design

and Planning).

8th Grade Math 8.G.7 Geometry determine unknown side lengths in right

triangles in real-world and mathematical

problems in two and three dimensions.

Apply the Pythagorean Theorem to find the

• Pythagorean Theorem 1




• Distance Formula • Distance between point and line

MM: Theorems, Pythagoras Geometric

8th Grade Math 8.G.8 Geometry distance between two points in a coordinate • Polar Coordinates 1 • Distance formula Plates I, II, and III. Occupations (Design


system.

Know the formulas for the volumes of

cones, cylinders, and spheres and use them

to solve real-world and mathematical

problems

• Polar Coordinates 2


• Applying Radical Equations 3

• Cylinder Volume and Surface Area

• Introduction to rate-of-change problems


and Planning).

• MM: Solids, Volume



Statistics and

Construct and interpret scatter plots for

bivariate measurement data to investigate

patterns of association between two

quantities. Describe patterns such as

clustering, outliers, positive or negative

association, linear association, and

nonlinear association.

Know that straight lines are widely used to

model relationships between two

quantitative variables. For scatter plots that

• Multiplying Polynomials 3

• Law of Large Numbers • •

• Calculating R-Squared • •

• Covariance and the Regression Line

• Fitting a Line to Data

• Proof (Part 1) Minimizing Squared Error to

Regression Line

• Proof (Part 3) Minimizing Squared Error to 8th Grade Math 8.SP.2

Probability suggest a linear association, informally fit a

Regression Line straight line, and informally assess the


Statistics and

Probability

model fit by judging the closeness of the

data points to the line.

Use the equation of a linear model to solve

problems in the context of bivariate

measurement data, interpreting the slope

and intercept. For example, in a linear

model for a biology experiment, interpret a

slope of 1.5 cm/hr as meaning that an

additional hour of sunlight each day is

associated with an additional 1.5cm in

mature plant height.


Regression Line

• R-Squared or Coefficient of Determination

• Second Regression Example

• ...and 1 more ...

• Calculating R-Squared • •




Regression Line


Regression Line


Regression Line



• ...and 1 more ...


Understand that patterns of association can

also be seen in bivariate categorical data by

displaying frequencies and relative

frequencies in a two-way table. Construct

and interpret a two-way table summarizing

data on two categorical variables collected

from the same subjects. Use relative

frequencies calculated for rows or columns

to describe possible association between the

two variables. For example, collect data

from students in your class on whether or

not they have a curfew on school nights and

whether or not they have assigned chores at

home. Is there evidence that those who

have a curfew also tend to have chores?

• Contingency Table Chi-Square Test • Integrated Humanities 1 and 2, Compare

and Contrast.

Know that numbers that are not rational are

• Number Sets • Converting 1-digit repeating decimals to MM: Fractions, Yellow Decimal Board called irrational. Understand informally that

fractions

8th Grade Math 8.NS.1 The Number System rational numbers show that the decimal

expansion repeats eventually, and convert a

• Number Sets 1 • Converting multi-digit repeating

decimals to fractions

• Number Sets 3

Udesceimraatiloenxaplaanpspioronxwimhaictihornespoefatisrreavtieonntaulally •

numbers to compare the size v`of irrational • Converting 1-digit repeating decimals to MM: Fractions, Yellow Decimal Board

fractions 8th Grade Math 8.NS.2 The Number System numbers, locate them approximately on a

number line diagram, and estimate the • Converting multi-digit repeating

decimals to fractions value of expressions (e g 2) For

Credit CCSS CCSS Category CCSS Sub-Category Khan Academy Work - Videos: Khan Academy Work - Exercises Exeter Work: 9-12

Algebra 1

Algebra 1 9-12.A-APR.5

Denver Montessori Junior/Senior High School: Grades 9 - 12 Math Curriculum Alignment to the Common Core State Standards

Understand that polynomials form a system

analogous to the integers, namely, they are closed

9-12.A-APR.1 Arithmetic with Polynomials and Rational

• Adding and Subtracting Polynomials 1



• Adding Polynomials

• Addition and Subtraction of Polynomials

Exeter MAT 11T / 120 / 130 :

Expressions under the operations of addition, subtraction, and

multiplication; add, subtract, and multiply

polynomials.

• Dividing Monomials

• Dividing multivariable polynomial with monomial

• Dividing polynomials 1

Algebra

Identify zeros of polynomials when suitable

Algebra 1 9-12.A-APR.3 Arithmetic with Polynomials and Rationalfactorizations are available, and use the zeros to

• Polynomial Equations in Factored Form

• Adding and subtracting polynomials

• Multiplying polynomials

Exeter MAT 11T / 120 / 130 :

Expressions construct a rough graph of the function defined by

the polynomial.

Algebra

Arithmetic with Polynomials and Rational

Expressions Use polynomial identities to solve problems

Rewrite simple rational expressions in different

forms; write a(x)/b(x) in the form q(x) + r(x)/b(x),

• Binomial Theorem (part 1) Exeter MAT 11T / 120 / 130 :

Algebra

• Multiplying and Dividing Rational Expressions 2

• Multiplying and Dividing Rational Expressions 3

• Simplifying Rational Expressions 1

Algebra 1 9-12.A-APR.6 Arithmetic with Polynomials and Rationa where a(x), b(x), q(x), and r(x) are polynomials • Simplifying Rational Expressions 2 Exeter MAT 11T / 120 / 130 :

Expressions

Algebra 1 9-12.A-CED.1 Creating Equations*


with the degree of r(x) less than the degree of b(x),

using inspection, long division, or, for the more

complicated examples, a computer algebra system.

Create equations and inequalities in one variable

and use them to solve problems. Include equations

arising from linear and quadratic functions, and

simple rational and exponential functions.

Create equations in two or more variables to

represent relationships between quantities; graph






• ...and 21 more ...

• Graphs of Linear Equations


• Multiplying expressions 0.5

• Multiplying expressions 1

• Graphing linear inequalities

• Multi-step linear inequalities

• One step inequalities

Algebra

Exeter MAT 11T / 120 / 130 :

Algebra

Exeter MAT 11T / 120 / 130 :

equations on coordinate axes with labels and scales. • Mixture problems 2

• Evaluating expressions with function notation

Algebra

Represent constraints by equations or inequalities, • Compound Inequalities 3


and by systems of equations and/or inequalities, and • Compound Inequalities 4

interpret solutions as viable or nonviable options in • Compund Inequalities

Exeter MAT 11T / 120 / 130 :

a modeling context. For example, represent

inequalities describing nutritional and cost

constraints on combinations of different foods.

Algebra 1 9-12.A-CED.4 Creating Equations* Create equations that describe numbers or

relationship

Explain each step in solving a simple equation as

following from the equality of numbers asserted at


• Multi-Step Inequalities

• Proportionality

• Rearrange formulas to isolate specific variables






• Compound inequalities

• Solving equations in terms of a variable

Algebra

Exeter MAT 11T / 120 / 130 :

Algebra

Algebra 1 9-12.A-REI.1 Reasoning with Equations and

Inequalities the previous step, starting from the assumption that • Solving Equations with the Distributive Property Exeter MAT 11T / 120 / 130 :

Algebra


Inequalities

the original equation has a solution. Construct a

viable argument to justify a solution method.

Understand that the graph of an equation in two

variables is the set of all its solutions plotted in the

coordinate plane, often forming a curve (which

could be a line).

• Solving equations with the distributive property 2

• Solving factored equations

• ...and 1 more ...


• Graphing using X and Y intercepts

• Significant figures

• Solving equations in terms of a variable

Exeter MAT 11T / 120 / 130 :

Algebra

Algebra 1 9-12.A-REI.4.b


Inequalities

Explain why the x-coordinates of the points where

the graphs of the equations y = f(x) and y = g(x)

intersect are the solutions of the equation f(x) =

g(x); find the solutions approximately, e.g., using

technology to graph the functions, make tables of

values, or find successive approximations. Include

cases where f(x) and/or g(x) are linear, polynomial,

rational, absolute value, exponential, and

logarithmic functions._

Graph the solutions to a linear inequality in two

• Solving Linear Systems by Graphing

• Graphical System of Inequalities

• Graphing Inequalities

• Graphing Inequalities 2


Exeter MAT 11T / 120 / 130 :

Algebra

variables as a halfplane (excluding the boundary in • Graphing systems of inequalities

Algebra 1 9-12.A-REI.12 Reasoning with Equations and the case of a strict inequality), and graph the • Graphing systems of inequalities 2 Exeter MAT 11T / 120 / 130 :

Inequalities solution set to a system of linear inequalities in two • Graphing systems of inequalities 3 Algebra

variables as the intersection of the corresponding

half-planes.

• System of Inequalities Application • Graphing and solving linear inequalities

• Graphing and solving systems of inequalities

• Graphing systems of inequalities

Algebra 1 9-12.A-REI.2

Reasoning with Equations and Inequalities


Inequalities

Solve simple rational and radical equations in one

variable, and give examples showing how

extraneous solutions may arise.

Solve linear equations and inequalities in one

variable, including equations with coefficients

represented by letters.

• Radical Equation Examples

• Simplifying Radical Expressions 2


• Compound Inequalities





• Equations and Inequalities

• Equations with Variables on Both Sides


• ...and 21 more ...

• Equations with variables on both sides

• Multi-step equations

Exeter MAT 11T / 120 / 130 :

Algebra

Exeter MAT 11T / 120 / 130 :

Algebra

Reasoning with Equations and

Inequalities Solve equations and inequalities in one variable

Prove that, given a system of two equations in two

• Factor by Grouping and Factoring Completely Exeter MAT 11T / 120 / 130 :

Algebra

• Solving Systems of Equations by Elimination


Inequalities

variables, replacing one equation by the sum of that

equation and a multiple of the other produces a

system with the same solutions.

Solve systems of linear equations exactly and

• systems of equations


Exeter MAT 11T / 120 / 130 :

Algebra


Inequalities approximately (e.g., with graphs), focusing on pairs • Graphings Systems of Equations

of linear equations in two variables.

• Graphing linear inequalities

Exeter MAT 11T / 120 / 130 :

Algebra

Algebra 1 9-12.A-SSE.1 Seeing Structure in Expressions Interpret expressions that represent a quantity in

terms of its context.

Algebra 1 9-12.A-SSE.1.a Seeing Structure in Expressions

Interpret parts of an expression, such as terms,

factors, and coefficients.

• Algebraic Expression Least Common Multiple

• Factor expressions by grouping

• Factoring and the Distributive Property



Exeter MAT 11T / 120 / 130 :

Algebra

Exeter MAT 11T / 120 / 130 :

Algebra

Algebra 1 9-12.A-SSE.1.b Seeing Structure in Expressions

Interpret complicated expressions by viewing one or • Algebraic Expression Least Common Multiple

more of their parts as a single entity. For example,

Exeter MAT 11T / 120 / 130 :

interpret P(1+r)^n as the product of P and a factor

not depending on P.

Algebra 1 9-12.A-SSE.2 Seeing Structure in Expressions Interpret the structure of expressions

Choose and produce an equivalent form of an


• Adding and Subtracting Rational Expressions

• Dividing and Simplifying Rational Expressions

• Factor by Grouping and Factoring Completely


• ...and 28 more ...

• Adding and Subtracting Rational Expressions

Algebra

Exeter MAT 11T / 120 / 130 :

Algebra

Algebra 1 9-12.A-SSE.3 Seeing Structure in Expressions expression to reveal and explain properties of the

quantity represented by the expression.

Use the properties of exponents to transform


• Exponent Properties Involving Products

Exeter MAT 11T / 120 / 130 :

Algebra

expressions for exponential functions. For example • Exponent Properties Involving Quotients

th i 1 15^t b itt

Page 85

Algebra 1 9-12.F-BF.4.b Building Functions

Algebra 1 9-12.F-BF.4.c Building Functions

Algebra 1 9-12.F-BF.4.d Building Functions

Algebra 1 9-12.A-SSE.3.c Seeing Structure in Expressions the expression 1.15^t can be rewritten as (1.15^1/12)^12t _ 1.012^12t to reveal the

approximate equivalent monthly interest rate if the

annual rate is 15%.

• Zero, Negative, and Fractional Exponents

• Exponent rules

• Simplifying expressions with exponents

Exeter MAT 11T / 120 / 130 :

Algebra

Algebra 1 9-12.A-SSE.4 Seeing Structure in Expressions

Derive the formula for the sum of a finite geometric • Sequences and Series (part 1)

series (when the common ratio is not 1), and use the

formula to solve problems. For example, calculate

mortgage payments.

Algebra 1 9-12.F-BF.1.a Building Functions Determine an explicit expression, a recursive

process, or steps for calculation from a context.

Write arithmetic and geometric sequences both

• Equations of Sequence Patterns

• Finding the 100th Term in a Sequence

• Inductive Reasoning 2

Exeter MAT 11T / 120 / 130 :

Algebra

Algebra 1 9-12.F-BF.2 Building Functions recursively and with an explicit formula, use them

to model situations, and translate between the two

forms.

• Patterns in Sequences 1

• Patterns in Sequences 2

• Sequences and Series (part 1)

• U12_L1_T3_we1 Inductive Reasoning 1

Identify the effect on the graph of replacing f(x) by • Algebra: graphing lines 1

f(x) + k, k f(x), f(kx), and f(x + k) for specific

values of k (both positive and negative); find the

• Algebra: Slope and Y-intercept intuition

• Connection between even and odd numbers and functions

Algebra 1 9-12.F-BF.3 Building Functions value of k given the graphs. Experiment with cases • Graphs of Square Root Functions Exeter MAT 11T / 120 / 130 :

and illustrate an explanation of the effects on the

graph using technology. Include recognizing even

and odd functions from their graphs and algebraic

expressions for them.

Algebra 1 9-12.F-BF.4 Building Functions Find inverse functions.

Algebra 1 9-12.F-BF.4.a Building Functions Build new functions from existing functions

Verify by composition that one function is the

inverse of another.

• Recognizing Odd and Even Functions

• Function Inverse Example 1

• Function Inverses Example 2


• Introduction to Function Inverses







• Even and odd functions

• Line graph intuition

• Shifting and reflecting functions

Algebra

Exeter MAT 210/220/230:

Integrated Mathematics

Exeter MAT 210/220/230:


Exeter MAT 210/220/230:


Read values of an inverse function from a graph or • Introduction to Function Inverses Exeter MAT 210/220/230:

a table, given that the function has an inverse.

Produce an invertible function from a non-invertible • Function Inverses Example 2


Exeter MAT 210/220/230:

function by restricting the domain.

Understand that a function from one set (called the




Algebra 1 9-12.F-IF.1 Interpreting Functions

domain) to another set (called the range) assigns to • Domain and Range 2 each element of the domain exactly one element of

the range. If f is a function and x is an element of its

Exeter MAT 210/220/230:

domain, then f(x) denotes the output of f • Introduction to functions Integrated Mathematics

corresponding to the input x. The graph of f is the

graph of the equation y = f(x).

• Understanding function notation

• Domain of a function

Use function notation, evaluate functions for inputs • Multiplying and Dividing Rational Expressions 1

Exeter MAT 210/220/230:



in their domains, and interpret statements that use

function notation in terms of a context.

Recognize that sequences are functions, sometimes

defined recursively, whose domain is a subset of the

integers. For example, the Fibonacci sequence is


• Sequences and Series (part 1)

• Domain of a function

• Range of a function


defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) • Sequences and series (part 2)

+ f(n-1) for n _ 1.

For a function that models a relationship between


two quantities, interpret key features of graphs and • Functional Relationships 1 tables in terms of the quantities, and sketch graphs


showing key features given a verbal description of

the relationship. Key features include: intercepts;

intervals where the function is increasing,

• Functions (Part III) Exeter MAT 11T / 120 / 130 :

Algebra

decreasing, positive, or negative; relative maximums• Graphing a line in slope intercept form

and minimums; symmetries; end behavior; an

periodicity.

Relate the domain of a function to its graph and,

• Testing if a relationship is a function



where applicable, to the quantitative relationship it • Domain and Range of a Function

describes. For example, if the function h(n) gives

Exeter MAT 210/220/230:

the number of person-hours it takes to assemble n

engines in a factory, then the positive integers

would be an appropriate domain for the function.





Calculate and interpret the average rate of change

of a function (presented symbolically or as a table)

over a specified interval. Estimate the rate of

change from a graph.

• Basic Rate Problem

• Slope and Rate of Change

Exeter MAT 11T / 120 / 130 :

Algebra

Algebra 1 9-12.F-IF.7 Interpreting Functions Graph functions expressed symbolically and show

key features of the graph, by hand in simple cases

Algebra 1 9-12.F-IF.7.a Interpreting Functions

Graph linear and quadratic functions and show

intercepts, maxima, and minima.

Graph square root, cube root, and piecewise-

• Functional Relationships 1





• Graphings Systems of Equations


• Absolute Value Equations

Exeter MAT 11T / 120 / 130 :

Algebra

Exeter MAT 11T / 120 / 130 :

Algebra

Algebra 1 9-12.F-IF.7.b Interpreting Functions



defined functions, including step functions and

absolute value functions.

Write a function defined by an expression in

different but equivalent forms to reveal and explain

different properties of the function.

Use the process of factoring and completing the

square in a quadratic function to show zeros,

extreme values, and symmetry of the graph, and

interpret these in terms of a context.

Use the properties of exponents to interpret

expressions for exponential functions. For example,

• Functions as Graphs

• Functions Part 2

• Graphs of Square Root Functions

• Functions (part 4)

• Factor by Grouping and Factoring Completely

• Graphs of Quadratic Functions

• Exponent Rules 1

• Factoring polynomials 1

• Factoring polynomials 2

• Factoring polynomials by grouping

• Factoring polynomials with two variables

Exeter MAT 210/220/230:


Algebra 1 9-12.F-IF.8.b Interpreting Functions identify percent rate of change in functions such as • Exponent Rules 2

y = (1.02)^t, y = (0.97)^t, y = (1.01)^12t, y =

(1.2)^t/10, and classify them as representing

exponential growth or decay. • Exponent Rules 3


Compare properties of two functions each

represented in a different way (algebraically,

graphically, numerically in tables, or by verbal

descriptions). For example, given a graph of one

quadratic function and an algebraic expression for

another, say which has the larger maximum.

Exeter MAT 11T / 120 / 130 :

Algebra

Algebra 1 9-12.F-LE.1 Linear, Quadratic, and Exponential Distinguish between situations that can be modeled • Linear, Quadratic, and Exponential Models Exeter MAT 11T / 120 / 130 :

Models with linear functions and with exponential functions. Algebra

Algebra 1 9-12.F-LE.1.a Linear, Quadratic, and Exponential

Models

Prove that linear functions grow by equal

differences over equal intervals, and that

exponential functions grow by equal factors over

equal intervals.

• Linear, Quadratic, and Exponential Models

• Direct Variation Models

Exeter MAT 11T / 120 / 130 :

Algebra

Recognize situations in which one quantity changes • Slope Example

Algebra 1 9-12.F-LE.1.b Linear, Quadratic, and Exponential

Models at a constant rate per unit interval relative to

another.

Construct linear and exponential functions,




• Graphing Using Intercepts


Exeter MAT 11T / 120 / 130 :

Algebra

Algebra 1 9-12.F-LE.2 Linear, Quadratic, and Exponential

Models

including arithmetic and geometric sequences, given• Slope Example

a graph, a description of a relationship, or two input-• Word Problem Solving 4

output pairs (include reading these from a table).

• Point slope form

• Slope intercept form

Exeter MAT 11T / 120 / 130 :

Algebra

Geometry 9-12.A-APR.4

Algebra 1 9-12.F-LE.3

Linear, Quadratic, and Exponential Models

Algebra 1 9-12.G-CO.1 Congruence

Observe using graphs and tables that a quantity

increasing exponentially eventually exceeds a

quantity increasing linearly, quadratically, or (more

generally) as a polynomial function.

Know precise definitions of angle, circle,

perpendicular line, parallel line, and line segment,

based on the undefined notions of point, line,

distance along a line, and distance around a circular

arc.

Prove the slope criteria for parallel and

perpendicular lines and use them to solve geometric


• Perpendicular Line Slope

• Perpendicular Lines

• Perpendicular Line Slope

• Equations of parallel and perpendicular lines

Exeter MAT 11T / 120 / 130 :

Algebra

Exeter MAT 210/220/230:


Algebra 1 9-12.G-GPE.5 Expressing Geometric Properties with

Equations problems (e.g., find the equation of a line parallel or

• Perpendicular Lines

perpendicular to a given line that passes through a

Exeter MAT 210/220/230: Integrated Mathematics


Equations

Algebra 1 9-12.G-SRT.1.a

Similarity, Right Triangles, and Trigonometry

Algebra 1 9-12.G-SRT.1.b Similarity, Right Triangles, and

Trigonometry

given point).

Find the point on a directed line segment between

two given points that partitions the segment in a

given ratio.

A dilation takes a line not passing through the

center of the dilation to a parallel line, and leaves a

line passing through the center unchanged.

The dilation of a line segment is longer or shorter in

the ratio given by the scale factor.

Use units as a way to understand problems and to

guide the solution of multi-step problems; choose

• Perpendicular lines 2

• Midpoint Formula



• Midpoint formula

Exeter MAT 210/220/230:


Exeter MAT 210/220/230:


Exeter MAT 210/220/230:


Exeter MAT 11T / 120 / 130 :

Algebra 1 9-12.N-Q.1 Quantities and interpret units consistently in formulas; choose • Mixture problems 3 Algebra

and interpret the scale and the origin in graphs and

data displays.

Algebra 1 9-12.N-Q.2 Quantities Define appropriate quantities for the purpose of

descriptive modeling.

Choose a level of accuracy appropriate to

• Speed translation

• Unit conversion

• Addition and Subtraction with Significant Figures

• More on Significant Figures

Exeter MAT 11T / 120 / 130 :

Algebra

Exeter MAT 11T / 120 / 130 :

Algebra 1 9-12.N-Q.3 Quantities

Algebra 1 9-12.N-RN.1 The Real Number System

limitations on measurement when reporting

quantities.

Explain how the definition of the meaning of

rational exponents follows from extending the

properties of integer exponents to those values,

allowing for a notation for radicals in terms of

• Multiplying and Dividing with Significant Figures

• Pure Numbers and Significant Digits

• Significant Figures

• Level 3 exponents

• Radical Expressions with Higher Roots


Algebra

Exeter MAT 11T / 120 / 130 :

rational exponents. For example, we define 5^1/3 to • Simplifying Radical Expressions 3

Algebra

be the cube root of 5 because we want (5^1/3)^3 =

5^(1/3)3 to hold, so (5^1/3) must equal 5.

• Simplifying Radical Expressions1

• Solving Radical Equations 2






Algebra 1 9-12.N-RN.2 The Real Number System Rewrite expressions involving radicals and rational

• Exponent Rules 3 exponents using the properties of exponents.

• Exponent Rules Part 1

• ...and 19 more ...

• Adding and subtracting radicals

• Multiplying radicals

• Simplifying radicals

Exeter MAT 11T / 120 / 130 :

Algebra

Algebra 1 9-12.N-RN.3 The Real Number System

Explain why the sum or product of two rational

numbers is rational; that the sum of a rational

number and an irrational number is irrational; and

that the product of a nonzero rational number and

an irrational number is irrational.

Interpret the slope (rate of change) and the

• Simplifying radicals • Square roots

• Square Roots and Real Numbers

• Square roots


Exeter MAT 11T / 120 / 130 :

Algebra

Algebra 1 9-12.S-ID.7 Interpreting Categorical and Quantitative

intercept (constant term) of a linear model in the Data

context of the data.

• Slope Example

• Slope of a line

Exeter MAT 11T / 120 / 130 :

Algebra



• Deductive Reasoning 3 Exeter MAT 11T / 120 / 130 :

Algebra

Geometry 9-12.A-SSE.2 Seeing Structure in Expressions Interpret the structure of expressions

• Deductive Reasoning 2 Exeter MAT 11T / 120 / 130 :

Algebra

Geometry 9-12.G-C.1 Circles Prove that all circles are similar. Exeter MAT 210/220/230:


• Area of Inscribed Equilateral Triangle (some basic trig used) Identify and describe relationships among inscribed

• Inscribed and Central Angles

angles, radii, and chords. Include the relationship

Geometry 9-12.G-C.2 Circles between central, inscribed, and circumscribed

angles; inscribed angles on a diameter are right

angles; the radius of a circle is perpendicular to the

tangent where the radius intersects the circle.

Construct the inscribed and circumscribed circles of

• Right Triangles Inscribed in Circles (Proof)

• 2003 AIME II Problem 7

• Inscribed angles 1



Exeter MAT 210/220/230:


Geometry 9-12.G-C.3 Circles a triangle, and prove properties of angles for a

quadrilateral inscribed in a circle.

• Area of Diagonal Generated Triangles of Rectangle are Equal

• Area of Inscribed Equilateral Triangle (some basic trig used)

• Inscribed and Central Angles

Exeter MAT 210/220/230:


Geometry 9-12.G-C.4 Circles Construct a tangent line from a point outside a

given circle to the circle.

Derive using similarity the fact that the length of the

arc intercepted by an angle is proportional to the

Exeter MAT 210/220/230:


Exeter MAT 210/220/230:

Geometry 9-12.G-C.5 Circles

Geometry 9-12.G-CO.1 Congruence

radius, and define the radian measure of the angle as

the constant of proportionality; derive the formula

for the area of a sector.

Know precise definitions of angle, circle,

perpendicular line, parallel line, and line segment,

based on the undefined notions of point, line,

• Circles: Radius, Diameter and Circumference

• Introduction to angles (old)

• Parallel Line Equation

• Parallel Lines


Exeter MAT 210/220/230:

Integrated Mathematics distance along a line, and distance around a circular • Parallel Lines 2 arc.

Geometry 9-12.G-CO.10 Congruence Prove geometric theorems


• ...and 1 more ...

• Area of Diagonal Generated Triangles of Rectangle are Equal

• Heron's Formula

• Part 1 of Proof of Heron's Formula

• Part 2 of the Proof of Heron's Formula

• Triangle Medians and Centroids (2D Proof)

Exeter MAT 210/220/230:



Prove theorems about parallelograms. Theorems

include: opposite sides are congruent, opposite

angles are congruent, the diagonals of a

parallelogram bisect each other, and conversely,

rectangles are parallelograms with congruent

diagonals.

• Rhombus Diagonals

• Basic triangle proofs

• Wrong statements in triangle proofs

• Basic triangle proofs

• Wrong statements in triangle proofs

Exeter MAT 210/220/230:



Make formal geometric constructions with a variety

of tools and methods (compass and straightedge,

string, reflective devices, paper folding, dynamic

geometric software, etc.). Copying a segment;

copying an angle; bisecting a segment; bisecting an

angle; constructing perpendicular lines, including

the perpendicular bisector of a line segment; and

constructing a line parallel to a given line through a

point not on the line.

• Angle bisector theorem

• Heron's formula

Exeter MAT 210/220/230:



Construct an equilateral triangle, a square, and a

regular hexagon inscribed in a circle.

Represent transformations in the plane using, e.g.,

transparencies and geometry software; describe

transformations as functions that take points in the

• 2003 AIME II Problem 7 Exeter MAT 210/220/230:




plane as inputs and give other points as outputs.

Compare transformations that preserve distance and

angle to those that do not (e.g., translation versus

horizontal stretch).

Given a rectangle, parallelogram, trapezoid, or

regular polygon, describe the rotations and

reflections that carry it onto itself.


• Quadrilateral types

Exeter MAT 210/220/230:




Develop definitions of rotations, reflections, and

translations in terms of angles, circles, perpendicular

lines, parallel lines, and line segments.

Given a geometric figure and a rotation, reflection,

or translation, draw the transformed figure using,

e.g., graph paper, tracing paper, or geometry

software. Specify a sequence of transformations

that will carry a given figure onto another.

• Congruency postulates

Exeter MAT 210/220/230:


Exeter MAT 210/220/230:



Use geometric descriptions of rigid motions to

transform figures and to predict the effect of a given

rigid motion on a given figure; given two figures,

use the definition of congruence in terms of rigid

motions to decide if they are congruent.

Exeter MAT 210/220/230:




Use the definition of congruence in terms of rigid

motions to show that two triangles are congruent if

and only if corresponding pairs of sides and

corresponding pairs of angles are congruent.

Explain how the criteria for triangle congruence

(ASA, SAS, and SSS) follow from the definition of

congruence in terms of rigid motions.

• Angles of parallel lines 2

Exeter MAT 210/220/230:



Exeter MAT 210/220/230:


• Alternate exterior angles

• Alternate exterior angles 2

• Alternate interior angles 2


Geometry 9-12.G-CO.9 Congruence Prove geometric theorems • Corresponding angles


• Same side exterior angles

• Same side exterior angles 2

• Same side interior angles

• Same side interior angles 2

• Vertical angles

Exeter MAT 210/220/230:


Geometry 9-12.G-GMD.1 Geometric Measurement and Dimension Explain volume formulas and use them to solve

problems

Geometry 9-12.G-GMD.2 Geometric Measurement and Dimension Explain volume formulas and use them to solve

problems

• Cylinder Volume and Surface Area Exeter MAT 210/220/230:


Exeter MAT 210/220/230:


• Applying Radical Equations 3

Geometry 9-12.G-GMD.3 Geometric Measurement and Dimension Use volume formulas for cylinders, pyramids,

cones, and spheres to solve problems._

Identify the shapes of two-dimensional cross-

Geometry 9-12.G-GMD.4 Geometric Measurement and Dimension sections of three-dimensional objects, and identify

three-dimensional objects generated by rotations of

two-dimensional objects.

Derive the equation of a circle of given center and

• Cylinder Volume and Surface Area


Exeter MAT 210/220/230:


Exeter MAT 210/220/230:


Geometry 9-12.G-GPE.1 Expressing Geometric Properties with

Equations


Equations

Geometry 9-12.G-GPE.3

Expressing Geometric Properties with Equations

radius using the Pythagorean Theorem; complete

the square to find the center and radius of a circle

given by an equation.

Derive the equation of a parabola given a focus and

directrix.

Derive the equations of ellipses and hyperbolas

given the foci, using the fact that the sum or

difference of distances from the foci is constant.

• Focus and Directrix of a Parabola 2

• Parabola Focus and Directrix 1

• Foci of a Hyperbola

• Foci of an Ellipse

• Proof: Hyperbola Foci

• Parabola intuition 1



Exeter MAT 210/220/230:


Exeter MAT 11T / 120 / 130 :

Algebra

Exeter MAT 11T / 120 / 130 :

Algebra


Equations


Equations





Use coordinates to prove simple geometric

theorems algebraically. For example, prove or

disprove that a figure defined by four given points

in the coordinate plane is a rectangle; prove or

disprove that the point (1, _3) lies on the circle

centered at the origin and containing the point (0,

2).



problems (e.g., find the equation of a line parallel or


given point).





given point).





given point).


• Equations of Parallel and Perpendicular Lines

• Parallel Line Equation

• Parallel Lines

• Parallel Lines 2

Exeter MAT 210/220/230:


Exeter MAT 210/220/230:


Exeter MAT 210/220/230:


Exeter MAT 210/220/230:



Equations


Equations

Geometry 9-12.G-MG.1 Modeling with Geometry



Geometry 9-12.G-SRT.1




Geometry 9-12.G-SRT.2 Similarity, Right Triangles, and

Trigonometry

perpendicular lines and use them to solve geometric • Parallel lines 3

problems (e.g., find the equation of a line parallel or • ...and 1 more ...

Use coordinates to compute perimeters of polygons • Distance Formula

and areas of triangles and rectangles, e.g., using the

distance formula._

Use geometric shapes, their measures, and their

properties to describe objects (e.g., modeling a tree

trunk or a human torso as a cylinder)._

Apply concepts of density based on area and

volume in modeling situations (e.g., persons per

square mile, BTUs per cubic foot)._

Apply geometric methods to solve design problems

(e.g., designing an object or structure to satisfy

physical constraints or minimize cost; working with

typographic grid systems based on ratios)._

Verify experimentally the properties of dilations

given by a center and a scale factor:

Given two figures, use the definition of similarity in

terms of similarity transformations to decide if they

are similar; explain using similarity transformations

the meaning of similarity for triangles as the equality

of all corresponding pairs of angles and the

proportionality of all corresponding pairs of sides.

Given two figures, use the definition of similarity in

terms of similarity transformations to decide if they

are similar; explain using similarity transformations

the meaning of similarity for triangles as the equality

of all corresponding pairs of angles and the

proportionality of all corresponding pairs of sides.






Exeter MAT 210/220/230:


Exeter MAT 210/220/230:


Exeter MAT 210/220/230:


Exeter MAT 210/220/230:


Exeter MAT 210/220/230:


Exeter MAT 210/220/230:


Exeter MAT 210/220/230:


Exeter MAT 210/220/230:



Trigonometry





Use the properties of similarity transformations to

establish the AA criterion for two triangles to be

similar.

Prove theorems about triangles. Theorems include: • Visual Pythagorean Theorem Proof

a line parallel to one side of a triangle divides the

other two proportionally, and conversely; the

Pythagorean Theorem proved using triangle

similarity.

Use congruence and similarity criteria for triangles

to solve problems and to prove relationships in

geometric figures.






• Triangle angles 1

Exeter MAT 210/220/230:


Exeter MAT 210/220/230:


Exeter MAT 210/220/230:


Understand that by similarity, side ratios in right

i l i f h l i h i l

• Basic Trigonometry Page 91


Trigonometry



triangles are properties of the angles in the triangle, • Basic Trigonometry II leading to definitions of trigonometric ratios for

acute angles. Explain and use the relationship between the sine

and cosine of complementary angles.

• Triangle angles 1

• Trigonometry 0.5

• Trigonometry 1

Exeter MAT 210/220/230:


Exeter MAT 210/220/230:



Trigonometry

Use trigonometric ratios and the Pythagorean

Theorem to solve right triangles in applied

problems._

• 30-60-90 Triangles II

• 45-45-90 Triangles


Exeter MAT 210/220/230:


Geometry 9-12.N-RN.2 The Real Number System Rewrite expressions involving radicals and rational • Deductive Reasoning 2 Exeter MAT 11T / 120 / 130 : exponents using the properties of exponents.

Geometry 9-12.S-CP.1 Conditional Probability & the Rules of Understand independence and conditional

Algebra

• Conditional statements Exeter MAT40S: Introduction to

Probability probability and use them to interpret data

Understand that two events A and B are

independent if the probability of A and B occurring

• Conditional statements

Statistics

Geometry 9-12.S-CP.2 Conditional Probability & the Rules of

together is the product of their probabilities, and Exeter MAT40S: Introduction to

Probability use this characterization to determine if they are

independent.

• Logical arguments and deductive reasoning Statistics

Understand the conditional probability of A given B

as P(A and B)/P(B), and interpret independence of

Geometry 9-12.S-CP.3 Conditional Probability & the Rules of A and B as saying that the conditional probability of

• Conditional statements and truth value

Exeter MAT40S: Introduction to

Probability A given B is the same as the probability of A, and

the conditional probability of B given A is the same

as the probability of B.

• Logical arguments and deductive reasoning Statistics

Recognize and explain the concepts of conditional

probability and independence in everyday language

Geometry 9-12.S-CP.5 Conditional Probability & the Rules of and everyday situations. For example, compare the

• Conditional statements and truth value


Probability chance of having lung cancer if you are a smoker

with the chance of being a smoker if you have lung

cancer.

Statistics

• Applications Problem Factoring Quadratics

• Factoring Quadratic Expressions

Factor a quadratic expression to reveal the zeros of • Factoring Special Products

Exeter MAT 11T / 120 / 130 :

Algebra 2 9-12.A-SSE.3.a Seeing Structure in Expressions

Algebra 2 9-12.A-SSE.3.b Seeing Structure in Expressions

the function it defines.

Complete the square in a quadratic expression to

reveal the maximum or minimum value of the

function it defines.

Use the properties of exponents to transform

• Quadratic Formula 3

• Solving a quadratic by factoring

• ...and 2 more ...

• Completing the square

• Completing the Square 1




• Quadratic Functions 2

• Solving Quadratic Equations by Completing the Square

• Exponential Decay Functions

Algebra

Exeter MAT 11T / 120 / 130 :

Algebra

expressions for exponential functions. For example • Exponential Growth

Algebra 2 9-12.A-SSE.3.c Seeing Structure in Expressions the expression 1.15^t can be rewritten as

(1.15^1/12)^12t _ 1.012^12t to reveal the • Interest (part 2) Exeter MAT 11T / 120 / 130 :

Algebra

approximate equivalent monthly interest rate if the • Introduction to compound interest and e

Algebra 2 9-12.A-SSE.4 Seeing Structure in Expressions

annual rate is 15%.

Derive the formula for the sum of a finite geometric

series (when the common ratio is not 1), and use the

formula to solve problems. For example, calculate

mortgage payments.

• Introduction to interest

• Geometric Sequences (Introduction)

• Geometric series sum to figure out mortgage payments

Algebra 2 9-12.F-BF.1 Building Functions Write a function that describes a relationship

between two quantities._

Combine standard function types using arithmetic

operations. For example, build a function that

• Exponential Growth Exeter MAT 210/220/230:


• Exponential Growth

Algebra 2 9-12.F-BF.1.b Building Functions models the temperature of a cooling body by adding

a constant function to a decaying exponential, and

relate these functions to the model.


Compose functions. For example, if T(y) is the

temperature in the atmosphere as a function of

• Parametric Equations 1

Page 92

output pairs (include reading these from a table). • Word Problem Solving- Exponential Growth and Decay

Page 93

Algebra 2 9-12.F-BF.1.c Building Functions

p p

height, and h(t) is the height of a weather balloon as • Parametric Equations 2

a function of time, then T(h(t)) is the temperature at

the location of the weather balloon as a function of • Parametric Equations 3 time.

Exeter MAT 210/220/230:


Algebra 2 9-12.F-BF.5 Building Functions



Understand the inverse relationship between

exponents and logarithms and use this relationship

to solve problems involving logarithms and

exponents.


two quantities, interpret key features of graphs and

tables in terms of the quantities, and sketch graphs


the relationship. Key features include: intercepts;


decreasing, positive, or negative; relative maximum

and minimums; symmetries; end behavior; and

periodicity._




change from a graph._

• Introduction to logarithm properties

• Introduction to logarithm properties (part 2)

• Introduction to Logarithms


• ...and 3 more ...


• Applying Quadratic Functions 1


• Operations with logarithms

Exeter MAT 310/320/330/340:

Advanced Integrated Mathematics

Exeter MAT 210/220/230:


Exeter MAT 210/220/230:


Algebra 2 9-12.F-IF.7.a Interpreting Functions Graph linear and quadratic functions and show


Graph polynomial functions, identifying zeros when

• ...and 12 more ... • Graphing parabolas in all forms

• Graphing parabolas in standard form

• Graphing parabolas in vertex form

• Graphing parabolas in all forms

Exeter MAT 11T / 120 / 130 :

Algebra

Exeter MAT 11T / 120 / 130 :

Algebra 2 9-12.F-IF.7.c Interpreting Functions

Algebra 2 9-12.F-IF.7.d Interpreting Functions


suitable factorizations are available, and showing

end behavior.

Graph rational functions, identifying zeros and

asymptotes when suitable factorizations are

available, and showing end behavior.





• Graphing parabolas in standard form

• Graphing parabolas in vertex form

• A Third Example of Graphing a Rational Function

• Another Rational Function Graph Example

• Asymptotes of Rational Functions

• Factoring Quadratic Expressions

• Factoring Special Products

• Quadratic Functions 2

• Solving Quadratic Equations by Completing the Square

• Factoring difference of squares 1



• Solving quadratics by taking the square root

Algebra

Exeter MAT 11T / 120 / 130 :

Algebra

Exeter MAT 11T / 120 / 130 :

Algebra

Use the properties of exponents to interpret

expressions for exponential functions. For example,


Algebra 2 9-12.F-IF.8.b Interpreting Functions identify percent rate of change in functions such as • Exponential Growth

y = (1.02)^t, y = (0.97)^t, y = (1.01)^12t, y =

Exeter MAT 11T / 120 / 130 :

Algebra

(1.2)^t/10, and classify them as representing

exponential growth or decay. • Exponential Growth Functions


Models

Distinguish between situations that can be modeled • Identifying Exponential Models

with linear functions and with exponential functions.• Identifying Quadratic Models

Exeter MAT 11T / 120 / 130 :

Algebra

Algebra 2 9-12.F-LE.1.a Linear, Quadratic, and Exponential

Models

Algebra 2 9-12.F-LE.1.c


Prove that linear functions grow by equal

differences over equal intervals, and that

exponential functions grow by equal factors over

equal intervals.

Recognize situations in which a quantity grows or

decays by a constant percent rate per unit interval

relative to another.

Construct linear and exponential functions,

• Identifying Exponential Models


• Exponential Growth Functions



Exeter MAT 11T / 120 / 130 :

Algebra

Exeter MAT 310/320/330/340:



Models

including arithmetic and geometric sequences, given• Geometric series sum to figure out mortgage payments

a graph, a description of a relationship, or two input-

Exeter MAT 11T / 120 / 130 :

Algebra

• Line Integrals and Vector Fields magnitudes (e.g., v, |v|, ||v||, v).

Page 94

Algebra 2 9-12.F-LE.4


For exponential models, express as a logarithm the

solution to ab^ct = d where a, c, and d are numbers

and the base b is 2, 10, or e; evaluate the logarithm

using technology.

• Solving logarithms Exeter MAT 310/320/330/340:



Models

Interpret the parameters in a linear or exponential

function in terms of a context.

Derive the equation of a circle of given center and

• Parametric Equations 1 Exeter MAT 210/220/230:


• Conic Sections: Intro to Circles


Equations

radius using the Pythagorean Theorem; complete

the square to find the center and radius of a circle

given by an equation.

• Equation of a circle in factored form

• Equation of a circle in non-factored form

• Recognizing conic sections

Exeter MAT 210/220/230:



Equations

Algebra 2 9-12.G-GPE.3


Derive the equation of a parabola given a focus and

directrix.

Derive the equations of ellipses and hyperbolas

given the foci, using the fact that the sum or

difference of distances from the foci is constant.

• Conic Sections: Hyperbolas 2

• Conic Sections: Hyperbolas 3

• Conic Sections: Intro to Ellipses

• Conic Sections: Intro to Hyperbolas

• Basic Complex Analysis

• Vertex of a parabola Exeter MAT 11T / 120 / 130 :

Algebra

Exeter MAT 11T / 120 / 130 :

Algebra

• Equation of a hyperbola

• Equation of an ellipse

Algebra 2 9-12.N-CN.1 The Complex Number System Perform arithmetic operations with complex

numbers

Algebra 2 9-12.N-CN.2 The Complex Number System Perform arithmetic operations with complex

numbers

Find the conjugate of a complex number; use

• Complex Numbers (part 1)

• Introduction to i and Imaginary Numbers

• Associative Law of Multiplication

• Associative property for multiplication


• Commutative Law of Addition

• Commutative Law of Multiplication

• Commutative Property for Addition

• Complex Numbers (part 1)

• Complex Conjugates

• Imaginary unit powers

• Adding and subtracting complex numbers

• Multiplying complex numbers

Algebra 2 9-12.N-CN.3 The Complex Number System conjugates to find moduli and quotients of complex • Complex Numbers (part 2)

numbers.


• Dividing complex numbers

Algebra 2 9-12.N-CN.4 The Complex Number System

Represent complex numbers on the complex plane

in rectangular and polar form (including real and

imaginary numbers), and explain why the

rectangular and polar forms of a given complex

number represent the same number.

• Exponential form to find complex roots

Algebra 2 9-12.N-CN.5 The Complex Number System

Represent complex numbers and their operations on

the complex plane

Calculate the distance between numbers in the


• Absolute value of complex numbers

• The complex plane

Algebra 2 9-12.N-CN.6 The Complex Number System complex plane as the modulus of the difference, and

the midpoint of a segment as the average of the

numbers at its endpoints.

• Applications Problem Factoring Quadratics




Algebra 2 9-12.N-CN.7 The Complex Number System Solve quadratic equations with real coefficients that

• Evaluating a polynomial at a given value have complex solutions.

Algebra 2 9-12.N-CN.8 The Complex Number System Use complex numbers in polynomial identities and

equations

Algebra 2 9-12.N-CN.9 The Complex Number System Know the Fundamental Theorem of Algebra; show

that it is true for quadratic polynomials.

Recognize vector quantities as having both

magnitude and direction. Represent vector

• Non-Linear Systems of Equations 1

• Non-Linear Systems of Equations 2

• ...and 13 more ...

• Gradient 1

• Quadratic formula

Algebra 2 9-12.N-VM.1 Vector and Matrix Quantities quantities by directed line segments, and use appropriate symbols for vectors and their

• Line Integrals and Vector Fields magnitudes (e.g., v, |v|, ||v||, v).

Page 94

• Gradient of a scalar field Exeter MAT 210/220/230: Integrated Mathematics

Algebra 2 9-12.N-VM.10 Vector and Matrix Quantities

Understand that the zero and identity matrices play

a role in matrix addition and multiplication similar

to the role of 0 and 1 in the real numbers. The

determinant of a square matrix is nonzero if and

only if the matrix has a multiplicative inverse.

• Identity property of 0

• Identity Property of 1

Exeter MAT 210/220/230:



Multiply a vector (regarded as a matrix with one

column) by a matrix of suitable dimensions to

produce another vector. Work with matrices as

transformations of vectors.

Exeter MAT 210/220/230:


Algebra 2 9-12.N-VM.12 Vector and Matrix Quantities Perform operations on matrices and use matrices in

applications

Find the components of a vector by subtracting the

Exeter MAT 210/220/230:


Exeter MAT 210/220/230: Algebra 2 9-12.N-VM.2 Vector and Matrix Quantities coordinates of an initial point from the coordinates

of a terminal point. Integrated Mathematics

Algebra 2 9-12.N-VM.4 Vector and Matrix Quantities Add and subtract vectors. Exeter MAT 210/220/230:


Algebra 2 9-12.N-VM.4.a Vector and Matrix Quantities

Add vectors end-to-end, component-wise, and by

the parallelogram rule. Understand that the

magnitude of a sum of two vectors is typically not

the sum of the magnitudes.

• Adding vectors

• Adding vectors

Exeter MAT 210/220/230:


Algebra 2 9-12.N-VM.4.b Vector and Matrix Quantities Given two vectors in magnitude and direction form,

determine the magnitude and direction of their sum.

Algebra 2 9-12.N-VM.4.c Vector and Matrix Quantities Perform operations on vectors

Exeter MAT 210/220/230:


• Adding vectors Exeter MAT 210/220/230:


Algebra 2 9-12.N-VM.5 Vector and Matrix Quantities Multiply a vector by a scalar. Exeter MAT 210/220/230:


Algebra 2 9-12.N-VM.5.a Vector and Matrix Quantities

Algebra 2 9-12.N-VM.5.b Vector and Matrix Quantities



Represent scalar multiplication graphically by

scaling vectors and possibly reversing their

direction; perform scalar multiplication component-

wise, e.g., as c(vx, vy) = (cvx, cvy).

Compute the magnitude of a scalar multiple cv

using ||cv|| = |c|v. Compute the direction of cv

knowing that when |c|v _ 0, the direction of cv is

either along v (for c > 0) or against v (for c < 0).

Use matrices to represent and manipulate data, e.g.,

to represent payoffs or incidence relationships in a

network.

Multiply matrices by scalars to produce new

matrices, e.g., as when all of the payoffs in a game

are doubled.

• Scaling vectors Exeter MAT 210/220/230:


Exeter MAT 210/220/230:


Exeter MAT 310/320/330/340:


Exeter MAT 310/320/330/340:


Algebra 2 9-12.N-VM.8 Vector and Matrix Quantities Add, subtract, and multiply matrices of appropriate

dimensions.

Understand that, unlike multiplication of numbers,

Exeter MAT 310/320/330/340:


Algebra 2 9-12.N-VM.9 Vector and Matrix Quantities matrix multiplication for square matrices is not a

commutative operation, but still satisfies the

associative and distributive properties.

Use statistics appropriate to the shape of the data

• Exploring standard deviation 1

Exeter MAT 310/320/330/340:


Algebra 2 9-12.S-ID.2 Interpreting Categorical and Quantitative distribution to compare center (median, mean) and Exeter MAT40S: Introduction to

Data spread (interquartile range, standard deviation) of

two or more different data sets.

Fit a function to the data; use functions fitted to

data to solve problems in the context of the data.

• Quadratic formula

Statistics

Algebra 2 9-12.S-ID.6.a Interpreting Categorical and Quantitative

Use given functions or choose a function suggested Exeter MAT 11T / 120 / 130 :

Data

Trigonometry 9-12.A-REI.4 Reasoning with Equations and

by the context. Emphasize linear, quadratic, and

exponential models.

Algebra

• Fun Trig Problem Exeter MAT 11T / 120 / 130 :

Inequalities Solve quadratic equations in one variable.

Trigonometry 9-12.F-BF.4 Building Functions Find inverse functions.

• Inverse Trig Functions: Arccos

• Inverse Trig Functions: Arcsin

• Inverse Trig Functions: Arctan


Algebra

Exeter MAT 210/220/230:


Trigonometry 9-12.F-BF.4.a Building Functions Build new functions from existing functions • Inverses of functions Exeter MAT 210/220/230:


Trigonometry 9-12.F-BF.4.b Building Functions

Verify by composition that one function is the

inverse of another.


• Inverse Trig Functions: Arctan

• Inverses of functions

Exeter MAT 210/220/230:


Page 95

Trigonometry 9-12.F-BF.4.c Building Functions Read values of an inverse function from a graph or • Inverse Trig Functions: Arctan

a table, given that the function has an inverse.

• Inverses of functions

Exeter MAT 210/220/230:


Trigonometry 9-12.F-IF.7.e Interpreting Functions

Graph exponential and logarithmic functions,

showing intercepts and end behavior, and

trigonometric functions, showing period, midline,

and amplitude.

• Determining the equation of a trigonometric function

• Graphing trig functions

• Graphs of trig functions

• More trig graphs

• Radians and degrees

Exeter MAT 210/220/230:


Trigonometry 9-12.F-TF.1 Trigonometric Functions Understand radian measure of an angle as the length

• The unit circle definition of trigonometric function of the arc on the unit circle subtended by the angle.

• Unit circle

Exeter MAT 310/320/330/340:


Explain how the unit circle in the coordinate plane • Graph of the sine function

enables the extension of trigonometric functions to • Radians and degrees Exeter MAT 310/320/330/340:

Trigonometry 9-12.F-TF.2 Trigonometric Functions all real numbers, interpreted as radian measures of

angles traversed counterclockwise around the unit

circle.

• The unit circle definition of trigonometric function

• Unit Circle Definition of Trig Functions

• Unit circle



Extend the domain of trigonometric functions using • The unit circle definition of trigonometric function Exeter MAT 310/320/330/340: Trigonometry 9-12.F-TF.3 Trigonometric Functions

the unit circle • Using Trig Functions


• Special right triangles


Trigonometry 9-12.F-TF.4 Trigonometric Functions Use the unit circle to explain symmetry (odd and

even) and periodicity of trigonometric functions.



• Graphs of sine and cosine

Exeter MAT 310/320/330/340:


Trigonometry 9-12.F-TF.5 Trigonometric Functions

Choose trigonometric functions to model periodic

phenomena with specified amplitude, frequency,

and midline._

• Determining the equation of a trigonometric function




Exeter MAT 310/320/330/340:



Understand that restricting a trigonometric function • Graphs of trig functions

to a domain on which it is always increasing or

always decreasing allows its inverse to be

constructed.

Exeter MAT 310/320/330/340:




Use inverse functions to solve trigonometric

equations that arise in modeling contexts; evaluate

the solutions using technology, and interpret them

Prove the Pythagorean identity sin2(_) + cos^2(_) =

1 and use it to find sin(_), cos(_), or tan(_) given

sin(_), cos(_), or tan(_) and the quadrant of the



• Fun Trig Problem

• Inverse trig functions

Exeter MAT 310/320/330/340:


Exeter MAT 310/320/330/340:


angle. • Trigonometric Identities • Trig identities 1


Prove the addition and subtraction formulas for

sine, cosine, and tangent and use them to solve

problems.

• IIT JEE Trigonometric Constraints

• IIT JEE Trigonometric Maximum

• IIT JEE Trigonometry Problem 1

• Proof: cos(a+b) = (cos a)(cos b)-(sin a)(sin b)

• Proof: sin(a+b) = (cos a)(sin b) + (sin a)(cos b)

• Trigonometric System Example

• Trigonometry Identity Review/Fun

• Law of cosines

• Trig identities 1

Exeter MAT 310/320/330/340:


Trigonometry 9-12.G-SRT.10 Similarity, Right Triangles, and

Trigonometry Prove the Laws of Sines and Cosines and use them

• Navigation Word Problem to solve problems.

• Proof: Law of Sines

• Ferris Wheel Trig Problem

Exeter MAT 310/320/330/340:



Trigonometry

Understand and apply the Law of Sines and the

Law of Cosines to find unknown measurements in

right and non-right triangles (e.g., surveying

problems, resultant forces).

Understand that by similarity, side ratios in right

• Ferris Wheel Trig Problem (part 2)

• Law of cosines

• Navigation Word Problem

• Proof: Law of Sines


Exeter MAT 310/320/330/340:



Trigonometry

triangles are properties of the angles in the triangle, • Unit Circle Definition of Trig Functions leading to definitions of trigonometric ratios for

Exeter MAT 210/220/230:


Trigonometry 9-12.G-SRT.7


Similarity Right Triangles an

acute angles.

Explain and use the relationship between the sine

and cosine of complementary angles.

Use trigonometric ratios and the Pythagorean

• Using Trig Functions Part II • Fun Trig Problem • Trigonometry 0.5

• Graphs of trig functions • Trigonometry 1

• Proof: cos(a+b) = (cos a)(cos b)-(sin a)(sin b)

• Proof: sin(a+b) = (cos a)(sin b) + (sin a)(cos b)

• The unit circle definition of trigonometric function

• Basic Trigonometry

• Basic Trigonometry II

• Ferris Wheel Trig Problem

• Ferris Wheel Trig Problem (part 2)

Exeter MAT 210/220/230:


Exeter MAT 210/220/230:

Page 96

Calculus 9-12.A-APR.5

Calculus 9-12.A-REI.4

Trigonometry 9-12.G-SRT.8 , Right , and Trigonometry

Theorem to solve right triangles in applied

problems._

• Graph of the sine function


• ...and 15 more ...


• Trigonometry 2

MAT



Trigonometry

Derive the formula A = 1/2 ab sin(C) for the area of • 2003 AIME II Problem 11.avi

a triangle by drawing an auxiliary line from a vertex

perpendicular to the opposite side.

Exeter MAT 310/320/330/340:




• Proof: d/dx(x^n) Exeter MAT 420/430/440/450:

Calculus


Calculus 9-12.A-CED.2 Creating Equations*

Create equations in two or more variables to

represent relationships between quantities; graph

• Epsilon Delta Limit Definition 2

• Introduction to Limits Exeter MAT 420/430/440/450:

Calculus equations on coordinate axes with labels and scales. • Introduction to Limits (HD)

• Limit Examples (part 1)

Calculus 9-12.A-CED.3 Creating Equations*

Represent constraints by equations or inequalities,

and by systems of equations and/or inequalities, and

interpret solutions as viable or nonviable options in

a modeling context. For example, represent

inequalities describing nutritional and cost

constraints on combinations of different foods.

• Epsilon Delta Limit Definition 2


Exeter MAT 420/430/440/450:

Calculus

Calculus 9-12.A-CED.4 Creating Equations* Create equations that describe numbers or

relationship

Understand that the graph of an equation in two

• Epsilon Delta Limit Definition 2 Exeter MAT 420/430/440/450:

Calculus

• Calculus BC 2008 2 a

Calculus 9-12.A-REI.10 Reasoning with Equations and

Inequalities

variables is the set of all its solutions plotted in the • Calculus: Derivatives 1 (new HD version)

coordinate plane, often forming a curve (which

Exeter MAT 420/430/440/450:

Calculus

could be a line). • Limit Examples (part 1)

Reasoning with Equations and

Inequalities Solve quadratic equations in one variable.

• Extreme Derivative Word Problem (advanced) Exeter MAT 420/430/440/450:

Calculus

Calculus 9-12.A-SSE.1.b Seeing Structure in Expressions

Interpret complicated expressions by viewing one or • Chain Rule Examples

more of their parts as a single entity. For example,

interpret P(1+r)^n as the product of P and a factor

not depending on P.

Exeter MAT 420/430/440/450:

Calculus

Calculus 9-12.A-SSE.2 Seeing Structure in Expressions Interpret the structure of expressions • Chain Rule Examples Exeter MAT 420/430/440/450:

Calculus

Calculus 9-12.A-SSE.3.a Seeing Structure in Expressions Factor a quadratic expression to reveal the zeros of • Limit Examples (part3) Exeter MAT 420/430/440/450: the function it defines. Calculus

Calculus 9-12.A-SSE.3.a Seeing Structure in Expressions Factor a quadratic expression to reveal the zeros of • Limit Examples w/ brain malfunction on first prob (part 4) Exeter MAT 420/430/440/450: the function it defines.

Calculus 9-12.F-BF.1 Building Functions Write a function that describes a relationship

between two quantities._

Compose functions. For example, if T(y) is the

temperature in the atmosphere as a function of

• Introduction to Limits


• Introduction to Limits

Calculus

Exeter MAT 420/430/440/450:

Calculus

Calculus 9-12.F-BF.1.c Building Functions

Calculus 9-12.F-IF.1 Interpreting Functions

height, and h(t) is the height of a weather balloon as

a function of time, then T(h(t)) is the temperature at

the location of the weather balloon as a function of

time.

Understand that a function from one set (called the • Squeeze Theorem

domain) to another set (called the range) assigns to

each element of the domain exactly one element of

the range. If f is a function and x is an element of its

domain, then f(x) denotes the output of f

corresponding to the input x. The graph of f is the

graph of the equation y = f(x).

Exeter MAT 420/430/440/450:

Calculus

Exeter MAT 420/430/440/450:

Calculus

Use function notation, evaluate functions for inputs • Introduction to Limits Exeter MAT 420/430/440/450:

Calculus 9-12.F-IF.2 Interpreting Functions in their domains, and interpret statements that use

function notation in terms of a context.


two quantities, interpret key features of graphs and

tables in terms of the quantities, and sketch graphs


• Calculus: Maximum and minimum values on an interval

Calculus

Calculus 9-12 F-IF 4 Interpreting Function the relationship Key features include: intercepts; Exeter MAT 420/430/440/450:

F-IF. Interpreting the . Key include:



Calculus

decreasing, positive, or negative; relative maximums

and minimums; symmetries; end behavior; and

periodicity._




Relate the domain of a function to its graph and,

where applicable, to the quantitative relationship it

describes. For example, if the function h(n) gives

the number of person-hours it takes to assemble n

engines in a factory, then the positive integers

would be an appropriate domain for the function._




change from a graph._

Graph functions expressed symbolically and show

key features of the graph, by hand in simple cases

• Squeeze Theorem

• Mean Value Theorem

• Calculus Graphing with Derivatives Example

• Calculus: Graphing Using Derivatives

• Graphing with Calculus

• Introduction to definite integrals

Exeter MAT 420/430/440/450:

Calculus

Exeter MAT 420/430/440/450:

Calculus

Exeter MAT 420/430/440/450:

Calculus and using technology for more complicated cases._ • Introduction to Limits

• More Limits

• ...and 2 more ...

Calculus 9-12.F-IF.7.a Interpreting Functions Graph linear and quadratic functions and show


• Calculus: Maximum and minimum values on an interval Exeter MAT 420/430/440/450:

Calculus

Graph polynomial functions, identifying zeros when • Calculus: Graphing Using Derivatives Exeter MAT 420/430/440/450:

Calculus 9-12.F-IF.7.c Interpreting Functions

Calculus 9-12.F-IF.7.d Interpreting Functions

suitable factorizations are available, and showing

end behavior.

Graph rational functions, identifying zeros and

asymptotes when suitable factorizations are

available, and showing end behavior.



Calculus

Exeter MAT 420/430/440/450:

Calculus

Calculus 9-12.F-IF.7.e Interpreting Functions

Graph exponential and logarithmic functions,

showing intercepts and end behavior, and

trigonometric functions, showing period, midline,

and amplitude.

• Visualizing Taylor Series Approximations

• Visualizing Taylor Series for e^x

Exeter MAT 420/430/440/450:

Calculus


Calculus 9-12.F-IF.8.a Interpreting Functions

Write a function defined by an expression in

different but equivalent forms to reveal and explain

different properties of the function.





• Limit Examples (part3) Exeter MAT 420/430/440/450:

Calculus

• Limit Examples (part3)

Exeter MAT 420/430/440/450:

Calculus

Calculus 9-12.G-GMD.1 Geometric Measurement and Dimension Explain volume formulas and use them to solve

problems

• Introduction to rate-of-change problems Exeter MAT 210/220/230:


Statistics 9-12.S-CP.1 Conditional Probability & the Rules of Understand independence and conditional

• Birthday Probability Problem

• Conditional Probability and Combinations



Probability probability and use them to interpret data

Understand that two events A and B are

independent if the probability of A and B occurring

• Probability and Combinations (part 2)

• Probability using Combinations



Statistics

Statistics 9-12.S-CP.2 Conditional Probability & the Rules of

together is the product of their probabilities, and • Independent Events 3 Exeter MAT40S: Introduction to

Probability use this characterization to determine if they are

independent.


• Probability of Dependent Events

• Probability of Dependent Events 2

Statistics

Understand the conditional probability of A given B • Conditional Probability and Combinations

as P(A and B)/P(B), and interpret independence of • Dependent Probability Example 1

Statistics 9-12.S-CP.3 Conditional Probability & the Rules of A and B as saying that the conditional probability of • Dependent Probability Example 2 Exeter MAT40S: Introduction to

Probability A given B is the same as the probability of A, and • Probability (part 6) Statistics

the conditional probability of B given A is the same • Probability (part 7)

as the probability of B. • Dependent probability

Construct and interpret two-way frequency tables

of data when two categories are associated with

each object being classified. Use the two-way table

as a sample space to decide if events are

i d d t d t i t diti l

• ANOVA 1 - Calculating SST (Total Sum of Squares) • ANOVA 2 - Calculating SSW and SSB (Total Sum of Squares Within and Between).avi • ANOVA 3 -Hypothesis Test with F-Statistic

independent and to approximate conditional

Statistics 9-12.S-CP.4 Conditional Probability & the Rules of probabilities. For example, collect data from a



Probability random sample of students in your school on their

favorite subject among math, science, and English.

Estimate the probability that a randomly selected

student from your school will favor science given

that the student is in tenth grade. Do the same for

other subjects and compare the results.

• Independent Events 2 • Pearson's Chi Square Test (Goodness of Fit) • Probability using Combinations

• Independent probability

Statistics

Recognize and explain the concepts of conditional


probability and independence in everyday language • Dependent Probability Example 1

Statistics 9-12.S-CP.5 Conditional Probability & the Rules of and everyday situations. For example, compare the • Dependent Probability Example 2


Probability chance of having lung cancer if you are a smoker • Probability (part 6) Statistics

with the chance of being a smoker if you have lung • Probability (part 7)

cancer.



Statistics 9-12.S-CP.6 Conditional Probability & the Rules of Use the rules of probability to compute probabilities • Dependent Probability Example 2

• Independent probability


Probability of compound events in a uniform probability model • Probability (part 6)




Statistics

Statistics 9-12.S-CP.7 Conditional Probability & the Rules of Use the rules of probability to compute probabilities Exeter MAT40S: Introduction to

Probability of compound events in a uniform probability model

Apply the general Multiplication Rule in a uniform • Probability (part 6)

Statistics

Statistics 9-12.S-CP.8 Conditional Probability & the Rules of probability model, P(A and B) = P(A)P(B|A) = • Probability (part 7) Exeter MAT40S: Introduction to

Probability P(B)P(A|B), and interpret the answer in terms of

the model.

Use permutations and combinations to compute



• Combinations


• Permutations

Statistics

Statistics 9-12.S-CP.9 Conditional Probability & the Rules of

probabilities of compound events and solve Probability

problems.

Understand statistics as a process for making

• Permutations and Combinations 1




• ...and 2 more ...






Statistics

Statistics 9-12.S-IC.1 Making Inferences and Justifying

Conclusions inferences about population parameters based on a

random sample from that population.





• ...and 4 more ...


Statistics

Decide if a specified model is consistent with results• Chi-Square Distribution Introduction

from a given data-generating process, e.g., using


Conclusions

simulation. For example, a model says a spinning

coin falls heads up with probability 0.5. Would a

result of 5 tails in a row cause you to question the

model?

Recognize the purposes of and differences among

• Pearson's Chi Square Test (Goodness of Fit)

• Type 1 Errors

• Surveys and Samples


Statistics


Conclusions sample surveys, experiments, and observational

studies; explain how randomization relates to each.

Use data from a sample survey to estimate a

• Confidence Interval 1





Statistics


Conclusions population mean or proportion; develop a margin of

• Margin of Error 2 error through the use of simulation models for


Statistics

random sampling. • Sampling Distribution of the Sample Mean

• Statistics: Sample vs. Population Mean


• ...and 1 more ...

• ANOVA 1 - Calculating SST (Total Sum of Squares)

• ANOVA 2 - Calculating SSW and SSB (Total Sum of Squares Within and Between).avi

• ANOVA 3 -Hypothesis Test with F-Statistic

Use data from a randomized experiment to compare • Chi-Square Distribution Introduction


Conclusions

Statistics 9-12.S-IC.6

Making Inferences and Justifying Conclusions

two treatments; use simulations to decide if

differences between parameters are significant.

Evaluate reports based on data.




• Contingency Table Chi-Square Test

• ...and 4 more ...

• Hypothesis Testing and P-values

• One-Tailed and Two-Tailed Tests

• T-Statistic Confidence Interval

• Box-and-whisker Plot


• Histograms



Statistics


Statistics

Statistics 9-12.S-ID.1 Interpreting Categorical and Quantitative Represent data with plots on the real number line • Sampling Distribution Example Problem Exeter MAT40S: Introduction to

Data (dot plots, histograms, and box plots).





• ...and 1 more ...

• Average or Central Tendency: Arithmetic Mean, Median, and Mode

Statistics

Statistics 9-12.S-ID.2 Interpreting Categorical and Quantitative distribution to compare center (median, mean) and Exeter MAT40S: Introduction to


two or more different data sets.




• Difference of Sample Means Distribution


• Range, Variance and Standard Deviation as Measures of Dispersion


Statistics

Statistics 9-12.S-ID.2 Interpreting Categorical and Quantitative distribution to compare center (median, mean) and • Standard deviation Exeter MAT40S: Introduction to


two or more different data sets. • Sampling Distribution of the Sample Mean 2

• ...and 1 more ...

• Variance

• Z scores 1

• Z scores 2

• Z scores 3

Statistics

Interpret differences in shape, center, and spread in • ck12.org Normal Distribution Problems: Qualitative sense of normal distributions

Statistics 9-12.S-ID.3 Interpreting Categorical and Quantitative

the context of the data sets, accounting for possible • Sampling Distribution of the Sample Mean Data


Statistics effects of extreme data points (outliers).


• Creating box and whisker plots

Use the mean and standard deviation of a data set

to fit it to a normal distribution and to estimate

Statistics 9-12.S-ID.4 Interpreting Categorical and Quantitative population percentages. Recognize that there are

• ck12.org Exercise: Standard Normal Distribution and the Empirical Rule

• ck12.org Normal Distribution Problems: Empirical Rule

• ck12.org Normal Distribution Problems: Qualitative sense of normal distributions

• ck12.org Normal Distribution Problems: z-score

• ck12.org: More Empirical Rule and Z-score practice



Data data sets for which such a procedure is not

appropriate. Use calculators, spreadsheets, and

tables to estimate areas under the normal curve.

Summarize categorical data for two categories in

two-way frequency tables. Interpret relative


• ...and 7 more ...

• Contingency Table Chi-Square Test

• Empirical rule

• Exploring standard deviation 1

• Z scores 1

• Z scores 2

• Z scores 3

Statistics

Statistics 9-12.S-ID.5 Interpreting Categorical and Quantitative frequencies in the context of the data (including Exeter MAT40S: Introduction to

Data joint, marginal, and conditional relative

frequencies). Recognize possible associations and

trends in the data.

Represent data on two quantitative variables on a

• Calculating R-Squared




Statistics


scatter plot, and describe how the variables are Data

related.

• Proof (Part 1) Minimizing Squared Error to Regression Line




• ...and 2 more ...


Statistics

Fit a function to the data; use functions fitted to

data to solve problems in the context of the data.


• Predicting with Linear Models


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interpret it as the mean of the probability

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answers obtained by guessing on all five questions

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four choices, and find the expected grade under

various grading schemes.

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DPMSS Application for performance school Page 103

Denver Public Montessori Secondary School

Performance School Application 2012

Respectfully Submitted

on behalf of the DPMSS Formation Committee by:

Katy Myers

1900 East St. Golden,

CO 80401 (303) 431-

2385

[email protected]



Performance School Application Guide for schools to open 2013-14 Page 104


EXECUTIVE SUMMARY

This section in its entirety will be provided to the Board of Education of Denver Public

Schools and will be posted online for the public to review, immediately upon

submission of this application.

Essential Information Form

Name of Proposed School Denver Public Montessori Secondary School

School Type (Select One) Performance School

Grade Configuration 7th - 12th (6th in first and second year only)

Model or Focus (e.g., Arts, College

Prep, etc)

Montessori

Proposed Region for School Attached to an existing DPS Montessori

elementary or centrally located to the four DPS

Montessori elementary schools.

Primary Contact Person Katy Myers; 303-431-2385;

[email protected]

Enrollment Projections: Delete unnecessary rows and/or provide additional columns if

you will not reach full enrollment by year five. Project your student headcount (not your

funded FTEs).

GRADE 2013-14 2014-15 2015-16 2016-17 2017-18 2018-19 2019-20

6 25

7 25 40 40 40 40 40 40

8 25 40 40 40 40 40

9 25 40 40 40 40

10 20 35 35 35

11 20 35 35

12 20 35

Total #

students

50

65

105

140

175

220

225

FRL % SPED % ELL %

Proposed Demographics Denison: 57

Lincoln 37

Academia Ana

Maria Sandoval:39

Gilpin: 89

Denison: 11

Lincoln: 6

Academia Ana

Maria Sandoval: 5

Gilpin:: 12

Denison: 19

Lincoln: 11

Academia Ana

Maria Sandoval: 41

Gilpin: 23



I. Culture: Denver Public Montessori Secondary School (DPMSS) will combine

Montessori best practices with current research on adolescent brain

development to provide a learning environment that promotes high

achievement for each student while also supporting them socially and

emotionally. Graduates, regardless of ethnicity or income status, will be

prepared for college or a career as well as demonstrate ingenuity, adaptability,

creativity, initiative and excellent communication and problem solving skills.

DPS currently has four Montessori magnet schools that end in either 5th

grade or 6th grade. There are approximately 133 4th grade and 128 5th grade

students. These students do not have an opportunity to continue Montessori

education within DPS. The purpose of this application is to give DPS Montessori

students the ability to continue Montessori education through high school

graduation. DPMSS will work with DPS and the Montessori elementary principals

to either centrally locate the secondary school to the Montessori elementary

schools, or join an existing Montessori school at their campus. DPS Montessori

school leaders recognize the need to continue Montessori education. Without a

secondary option, many students leave Montessori after 5th grade in order to

secure placement at a DPS middle school. Sixth grade students are crucial to

maintaining a high quality Montessori upper elementary classroom. However,

Montessori schools will only be able to retain these students if there is a high

quality Montessori option available to students when they move to 7th grade.

Montessori secondary education focuses on the whole child, self

construction, valorization and preparation for adult life. By creating a high

quality 7th through 12 grade program on these principles, students will

graduate with the academic skills necessary to thrive in both post secondary

education or career options, while at the same time have well developed

communication and problem solving abilities along with strong interpersonal

relationship skills. Finally, they will have developed creativity, ingenuity,

adaptability and initiative through the many problem solving, community

building and real world experiences they will encounter at DPMSS.

This application has the support of all four DPS Montessori elementary

principals. Surveys, both in English and Spanish, have recently been sent to

families in those schools, and, in just three weeks, 52 families indicated strong

interest. DPMSS has reached out to Montessori and community leaders both in

Denver and nationally. DPMSS has included the following people during the

development of this application: Dr. Martha Urioste, Principal Janice Spearman,

Principal Frank Vincent, Katy Mattis (incoming Denison Principal) , Principal

JoAnn Trujillo Hays, John Fowler, Judi Orion (AMI Trainer), David Kahn

(Executive Director of NAMTA), Virginia McHugh, (Director of AMI/USA), along

with Montessori administrators, teachers and parents. DPMSS recognizes that it

takes a strong community to build an excellent school and intends to build that

community during every stage of development.



II. Leadership: Katy Myers is an established Montessori leader. She was a

founding parent of Compass Montessori School which is a pre-k through 12th

grade charter school in Jefferson County, Colorado. Katy was the business

manager and assistant head of school for four years, and head of school for six

years. Katy has experience in all aspects of school leadership, including

budgeting, safety, accountability, staff evaluation, creating positive culture and

climate, and facilities. Katy has also been involved in the national Montessori

secondary movement for the last ten years. She is trained in Montessori

elementary (AMI) and Montessori adolescent education (NAMTA) and earned a

MEd in education leadership and administration at Arizona State University.

At Compass, Katy worked with staff to create an outcomes based

Montessori education system that includes graduation outcomes and written

outcomes for every level. During her tenure as head of school, Compass High

School moved from a non-performing school to a high performing school. In

2011, Compass won the Governor’s award for schools with the highest

2009-2010 academic growth rates in Colorado.

III. Education Plan: Montessori education is a constructivist model based on

creating an optimal prepared environment for students. For preschool through

6th grade, this means creating beautiful, spacious classrooms filled with

scientifically designed Montessori materials that allow students to acquire deep

mathematical, language, science and cultural knowledge. Each classroom

includes a Montessori guide that has obtained rigorous training in child

development, classroom content, and Montessori methodology. In the

September 28, 2006 issue of Science Magazine, Angeline Stoll Lillard published

findings of Montessori education study with the following conclusion:

Comparing outcomes of children at a public inner-city Montessori school with

children who attended traditional schools indicates that Montessori education

leads to children with better social and academic skills.

Montessori secondary education has been in development for 30 years.

During the last fifteen years, there has been signifiant increase in the number of

Montessori schools throughout the United States providing excellent education

from 7th through 12th grade. Leaders in the Montessori secondary education

movement have documented best practices, established training centers, and

provided a network of support to insure new schools can open successfully.

Montessori secondary education is designed for students who have attended

Montessori elementary schools. Montessori observed that this stage of a child’s

development provided excellent opportunity for a student to develop and hone

social and problem solving skills. Montessori wrote about what we now call the

value of 21st Century Learning Skills back in the early 1900s. She predicted that

if adolescent students were allowed to learn in an environment specially

designed for their specific stage of brain development, the result would be

adaptable, independent, ingenious and creative adults with excellent


communication and problem solving skills. She laid out a design for this type of

education in “From Childhood to Adolescence”.

Montessori secondary schools are divided into two “sub-planes”. The 7th

- 9th grade program is a land based program with real life problems solving

scenarios. Students combine didactic, academic lessons with real world

scenarios. They are daily working with both their head and their hands to

deeply internalize academic concepts. The 10th - 12th grade program is a

highly academic program preparing students for university. Having come

through the Montessori program to this point, students are well able and ready

to handle the most rigorous content. The high school remains centered on core

Montessori values. This includes Montessori trained teachers, long periods of

uninterrupted work time, key lessons, and a variety of methods whereby a

student can demonstrate mastery of knowledge. Assessments will include

rubrics, portfolios, presentations, quizzes on vocabulary and skills, end of unit

knowledge assessments plus all Federal and Colorado State mandated testing.

IV. Teaching: Along with being highly qualified, teachers and school leaders

employed at DPMSS must be Montessori trained through an accredited AMI or

AMS program, and have an orientation on adolescent Montessori education.

DPMSS will create a culture of shared learning among staff based on the

principals of recursive learning. For this application, recursive learning is

defined as the process of examining the principals of Montessori theory in

order to improve Montessori practice. Staff meetings will include seminars on

Montessori theory and experiential learning. There will be weekly level meeting

where staff can meet with their teams or across teams to problem solve.

Observation of staff will occur daily and, more formally, monthly using

established rubrics and feedback mechanisms designed to improve

performance.

V. Finance 2013-14 2014-15 2015-16 2016-17 2017-18

Number of Students 50 65 105 140 175

Per Pupil Revenue 221,850 288,453 465,933 621,180 776,523

Grant Funds *See V. for evidence 111,339

Private Funds

Other Sources

Total Revenue 333,189 288,453 465,933 621,180 776,523

Employee Salaries (inc. benefits) 285,933 285,933 451,957 595,380 753,250

Building Expenses

Services/Supplies 1,750 1,750 1,750 1,750 1,750

Other Expenditures 8,464 8,464 10,291 17,168 17,168

Total Expenses 296,147 296,147 463,998 614,298 772,169

NET INCOME 37,042 -7,694 1,935 6,882 4,354



A. Rationale

Section I. CULTURE

The current DPS Montessori schools are magnet schools managed by

Denver Public Schools. In order to maintain cohesiveness and continuity, it

makes sense for Denver Public Montessori Secondary School to also be

managed by Denver Public Schools. The performance school model combined

with innovative school status will give DPMSS the freedom necessary to create

an authentic Montessori secondary school while at the same time providing the

support and structure necessary to succeed within the DPS framework.

B. Mission Statement

Denver Public Montessori Secondary School will combine Montessori best

practices with current research on adolescent brain development to provide a

learning environment that promotes high achievement for each student while

also supporting them socially and emotionally. Graduates, regardless of

ethnicity or income status, will be prepared for college or a career as well as

demonstrate ingenuity, adaptability, creativity, initiative and excellent

communication and problem solving skills.

All students, regardless of ethnicity or income status, deserve a high

quality education and school choice. DPS recognized this fact when creating

Montessori elementary schools in four of its five regions. However, these

students do not currently have the ability to continue Montessori education

after 6th grade. DPMSS will create this option for students graduating from DPS

Montessori elementary programs. The school can either be located at an

existing DPS Montessori school or centrally located to all four schools.

Of the four DPS Montessori schools, one is rated as “Distinguished”, two

are rated at “Meets Expectations” and the fourth school was recently converted

via priority turn-around status to a Montessori school in order to improve

academic achievement. Data from the four schools indicate that students are

meeting or exceeding growth percentile benchmarks in reading, writing and

math. Areas of improvement include CELA growth and achievement gaps in

reading, writing, math and science. By creating a high quality Montessori

secondary school, DPMSS intends to continue the excellent Montessori

education students are receiving, while at the same time focus on narrowing

achievement gaps in reading, writing, math and science. DPMSS intends to

achieve the following goals within the first three years of opening:

• DPMSS will achieve and maintain a median growth percentile of at least 55 in

reading, mathematics and writing as reported on state assessments

(Transitional Colorado Assessment Program).

• DPMSS will increase the achievement in subcategories, including minority,

F&RL, student with disabilities and ELL and thereby decrease the achievement


gap by 5% per year while keeping Median Growth Percentiles above 55 for

each of the subgroup categories. Median Growth Percentiles will be measured

after the first year. Decreases in gaps will be measured after year two.

• Knowing that one of the four priorities in DPS is to better support ELLs, DPMSS

will also focus on improving academic achievement growth for ELL students.

We will increase the achievement of ELLs learners and decrease the

achievement gap between ELLs and Non-ELLs. Our goal will be to have an

achievement gap less than that of the district which is currently at 13%

difference for Math, 24% difference for Reading and 22% for Writing. DPMSS

will work to diminish achievement gap between ELLs and Non-ELLs so that the

difference will be less than 10% in Math and less than 20% in Reading and

Writing.

• DPMSS will achieve a rating of “exceeds” regarding parent satisfaction as

reported on the DPS School Performance Framework Stoplight Detailed Report

Card.

• DMPMSS will achieve a rating of “exceeds” regarding student engagement as

reported on the DPS School Performance Framework Stoplight Detailed Report

Card.

Montessori secondary education focuses on the whole child, self

construction, valorization and preparation for adult life. By creating a high

quality 7th through 12 grade program on these principles, students will

graduate with the academic skills necessary to thrive in both post secondary

education and career options, while at the same time have well developed

communication and problem solving abilities along with strong interpersonal

relationship skills. By graduation, they will have developed creativity, ingenuity,

adaptability and initiative through the many problem solving, community

building and real world experiences they will encounter at DPMSS.

C. Targeted Student Population

DPS currently has four Montessori magnet schools located in four of the

five DPS regions that end in either 5th grade or 6th grade.There are

approximately 133 4th grade and 128 5th grade students.Two of the four

Montessori elementary schools, Gilpin and Lincoln, end in 5th grade. The

optimal Montessori elementary design is for elementary to end in 6th grade. In

year one and possibly year two, DPMSS will provide an option for the graduating

5th graders. When the leadership at Gilpin and Lincoln believe the timing is

right, the intention is to work with these two Montessori schools towards

adding back 6th grade to their upper elementary classrooms. Year two or three,

depending on the success of bringing 6th grade back to Gilpin and Lincoln,

DPMSS would serve 7th and 8th and grow one grade at a time through grade

12. In its first year, DPMSS will serve 25 6th grade and 25 7th grade students.



The demographics for the existing four elementary schools are as follows:

FRL % SPED % ELL %


Lincoln 37

Academia Ana

Maria Sandoval:39

Gilpin: 89

Denison: 11

Lincoln: 6

Academia Ana

Maria Sandoval: 5

Gilpin:: 12

Denison: 19

Lincoln: 11

Academia Ana

Maria Sandoval: 41

Gilpin: 23

The demographics indicate that DPMSS will have over 50% of students who

qualify for the Federal Free and Reduced Lunch Program, about 10% of students

who qualify for special education services, and, depending on which schools

matriculates the majority of students to DPMSS, approximately 30% who qualify

for ELL services. Based on these percentages, the DPMSS principal and the

school psychologist / social worker will need to determine professional

development regarding best practices supporting students who qualify for FRL.

DPMSS will also have one of its full time staff qualified ELA-E and the Principal

and all other teachers will be at a minimum ELA - T qualified.

From these demographics, DPMSS may have only five to ten students who

qualify for special education services in its first year. DPMSS will hire a part-

time special education teacher to support these students while also work

closely with DPS to insure students are receiving the support they need.

Montessori education is individualized and designed to engage each

student at their level and then advance them through interesting, meaningful

work. In direct alignment with goals as set for in the Call for Quality Schools,

DPMSS will increase the achievement in subcategories, including minority, F&RL,

student with disabilities and ELL and thereby decrease the achievement gap as

outlined in our SMART goals set forth in Section I B.

D. School Culture

Montessori schools are designed on a culture of respect. All members of

the community are asked to respect themselves, each other and the

environment. Creating healthy, positive culture is a core component of

Montessori education. This goal is accomplished in several ways.

The first method for creating positive healthy culture is to create a

welcoming environment for staff, students, families and community members.

This began at the first stages of this application process. Members from all

sectors of the DPS Montessori community were invited to participate in the

application and submit ideas, thoughts and concerns. The applicants are

partnering fully with the DPS Montessori schools. Throughout the planning

year, the applicants will host multiple parent education nights to discuss the

benefits of Montessori education while also including perspective parents in the

design of the school. These parent nights will be held in both English and


Spanish. If there are families requiring additional languages, every effort will be

made to find interpreters. The goal is to create a deep sense of community and

inclusivity for all stakeholders.

Once school is open, students will be active members of the school

community. The Junior High (7th, 8th, 9th) and high school (10th, 11th, 12th)

will be set up into advisements. Students check in daily with their advisors to

review progress and set goals. Junior high and senior high School staff and

students will also hold weekly community meetings. There will be monthly all

school (7th - 12th) community meetings for celebrations and discussion.

A second core component of Montessori is peace education. Peace

education starts at the youngest grades and continues through high school. In

the junior high program, peace education manifests through positive behavior

support, conflict resolution, community service and lessons and discussion on

what it means to create a peaceful environment. High school continues this

practice but also adds a social justice class that allows students to explore

peace at a more national and global level.

A third component of Montessori education is the belief that all work is

noble and that work normalizes the child. What this means at the secondary

level is that students gain self confidence and self respect through challenging

work. DPMSS’ academic studies will be based on a culture of high challenge

combined with high skills and high support in order to create maximal

engagement or “flow”. This design is based on Dr. Mihaly Csikszentmihalyi’s

research as explained in Flow, The Psychology of Optimal Experience and flow

research in Montessori middle schools conducted by Dr. Kevin Rathunde.

Finally, Montessori schools provide individualized education that meets

each student at his or her level. All lessons and instruction are differentiated

and follow up work is initiated by the student based on his or her interests.

DPMSS will meet the needs of special education students through this

differentiated learning while still holding high expectations that appropriately

challenges each student as determined by their IEP and through teacher

observation. ELL learners will demonstrate learning both in their native

language and, with appropriate assistance as needed, in English. DPMSS will

employ at least one teacher who qualified ELA-E along with a full time highly

qualified Spanish teacher. At risk students will benefit from the inclusive

culture, the advisement model, and the academic program that is specifically

designed to help students find their voice and self-confidence through work.

D. Parent and Community Involvement: Prior to submitting the letter of intent,

the founding members of DPMSS contacted DPS Montessori principals, teachers

and community members to gauge interest in providing Montessori secondary

education for DPS Montessori students. Response was enthusiastic with the

caveat that the secondary program must be high quality, rigorous and



based on Montessori core principles. DPS Montessori community members

were invited to participate at every stage of this application, and their input has

been invaluable. The next step was creating an interest survey for existing

Montessori families. Surveys were sent out in English and Spanish in mid-

March. In just three weeks, 52 families indicated strong interest with surveys

responses still coming in.

Attached in Appendix F are emails of community support from the

following stakeholders: Katy Mattis, incoming Denison Montessori principal,

Principal Frank Vincent, Gilpin Montessori, Principal JoAnn Trujillo Hays,

Academia Ana Maria Sandoval, Principal Janice Spearman, Lincoln Montessori,

Dr. Martha Urioste, founding principal of Mitchell (now Denison) and Montessori

consultant, Judith Orion, Director of Training, The Montessori Institute Denver,

and Yamile Reina-Ayadi, Denison parent and DPS School Improvement Partner.

DPMSS is partnering with the North American Montessori Teaching

Association (NAMTA) for school design and teacher development. NAMTA,

presented to DPMSS a cash grant of $3000.00 in start-up funds along with an

additional $5000 for services in-kind donated from David Kahn and Laurie

Ewert-Krocker. David Kahn is the executive director of NAMTA and the

established global expert on Montessori adolescent education. Laurie Ewert-

Krocker is the founding director of The Hershey Montessori School, which is a

private, adolescent Montessori program that has been successfully operating

for fifteen years and has established curriculum and best practices that can be

replicated at DPMSS. Finally, DPMSS is partnering with Compass Montessori

School, a Jefferson County pre-k through 12th grade charter school located in

Wheat Ridge and Golden Colorado. Compass Montessori has an established,

high quality junior and senior high Montessori program. Compass Montessori

designed Montessori graduation outcomes, uses CSAP data to improve

Montessori instruction, and created record keeping systems that align

Montessori methods with education state standards. In 2010, Compass received

the Governor’s award for for schools with the highest 2009-2010 academic

growth rates in Colorado.

DPMSS has contacted the following organizations regarding partnering on

the urban farm program: the GrowHaus (in the Elyria-Swansea neighborhood),

GreenLeaf (a youth-internship urban farming program), and Sprout City Farms,

the non-profit that runs the farm at the Denver Green School. They are all

willing to sit down and talk about DPMSS and its inclusion of an urban farm. A

representative from DPMSS has meetings scheduled in April with these

organizations to determine how these partnerships might work and level of

commitment. Once the high school program is underway, DPMSS will partner

with local business and cultural institutions to establish student internships,

community service opportunities and expanded learning options.


DPMSS will embrace its families and community members in a variety of

ways. First, families will be included in the initial design. Although the core

Montessori mission and values must remain intact, families will provide

invaluable ideas regarding how to accomplish the school’s mission. Families

will be invited to participate in key decision making processes such as helping

to select the location of the school (as long as there are choices available), after

school activities, school committees and ideas on initiating school traditions,

fundraising and creating excellent communication structures. One of the best

ways for families to feel part of the school community is through community

volunteer events such as school work days. DPMSS will identify early on a

volunteer parent coordinator and then support that person to create school

work days along with numerous school volunteer opportunities.

DPMSS will also create a vibrant School Accountability Committee (SAC)

that will include no less then one staff member along with the head of school,

three parents and two community members. The SAC will assess school

performance based on agreed upon outcomes that include academic goals,

student well-being and community involvement. The SAC will meet once per

month to discuss school progress and make recommendations to the principal.

D. Parent Satisfaction

DPMSS intends to achieve a rating of “exceeds” in the DPS parent

satisfaction survey along with a high response rate. Parent satisfaction is a key

component for school success. The first step in insuring parent satisfaction is

clear communication regarding the school’s mission and vision along with

parent education regarding Montessori adolescent education. This

communication must happen prior to parents choosing DPMSS for their student.

Once students are enrolled, DPMSS will manifest multiple ways to connect with

parents and gauge satisfaction. Some methods will be as simple as the principal

being outside during drop off and pick-up so parents can engage in quick

conversation if necessary. The principal will also maintain an open door policy

along with a school policy that all parent phone or email messages must be

replied to within 24 hours (except during week-ends or holidays).

Each year, the chairperson of the school accountability committee will

insure that the DPS parent satisfaction survey measuring parent satisfaction

regarding the school achieving established outcomes is delivered to all parents

and guardians. All surveys will be delivered in English and the parent’s native

language. Surveys will be anonymous but the SAC chairperson will assess

percentage of surveys returned based on school population. If that percentage

is less than 75%, the SAC committee will assess the current population and find

solutions on how to bring that percentage up to 75%. Should parent satisfaction

not meet the standard on the SPF rubric, DPMSS will take the following steps: 1)

Hold community meetings to determine the root of parent dissatisfaction, 2)



increase parent education to insure that parents are comfortable with the

Montessori Method and how it is being implemented at DPMSS, 3) create a

strategic plan that includes tactical and strategic steps to resolve concerns.

E. Student Engagement

The goal for student attendance is 95% or better every school year.

Montessori schools are designed as a place where students feel safe, welcome

and love school. Because Montessori education is designed on student self-

construction and student choice, students have the ability to deeply study

subjects that are of interest to them. These studies combined with meaningful

work result in students demonstrating competency and therefore gaining in self

respect and self worth. If a student starts to demonstrate a lack of engagement,

the advisor will connect with the student to determine the cause. If needed, the

student and their family will meet with the advisor to determine how to re-

engage the student towards meaningful work.

Attendance will be conducted at the beginning of the school day, prior to

lunch and mid-afternoon. If a students receives more than three excused

absences in a month, the advisor will contact the family to make sure all is well.

If the student receives any unexcused absences, again, the advisor will contact

the family to determine why the student is not in school and ask how can we

support the student and the family. If the student has three or more unexcused

absences in a month, or is approaching more than ten unexcused absences in a

semester, the principal will actively work with the family while at the same time,

initiate a truancy plan as outlined by DPS. At all times, DPMSS will adhere to the

DPS attendance policies.

Student satisfaction will also be measured in multiple ways. The school

will track on-time, daily attendance and work with students who are

demonstrating a lack of engagement through tardiness or poor attendance.

Advisors will address student concerns at the daily and weekly community

meetings. Both the advisors and the principal will maintain an open door policy

to address student concerns and complaints. Finally, the principal will insure

that the DPS student satisfaction survey is delivered to every student. Students

will be given access to the survey during school hours in a manner that allows

them to maintain confidentiality.

DPMSS intends to achieve a rating of “exceeds” on the SPF for student

attendance and on the DPS student satisfaction survey. Should the results of the

survey not meet the standard on the SPF rubric, the school will invite students

to more clearly articulate concerns through both an anonymous forum and a

community forum. Staff will then work with students to create a strategic plan

that includes both tactical and strategic steps to address student concerns.

Follow-up meetings will be held twice per month until concerns are

satisfactorally addressed.


Section II. LEADERSHIP

A. Leadership Team Personnel

DPMSS has identified the following characteristics for successful

leadership of a public Montessori school. The leader must be trained both in

Montessori elementary education and in Montessori adolescent education. The

leader must hold a Master’s degree in Education and Administration or similar

school leadership program. The leader must have experience leading a public

school, preferably a public Montessori school. He or she must have experience

working with adolescents and preferably teaching adolescents. Finally, the

leader must demonstrate a leadership style that is reflective of Montessori core

values including respect, inclusivity, shared decision making, recursive learning,

and empowering staff to work at their highest level.

DPMSS will be led by Katy Myers. Katy Myers is an established Montessori

leader. She was a founding parent of Compass Montessori School which is a

pre-k through 12th grade charter Montessori school in Jefferson County,

Colorado. Katy led the Compass steering committee composed of nine parents

through the process of writing the charter application, working with Jefferson

County School District to achieve approval of the charter, hiring the founding

principal and staff, locating, financing and purchasing the Wheat Ridge facility,

designing and remodeling the facility, purchasing furniture, fixtures and

Montessori materials, and enrolling 150 students. Two years later, Katy was

hired as the Compass business manager and assistant head of school. Her

primary role was to start the Compass Montessori Secondary School. During

that time, Katy worked with the head of school and a parent committee to

locate, purchase, finance and build the Compass Montessori Golden campus.

This included obtaining $5.5 million in CECFA bond financing, hiring both an

architect and contractor, and working closely with staff and parents to create

the beautiful 35,000 square foot campus that has two buildings, a working

farm, commercial kitchen and an art studio with kiln. The project was

completed on time and under budget.

Compass opened the Golden campus in 2002 with 180 students grades

7th - 10th and twelve full time staff. During the next few years, there were

successes but also many challenges. In analyzing the situation, Katy realized

that she was missing key education components to be a successful leader in

this public, secondary Montessori environment. After the first year, Katy

attended Montessori adolescent training through the North American

Montessori Teachers Association. The following year, Katy applied and was

accepted to the Federally funded Leadership for Education Entrepreneurs

program at Arizona State University. There she obtained her Master’s in

Education and Administration. She then enrolled in the elementary education



diploma program through Association Montessori Internationale, which will be

completed this June.

Through observation and data analysis, Katy and the Compass leadership

team began determining best practices that had to be implemented for

Compass to succeed. In 2005, Katy became Head of School of the Golden

Campus and instituted the following reforms at the school. First, the secondary

program was downsized so that a super-majority of students entering 7th

grade came from Compass 6th grade. This insured that the junior high program

had a majority of students and families that were familiar with Montessori and

specifically choosing Montessori to continue their education. Katy then worked

with staff to create Montessori high school graduation outcomes. Staff took

these outcomes and backward mapped them all the way to Compass

kindergarten, so that staff had a clear roadmap towards educating students to a

successful graduation and beyond. Finally, Katy, working with staff, analyzed

CSAP benchmark data provided by Jefferson County to determine what areas of

instruction needed improvement. She then worked with staff to determine what

Montessori materials, key lessons and Montessori based curriculum matched

those instructional areas and created professional development to improve

instruction using Montessori methods. During this process, Compass High

School moved from “non-performing” to “performing” to “high-performing”. In

2011, Compass won the Governor’s award for schools with the highest

2009-2010 academic growth rates in Colorado.

During this time, Compass became an early adopter of the Response to

Intervention (RtI) model for identifying students requiring special education

services and insuring that all student received strategic, targeted interventions

when demonstrating need for such intervention. The RtI model matched well

with the Montessori method, and staff embraced this innovative approach to

improving student achievement for all students.

In 2008, Katy became head of school over Compass Wheat Ridge campus

as well. Compass Wheat Ridge is a pre-k through 6th grade Montessori charter

school that then matriculates to the Golden campus. At that time, Compass

Wheat Ridge was experiencing decreasing CSAP scores, high teacher turnover

and was in a budget crisis that was bringing the school to the edge of

bankruptcy. During the three years that Katy was head of school over both

Compass Wheat Ridge and Compass Golden, Katy was able to bring the Wheat

Ridge budget from a projected deficit of ($180,000) to a positive cash flow of

$40,000. She improved the culture and community of the school by creating a

shared leadership model resulting in very high staff and student retention. Katy

added Montessori professional development and created a culture of high

student behavior and academic expectations. By 2010, CSAP scores had risen

dramatically and the school was thriving as indicated by staff, parent and

student surveys.


While working locally within Compass to document best practices, Katy

also worked with the national Montessori secondary school movement through

NAMTA. Katy collaborated with other Montessori administrators throughout the

U.S. and Mexico to determine what exactly high quality secondary Montessori

education looks like and how it could be measured. Because of her experience

in public charter Montessori education, Katy has been a frequent presenter at

NAMTA conferences and most recently teamed with three other experienced

administrators to lead a four day Montessori leadership training for current and

prospective Montessori administrators who came from as far away as the

Philippines and Monaco to attend.

DPMSS will work with the “Self-Governance” leadership model that is

successfully being implemented at Compass Montessori School. An outline of

this model is included in Exhibit G. During year one and two, the school will

have up to 65 students. In order to be economically sustainable, the school

leader will also work half time in the classroom. During that time, she will work

with the other advisors to create a culture of shared leadership. Key leadership

roles and responsibilities will be reviewed with staff to insure reasonable

redundancies can be created. In year two, a junior high program director will be

identified and that person will start attending professional leadership and

administration development as offered through DPS. In year three, the school

principal will decrease teaching hours in order to focus on the well being of the

105 students, data analysis, and professional development for staff. She will

also conduct curriculum and programmatic review to insure that 9th grade is

successfully meeting DPS high school standards and that DMPSS is ready to

move forward with adding the high school program. Also In year three, a high

school program director will be identified and will start attending professional

leadership and administration development as offered through DPS. In year

four, the leadership team will consist of the principal, the junior high and the

senior high program directors. At that point, the principal will insure that both

program directors have the knowledge base needed to assume the principal

role of the school should that event be necessary.

The principal’s roles and responsibilities include creating and maintaining

the school’s mission and vision, hiring and evaluating staff, maintaining a

culture of high expectation regarding behavior and academic achievement,

creating and reviewing measurable data systems to insure the students are

obtaining a rich and rigorous education, creating and linking staff to

professional development, visiting classrooms every day and conducting

monthly, longer staff observations, creating and maintaining a welcoming

environment for all community members, high level student discipline and

attendance.

The program director’s roles and responsibilities include maintaining a

culture of high expectations regarding student behavior and academic



achievement, daily check in with fellow staff, weekly staff meetings to insure

that the school is holding to its mission and vision, ground level parent

communication, and resolving low level student conflict and discipline. Program

Directors will also be advisors / teachers.

Program directors must be highly qualified teachers who are Montessori

trained in both elementary and adolescent education. They need to have

completed or be willing to complete a Master’s level leadership program. They

must demonstrate either in their DPMSS position or in past positions they they

can create a culture of respect, inclusivity, shared decision making, recursive

learning, and empowering staff to work at their highest level.

B. Leadership Team Coaching and Evaluation

DPMSS will use a variety of data points and observation to determine the

school leader’s need for coaching and professional development. First, the SAC

team will review monthly achievement data and the annual SPF to see if the

school has met set targets. Second, the SAC will review annual parent, staff and

student surveys to determine the overall health of the school and community

opinions of the school. Third, the SAC will meet with a Montessori consultant

who will be hired in year 1, 2, 3 and year 5 to observe the school and provide

feedback to the SAC, school leadership and staff.

The SAC will use the DPS Framework for Effective School Leadership as

their evaluative tool. The principal will also welcome designated DPS leadership

to observe the school and provide feedback using the DPS Framework. Every

month, the principal will meet with the SAC to discuss the school’s successes

and challenges based on data and observation. During those meetings, the

principal will seek out feedback regarding current leadership effectiveness. The

principal will also solicit feedback from staff and community members during

informal meetings. At all times, the DPMSS principal will model the value of

recursive learning, seeking and accepting feedback, and inclusive problem

solving in order to continue to evolve towards distinguished leadership.

Should the SAC and/or DPS leadership determine that the principal

require additional coaching and professional development, the principal, SAC

and DPS Leadership will create a professional development plan along with

benchmarks to measure progress. Progress will be reviewed monthly. If, after

six months, the principal has not made satisfactory improvement, DPS will

replace the him or her with a program director and begin the search for a new

principal.

B. School Personnel Structure

DPMSS will have 50 students for the first year of operation and 65

students in the second year. During that time, DPMSS will enroll one full time

licensed teacher who is ELA-T qualified, one full time teacher who is highly


qualified in Spanish and is also ELA - E qualified along with part-time staff for

special education, psychologist/social worker, nurse, office support, and

principal.2

The principal will work half time as head of school and half time as a

teacher / advisor which brings the total number of teachers to 2.5. (including

the Spanish / ELA-E teacher). After that time, the school will grow by 40

students per year. Staff will be added to maintain a teaching ration of 25

students to 1 teacher. Hours for the part time staff will increase based on the

number of special education students being served. The principal will relinquish

all teaching duties and become a full time position in year six.

An organization chart is included as Appendix I and a Staff Roster is

included as Appendix J.

C. Student Enrollment

DPMSS is designed to be the secondary school for DPS Montessori

elementary schools. The entire curriculum is designed as a continuation of the

Montessori elementary curriculum, the Montessori methodology and the

education design structures students have experienced throughout their

elementary Montessori experience. Priority enrollment will be given to all

students graduating from Dension, Academia Ana Maria Sandoval, Lincoln and

Gilpin Montessori schools along with any DPS Montessori elementary schools.

Each of these schools currently have a diverse population representative of

Denver. DPMSS will not deny admissions to any student based on income

status, academic achievement, disabilities or at risk of academic failure. DPMSS

staff will meet with designated staff of the sending schools to discuss transition

of students and to review any IEP, ALP, ILP, and ELL plans along with discussing

learning styles, RTI and productive strategies for all students matriculating to

DPMSS.

Should there still be available spots at DPMSS, DPMSS will accept students

via the following DPS approved choice enrollment process:

Beginning with the 2012-13 school year, DPS will offer the SchoolChoice

enrollment process. Enrollment will follow five steps for any student who wants

or needs to attend a new school as of 2012-13, especially “transitioning”

students.

1. Research DPS schools by reviewing the SchoolChoice Enrollment Guide and

online resources, and by visiting schools of interest.

2. Prioritize your student’s top five preferences and list them in order on the

SchoolChoice form.

3. Complete any extra enrollment steps and submit them to your schools of

interest if they are required. Submit your SchoolChoice form by January 31.

2 Clarification to CDE: ELA qualified teachers will also meet state highly qualified requirements.



4. SchoolChoice will combine your student’s top five preferences with each

school’s admissions priorities and available space. For schools with more

interested students than available space, students will be randomly

assigned a lottery number that will determine the order in which they are

enrolled with a school.

5. Students will be awarded a seat at their highest-preference school with an

available seat in March 2013.


A. Curriculum

Section III: EDUCATION PROGRAM.

The 6th grade through 12th grade Montessori curriculum that DPMSS will

implement is rigorous, innovative, interesting and is designed to engage

students to produce optimal academic achievement as well as social and

emotional maturity and well-being. Montessori adolescent curriculum has been

designed and tested over the last fifteen years at both private and public

Montessori schools. This curriculum, referenced throughout this application as

the National Montessori Curriculum, has been collected, refined and reported

through The NAMTA Journal, A National Montessori Curriculum Report, The

NAMTA Journal, Volume 37, No. 1, Winter 2012. DPMSS will design its program

using this curriculum. Recently, the National Montessori Curriclum for the

Adolescent Program from Twelve to Fifteen/Sixteen Years was reviewed by the

Australian Curriculum Assessment and Reporting Authority. Their findings, as

reported in A National Montessori Curriculum Report, are as follows: ACARA

(Australian Curriculum Assessment and Reporting Authority) established an

extremly rigorous recognition process to determine the extent to which a well-

established alternative national curriculum can deliver comparable educational

outcomes for students to those based on the Australian National Curriculum.

ACARA have advised that (the National Montessori Curriculum) aligns with the

Melbourne Declaration on Educational Goals for Young Australians, meets the

particular principles and guidelines in relation to the Shape of the Australian

Curriclum v3 paper, and allows for broadly comparable educational outcomes in

English, mathematics, science and history by the end of year 10.

Although DPMSS will use the National Montessori Curriculum, DPMSS will

also use the Colorado Academic Standards (CAS), the Common Core Standards

(CCS)and the Higher Education Admission Requirements (HEAR) as its education

standards. DPMSS will compare the Montessori National Curriculum to the CAS

and the CCS to insure that there are no gaps and that the students are

achieving the benchmarks as stated in these standards.

The priorities for the secondary program are first to provide the optimal

environment for student achievement. This will include a beautiful physical

environment that includes an urban farm, an art and micro-economy studio

with kiln, a commercial kitchen and science laboratories. The school will need

to be located in an area that allows for public transportation to the local cultural

institutions. For high school, the prepared environment will include

professional work environments, a laboratory fitted out for advanced chemistry,

biology and physics instruction, an art studio fitted out for advanced work in a

variety of artistic media, and computers with refined publishing and

demonstration software.



The next priority is to extend and deepen the Montessori education

students have received through their elementary program. By sixth grade, the

Montessori students will have completed most of the elementary Montessori

materials. DPMSS will build upon the skills and knowledge acquired through the

materials via a carefully constructed curriculum that recognizes the specific

stage of brain development students are entering upon adolescence.

Here is one example of this extension as related to math. Upon entering

DPMSS, students should have completed Montessori math materials up through

the trinomial cube, measurement, volume, mathematical laws, introduction to

algebra, Pythagoras theorem, and geometry. At this point, students need to

practice their skills while using these skills to solve challenging problems. They

also need to advance their skills through algebra, advanced geometry and into

trigonometry and calculus. In the 7th, 8th and 9th grades, students will practice

math skills solving real problems that involve the urban farm, culinary arts and

micro-economies. They will also receive direct instruction in math along with

working a self-paced on-line math program to continue to practice, develop

and build math knowledge.

By 10th grade, students will be ready for direct instruction in advanced

algebra, geometry, trigonometry and calculus. The curriculum in high school

will be a combination of small group lesson and on-line math curriculum to

allow the students to advance at his or her own rate while, at the same time,

insuring they have the support they need to continue making, at a minimum,

one year of academic progress in one year’s time.

DPMSS is also committed to providing a strong Spanish language

program and support dual language acquisition. It will have one teacher in both

the junior and senior high who is highly qualified in Spanish and Montessori

trained and who is also qualified ELA - E. At least one Occupation per year will

be delivered in Spanish to offer an immersion experience and to extend the

dual education students have received at Academia Ana Maria Sandoval.

DPMSS will be using the National Montessori Curriculum for grades 7-9

for science, history and language arts. DPMSS will use an on-line math

curriculum that is individualized for each student combined with small group

lessons. The small group lessons will be designed to meet each student at the

particular benchmark the student is currently working, and the teacher will use

a variety of instructional methods, including Montessori math materials, to

assist the student in mastering that benchmark and preparing to work on the

next on-line unit. Students will also apply math towards a variety of hands-on

projects utilizing the farm, the culinary arts program and micro-economy. The

7,8,9 Spanish curriculum will be the TPRS curriculum. TPRS matches the

meaningful, relative approach that defines Montessori education.


The high school, grades 10, 11 and 12, will use an integrated college

prepatory curriculum such as the curriculum currently in place at Compass

Montessori High School in Jefferson County. The Compass three year SPF results

for this curriculum are a median growth percentile of 58 for reading, 54 for

mathematics and 66 for writing and an academic achievement score for science

of 59%. The academic growth gaps achieved a level of “exceeds” for reading

and “writing” and meets for math. The three year ACT composite is 21.7.

Although the curriculum for high school will be similar to advance

placement curriculum in DPS for English, history, math, science and Spanish,

there will still be innovative differences. First, the curriculum will be integrated

so that literature studied in language arts will support the history curriculum for

an overall integrated humanities curriculum. The math and science teacher will

work together to insure students are obtaining the mathematical skills needed

to work out currently studied complex scientific equations. Linkages between

science, math and history will be explored. Throughout all areas of study, there

will be indepth reading and writing instruction.

The junior high program will include 6th grade in its first and possibly

second year. Currently, 6th grade is offered at Denison and Academia Ana

Maria Sandoval, but not at Lincoln or Gilpin. When the leadership at Gilpin and

Lincoln believe the timing is right, the intention is to work with these two

Montessori schools towards adding back 6th grade to their upper elementary

classrooms. Year two or three, depending on the success of bringing 6th grade

back to Gilpin and Lincoln, DPMSS would serve 7th and 8th and grow one grade

at a time through grade 12. The long range design is for the junior high to be

composed of 7th, 8th and 9th grade. There will be 120 students divided into

five advisements of 24 students each. All five teacher / advisors will be

Montessori trained. There will be a highly qualified math teacher, language arts

teacher, social studies teacher, science teacher and Spanish teacher.

The high school will be composed of 105 students. There will be four

teacher/advisors including a highly qualified math teacher, language arts

teacher, social studies teacher and science teacher. There will be a fifth teacher

who will be highly qualified in Spanish and ELA-E. These same teachers will

offer afternoon electives in subject areas that they are qualified to teach.

The junior high program has, as a key component, a curriculum called

Occupations. In the NAMTA National Montessori Curriculum Report,

Occupations is defined as follows: “Through work, the students in the

Montessori adolescent community engage with the natural environment and the

wider society. The work undertaken within the community which has purposeful

problem solving and economic contributions but which draws on necessary

academic expertise is called Occupations. Occupations in the adolescent

community have the following characteristics: The work is meaningful to the

students, the work is both physically and intellectually challenging, the work is



valued in the wider community, society and culture, and the work has economic

validity. Occupations with these characteristics inspire students to engage in

the work with integrity and passion, to develop their own interests and

expertise, to gain recognition for their contribution and to experience a sense

of ownership and accomplishment.” The NAMTA Journal, Volume 37, Number 1,

Winter 2012. The scope and sequence and an example of a science Occupation

are included in Appendix K.

Staff at DPMSS will create Occupations and humanities units that are

meaningful to the target population and inclusive of diverse cultures and

academic learning styles. Occupations integrate all of the core subject areas,

with a focus on Science. Humanities is taught using a similar scope and

sequence as Occupations but with a focus on history. An example of the

Humanities curriculum is in Exhibit C. Throughout the school day, students will

be engaged in the various Occupations and Humanities. During this time,

additional small group lessons will occur providing direct instruction in math,

ELA, and Spanish. Here is the curriculum summary as outlined in A National

Montessori Curriculum Report and adapted to DPMSS:

Pedagogy: The themes that govern the approach to pedagogy implemented in

the Montessori adolescent community are synthesis and integration. Montessori

adolescent pedagogy integrates concrete and active learning experiences with

opportunities for reflective and contemplative study of increasingly abstract

concepts and ideas. Second, the pedagogy integrates intellectual and ethical

development, creative expression and the academic disciplines, giving students

the opportunity to apply discipline knowledge, judgement and creative skills to

problem solving in projects that require physical activity, ethical choices, self-

expression and abstract application of interdisciplinary knowledge. The focus of

the pedagogy is the adolescent’s civic, ethical and social development as well

as the adolescent’s adaptation to the demands of the changing natural and

human world.

The expansive nature of the curriculum, and the pedagogy used to

implement the curriculum, ensures that the curriculum can be adjusted to

accommodate knowledge, skills and understandings required by the CAS, the

CCS, and the State assessments. Students become active participants with

teachers in the task of identifying individual learning needs and, where needed,

to design individualised learning programs to meet these requirements and

demands. The goal is to hand over to students increasing responsibility for

planning and managing their own learning as one aspect of the overall aim of

the Montessori learning environment prepared for adolescents: to prepare

students for social and economic independence.


The National Montessori Curriculum Summary

Intellectual Development (cross-curricular)

· civility, citizenship, civics and community life (civil society and moral

development)

· mathematics, including arithmetic, geometry, algebra and measurement

· language, English language, as well as at least one language other than

English

Self-Expression (cross-curricular)

· language for creative expression

· music

· visual arts

Preparation for adult life and contemporary culture

· Science curriculum embedded in the Occupations

· the study of the Earth and living things, incorporating studies in:

• Earth and space sciences: cosmology, including astronomy;

geology and physical geography, including the geology and

geography of prehistoric periods

• Biological sciences: biology, including studies in botany,

zoology, ecology, physiology, comparative anatomy health

sciences, and ecology(sustainability)

· the study of human progress and civilisation, incorporating studies in:

• Physical sciences: physics and chemistry

• Contemporary sciences: mechanics and engineering, history of

science and technology, including genetics

Occupations

· practical daily life tasks, including maintenance of the community

environment

· working on and being stewards of the land, including care of the natural

environment, horticulture, agriculture and animal husbandry

· participating in the micro-enterprises of the adolescent community

History and the humanities curriculum

· the study of humanity

· the study of the building of human civilisation

These studies incorporate studies in geography, anthropology, politics and

economics.

By high school, (10th - 12th), Montessori students are well adept at

taking charge of their education, and are eager for further intellectual

challenge. At this point, the curriculum looks similar to more traditional college

preparatory curricula. However, the delivery of curriculum maintains the core

values of Montessori and are designed specifically for students who have

progressed through Montessori education. Instruction is delivered via key

lessons that convey to the students fundamental concepts and serve as



“jumping off” points for further exploration. Studies are self-directed in an

environment of high expectations and high support. Teacher/advisors work

with students to insure that students have the advanced skills necessary to

explore advanced concepts.

In combination with the challenging academic setting, high school

students are also encouraged to go out to local cultural institutions to further

study. DPMSS intends to create partnerships with the Museum of Nature and

Science, the Denver Zoo, the Denver Botanic Gardens, the Denver Art Museum

and other local cultural centers so that our students can easily access experts

within those settings. DPMSS will also create partnership with CU Denver and

Metropolitan State College of Denver so that students who wish to dually enroll

in some classes during their senior year have the ability to do so. Another key

experience for high school will be international travel. DPMSS will determine

appropriate fund raising venues so that all students will be able to attend at

least one international trip during high school.

In 2003, Dr. Kevin Rathunde published a study titled “A Comparison of

Montessori and Traditional Middle Schools: Motivation, Quality of Experience,

and Social Context.” With the help of co-investigator Mihaly Csikszentmihalyi,

Dr. Rathunde compared the experiences and perceptions of 150 middle school

students in Montessori and 150 middle school students in traditional schools

using the Experience Sampling Method (ESM). The ESM statistical procedure

allowed Dr. Rathunde to determine, in an objective manner, whether there were

significant differences between the two groups of students (Montessori and

Traditional) and to adjust or “control” for any differences that were due to other

factors such as background variables.

The statistical analysis revealed that there were strong differences

between the Montessori and Traditional students. The differences included:

1) Montessori students reported a significantly better quality of experience in

academic work than the traditional students,

2) Montessori students appeared to feel more active, strong, excited, happy,

relaxed, sociable, and proud while engaged in academic work,

3) Montessori students enjoyed themselves more, they were more interested in

what they were doing, and they wanted to be doing academic work more than

the traditional students,

4) Montessori students reported significantly higher percentages of

undivided interest, higher motivation and higher levels of importance with

regard to schoolwork,

5) Montessori students reported more conditions where the challenges and

skills used while doing academic work were above average.

B. School Schedule & Calendar: The school calendar and School Day Schedule

are outlined in Appendix L. The junior high portion of DPMSS will be

centered around an urban farm. In order to take advantage of the short


growing season in Colorado, DPMSS will start one week earlier than Denver

Public Schools. DPMSS will also end one week later. During the year, DPMSS will

have a one week fall break in late October and extend spring break to two

weeks. Prior to school opening year one, there will be 10 non-contact days

before the first day of school. The schedule for this professional development is

described in Section IV C.

The DPMSS junior and senior high curriculum is outcomes based, with the

outcomes measured via benchmarks achieved as noted in the farm school and

high school portfolios, and data gathered through the on-line math

assessments, mastery level quizzes, end of unit assessments and completed

follow-up work. The schedule is therefore individualized to meet the needs of

every learner, including students needing intervention or acceleration.

The junior high school day will start at 8:00 and run until 3:30. There will

be one half hour for lunch and one half hour for outdoor recreation time and

6.5 hours for academic work time. On Wednesdays, the school day will end at

1:30 so that teachers can meet to review student progress and for integrated

planning. A supervised study hall will be offered from 1:30 to 3:30 for those

students who are not able to go home at 1:30 on Wednesdays. The day will

start at 8:00 in advisement. Students will then proceed to their Academic Work

Time, which includes lessons in all curriculum subjects, for the remainder of

the day. During this time, students will meet in small group lessons for math,

Spanish and ELA instruction. All other instruction, including enrichment, will be

integrated into Occupations and/or humanities with lessons and work time

scheduled throughout the Academic Work Time. A sample of a student’s

schedule is included in Appendix L. After lunch, there will be a 45 minute quiet

work time dedicated to reading and journal writing. During this time, advisors

will also do individual portfolio review with students. Students will then proceed

back into Academic Work Time. Students will meet back in advisements at 3:10

to restore the environment and have a closing meeting.

Teachers, including the special education teacher and ELA-E teacher, will

plan lessons for the entire week. All teachers will list their lessons for the

following week on Thursday. Students will then sign up for their lessons on

Friday for the following week. Advisors will review what lessons their students

have signed up to insure that there are no gaps. Staff will note what students

need additional intervention through data gleaned at the Wednesday afternoon

staff integration time, portfolio checks, review of data from the on-line math

program, assignments and assessments. Teachers will include these lessons in

their weekly lesson plan and advisors will insure that students are signed up to

attend those lessons. The ELA-E teacher will also have lesson sign up times for

every day and review the lists to insure that every ELL student is receiving direct

instruction for 45 minutes per day.



A teacher will start their school day with their advisement, working with

students to insure they are ready for the day and the week. Teachers then

spend the morning teaching lessons. When they are not teaching lessons, they

are available to students to answer questions, assess work, and observe

students. Teachers will eat lunch with the students and attend recess,

alternating the schedule so that each teacher will have a 30 minute break. After

lunch, teachers will conduct a portfolio check and individual advising with

students. Teachers will then teach additional lessons and continue to work with

students until 3:10. At 3:10, teachers will work with students to restore the

environment and talk with students about their successes and challenges for

the day. On Wednesday afternoons, teachers will have two hours of staff

integration time to review data, discuss students and determine what additional

lessons, interventions, and challenges students need to maintain an optimal

learning environment.

A student might spend his day as follows: Monday he will start in

advisement. There, advisors will talk to the students about their weekly

schedule, inform students of any gaps and require students to adjust their

schedules to fill the gaps, and insure students are organized and ready for the

week. After the advisor has signed off on the student’s weekly lesson plan,

students will start their Academic Work Time. During Academic Work Time, a

student might then choose to spend time on the on-line math program or other

follow up work. He would then attend the various lessons he signed up for that

day. In-between lessons, he is working on chosen follow up work that could

include project based work, writing a research paper, reading documents in

preparation for seminar, and the on-line math program. The students will be

allowed to choose their work, but they will not be allowed to choose not to

work. Although social interaction is a part of every Montessori classroom, the

culture at DPMSS will require that social interaction is not interfering with

student work. This is a balance that has been worked on in Montessori

adolescent programs throughout the country, and best practices have been

ascertained. One best practice that keeps students on task is to insure they

have choice. A second best practice is to insure that the work is meaningful and

engaging. A third best practice is to hold a culture of high challenge, high skills

and high support. And finally, the most important best practice, is to insure

that a supermajority of the students have come up through Montessori

education and therefore have worked in classrooms that have schedules very

similar to the adolescent program. If an adolescent program implements these

best practices, this schedule is the optimal schedule for students to succeed.

During lessons, students will note in their portfolios the lesson received,

the benchmarks related to the lesson, and ideas for follow up work. When

follow-up work is turned in, the advisor and the student will assess the follow

up work to see if it demonstrates that the student is proficient in those


benchmarks. After lunch, students will have 45 minutes of quiet time for

journaling, reflection and reading. During this time, advisors will individually

meet with students for portfolio check and individual advisement. After this

time, students will again begin Academic Work Time. At the end of the day,

students will meet back in advisement to restore their environment and discuss

their successes and challenges for the day.

For high school, the schedule will be also 8:00 - 3:30. There will be 45

minutes for lunch. The mornings will be blocks of small group lessons and

independent work time. The afternoon will be comprised of two one-hour

electives. From 2:30 - 3:30, students can study, practice school team sports

such as Ultimate Frisbee or rehearse dramatic or other student productions,

and staff will be available to students for advisement and tutoring. On

Wednesday afternoons, students will leave school at after lunch to attend

internships, mentorships or volunteer work. Advisors will work with student to

obtain appropriate placements. Advisors will work closely with the supervisors

for the off-campus learning opportunities to insure students are arriving on

time, and appropriately contributing and demonstrating the core values of our

Montessori program. This schedule has been modeled after the Compass

Montessori High School schedule, where it is extremely successful as measured

by observation, student and staff satisfaction and student academic growth.

C. Progress Monitoring and Assessment

This description of Montessori assessment is from the NAMTA National

Montessori Curriculum Report and has been adapted to specifically address the

Montessori adolescent program and the assessment design for DPMSS.

The Montessori curriculum is organized in a developmental sequence

from one phase of learning to the next. Individual students, however, are able

to work successfully through elements of the curriculum in a sequence unique

to themselves. Assessment in Montessori classrooms, therefore, is based on

each student’s mastery of skills and knowledge at any point in the sequence.

Students display their progress and achievement through a variety of modes,

including spoken and written language, interaction with others, creative arts

such as drama, visual arts, model-making and importantly, through applying

what they have learned in practical ways.

Formative Assessment: Montessori teachers, working closely with the

adolescents, keep careful records to ensure the students are provided with

appropriate lessons when they are ready. Daily observation of students and

detailed record-keeping help teachers plan the lessons individuals will need

next. Working together, the adolescent students and the Montessori teachers

keep records of lessons given,the follow-up work completed by each students,

student progress and achievement, difficulties encountered by individual

students and how those difficulties were resolved. Montessori teaching and



learning practices provide enhanced opportunities for formative assessment.

Here are some examples:

Because Montessori Junior high and Senior High teachers have students in

their class for three years, they come to know each student in a way that is not

possible when students move to new classes with new teachers every school

year. Through close observation over three years, Montessori teachers become

very aware of their students’s learning styles, strengths and areas requiring

further development.

Because most lessons are presented to individuals or small groups, the

teacher can easily observe and record levels of understanding and mastery in

individuals. Before a lesson draws to a close, all students in the lesson are given

the opportunity to show they understand the newly acquired skills or content.

Any student who needs further teaching can review the lesson when it is

presented to the next group of students ready for the lesson.

When students choose their own work extensions, they reveal a great

deal about their interest and ability at any point in time, which teachers are

then able to observe and record. During regular individual conferences with the

teacher, students become co-assessors of their work with the teacher. Junior

and senior high students are given rubrics prior to any assignment which they

can then use to assess their work. Students will also be provided with a detailed

Junior High or Senior High portfolio that identifies all standards and

benchmarks for their grade levels. They will then record the date they received

lessons addressing these benchmarks and also provide evidence of

understanding and academic achievement related to the benchmark.

Summative Assessment: Learning achievement in Montessori classrooms is

recorded through observation, the compilation of portfolios and detailed

records of progress. Progress will also be measured against achievement

benchmarks that are based on the Colorado Academic Standards and the

Common Core Standards. In these ways each student’s progress can be

expressed in terms meaningful to the student, as well as to teachers, parents

and the wider community.

The DPMSS SMART Goals are listed in Section I B. These SMART Goals will

be achieved in the following manner:

At the beginning of the school year, students’ math skills will be assessed

via the on-line math program’s assessment tools. One example of an on-line

math program is Renaissance math and their STAR assessment. DPMSS will

review the current on-line math offerings during its planning year to determine

which program is the most successful and most compatible with the Montessori

program. Students will take weekly and end of unit on-line assessments which

are summarized within the on-line program. Teachers will check student


progress weekly to determine what math lessons students need in order to

continue making appropriate progress for that particular student. Teachers will

incorporate Montessori math materials along with more traditional math

instruction techniques during math lessons. If students are not making adequate

progress in math, despite additional support from teachers, then staff will begin

the RTI process.

Also at the beginning of the year, students will receive the DRA -2 to

determine reading levels. The principal, working with staff, will review this data

to determine what areas each individual students requires assistance in order to

continue to make adequate progress with reading. Students will be allowed to

choose their own literature books from a list provided by the school. Staff will

then work with students to make adequate progress in all aspects of reading,

including vocabulary, literary technique and structure, reading elements, and

the ability to analyze text. Reading instruction will occur via literature circle,

seminar and book clubs. During the first year, staff will administer the DRA-2

again half-way through the year and at the end of the year in order to obtain

data on effective reading instruction. Staff will continue to use the DRA-2 for

new students and students who are demonstrating difficulty with reading as

observed in seminar and literature circles, previous DRA-2 assessments and

State assessments. If a students continues to demonstrate a lack of progress

with reading after receiving additional lessons, staff will begin the RTI process.

The third assessment students will complete at the beginning of the year

is a writing assessment. Teachers will review the student’s written work using a

rubric based on Colorado Academic Standards for that grade level. Teachers will

identify what small group instruction each student requires, and place that into

the schedule. Students will be required to complete writing assignments

throughout each Occupations. Teachers will review progress, again based on

the CAS rubric, and continue to develop lessons plans for each individual

student. Should students continue to demonstrate a lack of progress after

additional teacher support, staff will begin the RTI process. DPMSS will use the

6 +1 Trait Writing Curriculum as a guide for lesson development.

At all times, the expectation is that students will be working at or beyond

grade level as determined by the on-line math assessments, the DRA-2, and

the writing rubric. If students are not working at grade level, staff will create a

lesson plan to bring students to grade level. That lesson plan will be a part of

that individual students junior or senior high portfolio.

Every month, the principal will review student portfolios to determine

percentage gained regarding achieved benchmarks. The principal will also

review data compiled from the on-line math program, the DRA-2, writing

samples, quizzes and end of unit assessments. Because the school will only

have 50 and 65 students in its first two years, the principal will be able to take



a hands on approach to data review. As the school grows, some of these duties

regarding individual student data management will transfer back to the

program directors, and the principal will focus on overall school data trends.

This data will be reviewed monthly with the SAC Committee. Individual student

performance will be presented to parents during two parent/teacher/student

conferences per year. At these conferences, students will walk their families

through their portfolios. Teachers, students and families will discuss student

achievements, student challenges, and create goals for further progress.

The principal will use data management systems as recommended by

DPS. During the planning year, DPMSS will design electronic junior and senior

high portfolios that can be filled in by both teachers and students. Once State

assessment data and SPF are released after year one, the principal will review

data based on prioritized benchmarks. The principal will identify gaps in DPMSS

achievement as compared to other DPS schools and state averages. The

principal will work with staff to determine causes for these gaps and identify

small group Montessori lessons to improve student achievement.

The SAC committee will review student data monthly through reports

compiled by the principal. When the SPF is released, the SAC will work with the

principal to analyze successes and challenges, and create a formal report for all

stakeholders. This report will include SMART goals on those areas where the

school did not achieve satisfactorily. The SAC and the principal will also work

together with staff to create the Unified Improvement Plan that will include the

SMART goals along with other areas identified as needing improvement.

DPMSS high school graduation requirements will reflect the HEAR

requirements including four years of English, four years of Mathematics, three

years of Natural/Physical Science including two lab-based units, three years of

Social Sciences (with at least one unit of U.S. and one unit of World History), one

year of Foreign Language and two years of Academic Electives. Starting in

eighth grade, every DPMSS will develop a personal education plan which will

become part of their junior and then their senior high portfolios. These plans

will be completely integrated with their portfolios to insure students are

receiving 100% of the credits needed to graduate. Occupation curriculum will be

compared to course objectives for traditional classwork to determine

appropriate credit for ninth grade. Tenth through 12th grade classes will have

the same course objectives as traditional schools for the academic areas.

Students will receive grades and transcripts starting in 9th grade.

DPMSS is designed to respect stages of adolescent development, and

promotion and retention criteria will reflect this value. Students will be

expected to be promoted within their established class. A key time for

evaluation will occur towards the end of the ninth grade year. If a student is

demonstrating significant gaps in academic achievement, social and/or


emotional growth to the level that they may not yet thrive in the high school, a

conference will be called between the student, their family, the principal and

the student’s advisor to determine if the student should spend an additional

year in the junior high. In high school, if a student is not on track to meet all

DPMSS graduation requirements, the student, their family, the principal and the

student’s advisor will meet to create a plan in order for the student to graduate.

One possible outcome of that plan may be for the student to spend an

additional semester or year at DPMSS until all graduation requirements are met.

If a student has exceeded graduation requirements before the end of

their 12th grade year, that student will have the option to graduate early or

dually enroll in UCD, Metropolitan State, or another college that offers dual

enrollment. Again, a meeting will be called between the student, their family,

the principal and the student’s advisor to determine the best course of action.

At all times, if a student is demonstrating academically, socially or

emotionally that he or she is struggling to make academic progress in the

school in order to achieve or maintain grade level, the advisor will meet with

the student and their family to analyze the cause. If improvement does not

occur, the advisor will work with staff to initiate RTI.

Compass Montessori High School created graduation outcomes for its

students. DPMSS will adopt the outcomes as a starting point for creating its own

outcomes reflective of is target population. The outcomes are as follows:

Outcome One : Is an experienced thoughtful writer and reader, adjusts

use of spoken, written, and visual language, to respond to the needs of society,

to acquire new information and for personal fulfillment.

Outcome Two: Has developed a mathematical mind: experienced use of

the power of mathematical thinking in problem solving and paradigm

formation.

Outcome Three: Is competent and knowledgeable in life sciences,

physical sciences and advancing technology.

Outcome Four: Is economics literate and an ethical entrepreneur

Outcome Five: Is effective and capable of expressing ideas, contributing

to a community of inquiry, actively listening and collaborating

Outcome Six: Is locally and globally aware, well worldly traveled in fact or

through reading of human encounters; historical minded and historically

literate about human history and the human condition.

Outcome Seven: Is physically active, a participant in activities that create

mental / physical challenges that foster whole person development.

Outcome Eight: Is a developing artist, song writer, poet, musician, actor,

etc.through practice, experience in, appreciation for and understanding of the

arts.



Outcome Nine: Is aware and knowledgeable of self-construction and

actualization; has an immense sense of humor and an ingenious love of

learning.

When our high school students have achieved these outcomes, the result

will be graduates, regardless of ethnicity or income status, who will be prepared

for college or a career as well as demonstrate ingenuity, adaptability, creativity,

initiative and excellent communication and problem solving skills.

D. English Language Learner Students

Montessori education is an individualized inclusive approach for all

students in all cultures. It is a world recognized curriculum with Montessori

schools in nearly every country. Providing excellent ELA education is

completely in line with the DPMSS mission and vision. With their educational

focus of connecting the hand and the mind in all learning activities, DPMSS

teachers will be well prepared to assist ELL learners to acquire English in a fun,

engaging and meaningful manner. Prior to opening DPMSS, the principal will

attend DPS professional development regarding meeting the needs of ELL

learners. The Spanish teacher will attend all required DPS professional

development and classes to obtain ELA-E certification. The principal and all

other DPMSS teachers will obtain a minimum level of training to obtain ELA-T

certification. The principal and teachers will be expected to continue to attend

DPS ELA professional development in order to insure that best practices for ELA

are being implemented at DPMSS.

When a student enrolls at DPMSS, the administrative assistant will insure

that the newly enrolled family receives and completes a DPS Home Language

Questionnaire translated to the family’s native language. The administrative

assistant will compile the information and give to the principal a list of all

students who qualify for ELL services because their families speak a language

other than English at home. The administrative assistant will also give to the

principal a list of all incoming students who are already receiving ELA services

at their elementary schools.

Within the first two weeks of school, the principal will insure that the

ELA-E certified teacher gives the CELA Placement Test to the list of students

who qualify for ELL services and who are not currently receiving ELA services.

The ELA-E teacher will use the data gleaned from the CELA Placement Test to

determine the level of ELL services each student requires and give that

information to the principal. The ELA-E teacher will also review the ELL plans

for all incoming designated ELL students.

Within 30 days of school opening, the principal will send to all ELL

eligible students’ families a letter written in English and in their native language

stating that their student is eligible for a language instruction education

program and ELL services. The school will describe how ELL services will be


provided at DPMSS. The school will request permission from the families to

begin ELL services for their students. The principal and the ELA-E teacher will

talk to any families with questions using interpreter assistance as needed.

During the planning year, DPMSS will research ELA curriculum to

determine what scientifically proven curriculum matches best with Montessori

curriculum and instruction. The chosen curriculum will provide lessons and

plans to support full implementation of State ELD standards. The ELA-T teacher

will use DPS established best practices to implement the curriculum. Examples

of these best practices include:

The teacher will provide a minimum of 45 minute block instruction for all

ELL students. The teacher will implement the ELD block in target language daily,

implementing the instructional components of the curriculum to design lessons

that provide explicit instruction of English language development in the four

domains: listening, speaking, reading and writing daily. There will be clearly

defined content and language objectives posted and articulated in student

friendly language at the beginning of lesson and revisited at the end of the

lesson. Lessons will address identified standards and meet students’ language

proficiency levels and academic needs as determined by ongoing observation

and assessment. There will be focused, appropriate lessons that introduce and/

or support social and academic language development in the four domains.

The teacher will create a positive classroom culture to support student

learning. The teacher will use a variety of techniques to make content concepts

clear and accessible including modeling, visuals, hands-on activities,

demonstrations, gestures, body language, and sufficient wait time for student

responses. The teacher will consistently use effective strategies to promote

academic language and learning (ex. chants, songs, graphic organizers,

cooperative groupings, Total Physical Response, visuals). The teacher will

provide frequent opportunities for interaction and discussion between and

amongst teacher and students. The teacher will encourage elaborated

responses to clarify lessons and and key concepts. The teacher will incorporate

and model sentence stems and patterns differentiated for student’s language

proficiency levels.

Daily lessons will be a combination of the selected curriculum and

Montessori curriculum. The teacher will rely on the selected curriculum to

insure that lessons are sequential, purposeful and address oral, reading, and

written language development, building background, language functions and

structures, grammar skills, vocabulary, comprehension strategies, reading

strategies and reading components (word work, fluency, vocabulary, writing

strategies and genres). With teacher modeling, there will be active student

involvement, with significant opportunities for accountable talk and extended

discourse to practice different functions of language, vocabulary, and, reflecting



a balance of student and teacher talk, extended student language and modeled

correct language use. There will be a deliberate balance between teacher/

student talk striving for 80% student talk and 20% teacher talk. The Montessori

curriculum will include sheltered instruction within the different Montessori

environments including the farm, art studio and the commercial kitchen.

The ELA-E teacher will conduct, review and use end of unit and ongoing

progress monitoring (both individual and group) to assess progress in oral

language, reading and writing. Assessments will include progress tests, writing

samples, and oral interaction that assess stages of language acquisition. The

teacher will keep a body of evidence to monitor student progress and

encourage self-assessment. The ELA-E teacher will provide this data to the

principal and the student’s advisor. The principal will compile the data and

include ELA progress monitoring in the monthly reports that the principal

shares with the SAC. Advisors will include student data in student conferences

and parent/student/advisor conferences to set learning goals and communicate

with parents. The ELA-E teacher will link goals to students independent

reading, speaking and writing levels and will consistently provide effective

feedback to students that focuses on what the students can do.

When a student has demonstrated proficiency in all four domains as

measured by CELA testing and is at a minimum partially proficient in all State

mandated tested areas, the student, the student’s family, the ELA -E teacher

and the student’s advisor will meet to determine if the student is ready to exit

the ELL program and be redesignated as no longer requiring ELL services. This

team will determine appropriate ways to monitor student progress over the

next two years to insure that the student continues success. If the student

demonstrates, through student work or State mandated testing, a need for

continue ELL services, the student, with parent permission, will be incorporated

back into the ELL program, or receive supplemental targeted instruction

E. Special Education Students

DPMSS will use the Response to Intervention (RtI) model to identify

students requiring special education.3

The RtI model requires that achievement

data and a body of evidence is maintained for all students. DPMSS will insure

that universal screening is happening through the DRA-2, weekly on-line math

assessments, observation, mastery level quizzes and end of unit assessments

for both the junior and senior high. If a student is demonstrating a lack of

appropriate progress, the student’s advisor will contact and discuss concerns

with parents and work with teachers to begin implementation of strategic

3 Clarification to CDE: The RtI process will not be used in a way that will delay identification of a student who is suspected of

having a disability. Further, RtI is a general education process and framework for providing a multi-tiered system of support to all students.

Page 136


interventions with fidelity. Staff will document these interventions and whether

or not the interventions are successful during a predetermined length of time

such as 8 - 12 weeks. The documentation will occur on a secure, shared

document format so that all teachers can review what interventions are being

tried for each student, and share their own observations of successful

interventions. Progress will be monitored via observation, weekly written

samples, weekly on-line math assessments, participation in seminar, mastery

quizzes and end of unit assessments, and DRA-2 assessment.

If the student responds to the interventions, they will remain in place as

long as necessary. If the student does not respond to the interventions as

documented by insufficient progress towards specific benchmarks in the given

area of concern, the advisor will bring the student to the monthly convened

student intervention team. The student intervention team will consist of the

principal, the special education provider, and at least two additional teachers.

The student’s parents will also be invited to participate in this meeting only

during the time that their particular student is being discussed. At student

intervention team, the team will review the student performance data collected

before and during interventions. The team will then discuss further

interventions for the teachers to use for that student within a determined

number of weeks. Teachers will implement the interventions with fidelity and

record the student’s response to the interventions. Progress will again be

monitored via observation, weekly written samples, weekly on-line math

assessments, participation in seminar, mastery quizzes and end of unit

assessments, and DRA-2 assessment.

If, after trying a variety of interventions, the student is still not making

sufficient progress as compared to his/her peers, the special education

provider will begin the process to determine if the student qualifies for special

education services. This process will follow all Federal and Colorado special

education guidelines including parent notification, a complete record review,

additional testing if needed and appropriate written permission. Once the

assessment process is completed, the special education provider will convene

an initialization meeting that consists of the student, the student’s family, the

student’s advisor, the general education teacher, the principal, the special

education provider, the psychologist/social worker, the school nurse, and any

other experts necessary to create a holistic picture of what the student requires

in order to achieve a free, appropriate, public education and to thrive at DPMSS.

If this team determines that the student requires special education services, the

team will then determine how much and what type of services the student

requires and set initial goals for the student. The special education provider,

the student’s advisor, and the family will continue to work together to set

appropriate goals for the student. Progress on these goals will be monitored by

the student advisor and the special education provider.

DPMSS will accept students coming from DPS Montessori schools without

discrimination towards students with disabilities. Prior to the start of every

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school year, the DPMSS special education provider will review the list of

incoming students to determine who is currently on an individualized education plan (I.E.P). The provider will review the I.E.P. and conduct transition meetings

with the student, the student’s families and the special education team from

the sending school. Goals will be reviewed to insure they align with the DPMSS

junior high program.4

Progress will be monitored by both the special education

provider and the student’s advisor via observation, weekly written samples,

weekly on-line math assessments, participation in seminar, mastery quizzes

and end of unit assessments, and DRA-2 assessment.

The student’s I.E.P. will be formally reviewed no less than once per year

with documentation of progress written quarterly. During the annual review,

student goals will be discussed to determine if goals have been met and if new

goals need to be set based on a collected body of evidence of both formal and

informal assessment. Every three years, the special education provider will

convene a triennial meeting to determine if the student still requires special

education services.5

At that meeting, all student progress, including scores on

State standardized assessments, DPMSS internal assessment, the student’s

portfolio and a body of evidence gleaned from observation and student work

will be discussed, along with any required testing. The meeting will consist of

the special education provider, the principal, the student, the student’s family,

the student’s advisor, the psychologist / social worker, the school nurse, and

any additional staff or experts deemed necessary for this meeting based on the

student’s needs. If the team determines that the student no longer requires

special education services, the I.E.P. will be terminated. The team will then

determine appropriate progress monitoring for the next year to determine if the

I.E.P. needs to be re-opened as well as make appropriate recommendations to

the general educator in supporting the student. If the team determines that the

I.E.P. needs to stay in place, the team will evaluate services provided, adjust as

deemed necessary, and create new short term and long term goals.

The DPMSS special education teacher and the psychologist / social

worker will be highly qualified and duly licensed as such by C.D.E. to serve

students from 6th grade to 12th grade. The school nurse will be a licensed

nurse by the State of Colorado. All other experts used in the I.E.P. process will

hold appropriate C.D.E. or State licensing in their respective area of expertise.

During the first few years, DPMSS will require only part time staff. DPMSS

intends to partner with other schools within DPS to share employees for special

education provider, psychologist / social worker and school nurse.

Montessori education is an ideal match for serving students with

disabilities. All students are educated in an individualized manner, with

personal goals and personalized progress monitoring. Lessons are presented in

small group format with multiple opportunities to check for understanding, ask

4 Clarification to CDE: All goals in the IEP will be developed to meet the individual needs of the students, resulting from the

disability. 5 Clarification to CDE: The triennial meeting will be a triennial evaluation and meeting and a regular education teacher will be

a required member of the IEP team. Page 138


questions, and demonstrate knowledge. All lessons are differentiated to meet

the needs of attending students. Students are then allowed to demonstrate

learning in a wide variety of ways. In Montessori, the special education provider

is integrated into the classroom, working side by side with all students, with

and without I.E.Ps. At the same time, the special education provider insures that

students with I.E.Ps are receiving the required minutes of service. If the special

education teacher needs to meet with I.E.P. students one on one or in small

groups, the schedule easily allows for these types of pull-out lessons.

Secondary Montessori Special Education involves awareness of the student

to understand his/her disability and learning style. Much like regular education,

DPMSS will encourage students to become self directed learners and find

strategies that work for them. As they ready themselves for the next level,

students learn to become increasingly more independent in their learning. They

learn to ask for help from a variety of resources and ask for accommodations

based upon their need. Students learn to be their own best advocates and are

then able to carry this skill to college and post secondary careers.

A student’s disability is treated as a learning difference. In Montessori,

students recognize that all students learn differently, and staff work with all

students to determine optimal learning styles. Because of this culture, students

with disabilities leave behind much of the stigma around being a different type

of learner. Instead, they embrace their differences, understand strategies they

need to succeed, and work with the special education provider and their

teachers to receive accommodations necessary for academic achievement.

The strategies used by the special education provider will vary depending

on student disability. The provider will use the existing Montessori materials,

key lessons and curriculum as the basis for instruction. If a student requires

additional, outside curriculum such as Wilson Reading Systems, the special

education provider will consult with DPS to determine the most current highly

effective curriculum for the specific targeted intervention. Any outside

curriculum used will be scientifically proven to help students with that

particular targeted intervention. For our high school students with I.E.P.s, the

special education provider will work with the student, the student’s family, and

the student’s advisor to create transition plans to assist the student in

identifying and determining post secondary options.

The principal and teaching staff will attend DPS sponsored professional

development regarding RtI. If DPS does not have such professional development

available, DPMSS will work with the special education provider to create this

professional development including bringing in consultants if needed. The

special education provider and the psychologist/social worker will seek out

professional development as provided by DPS to insure they have the latest

understand of adolescent brain development and how that applies to students

with disabilities, application of RtI, and current high quality and scientifically

proven interventions that will blend well within the Montessori environment.

The special education provider and the psychologist/ social worker will then

share this information with the general education staff.



E. Academic Intervention and Acceleration

The DPMSS schedule is designed so that teachers are easily able to

schedule and conduct small group lessons. These lessons will be created to

meet the needs of the variety of learners at DPMSS, including special education,

ELL, gifted and talented and intervention students. There will be key lessons to

advance the curriculum, targeted intervention lessons for students

demonstrating a need for additional support, and challenge lessons for

students demonstrating a need and ability to work beyond the established

curriculum. Montessori education uniquely supports all types of learners

because of its focus on individualized education.

During the Wednesday afternoon staff integration time, the principal and

the teachers will review data gleaned from on-line math assessments, the

writing samples and the DRA-2, along with observations, and body of evidence

including student portfolios. Through these meetings, staff will determine what

students are succeeding with tier I intervention and therefore only needing key

lessons. Staff will also identify tier II students who are lagging behind their piers

and demonstrating weak progress. Staff will collaborate and determine what

targeted lessons these students require and plan for those lessons. Staff will

work together to determine specific interventions and document the use and

success or lack of success of these interventions in a secured, shared document

format. If students continue to demonstrate a lack of success after different

interventions are attempted, the student will need tier III intervention and will

be referred to the student intervention team as described in the Section D.

Targeted interventions in math will include revisiting the elementary

Montessori math materials. These materials provide concrete representations of

advanced math concepts in a manner that allows students to understand the

concepts with their hands as well as their heads. Additional targeted

intervention includes small group lessons that meet students at the level they

need to make progress. The on-line math program will support these

interventions as math programs such as Renaissance Math are designed to

meet the individual skills and challenges required by the individual student.

Targeted interventions in reading will include small group lessons or one

on one assistance depending on the individual student’s needs. At this level,

deficiencies are often in fluency and/or comprehension. Comprehension can be

improved by working with students to practice pulling out important

information or highlighting. Fluency typically improves with practice, practice,

practice as most struggling readers avoid reading. Teachers will create safe,

small group lessons that allow students to practice reading. Students will also

be allowed to choose their literature books, from a list generated by the school,

so that they have more ownership of the books that they are reading. Targeted

interventions in writing will incorporate the 6+1 Trait Writing program.


Teachers will determine what traits students need reinforcement on and create

small group lessons using this scientifically proven curriculum.

Montessori education meets the needs of students requiring additional

challenge. Montessori students determine what follow up work they want to

investigate within the curriculum. Because of the open ended nature of this type

of approach, students are able to take their follow up work as wide and as deep

as they choose. Presentations of learning can be accomplished using a variety

of modalities including PowerPoint, dramatis personae, extended essay, song

writing, poetry and creating physical models. The goal of the teachers and

student advisors is to insure that students are working a majority of the time to

the top level of their ability. Should a student demonstrate a lack of

engagement, the student’s advisor will meet with the student to determine what

additional skills a student requires to reach the next level of learning. These

challenge lessons will then be designed and delivered.

Dr. Mihaly Csikszentmihalyi through his research created a chart that

demonstrates optional flow or engagement. (Flow, the Psychology of Optimal

Experience, p. 74) The chart demonstrates that optimal flow, or engagement,

occurs at the intersection of challenge and skills. If a person in experiencing

high challenge and low skills, the result is anxiety. If the person is experiencing

high skills but low challenge, the result is boredom. The goal at DPMSS is to

insure that students are fully supported so that they are working at the exact

intersection of high challenge and high skills in order to make optimal

academic along with social and emotional progress.

At DPMSS, a high school student who is at risk of dropping out or not

graduating will be identified long before the situation becomes a crisis.

Through the integrated planning time and review of data, staff will be aware of

students who are not making adequate academic progress and work with the

student and the student’s family to create a plan for the student to get back on

track. Student advisors will create professional, trusting relationships with

students so that they will be aware if a student is experiencing challenges

beyond school that affect their ability to succeed at school. In this event,

advisors will link the student and the school psychologist / social worker to

insure the student is getting support needed outside of school to succeed at

school. Students needing additional academic support will receive this support

through the RtI process. If a high school student is still struggling with

obtaining credits necessary for graduation, the student, the student’s advisor,

the student’s family and the high school program director will meet to create a

graduation plan that may include summer studies, on-line education,

partnership with other DPS schools, an additional year at DPMSS, and any other

support necessary to insure that the student graduates ready and able to attend

college or succeed in a career.



G. Gifted and Talented Students

Montessori education is an ideal match for students who are identified as

gifted and talented. Because the majority if not all of the students will be

coming from DPS Montessori schools, gifted and talented students should

already be identified and have ALPs. For the first two years of the school, the

principal will also be the GT coordinator. That task will eventually be delegated

to a selected and trained teacher. Both the principal and, when selected, the

staff GT coordinator will attend DPS sponsored professional development for

identifying and serving GT students. The principal will also conduct

professional development for the staff to insure the needs of GT students are

being addressed at DPMSS.

When a GT student is enrolled at DPMSS, the principal will review ALPs of

all incoming GT students and discuss the ALPs with sending teachers and GT

coordinators. At the start of the school year, the principal, the student, the

student’s advisor and the student’s family will meet to review the ALP and

discuss how best DPMSS can support the student towards reaching ALP goals.

Montessori students determine what follow up work they want to

investigate within the curriculum. Because of the open ended nature of this type

of approach, students are able to take their follow up work as wide and as deep

as they choose. For GT students, further connection to challenging curriculum

may be required. Depending on the situation, this could occur via connecting

the students to outside experts related to the Occupation, having the student

research and co-teach with staff key lessons, having the student design and

implement management roles, and having students create polished,

professional presentations that can be shared with the greater community. For

High School, students can take on-line coursework that better meets their

academic level and can dually enroll in college coursework. Students can also

create and co-teach with staff elective coursework and test preparation classes.

All of these options will be available to all students, regardless of if they

have a GT designation or not. This will allow students who perhaps qualify for

GT designation but have chosen not to purse the designation to also work at

their highest levels. If a DPMSS student who does not have a GT designation

and who demonstrates the potential to qualify for GT designation and also they

(or their family) desires to pursue the GT designation, the principal will follow

the GT designation criteria as outlined on the DPS Gifted and Talented website

to determine if the student qualifies for GT services.

H. Supplemental Programming

Montessori adolescent programs are designed to address the social,

emotional and mental well being for students. The advisor model and three

year cycle are designed so that teachers create professional, positive


relationships with students and are able to understand students’ abilities at a far

deeper level than if they only had students for one class or one year. During this

time, the student’s advisor is also able to create positive partnership with the

student’s family so that there is an entire network of communication and

support for students. Throughout Montessori education, students are strongly

encouraged to develop and use their voice, to advocate for themselves and to

figure out solutions to their challenges with adult support. If a student requires

further intervention than the advisement model can support, the advisor will

connect the student to the school psychologist / social worker so that he or she

can determine appropriate resources for the student.

Nurturing physical health is also a core value of Montessori. One of the

purposes of the urban farm is to connect students to a wide variety of

organically grown food. The food grown will be added to the school lunch

program so that students have fresh vegetables that they have grown

themselves. The outdoor work is physical and requires students to challenge

themselves in order to complete the required tasks. Because the students are

working side by side with their friends and with an adult, the students

partcipate generally with a positive attitude. One of the Occupations will be

focused on adolescent development, nutrition and health. Students will learn

the science of adolescent development and nutrition, and have the opportunity

to ask questions and discuss the negative affects of alcohol and drug use on

the developing brain.

Another core value of Montessori education is the creation of positive

communities. There is extensive conversation regarding creating community,

supporting positive behavior and being inclusive. Students are invited to bring

up community concerns at daily advisement meetings and weekly community

meetings. Behavior that resembles bullying, exclusivity, discrimination,

prejudice and any other non-inclusive behavior is immediately addressed and

processed with involved parties. Montessori students take pride in their healthy

communities, and they advocate in a variety of ways to maintain them.

The junior high will have a supervised study hall on Wednesday

afternoons to give students an opportunity for a quiet environment to catch up

on work. DPMSS will also work to find background checked parent or

community volunteers to create afterschool clubs and team sports. One sport

that Montessori students gravitate towards is Ultimate Frisbee. DPMSS intends

to create a high school ultimate frisbee team, but will need to do so with

volunteer support.

DPMSS will partner with existing summer school programs if the

student’s advisor, the principal, the student and the student’s parents

determine a student would benefit by attending summer school.

Volunteer programs have been addressed in the schedule portion of this

application.



Section IV: TEACHING

The primary goal for teacher coaching is to create a recursive learning

environment where teachers can evaluate and improve their practice through

reflective conversation with other teachers, the principal, peer observers and

Montessori consultants. Our definition of a recursive learning environment is

the process of improving Montessori practice by examining the principles of

Montessori theory and how it applies to adolescent education. Colleagues then

share their acquired knowledge and skills with one another resulting in the

knowledge being reinforced for the “teacher” and spread exponentially among

the other staff members. At DPMSS, we will focus on implementing Montessori

theory and understanding adolescent brain development. The school will be

constructed around how these two factors can be maximized to insure an

optimal learning environment.

The tools we will use for teacher observation include the Framework for

Effective Teaching used by principals and peer evaluators to evaluate

Montessori teachers in DPS. Another tool we will use will be an observation

rubric specifically created for DPMSS. That rubric will include prepared

environment, engagement of students, quality of key lessons, portfolio quality

and completion, ability of teacher to link students to high quality follow up

work, overall quality of the Occupation including involvement of outside

experts, initial engaging experiences (first period lessons), challenging and

interesting follow up work (second period) and high quality presentations of

learning (third period). The third tool we will use is data review. This includes

student portfolio review, review of the on-line math assessments, review of

mastery and end of unit assessments, review of writing samples throughout the

year and standardized test results. At least 50% of a teacher’s overall evaluation

will be based on review of student data.

DPMSS is an integrated learning environment that allows teachers to work

together or separately depending on the need for that day. Additionally, DPMSS

will require that teachers formally observe each other using the DPMSS

Observation Rubric at least twice per year. Staff will then use the results of this

observation as an opportunity for recursive learning during integrated staff

time. The school leader will observe teachers once per month alternating

between the Framework for Effecting Teaching Evidence Guide and the DPMSS

Observation Rubric. This information will again be brought to staff in a non-

threatening way during teacher integration time. DPMSS will also welcome

observations by LEAP peer observers.

During the weekly staff integration time, there will be dedicated time on

the agenda to discuss teacher observation and student data. The goal always is

to create a recursive and reflective learning environment to insure that we are

improving the Montessori program and student outcomes. If personnel issues


arise from the observations, that will be handled privately through the teacher

evaluation process.

B.Teacher Evaluation

Prior to the new school year, DPMSS will create a teacher self-evaluation

tool based on the desired outcomes of the school, the DPMSS observation

rubric, SMART goals as set forth in this application and thereafter in the Unified

Improvement plan, and the Framework for Effective Teaching. This evaluation

tool will be discussed during professional development. Teachers will then be

given time during professional development days to thoughtfully identify areas

of strength and to create goals for areas of improvement. The principal will

review the self-evaluation tool individually with each teacher and work with the

teacher to add strengths and areas of improvement.

No less than two times per year, the principal will meet with the teacher

to review the self-evaluation tool and determine progress based on

observations and data. The second meeting will be the formal teacher

evaluation and it will be between the principal and the teacher, using

information gathered from peer observations, peer observer observations,

principal observations and data on student performance as demonstrated

through student portfolios, weekly on-line math assessments, DRA-2

assessments, writing samples evaluated against a grade leveled rubric, mastery

quizzes and end of unit assessments. At least 50% of the evaluation outcome

will be based on student improvement as demonstrated through data. Prior to

the formal evaluation, the teacher will fill out their self-evaluation based on

goals set at the beginning of the school year.The teacher will share that

document with the principal in advance, so that the principal can better prepare

for the formal evaluation.

At the formal evaluation, the teacher and the principal will discuss

strengths and successes. They will also discuss goals and what goals were met,

where progress was made, and where progress did not occur. Together, the

principal and the teacher will create a plan to assist the teacher towards

meeting goals necessary to improve student outcomes.

If a teacher is not making progress as determined through observation

and data, the principal will inform the teacher privately after each monthly

observation. The principal will encourage the teacher to bring forward their

challenges at the weekly staff integration meeting for advice and support. The

principal will also find professional development to assist the teacher, and work

personally to coach the teacher. If, after additional professional development

and coaching, the teacher continues to not make reasonable progress as

determined through observation and data, the principal will create a formal

performance improvement plan based on the goals set forth in the Teacher

Self-Evaluation rubric. This plan will require improvement as determined



through observation and data within 60 days or by the end of the school-year

depending on the timing of the performance improvement plan. If improvement

is not made, DPMSS will have the option to terminate or not renew the teacher’s

contract. Prior to school opening, DPMSS will create a staff policy handbook that

will include a grievance procedure that will allow staff sufficient opportunity to

appeal in the event they feel their contract has been wrongfully terminated.

C. Professional Development

The principal at DPMSS will ultimately be responsible for managing and

evaluating professional development. There will be several areas of professional

development. The first area will be DPS sponsored. This will include RtI, ELA-T

and ELA-E, Positive behavior support, and any other DPS professional

development that will insure our staff is well educated in providing an optimal

education to a diverse student body.

The second area of professional development will be on Montessori

education and adolescent brain development. All teaching staff will be required

to attend training on Montessori adolescent education such as the AMI

Montessori Orientation to Adolescent Education. This five week intensive course

of study includes all aspects of adolescent Montessori education. During the

school year, each member of the teaching staff and leadership team will lead a

seminar based on Montessori literature. The North American Montessori

Teachers Association has given DPMSS a $3,000 grant and an additional $5,000

in-kind for professional development. The principal will create a professional

development plan to utilize this grant throughout the first three years.

The third area of professional development will be led by the principal

and will be on data collection and evaluation. The principal, working with DPS,

will work with staff to create appropriate data collection tools and methods

whereby the data is frequently reviewed.

The fourth area of professional development will be led by the special

education provider and/or the psychologist social worker. This area will cover

adolescent brain development, differentiated learning, implementing effective

teaching strategies with students who have special needs, and ongoing

professional development on RtI. The Special Education teacher and/or school

psychologist/social worker will attend professional development on these

topics at DPS and review materials and/or attend workshops by professionals

such as Dr. Steve Hughes and the Gurian Institute.

Prior to the first day of the first school year, DPMSS will have ten

professional development (PD) days in order to insure that we are fully prepared

for the very first day of school. During this time staff will attend DPS

professional development for ELA and RtI. Because staff will already be trained

in Montessori at both the elementary and adolescent levels, a majority of the


planning time will allow for staff to prepare their environments and review

curriculum for the first series of Occupations. The Occupations curriculum

requires a deep understanding of the land, the local area, public transportation,

and local community resources. Staff will work with the principal to make sure

that all necessary materials to run successful Occupations are readily available

so that the school year can start as smoothy as possible. There will also be

professional development around positive behavior support and Discipline

through Love and Logic offered by the Love and Logic Institute. The principal

will review with staff the DPMSS farm school portfolio, rubrics, record keeping,

assessment and all other tools necessary to frequently and accurately obtain

data regarding student achievement.

After the first year, DPMSS will have five PD days prior to the first day of

school. During the school year, DPMSS will have an additional five professional

development days. The topics for the professional development days during the

first school year will be as follows: Record keeping and assessment, RtI and

meeting the individual learning needs for all of students, review of and creating

best practices for writing and implementing Occupations curriculum, further

work regarding RtI and meeting the individual learning needs for all students,

and understanding the Urban Farm and how it applies to Montessori adolescent

education. In addition, on Wednesday afternoons from 1:30 - 3:30, staff will

attend staff integration meetings. These meetings will include data review,

discussion on recent observations, curriculum review and student discussion.

DPMSS will have monthly ninety minute staff meetings on where the

primary focus is Montessori theory and understanding adolescent brain

development.These staff meetings will support the recursive learning

environment. The meetings will allow for reflective conversation to evaluate

and improve practice. Staff will improving Montessori practice by examining the

principles of Montessori theory and how it applies to adolescent education.

Colleagues will share their acquired knowledge and skills with one another

resulting in the knowledge being reinforced for the “teacher” and spread

exponentially among the other staff members.

D. Teacher Recruitment, Hiring, and Retention

DPMSS teachers will be Montessori trained at the elementary level. If a

teacher is identified who has not yet obtained this Montessori training, they will

be required to do so during summer sessions. DPMS teachers will also have

attended Montessori adolescent training. Again, if a teacher is identified who

has not obtained Adolescent Orientation, they will be required to do so during

summer session. Every effort will be made to find high quality teachers who

already have one if not both of these trainings.6

DPMSS will recruit teachers through the NAMTA, AMI, AMS and Public

Montessorian websites. In the first year, DPMSS intends to hire a licensed

teacher who is highly qualified in science and math and is Montessori trained.




There are teachers who have all of these designations. However, it is highly

likely that DPMSS will hire someone who has most but not all of these

designations.7

Upon selecting the right teacher, DPMSS will work with that

individual to obtain summer training or enroll in coursework so that they have a

clear, achievable path to obtaining all of these designations. The second

teacher hired will be a licensed teacher highly qualified in Spanish, ELA-E

certified and Montessori trained. Again, it is highly likely that DPMSS will hire

someone who has most but not all of these designations.8

Upon selecting the

right teacher, DPMSS will work with that individual to obtain summer training or

enroll in coursework so that they have a clear, achievable path to obtaining all

of these designations.

The junior high and senior high program directors will be selected from

the existing staff as long as there are candidates ready, willing and qualified to

take on these leadership positions.

During the first two years, DPMSS will be serving 6th, 7th and 8th grades

in an integrated learning environment. Teachers are highly qualified to teach

these levels if they have k-8 elementary licensure. Prior to adding the 9th

grade, DPMSS will need to have teachers in place who are highly qualified to

teach secondary math, science, language arts, social studies and Spanish.

DPMSS will begin recruitment, identification and training of these teachers

during the first two years so that all teachers are highly qualified in their

subject area and Montessori trained. DPMSS will continue to aggressively reach

out locally and nationally to find teachers who are excited about teaching in a

public Montessori secondary environment and willing to complete the rigorous

training in order to do so.

DPMSS will request a waiver regarding licensed staff in order to insure the

best possible Montessori teachers are hired. All teachers will still be required to

be highly qualified (as determined by a bachelors degree, 24 hours of

completed coursework in their subject area, and/or passing the PRAXIS or

PLACE testing for their subject area) prior to hiring. All unlicensed teachers will

be required to pursue alternative teaching licensure through programs

approved by DPS.

Teacher retention will be the highest priority at DPMSS. Montessori

adolescent programs work best when there is a consistent, well trained, highly

effective staff. DPMSS will operate under the principals of shared leadership.

The culture at DPMSS will be respectful, inclusive and consistent. As

demonstrated at Compass Montessori School in Jefferson County, CO, a positive

inclusive school culture results in high staff retention, even during difficult

times such as the recent decline in school funding.


Colorado teaching license and demonstrating subject matter competency. 8 Clarification to CDE: All teachers who teach core content classes will meet the Highly Qualified requirements by holding a



Section V: FINANCE

A. Budget and Policy Narrative

The DPMSS school leader will be in charge of managing and overseeing

the school budget. Katy Myers has ten years of experience managing the

Compass Montessori School budget. Compass is a Jefferson County Public

School located in Wheat Ridge and Golden. The two campuses were treated as

separate business units, and Katy managed the budgeting, variance reports,

audit process and all aspects of the school’s finances. When Katy departed

Compass in 2011, both schools had positive fund balances. The Golden fund

balance was over $200,000. The Wheat Ridge fund balance was at a prospective

($180,000) when Katy took over that site in 2008. By 2011, the Wheat Ridge

fund balance was at $40,000. By the end of this year, based on the budget Katy

created last year, that Wheat Ridge fund balance will be closer to $100,000.

Based on the budget template provided, DPMSS will be cash positive by

year 3. In year 0, year 1 and year 2, DPMSS will rely on a $300,000 grant for

performance schools to cover salaries until the school reaches enrollment of

105. DPMSS will maintain a cash positive budget throughout the next four

years, including when it reaches steady state enrollment of 225 students and

10 teachers and related administration and support staff.

A minimum of 95% of allocated SBB revenue will be spent on salaries to

support a student - teacher ratio of 25 to 1. In year one and two, the school will

have 50 and then 65 students. Because of this small size, the principal will be

paid 50% at the principal’s salary level and 50% at the teacher’s salary level. The

principal will spend 50% of her time teaching. In years three, four and five, the

principal will spend 75% of her work time on principal duties and the remaining

25% teaching. Her salary will reflect this distribution. In year six, the school will

require and be able to afford a full time principal.

For years one and two, DPMSS projects a population of students requiring

special education services of about 10% of the total population. At 50 and 65

students, that equates to 5 and then 7 students. Therefore, the school is

planning on special education staffing of 25% FTE or 10 hours per week. DPMSS

hopes to partner with other small DPS schools to share resources. As the school

grows, the percentage of this position grows as well until year six when it is a

full time position. DPMSS also intends to hire a school pschologist / social

worker for the equivalent of one day per week during year one and two. As the

school grows, this position will also grow until year seven when it will remain at

28 hours per week.

For school nurse, DPMSS intends to use the clinic aid model often used in

charter schools. The office support will also be the clinic aid and will be

delegated to dispense medications in the manner authorized by law. The school



nurse will supervise the clinic aid in these duties. For years one and two, the

school nurse will come to the school twice a week for two hours to review

records and insure the school is in compliance. As the school grows, the hours

for school nurse will grow as well until year seven, when this postion will

remain at twelve hours per week.

During year 0 and year 1, DPMSS will use a performance school grant to

retrofit a DPS facility to insure that the school has a commercial kitchen, science

laboratories, an art studio with a kiln, and the ability to create an urban farm.

The ideal environment will have a gym and a performance space. DPMSS intends

to create a 2 to 1 ratio of students to computers. DPMSS will work with DPS to

create an efficient technology plan that could incorporate the use of thin client

or other inexpensive but effective computer hardware set ups. All staff will have

a laptop or tablet in order to efficiently record what students are attending

which lessons and related follow up work.

DPMSS will require classroom materials including a well stocked

laboratory to handle high school chemistry, biology and physics, reference,

non-fiction research books and fiction books for the library, literacy books, and

classroom materials to allow for the instruction of a wide variety of

Occupations , US history, Civics, Economics, A.P. World History, A.P.

Environmental Science, A.P. Biology, Advanced Algebra, Geometry,

Trigonometry and Calculus, A.P. Spanish and A.P. Language Arts. DPMSS will

also require access to an on-line math program for every enrolled student plus

a wide variety of math resources.

Non-typical expenses will include materials to build and maintain an

urban farm, including a water system. One very successful Occupation in other

Montessori adolescent programs is a culinary arts program that provides lunch.

Compass Montessori is its own School Food Authority and provides lunch for

the entire 330 student Golden campus. If DPMSS is able to work with the DPS

lunch program to create a similar opportunity, that would be ideal. DPMSS will

also require a complete set of Montessori materials equal to one large

classroom in an elementary setting.

DPMSS will use proceeds from the performance school start up grants to

buy the typical and non-typical classroom materials and technology. Once all

purchases are made via grant funding, DPMSS will set up a replacement

schedule to make sure that classroom materials are replaced in a methodical

manner and that school technology is updated every three years.

An ongoing need will be travel money for extended overnight trips. The

junior high program will travel within Colorado and adjacent states to visit

farms, ranches and historic sites related to the Occupations and humanities

curriculum. The high school will have one international trip per year. DPMSS will

create an ongoing fundraising effort to assist in funding these trips. No student

will be excluded from going on a trip due to inability to pay for the trip.

The next two pages is evidence supporting grant estimates.


Start Up Grant

Lauren Masters <[email protected]>

Wed, Mar 21, 2012 at 7:36 PM

To: "Murray, Alison" <[email protected]> Cc: "Neal, Mathew"

<[email protected]>, "Proctor, Grant"

<[email protected]>, Katy Myers <[email protected]>

Hi all,

Alison - thank you so much for your quick response and for being so

willing to help (as always)! I think a quick phone call or a look at Katy's budget

template thus far would be really helpful. Katy - your other budget questions

re: nursing and social worker requirements are something that Alison can help

answer.

I also wanted to provide some further clarity (on top of Mathew's email)

about the start up grants for new performance schools. Performance schools

get 2 sources of grants from DPS - 1) FFE and 2) start up funds to cover non

FFE.

1) FFE: All new approved performance schools will receive a separate grant

fund for FF&E, which is why there are not line items for curriculum materials,

furniture, computers, etc. on the budget form. Those expenses are covered

separately. This also includes maintenance facility upgrades for DPS sites that

are required to fit the school into a DPS building. Please note these facility

upgrades cover the bare minimum to retrofit a school into a space and some

schools want to use funds to do additional facility upgrades as Mathew

mentioned (again very site specific).

2) Start up funds:Tends to be @ $300-400,000 for non-FF&E (largely to

fund operating deficits as enrollment ramps up)over year 0, year 1, and year 2.

Schools should be sustainable on PPR by year 2 or 3. Mathew did a great job

describing the typical year 0 expenses, but year 1 and year 2 also normally have

operating gaps that need to get filled as the school's enrollment grows, so it is

not unusual to see start-up funds go towards salaries and PD (and not

facilities). Alison and Grant have a great perspective on this as well from past

experience. While 300-400K has been the available amount in the past, the pot

of money that funded past new performance schools continues to dwindle so I

just want to also add a disclaimer to be as conservative as you can with start up

funding (i.e. as close to $300K over year 0 - year 2 that you can get your

budget at, the better).

I hope this helps. Let me know if you have any outstanding budget

questions once you talk to Alison.

Thanks!

Lauren







Denver Public Montessori Secondaty School

N· A· M · T·A

13693 Butternut Road

Burton, Ohio 44021

tel 440.834.4011

fax 440.834.4016

[email protected]

www.montessori-namta.org

March 19, 2012

Katy Myers

10923 Magnolia Dr.

Apt. B,

Cleveland, OH 44106.

Dear Katy,

Montessori Development Partnerships and the North American Montessori

Teachers' Association have authorized a cash grant of $3000.00 in start-up

funds to be used primarily for Montessori consultancy and services from

Project 2012. Services in kind constitute an additional $5000 in honoraria

donated from David Kahn and Laurie Ewert-Kroeker (and others) in providing

on-site programming and materials for the project. The $3000.00 will be

disbursed in June.

We have elected your program for sponsorship because of our faith in your

history of making Montessori secondary programs work, especially

demonstrated in the viability and authenticity of Compass Montessori School

located in Golden, Colorado. Having had contact with Montessori High

School at University Circle and Hershey Montessori School Farm Program,

we are hoping you adopt some of our successful curriculum design and

orientation creating a unique blend of school cultures that will inevitably lead

the country in Adolescent work.

With best wishes for Denver Public Montessori Secondary School.

Si 0 k:t..._ David Kahn Executive Director, NAMTA

Executive Director, MDP

ein affiliation with the Association Montessori In temationale-Amsterdam, Netherlands



http://www.montessori-namta.org/


Optional Section VI: Innovation School Status

DPMSS will be requesting Innovation Status through the DPS Innovation

School Application. The 6th grade through 12th grade Montessori curriculum

that DPMSS will implement is rigorous, innovative, interesting and is designed

to engage students to produce optimal academic achievement as well as social

and emotional maturity and well-being. Montessori adolescent curriculum has

been designed and tested over the last fifteen years at both private and public

Montessori schools. This curriculum, referenced throughout this application as

Montessori National Curriculum, has been collected, refined and reported

through The NAMTA Journal, A Montessori National Curriculum Report, The

NAMTA Journal, Volume 37, No. 1, Winter 2012. DPMSS will design its program

using this curriculum. Recently, the Montessori National Curriclum for the

Adolescent Program from Twelve to Fifteen/Sixteen Years was reviewed by the

Australian Curriculum Assessment and Reporting Authority. Their findings, as

reported in A National Montessori Curriculum Report, are as follows: ACARA

(Australian Curriculum Assessment and Reporting Authority) established an

extremly rigorous recognition process to determine the extent to which a well-

established alternative national curriclum can deliver comparable educational

outcomes for students to those based on the Australian National Curriculum.

ACARA have advised that (the National Montessori Curriculum) aligns with the

Melbourne Declaration on Educational Goals for Young Australians, meets the

particular principles and guidelines in relation to the Shape of the Australian

Curriclum v3 paper, and allows for broadly comparable educational outcomes in

English, mathematics, science and history by the end of year 10.

In order to effectively implement the curriculum, DPMSS will need to

adopt its own schedule, its own standards for hiring teachers, its own school

calendar and professional development plan, its own assessments, and, of

course the National Montessori Curriculum. If DPMSS is not able to achieve

innovation school status, it is highly unlikely that the school will open. For a

school to achieve excellence, it must hold on to its vision and implement the

vision as clearly and effectively as possible. DPMSS will require the innovative

school status to maintain fidelity to its mission and vision.

Examples of the DPMSS curriculum are included in Exhibits C and K.

DPMSS will be using the National Montessori Curriculum for grades 7-9 for

science, history and language arts. DPMSS will use an on-line math curriculum

that is individualized for each student combined with small group lessons. The

small group lessons will be designed to meet each student at the particular

benchmark the student is currently working, and the teacher will use a variety

of instructional methods, including Montessori math materials, to assist the

student in mastering that benchmark and preparing to work on the next on-

line unit. Students will also be expected to apply math towards a variety of



hands-on projects utilizing the farm, the culinary arts program and micro-

economy. The 7,8,9 Spanish curriculum will be the TPRS curriculum. TPRS

matches the meaningful, relative approach that defines Montessori education.



Montessori High School in Jefferson County. The Compass three year SPF results

for this curriculum are a median growth percentile of 58 for reading, 54 for

mathematics and 66 for writing and an academic achievement score for science

of 59%. The academic growth gaps achieved a level of exceeds for reading and

writing and meets for math. The three year ACT composite is 21.7.

Although the curriculum for high school will be similar to advance

placement curriculum in DPS for English, history, math, science and spanish,

there will still be innovative differences. First, the curriculum will be integrated

so that literature studied in language arts will, at the same time, support the

history curriculum for an overall integrated humanities curriculum. The math

and science teacher will work together to insure students are obtaining the

mathematical skills needed to work out currently studied complex scientific

equations. Linkages between science, math and history will be explored.

Throughout all areas of study, there will be in-depth reading and writing

instruction. This integrated approach will be supported by the innovative

schedule.

The schedules for both the junior high and the senior high will support

the Montessori approach. There will be minimal required transition times.

Instead, students will be called to small group lesson as those lessons are

needed to support the next level of study. This schedule is currently in place at

Compass Montessori high school. During the morning, students are

independently working on a variety of assignments and further exploration of

their current units of study. At the same time, teachers are giving small group

lessons to students in math, science, language arts and history. The culture of

respect and hard work is resolutely held by both the staff and the students. One

hundred percent of the students are on task and engaged because they are

enjoying their academic studies. This on task and engaged behavior is the

hallmark of Montessori education, and this is what we intend to create at

DPMSS.

DPMSS has outlined in Exhibit D the State, District and collective

bargaining wavers that it is requesting.


Appendix A: Letter of Intent

This letter of intent (LOI) will provide formal notice to the Office of School Reform and

Innovation in Denver Public Schools regarding an applicant’s intention to submit a new

school proposal for the 2013-2014 school year cycle.

The information presented in the LOI is non-binding.

Name of Proposed

School:


Type of School: Performance

Grade Configuration: 7th - 12th (6th grade in first year only)

Model or Focus: Montessori secondary education

Primary Contact Person:

Phone:

Email:

Katy Myers

303-431-2385

[email protected]

Region: Preferably attached to an existing DPS Montessori

elementary school or centrally located to serve the four

existing Montessori elementary schools

Proposed Leader (if

known):

Katy Myers

Replication: No

Contract with ESP/EMO: No

Enrollment Projections: Provide additional rows and columns if necessary.

GRADE 2013-14 2014-15 2015-16 2016-17 2017-18

6 25 0 0 0 0

7 25 40 40 40 40

8 25 40 40 40

9 25 40 40

10 20 35

11 20

Total # of Students 50 65 105 140 175

FRL % SPED % ELL %


Lincoln 37

Academia Ana

Maria Sandoval:39

Gilpin: 89

Denison: 11

Lincoln: 6

Academia Ana

Maria Sandoval: 5

Gilpin:: 12

Denison: 19

Lincoln: 11

Academia Ana

Maria Sandoval: 41

Gilpin: 23




Mission of School: Denver Public Montessori Secondary School will combine

Montessori best practices with current research on adolescent brain development to provide a learning environment that promotes high achievement for each student while also supporting them socially and emotionally. Graduates, regardless of ethnicity or income status, will be prepared for college or a career as well as demonstrate ingenuity, adaptability, creativity, initiative and excellent communication and problem solving skills.

Provide a brief

overview of the

education program of

the proposed school:

Denver Public Montessori Secondary School will provide a

continuation of Montessori education to students primarily coming from the DPS Montessori elementary programs. The school will combine Montessori best practices with current research on adolescent brain development to provide a learning environment that promotes high achievement for each student while also supporting them socially and emotionally. The junior high (7th, 8th and 9th) will be centered around an urban farm containing real life, hands on experiences that extend and deepen rigorous academic learning. The high school (10th, 11th and 12th), will partner with local Denver cultural institutions along with community colleges in order to

prepare each graduate for college or a career. .


Appendix B: School Facility Questionnaire

Core Classroom Requirements Years 1-3:

Baseline assumption for number of students per classroom: _25_

Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7

50 65 105 140 175 210 225

School Name: Denver Public Montessori Secondary School

Primary Contact for Facility Planning: Katy Myers

Telephone: 303-431-2385 Email: [email protected]

School Type: Performance School Charter School

Grade levels and student enrollment estimates for the first five years:

2013-2014 2014-2015 2015-2016 2016-2017 2017-2018

Grades 6th - 7th 6th - 8th 7th - 9th 7th - 10th 7th - 11th

Enrollment 50 65 105 140 175

Region: Centrally located to serve the current four DPS Montessori elementary schools

or attached to an existing DPS Montessori elementary school

Description of the facility/ies under consideration including available square footage

and quotes (for years 1-5) from property owners:

1.

2.

3.

Are you interested in investigating the possibility of occupying a district-owned

facility?

Yes




Administrative/Support Spaces

Main Office Yes

If yes, list number of private offices needed (e.g., principal, AP, etc.): 3

Satellite Office Yes

Work Room/Copy Room Yes

Supplies Storage Yes

Teacher Work Room(s) Yes

If yes, list number of teacher work/planning rooms needed: 2

Specialty Classroom Needs

Number of Science Labs: 2

Number of art rooms ( one with kiln): 2

Number of computer labs: 0

Library Media Center (LMC) Yes

Performance/Dance Room Yes

Auditorium Yes

Other (list room type and number): Commercial Kitchen 1

Physical Education/Athletic Requirements

Gymnasium Yes

Locker Rooms No

Weight Room No

Field(s) – soccer, football, multipurpose Yes

Baseball Field No

Softball Field No

Other (please list): Land suitable to start an urban farm

Other Needs

Playground(s)

No

Large space for class/school assemblies (e.g., morning meeting,

cafeteria)

Yes

Spaces not addressed and/or special considerations: DPMSS would like to eventually

run its own school lunch program using a commercial kitchen on site.


Appendix C: Questions for Schools Requesting Waivers

Schools requesting waivers from district curriculum, DPS’s benchmark assessment

program, and/or promotion and graduation policies are required to complete the

below questions in this appendix.

A. Instructional Design & Curricular Materials

Denver Public Montessori Secondary School (DPMSS) will combine

Montessori best practices with current research on adolescent brain

development to provide a learning environment that promotes high

achievement for each student while also supporting them socially and

emotionally. Graduates, regardless of ethnicity or income status, will be

prepared for college or a career as well as demonstrate ingenuity, adaptability,

creativity, initiative and excellent communication and problem solving skills.

In order to accomplish this mission, DPMSS will be requesting Innovation Status

through the DPS Innovation School Application.

Dr. Montessori designed an education program with 21st Century

outcomes long before there was a definition of 21st Century outcomes.

Through her extensive observation, research and innovative practice, she

developed a curriculum for children from age 0 - 12. She also created a

curriculum framework for students ages 12 - 18. That framework is outlined in

her book, From Childhood to Adolescence, published in 1948.

In 1996, a concentrated effort began to bring Montessori’s adolescent

framework to life through carefully run school programs. This effort was led by

the Northern American Montessori Teacher’s Association (NAMTA). NAMTA

gathered curriculum and best practices from existing schools throughout the

United States. NAMTA also partnered with the Hershey Montessori Foundation

to create an exemplary school that contained every element of Montessori’s

vision as presented in From Childhood to Adolescence. At this school, the

Occupations curriculum and the Montessori adolescent humanities curriculum

has been developed, implemented and modified through practical application

research. In 2001, NAMTA started the AMI Montessori Orientation to Adolescent

Studies for adolescent teachers. This intensive five week summer course trained

teachers on pedogy, curriculum and curriculum implementation. Every year,

there are conferences on various aspects of program implementation. The

Montessori adolescent program has arrived at a point where it is replacatable

and can work in both private and pubic school environments.

In 2011, The Montessori Australian Foundation partnered with NAMTA to

create a full 0 to 16 Montessori curriculum alignment to the Australian

Educational Goals for Young Australians. This curriculum alignment project

was published through The NAMTA Journal, A National Montessori Curriculum

Report, The NAMTA Journal, Volume 37, No. 1, Winter 2012. The National

Montessori Curriclum for the Adolescent Program from Twelve to Fifteen/

Sixteen Years was reviewed by the Australian Curriculum Assessment and



Reporting Authority. Their findings, as reported in A National Montessori

Curriculum Report, are as follows: ACARA (Australian Curriculum Assessment

and Reporting Authority) established an extremly rigorous recognition process

to determine the extent to which a well-established alternative national

curriclum can deliver comparable educational outcomes for students to those

based on the Australian National Curriculum. ACARA have advised that (the

National Montessori Curriculum) aligns with the Melbourne Declaration on

Educational Goals for Young Australians, meets the particular principles and

guidelines in relation to the Shape of the Australian Curriclum v3 paper, and

allows for broadly comparable educational outcomes in English, mathematics,

science and history by the end of year 10.

DPMSS will use the National Montessori Curriculum, as presented in the

NAMTA journal and modified to meet the cultural orientation of our target

students and all CAS and CCS standards. The 6th grade through 12th grade

Montessori curriculum is rigorous, innovative, interesting and is designed to

engage students to produce optimal academic achievement as well as social

and emotional maturity and well-being.

Montessori is inquiry based. Self-direction, collaboration,information

literacy, critical thinking and reasoning and invention are all core components

of the Montesssori curriculum. Montessori education teaches students how to

learn, how to acquire information, and how to make connections. Montessori

wrote, “Here is an essential principle of education: to teach details is to bring

confusion; to establish the relationship between things is to bring knowledge.”

The curriculum, the schedule, the pedagogy and even the assessments are all

created to foster an environment that allow students to explore, to work

together, to work independently, and most importantly, to become confident,

competent adults who know how to problem solve because they have been

practicing this skill for years.

Students who leave Montessori programs to go to traditional schools are

easily able to make this transition. They have learned to create healthy, trusting

relationships with teachers because of the advisor model. Students are able

and willing to seek out adults at school for help. They are confident speakers

and able to use their voice. They understand that they are in charge of their

education. Even though they may not have been using traditional curriculum,

Montessori students are easily adaptable and are used to challenges.

Montessori said, “For success in life depends in every case on self-confidence

and the knowledge of one’s own capacity and many-sided powers of

adaptation.”

Montessori education is individualized education. The schedule, small

group lessons, individualized assessment and follow up work that is based on

the students’ interests and explorations allow for every type of learner to excel.


This includes students with special needs, ELL learners, accelerated learners

and students from every culture.

One example of the DPMSS junior high curriculum is included in Exhibit

K. DPMSS will be using the National Montessori Curriculum for grades 7-9 for

science, history and language arts. DPMSS will use an on-line math curriculum

that is individualized for each student combined with small group lessons. The

small group lessons will be designed to meet each student at the particular

benchmark the student is currently working, and the teacher will use a variety

of instructional methods, including Montessori math materials, to assist the

student in mastering that benchmark and preparing to work on the next on-

line unit. Students will also be expected to apply math towards a variety of

hands-on projects utilizing the farm, the culinary arts program and micro-

economy. The 7,8,9 Spanish curriculum will be the TPRS curriculum. TPRS

matches the meaningful, relative approach that defines Montessori education.



Montessori High School in Jefferson County. The Compass three year School

Performance Framework results for this curriculum are a median growth

percentile of 58 for reading, 54 for mathematics and 66 for writing and an

academic achievement score for science of 59%. The three year academic

growth gaps achieved a level of exceeds for reading and writing and meets for

math. The three year ACT composite is 21.7. Grove High School, located in

Redlands, CA, is another public Montessori charter school that has a farm

school program for its junior high and college preparatory program for its high

school, very similar to the design we are proposing. Their California State

School Accountability Report Card shows Grove at a 2011 API growth level of

857, well above the 800 median and an overall 2010 proficient and advanced

rate in English Language Arts of 77 % and Science at 66%.

By high school, (10th - 12th), Montessori students are well adept at

taking charge of their education, and are eager for further intellectual

challenge. Although the curriculum for high school will be similar to advance

placement curriculum in DPS for English, history, math, science and spanish,

there will still be innovative differences. The delivery of curriculum maintains

the core values of Montessori and are designed specifically for students who

have progressed through Montessori education. Instruction is delivered via key

lessons that convey to the students fundamental concepts and serve as

“jumping off” points for further exploration. Studies are self-directed in an

environment of high expectations and high support. Teacher/advisors work

with students to insure that students have the advanced skills necessary to

explore advanced concepts.

In combination with the challenging academic setting, high school

students are also encouraged to go out to local cultural institutions to further



study. DPMSS intends to create partnerships with the Museum of Nature and

Science, the Denver Zoo, the Denver Botanic Gardens, the Denver Art Museum

and other local cultural centers so that our students can easily access experts

within those settings. DPMSS will also create partnership with CU Denver and

Metropolitan State College of Denver so that students who wish to dually enroll

in some classes during their senior year have the ability to do so. Another key

experience for high school will be international travel. DPMSS will determine

appropriate fund raising venues so that all students will be able to attend at

least one international trip during high school.

Here is an example of a high school Humanities Unit from Compass

Montessori High school:

Modern American Studies

Reconstruction to Modern Times

Curriculum Summary

English & American History credit - ½ each per semester

Required Textbooks

American History: Taking Sides: Clashing Views on Controversial Issues in

American History. Vol. II: Reconstruction to the Present.

Larry Madaras & James M. SoRelle, eds. Guilford, CT:

Dushkin/McGraw Hill, 2000. Eighth edition.

Modified: Reasoning with Democratic Values: Ethical Problems in

United States History, Volume 2. Alan L. Lockwood and

David E. Harris, eds. Teacher College Press, 2002

Geography: Geography Coloring Book, by Wynn Kapit. Third Edition

English: Short Takes: Model Essays for Composition. Elizabeth

Penfield. New York: Longman, 2002. Seventh Edition.

Literature, American Authors as assigned.

AP English: The Norton Reader. Peterson, Linda H., and John C.

Brereton, eds. New York: W. W. Norton & Co.


Overview:

American Studies surveys significant social, cultural, and political developments

in United States society from the late nineteenth century to the present. This

course explores the political and social meanings of cultural conflict and

national identity through close analysis and classroom discussion of historical

documents, literature, and scholarly writings. How ideas about race, gender,

sexuality, class, and religion have shaped legal and political contests in past

and modern society are examined. Students will engage these issues through

seminars, lectures, and course readings. Students will not only be expected to

know the "facts" but also to understand and interpret those facts and their

interrelationships in both historical and modern context.

Literature and writing work focuses upon the themes of each quarter’s studies.

Essay writing in description, exposition, argumentation, classifying, comparing,

contrasting and narrative are covered within this course. Required literature

includes classic, modern, short stories and poetry from American authors.

1st

Quarter: “How do you get to Carnegie Hall? Lessons from the Gilded

Age”

In this quarter we will examine America after the Civil War until 1910. Themes

of study will include urbanization, imperialism, industrialization and

immigration.

Literature - Examples: The Jungle, Devil in the White City, 42nd Parallel,

Fountainhead

2

nd Quarter: “War, Roar, Bust & Dust”

Topics in this quarter will include WWI, the Roaring Twenties, including the

Harlem Renaissance, The Great Depression and the Dust Bowl. Themes will

include progressivism, economics, labor unrest and isolationism.

Literature – Examples: Johnny Got his Gun, The Grapes of Wrath, The Heart is a

Lonely Hunter, The Great Gatsby, To Kill a Mockingbird, Poetry selections -

Langston Hughes

3

rd Quarter: “WW-II to MCMXC-II”

Overview of the U.S. involvement in the Second World War and the cold war until

the fall of the Berlin Wall is presented. Topics of study will include WWII, the

Korean and Vietnam conflicts, Civil Rights Movement, The Counterculture, the

70’s and 80’s. Themes of study will include propaganda, conflict among

conformity, popular culture & consumerism.



Literature – Examples: The Things they Carried, Slaughterhouse Five, Catch 22,

One Flew over the Cuckoo’s Nest

4

th Quarter: “The State of the Union”

An examination of our current political and social climate both domestically and

internationally. This term will investigate cultural aspects of Latin America,

partly in preparation for a May 2008 trip to Costa Rica. A brief survey of cultural

aspects of Latin America’s cultural, social economic, racial, and environmental

concerns. In addition, a weekly survey of current issues of concern to the U.S.-

Latin American relations.

Literature - Examples: 1984, Clockwork Orange, Anthem, 100 Years of

Solitude, Like Water for Chocolate, Love in the time of Cholera

The National Montessori Curriculum aligns with nearly every benchmark

of the Colorado Academic Standards and Common Core Standards. Below are a

few examples. During the planning year, DPMSS will completely adapt the

National Montessori Curriculum to the Colorado Academic Standards and

Common Core Standards. Assessments will then be created using the CAS

aligned curriculum. Because the junior high will integrate grades 7, 8 and 9, all

alignment will be based on the 9th grade standards. For high school, alignment

will be based on the 12th grade standards.

English Instruction - Grades 7 - 9 (partial example)

Content Strand

Knowledge, Skills and Understandings Activities and Resources

Typically students will:

Reading Understand the role reading plays in social life, and its applications in the life of the adolescent community and in

the wider community Understand the purpose for reading, and how to read

different formats, including literar y, factual and persuasive

texts of different types in paper-based, digital or multimedia

forms Read, respond to and interpret a range of literar y texts,

including shor t stories, novels, plays, and poetr y

Recognise and label the elements of a literar y text,

including:

- the setting, plot, characterization, dialogue, climax and

denouement of a narrative

- the form, metre and rhyme scheme of a poem Recognise literar y technique and structures, including

figures of speech such as:

- metaphor and simile

- personification

- hyperbole and irony

- pun

- alliteration Par ticipate in a book group to share and discuss ideas and

interpretive questions collaboratively Respond personally, analytically and critically to a variety of

literar y works by:

- interpreting, analysing and evaluating different

perspectives on issues, events, situations, individuals or

groups

- identifying and analysing implicit and explicit values, beliefs

and assumptions Read for enjoyment beyond assigned reading tasks Appreciate the diversity of the literary tradition through

reading works by authors from many racial, ethnic, and

cultural groups

Activities include: - evaluating the expression of

comparable ideas across a

variety of sources for a variety

of audiences

- analysing how individual,

groups, events and places are

represented in literar y, factual

and persuasive texts in order

to influence audience

perception or opinion

- designing a checklist for

evaluating the quality of

information found in sources

such as websites, magazines,

adver tisements, television and

newspaper current affairs e.g.

credibility, accuracy, reliability,

fact distinguished from opinion

- using evidence from literar y,

factual and persuasive texts to

reveal how authors create

emotional responses, influence

and/or position an audience

e.g. through comparison,

contrast, exaggeration,

juxtaposition, the changing of

chronological order, or the

expansion and compression of

time

- analytical, interpretive and

evaluative comprehension tasks

related to intellectual

development and creative

expression

Resources include:

- classical and contemporar y

literature

- texts from popular culture

- inter views with authors




Read to build understanding of subject matter across the

curriculum Read closely, analytically and critically a range of non-fiction/

factual texts, including information texts, biography, newspaper

and journal articles by interpreting, analysing and evaluating

different perspectives on issues, events, situations, individuals

or groups Read a range of persuasive texts, including speeches, media

commentary, essays, journal articles and opinion pieces Recognise and describe an author’s intention and point of

view Use annotation and citation effectively when interpreting a

text Build and expand, through reading, an increasingly mature and

sophisticated vocabulary relevant to range of contexts and

language varieties

- literar y criticism - study guides

- librar y

- reference and research

materials (paper-based, digital,

web-based, multimedia)

Reading for life

Read for information across the curriculum and beyond (e.g. mass media and popular culture in community and

Occupations contexts) Read to ‘do’ i.e. reading to learn how to complete practical

tasks and how to use equipment and technology Read for enjoyment and enter tainment Read as a study skill:

- applying reading strategies such as skimming, scanning,

vocabular y building, text analysis and synthesis,

summarising, paraphrasing, acknowledging sources and

note-taking to achieve study goals

- establishing reading goals and priorities as par t of larger

research or other projects

- developing analytical, interpretive, evaluative and critical

reading skills

Activities include: - preparation for seminars,

meetings, presentations and

debates

- research, analytical, interpretive

and evaluative comprehension

tasks related to the under taking

of practical and community

projects

- lunchtime book club

- reading out loud for an

audience as performance e.g.

stor y-telling, choral reading, and

information sharing Resources include:

- literar y texts, reference and

research materials (paper-

based, digital, web-based,

multimedia)

- DIY instructions and operating

manuals (paper-based, digital,



Colorado

Academic

Standard for

Grade 9

Students Can:

a. Determine a theme or central idea of a text

and analyze in detail its development over

the course of the text, including how it

Concepts and skills students

master:

Increasingly complex literary

elements in traditional and

contemporary works of emerges and is shaped and refined by specific literature require scrutiny and details; provide an objective summary of the text. (CCSS: RL.9-10.2)

b. Analyze how complex characters (e.g., those

with multiple or conflicting motivations)

develop over the course of a text, interact

with other characters, and advance the plot or

develop the theme. (CCSS: RL.9-10.3)

c. Analyze how an author's choices concerning

how to structure a text, order events within it

(e.g., parallel plots), and manipulate time

(e.g., pacing, flashbacks) create such effects

as mystery, tension, or surprise. (CCSS: RL.

9-10.5)

d. Analyze a particular point of view or cultural

experience reflected in a work of literature

from outside the United States, drawing on a

wide reading of world literature. (CCSS: RL.

9-10.6)

e. Identify the characteristics that distinguish

literary forms and genres

◦ Analyze how an author draws on and transforms source material in a specific work (e.g., how Shakespeare

treats a theme or topic from Ovid or

the Bible or how a later author draws

on a play by Shakespeare). (CCSS:

RL.9-10.9)

◦ Use literary terms to describe and

analyze selections

f. By the end of grade 9, read and comprehend

literature, including stories, dramas, and

poems, in the grades 9-10 text complexity

band proficiently, with scaffolding as needed

at the high end of the range. (CCSS: RL.

9-10.10)

comparison



Colorado

Academic Students Can: Concepts and skills students

master: Standard for a. Determine a central idea of a text and analyze Increasingly complex Grade 9 its development over the course of the text,

including how it emerges and is shaped and

refined by specific details; provide an

objective summary of the text. (CCSS. RI.

9-10.2)

b. Analyze in detail how an author's ideas or

claims are developed and refined by

particular sentences, paragraphs, or larger

portions of a text (e.g., a section or chapter).

(CCSS: RI.9-10.5)

c. Evaluate clarity and accuracy of information

through close text study and investigation via

other sources

d. Analyze how the author unfolds an analysis

or series of ideas or events, including the

order in which the points are made, how they

are introduced and developed, and the

connections that are drawn between them.

(CCSS: RI.9-10.3)

e. Use flexible reading and note-taking

strategies (outlining, mapping systems,

skimming, scanning, key word search) to

organize information and make connections

within and across informational texts

f. Critique author's choice of expository,

narrative, persuasive, or descriptive modes to

convey a message

g. Delineate and evaluate the argument and

specific claims in a text, assessing whether

the reasoning is valid and the evidence is

relevant and sufficient; identify false

statements and fallacious reasoning. (CCSS:

RI.9-10-8)

h. By the end of grade 9, read and comprehend

literary nonfiction in the grades 9-10 text

complexity band proficiently, with

scaffolding as needed at the high end of the

range. (CCSS: RI.9-10.10)

informational texts require

mature interpretation and

study

Content Strand

Knowledge, Skills and Understandings A c t i v i t i e s a n d Resources


Writing Introduce, consolidate and/or review knowledge about: - written texts, their purposes and structure

- the structure of paragraphs

- the study of grammar : the function of words, groups

and phrases, the analysis and composition of clauses

and sentences

- the study of style

- word study, spelling and etymology

- punctuation

- handwriting and keyboarding

Activities include: - modelled and guided writing

activities in which students

develop written composition

skills

- composition of a range of

written texts to achieve

purposes across all curriculum

domains

- writer’s conferences

- engaging in real life tasks that

demand written texts to achieve

a range of purposes Resources include:

- model texts

- purposeful writing contexts

across the curriculum

- a range of writing media (paper-

based, digital, web-based,

multimedia)

Writing as experi-

ence

Uses the steps of the writing process as a means to composing texts:

- planning: generating ideas, selecting a topic/focus,

gathering and collating details, building vocabular y,

organising information

- seeking and responding to feedback

- editing to improve clarity and effectiveness

- proofreading for spelling and punctuation

- publishing (handwriting/word processing, illustrating,

presenting)

Build a reper toire of text structures to achieve a range of

purposes, including:

- describe, recount, narrate

- respond, interpret, critique

- instruct, explain, repor t

- persuade

Write for a range of audiences:

- from informal to formal

- from peers to an audience of higher or lower status in

the context e.g. more or less exper t, older or younger




Write for a range of media, including written text, spoken

presentation or dialogue, digital media, and multimedia

Write in a range of forms, including notes and messages,

letter, essay, ar ticle, shor t answer, prose, poetr y

Write spontaneously for practical purposes and

enjoyment

Develop a personal voice in writing

Share drafts with ‘critical friends’ (e.g. other students,

teachers, parents) in order to gather ideas for revision

and respond to suggestions

Develop criteria for evaluating own and others’ texts

Improve awareness and master y of the conventions of

language (paragraphs, spelling, punctuation) and the effect

of conventional usage on clarity

Develop a range of strategies for organising ideas and

content prior to writing, including graphic organisers,

concept mapping, note-taking, file system, bibliography

Draw from multiple sources and integrate into own work

with correct citation and no plagiarism

Use word processing, graphics, and publishing as a

medium of exchange

Evolve a personalised style sheet


Colorado

Academic Students Can: Concepts and skills students

master: 1. Literary and Standards a. Write narratives to develop real or imagined narrative texts develop a for Grade 9 experiences or events using effective

technique, well-chosen details, and well-

structured event sequences. (CCSS: W.

9-10.3)

◦ Engage and orient the reader by setting out a problem, situation, or observation, establishing one or

multiple point(s) of view, and

introducing a narrator and/or

characters; create a smooth

progression of experiences or events.

(CCSS: W.9-10.3a)

◦ Use a variety of techniques to sequence events so that they build on one another to create a coherent

whole. (CCSS: W.9-10.3c)

b. Write literary and narrative texts using a

range of poetic techniques, figurative

language, and graphic elements to engage or

entertain the intended audience

c. Refine the expression of voice and tone in a

text by selecting and using appropriate

vocabulary, sentence structure, and sentence

organization

d. Review and revise ideas and development in

substantive ways to improve the depth of

ideas and vividness of supporting details

e. Explain strengths and weaknesses of own

writing and the writing of others using

criteria (e.g., checklists, scoring guides)

controlling idea or theme with

descriptive and expressive

language



Students Can:

a. Write arguments to support claims in an


master: 2. Informational and persuasive

analysis of substantive topics or texts, using texts develop a topic and valid reasoning and relevant and sufficient evidence. (CCSS: W.9-10.1)

1. Introduce precise claim(s), distinguish the claim

(s) from alternate or opposing claims, and create

an organization that establishes clear

relationships among claim(s), counterclaims,

reasons, and evidence. (CCSS: W.9-10.1a)

2. Develop claim(s) and counterclaims fairly,

supplying evidence for each while pointing out

the strengths and limitations of both in a manner

that anticipates the audience's knowledge level

and concerns. (CCSS: W.9-10.1b)

3. Use words, phrases, and clauses to link the major

sections of the text, create cohesion, and clarify

the relationships between claim(s) and reasons,

between reasons and evidence, and between

claim(s) and counterclaims. (CCSS: W.9-10.1c)

4. Use appropriate rhetorical appeals and genre to

engage and guide the intended audience

5. Anticipate and address readers' biases and

expectations

6. Revise ideas and structure to improve depth of

information and logic of organization

7. Explain and imitate emotional, logical, and

ethical appeals used by writers who are trying to

persuade an audience

8. Establish and maintain a formal style and

objective tone while attending to the norms and

conventions of the discipline in which they are

writing. (CCSS: W.9-10.1d)

9. Provide a concluding statement or section that

follows from and supports the argument

presented. (CCSS: W.9-10.1e)

establish a controlling idea or

thesis with relevant support


Students Can:

a. Demonstrate command of the conventions

of standard English capitalization,

punctuation, and spelling when writing.

(CCSS: L.9-10.2)

◦ Identify comma splices and fused sentences in writing and revise to eliminate them

◦ Distinguish between phrases and clauses and use this knowledge to write varied, strong, correct, complete sentences

◦ Use a colon to introduce a list or

quotation. (CCSS: L.9-10.2b)

◦ Spell correctly. (CCSS: L.9-10.2c) b. Produce clear and coherent writing in which

the development, organization, and style are

appropriate to task, purpose, and audience.

(Grade-specific expectations for writing

types are defined in expectations 1 and 2

above.) (CCSS: W.9-10.4)

c. Develop and strengthen writing as needed

by planning, revising, editing, rewriting, or

trying a new approach, focusing on

addressing what is most significant for a

specific purpose and audience. (CCSS: W.

9-10.5)

d. Use technology, including the Internet, to

produce, publish, and update individual or

shared writing products, taking advantage of

technology's capacity to link to other

information and to display information

flexibly and dynamically. (CCSS: W.9-10.6)


master:

3. Writing for grammar, usage,

mechanics, and clarity requires

ongoing refinements and

revisions



A core component of Montessori education is that it is integrated. Here are

examples of how Reading, Writing and Communicating are integrated across

all curriculums.

English Across the Curriculum

English is embedded in all areas of the curriculum, wherever language skills are needed to engage

productively with curriculum content. How English is embedded in specific curriculum areas is summarised

in the table below.

The Domain of Intellectual Development

Spoken language Composing written and multimodal texts

Reading

Citizenship, civics and community life

- use a range of media to communicate with the wider

community (e.g. telephone,

social networking, video

conference, Skype)

- discuss ideas in conversation

with others within and beyond

the adolescent community

- par ticipate in seminars and

debating

- deliver presentations within and

beyond the adolescent

community

- par ticipate in a council meeting,

conflict resolution conference

- take notes - summarise reading material

- present research, analysis and

proposals for projects and change

- publish flyers, ar ticles, opinion

pieces, newsletters and newspapers

- incorporate text into char ts,

timelines, and power points

- read for pleasure - read to know what surrounding

community and society is

reading and talking about, e.g.

positions taken and the opinions

expressed in the mass media

and popular culture

- research primar y and secondar y

sources

- read literar y and philosophical

works

- read non-fiction, including text

books, reference books,

newspapers, journals, websites

- review and respond to the

writing of others

Mathematics

- demonstrate proofs/problems - explain problem-solving

strategies

- use the vocabular y of mathematics effectively

- record the analysis of mathematical

problems and strategies used

- write word problems

- write text to accompany timelines,

graphs, char ts and multimedia

presentations on mathematics

topics

- prepare visual texts including

graphs, diagrams, char ts, timetables

- prepare historical accounts related

to mathematical topics and

biographies of mathematicians

- read stor y/word problems - research mathematics through

histor y, including the biographies

of mathematicians

- read current texts on topics in

mathematics

English and languages other than English

- read aloud for self or an audience

- recite poetr y

- engage in stor y-telling to a

variety of audiences

- par ticipate in quizzes,

discussions, book groups and

debates

- take notes - keep a journal/diar y

- apply knowledge about grammar to

the composition of sentences/

clauses

- write effective paragraphs

- draft essays and ar ticles

- compose poetr y, fiction, scripts and

other literar y texts

- write to persuade

- revise, edits and proofread texts

- use spelling and punctuation

effectively

- present/publish written text

effectively, including hand-written,

typed, multimodal and digital text

- solve puzzles and brainteasers - apply knowledge about grammar

to the analysis of sentences/

clauses

- research primar y and secondar y

sources


works

- read non-fiction/factual texts,

including text books, reference

materials, newspapers, journals,

current affairs

- apply reading strategies e.g.

reading for the main idea,

skimming, scanning

- review and respond personally

and critically to the writing of

others

- prepare for assessment




The Domain of Self-Expression

Spoken language Written language and multimedia

Reading

English for self-expression

- follow and give instructions related to a range of techniques

for creative expression

- read aloud as performance for a

range of audiences

- par ticipate in acting exercises

and the reading of scripts

- perform in videoed stories,

plays, dramatis personae

- perform poetr y and songs

- discuss ar tworks with others in

groups and seminars

- communicate with ar tists,

specialists and others involved in

creative industries in the

community

- take notes on aspects of literar y texts, including setting, character,

plot, atmosphere, themes, motifs,

symbols

- keep a journal/creative diar y to

record personal responses to

ar tworks

- write creatively in a range of genres

- prepare stor y boards and scripts for

plays and videos

- write poetr y and song lyrics

- write captions and synopses for

ar tworks and exhibitions

- write reviews, analysis, interpretation

and criticism of artworks

- prepare projects related to creative

expression, past and present

- read creative writing across a range of genres and media

- read scripts, poetr y and other

language for performance

- recognise aspects of literary texts,

including themes, motifs, symbols,

figurative language (analogy,

metaphor, simile), characterisation,

imagery, mood and atmosphere,

point of view

- analyse the style of a literar y or

other ar t work

- read and evaluate responses of

others to creative expression/

ar tworks, including own creative

work

- read reference works and

criticism related to creative

expression, past and present


The Domain of Preparation for Adult Life and Contemporary Culture

Science (integrated into Occupations)

- follow and give instructions and demonstrations related to

science experiments and

projects

- par ticipate in discussions and

problem-solving exchanges

- present at seminars and at

community events

- communicate with exper ts,

specialists and others involved in

science and technology in the

community

- par ticipate in debates and

performances related to issues

in science and technology

- par ticipate in quizzes

- use the vocabular y of science effectively

- take notes from talks, lectures and

reference material

- write summaries and outlines

- record data in journal/diar y

- prepare laborator y and research

repor ts

- write scientific explanations

- write analytical essays

- prepare multimodal and multimedia

project presentations, that include,

for example, maps, graphs,

diagrams, char ts, timelines

- consult a range of primar y and secondar y sources

- evaluate the credibility, reliability,

and accuracy of sources

- read published reference and

text books and ar ticles as well

as work produced by peers

- sur vey and evaluate a range of

positions and opinions taken on

issues in science and technology

History/Humanities

- par ticipate in discussions and seminars

- deliver spoken presentations at

seminars and community events

- communicate with exper ts,

specialists and members of the

wider community

- par ticipate in debates and

performances related to histor y

topics

- par ticipate in quizzes

- take notes - keep a journal/diar y

- write essays, ar ticles and proposals

- write to recount and account for

historical events

- write to persuade

- present research/projects in

written, multimodal and multimedia

form

- research a range of primar y and secondar y sources

- evaluate the credibility, reliability,

and accuracy of sources


works related to the study of

histor y

- read text books, reference

books, newspapers, journals,

websites

- review and respond critically to

the historical writing of others

- sur vey and evaluate a range of

positions and opinions taken by

writers on issues in histor y and

current affairs



Here is a sample lesson plan demonstrating scope and sequence for a

Humanities unit:

Humanities Project: Early Agriculture – The Incas

The project is initiated by a group of students with an adult guide, and the

input of other specialists as needed. The project would span one school term.

Goals

Engagement to inspire wonder in a past civilisation and the relics it leaves behind today

Key Concepts/

Mastery

− to experience the Incan culture as an early agricultural, complex social structure − to understand that the ways in which early agricultural societies developed was affected

by the natural environment and their understanding of their place within the

environment

− to understand that the Incan people made use of limited resources in enterprising ways in order to meet their fundamental human needs

Skills − take notes from lectures and presentations − make oral summaries of key ideas for the group

− develop public speaking and presentation techniques

− develop dramatic performance skills

− write summaries of key ideas from readings

− take notes for research using a variety of frameworks

− prepare and draft a research paper

− choose relevant readings from a variety of texts, including multimodal texts

− use referencing conventions and prepare bibliographies effectively

− develop skills in public speaking

Work Manage-

ment

− use work time effectively without disturbing others − manage paperwork effectively

First Period of the Project

In this period students participate in introductory activities that open up the

topic and key concept lessons.

The first period of the Incas project might include introductory activities such

as the following:

• introducing to concepts

• building vocabulary

• initiating the challenge

• eliciting students’ areas of interest and ideas for problem solving

• connecting the project to a micro-enterprise in the adolescent community

• telling an Inca creation story

• watching a DVD: Lost Civilisations: Macchu Picchu


Students then pose one or more key questions. The key questions for the Inca

project might be:

What was it like to be an everyday Incan?

How was such a large empire so quickly overrun?

What were the similarities and differences between colonization of South

America and colonization of the United States?

The answer to these questions determines the key concept lessons to follow.

Below are a series of key concept lessons that might be presented in the first

period of the Incan project.

Lesson Title Description

Lesson 1 Orientation in space and time: South American

Students design a timeline of the Incan stor y and create a map to show boundaries of Incan

empire.

Lesson 2 Incan government & social structures Students discuss the running of a large empire, - its necessar y structures, its difficulties - and

compare with the running of modern nations.

Lesson 3 Quipu recording system Students discuss the lack of alphabet and the use of different systems of recording and

remembering.

Lesson 4 Incan agriculture Students explore the methods of farming and the types of domesticated plants and animals of

South America.

Lesson 5 Pizarro and the conquest of the Incas Students read accounts of the conquest and present a seminar to discuss the topic.

Further activities might include:

• making connections with the adolescent community, its land and micro-

enterprises, for example, the growing of vegetables originating from South

America such as corn, potatoes and tomatoes

• cooking using ingredients originating from South America e.g. Quinoa salad,

chocolate

Students will be provided with a range of resources to explore the key concepts

and the discussion question further. These will include a range of reference and

research materials (paper-based, digital, web-based, multimedia).

During the first period of the project students build a shared specialised

vocabulary to talk about the topic. This vocabulary might include:

• Inca, Coya, Amerindians, Sapa Inca

• Quipu, Curaca

• Francisco Pizarro, Atahuallpa, civil war

• Macchu Picchu, Camayoc, Tahuantinsunyu

• llama, alpaca, Quecha, Cuzco



Second Period of the Project

The second period of the project includes whole group and individual

explorations and activities engaging in enquiry, research, dialogue with

experts, experimentation, field trips and practical activities. Second period

explorations and activities might include the following:

Activity Title Description

Activity 1 Map of South America Students create a 2D or 3D map of South America, showing topography, current political borders and extent of Incan

empire.

Activity 2 Incan time measurement; Incan number base system

Students measure time taken to boil a potato and use their results to recreate their daily timetable in the Incan number

base system.They discuss use of different base systems in

different periods of histor y.

Activity 3 Ar tefact creation Students create ar tefacts using clay, based on the type of ar tefacts found in Inca ruins.

Activity 4 Cooking Students create a salad using corn, quinoa and hot chocolate.They discuss traditional foods.

Activity 5 Drama Students are given small scenes to recreate using the information they have gleaned through research and

concept lessons.

The students then undertake individual research tasks of their own choosing

related to the project.

Third Period of the Project

During the third period of the project students demonstrate their knowledge

and mastery of the topic through tasks such as the following:

Spoken language

• prepare a monologue delivered by Pizzarro, Sapa Inca or an Incan layman

• perform a play or mime recreating the story of the conquest

• perform a play recreating ‘day in the life of’ an Incan

• perform an interview between Pizarro and Sapa Inca

Written language

• end of unit quiz

• providing definitions

• research project on how the Incas met their fundamental needs (e.g. food,

architecture, medicine)

• compose a narrative based on Incan legends and information about Incan

culture

• recreate the journal of a Spanish conquistador or of a vanquished Incan


Creative expression

• create an archaeological ancient artefact, or musical instrument or artwork

• prepare a dramatic production of conquest or daily life of Incans

DPMSS will require classroom materials including a well stocked

laboratory to handle high school chemistry, biology and physics, reference,

non-fiction research books and fiction books for the library, literacy books, and

classroom materials to allow for the instruction of a wide variety of

Occupations, US history, Civics, Economics, A.P. World History, A.P.

Environmental Science, A.P. Biology, Advanced Algebra, Geometry,

Trigonometry and Calculus, A.P. Spanish and A.P. Language Arts. DPMSS will

also require access to an on-line math program for every enrolled student plus

a wide variety of math resources.

Non-typical expenses will include materials to build and maintain an

urban farm, including a water system. One very successful Occupation in other

Montessori adolescent programs is a culinary arts program that provides lunch.

Compass Montessori is its own School Food Authority and provides lunch for

the entire 330 student Golden campus. If DPMSS is able to work with the DPS

lunch program to create a similar opportunity, that would be ideal. DPMSS will

also require a complete set of Montessori materials equal to one large

classroom in an upper elementary setting at a projected cost of $8,000.

DPMSS will use proceeds from the performance school start up grants (as

evidenced in section V. Finance) to purchase the typical and non-typical

classroom materials and technology. DPMSS will set up a replacement schedule

to make sure that classroom materials are replaced in a methodical manner and

that school technology is updated every three years.

In the September 28, 2006 issue of Science Magazine, Angeline Stoll

Lillard published findings of Montessori education study with the following

conclusion: Comparing outcomes of children at a public inner-city Montessori

school with children who attended traditional schools indicates that Montessori

education leads to children with better social and academic skills.

In 2003, Dr. Kevin Rathunde published a study titled “A Comparison of

Montessori and Traditional Middle Schools: Motivation, Quality of Experience,

and Social Context.” With the help of co-investigator Mihaly Csikszentmihalyi,

Dr. Rathunde compared the experiences and perceptions of 150 middle school

students in Montessori and 150 middle school students in traditional schools

using the Experience Sampling Method (ESM). The ESM statistical procedure

allowed Dr. Rathunde to determine, in an objective manner, whether there were

significant differences between the two groups of students (Montessori and

Traditional) and to adjust or “control” for any differences that were due to other

factors such as background variables.



The statistical analysis revealed that there were strong differences between the

Montessori and Traditional students. The differences included:

1) Montessori students reported a significantly better quality of experience in

academic work than the traditional students,

2) Montessori students appeared to feel more active, strong, excited, happy,

relaxed, sociable, and proud while engaged in academic work,

3) Montessori students enjoyed themselves more, they were more interested in

what they were doing, and they wanted to be doing academic work more than

the traditional students,

4) Montessori students reported significantly higher percentages of

undivided interest, higher motivation and higher levels of importance with

regard to schoolwork,

5) Montessori students reported more conditions where the challenges and

skills used while doing academic work were above average.

ACARA (Australian Curriculum Assessment and Reporting Authority)

established an extremly rigorous recognition process to determine the extent

to which a well-established alternative national curriclum can deliver

comparable educational outcomes for students to those based on the

Australian National Curriculum. In 2011, ACARA advised that the National

Montessori Curriculum aligns with the Melbourne Declaration on Educational

Goals for Young Australians, meets the particular principles and guidelines in

relation to the Shape of the Australian Curriclum v3 paper, and allows for

broadly comparable educational outcomes in English, mathematics, science and

history by the end of year 10. The complete curriculum alignment has been

published in the NAMTA Journal, Volume 37, Number 1, Winter 2012.

B. Alternative Benchmark Assessment Program

At the beginning of the school year, students’ math skills will be assessed

via the on-line math program’s assessment tools. One example of an on-line

math program is Renaissance math and their STAR assessment. DPMSS will

review the current on-line math offerings during its planning year to

determine which program is the most successful and most compatible with the

Montessori program. Students will take weekly and end of unit on-line

assessments which are summarized within the on-line program. Teachers will

check student progress weekly to determine what math lessons students need

in order to continue making appropriate progress for that particular student.

Teachers will incorporate Montessori math materials along with more

traditional math instruction techniques during math lessons.

Also at the beginning of the year, students will receive the DRA -2 to

determine reading levels. The principal, working with staff, will review this data


to determine what areas each individual students requires assistance in order

to continue to make adequate progress with reading. Students will be allowed

to choose their own literature books from a list provided by the school. Staff

will then work with students to make adequate progress in all aspects of

reading, including vocabulary, literary technique and structure, reading

elements, and the ability to analyze text. Reading instruction will occur via

literature circle, seminar and book clubs. During the first year, staff will

administer the DRA-2 again half-way through the year and at the end of the

year in order to obtain data on effective reading instruction. Staff will continue

to use the DRA-2 for new students and students who are demonstrating

difficulty with reading as observed in seminar and literature circles, previous

DRA-2 assessments and State assessments.

The third assessment students will complete at the beginning of the year

is a writing assessment. Teachers will review the student’s written work using a

rubric based on Colorado Academic Standards for that grade level. Teachers will

identify what small group instruction each student requires, and place that into

the schedule. Students will be required to complete writing assignments

throughout each Occupations. Teachers will review progress, again based on

the CAS rubric, and continue to develop lessons plans for each individual

student. DPMSS will use the 6 +1 Trait Writing Curriculum as a guide for lesson

development.

At all times, the expectation is that students will be working at or beyond

grade level as determined by the on-line math assessments, the DRA-2, and

the writing rubric. If students are not working at grade level, staff will create a

lesson plan to bring students to grade level. That lesson plan will be a part of

that individual students junior or senior high portfolio.

Every month, the principal will review student portfolios to determine

percentage gained regarding achieved benchmarks. The principal will also

review data compiled from the on-line math program, the DRA-2, the rubric -

measured writing samples and mastery assessment scores created by each

teacher for their Occupations. Because the school will only have 50 and 65

students in its first two years, the principal will be able to take a very hands on

approach to data review. As the school gets larger, some of these duties

regarding individual student data management will transfer back to the

program directors, and the principal will focus on overall school data trends.

This data will be reviewed monthly with the SAC Committee. Individual student

performance will be presented to parents during two parent/teacher/student

conferences per year. At these conferences, students will walk their families

through their portfolios. Teachers, students and families will then discuss

student achievements, student challenges, and create goals for further

progress.



Once State assessment data and SPF are released after year one, the

principal will review data based on prioritized benchmarks. The principal will

identify gaps in DPMSS achievement as compared to other DPS schools and

state averages. The principal will work with staff to determine causes for these

gaps and identify small group Montessori lessons to improve student

achievement.

Here is an example of the portfolio that will be used for the junior high

program. This is excerpted from the Compass Montessori Farm School

Portfolio. DPMSS will create similar junior high and senior high portfolios based

on CAS benchmarks.


Outcome One Is an experienced thoughtful writer and reader, adjusts use of spoken,

written, and visual language, to respond to the needs of society, to acquire new information and

for personal fulfillment.

Mastery Works

WRITING

! Utilizes effective writing process in a variety of genres such as:

o Letters ! Lesson: ! Work Sample

o Expository essays ! Lesson: ! Work Sample

o Process Analysis essays ! Lesson: ! Work Sample

o Narrative Essays ! Lesson: ! Work Sample

o Experienced research writer ! Lesson: ! Work Sample

o Writes detailed papers on topics relevant to study

! Lesson: ! Work Sample

o Uses a variety of reliable sources and cites appropriately, avoiding any use of plagiarism, using MLA format inside text and on bibliography


o Writing reflects a scholarly tone ! Lesson: ! Work Sample

o Discerns pertinent information from sources


o Synthesizes information to form original thoughts, supports thoughts with examples


! Uses journaling/reflective writing for self- expression


! Writes in a variety of creative styles such as, poetry, journalistic, storytelling/fiction


! Additional Six Trait Skills :

o Writes with voice ! Lesson: ! Work Sample

o Extends vocabulary skills ! Lesson:

! Work Sample

o Effectively uses the editing process ! Lesson:

! Work Sample o Utilizes conventions in writing

(grammar & punctuation) ! Lesson: ! Work Sample

READING ! Reads for recreation

o Book List

! Reads a variety of styles; fiction, non-

fiction, autobiography, biography, poetry o Book List

! Able to answer factual, interpretive and

evaluative questions based on assigned reading


! Synthesizes information to form own

thoughts/opinions ! Lesson: ! Work Sample

COMMUNICATION ! Write a narrative essay describing a situation

where you used your best communication skills this year. o Can communicate effectively in a

variety of settings and situations to acquire new information, and to self- advocate

o Open minded, flexible thinker o Active listener

! Lesson: ! Work Sample:



C. Alternative Graduation & Promotion Standards

DPMSS high school graduation requirements will reflect the HEAR

requirements including four years of English, four years of Mathematics, three

years of Natural/Physical Science including two lab-based units, three years of

Social Sciences (with at least one unit of U.S. and one unit of World History), one

year of Foreign Language and two years of Academic Electives. Starting in

eighth grade, every DPMSS will develop a personal education plan which will

become part of their junior and then their senior high portfolios. These plans

will be completely integrated with their portfolios to insure students are

receiving 100% of the credits needed to graduate. Occupation curriculum will be

compared to course objectives for traditional classwork to determine

appropriate credit for ninth grade. Tenth through 12th grade classes will have

the same course objectives as traditional schools for the academic areas.

Students will receive grades and transcripts starting in 9th grade.

One additional high school graduation requirement is that all graduates

apply to three colleges or universities. The intention of this requirement is that

all DPMSS graduates are aware that they have the ability to attend college, even

if they are choosing not to attend directly after graduation.

DPMSS is designed to respect stages of adolescent development, and

promotion and retention criteria will reflect this value. Students will be

expected to be promoted within their established class. A key time for

evaluation will occur towards the end of the ninth grade year. If a student is

demonstrating significant gaps in academic achievement, social and/or

emotional growth to the level that they may not thrive in the high school

environment, a conference will be called between the student, their family, the

principal and the student’s advisor to determine if the student should spend an

additional year in the junior high. In high school, if a student is not on track to

meet all DPMSS graduation requirements, the student, their family, the principal

and the student’s advisor will meet to create a plan in order for the student to

graduate. One possible outcome of that plan may be for the student to spend

an additional semester or year at DPMSS until all graduation requirements are

met.

If a student has exceeded graduation requirements before the end of

their 12th grade year, that student will have the option to graduate early or

dually enroll in UCD, Metropolitan State, or another college that offers dual

enrollment. Again, a meeting will be called between the student, their family,

the principal and the student’s advisor to determine the best course of action

for that student.


Compass Montessori High School created graduation outcomes for its

students. DPMSS will adopt the outcomes as a starting point for creating its own

outcomes reflective of is target population. The outcomes are as follows:

Compass Montessori Student Outcomes

Outcome One

Is an experienced thoughtful writer and reader, adjusts use of spoken,

written, and visual language, to respond to the needs of society, to

acquire new information and for personal fulfillment.

Outcome Two

Has developed a mathematical mind: experienced use of the power of

mathematical thinking in problem solving and paradigm formation.

Outcome Three

Is competent and knowledgeable in life sciences, physical sciences and

advancing technology.

Outcome Four

Is economics literate and an ethical entrepreneur

Outcome Five

Is effective and capable of expressing ideas, contributing to a community

of inquiry, actively listening and collaborating

Outcome Six

Is locally and globally aware, well worldly traveled in fact or through

reading of human encounters; historical minded and historically literate

about human history and the human condition.

Outcome Seven

Is physically active, a participant in activities that create mental / physical

challenges that foster whole person development.

Outcome Eight

Is a developing artist, song writer, poet, musician, actor, etc.through

practice, experience in, appreciation for and understanding of the arts.

Outcome Nine

Is aware and knowledgeable of self-construction and actualization; has

an immense sense of humor and an ingenious love of learning.

When our high school students have achieved these outcomes, the result will be

graduates, regardless of ethnicity or income status, who will be prepared for

college or a career as well as demonstrate ingenuity, adaptability, creativity,

initiative and excellent communication and problem solving skills.



Appendix F

Evidence of Support


N· A· M · T·A

13693 Butternut Road

Burton, Ohio 44021

tel 440.834.4011

fax 440.834.4016

[email protected]

www.montessori-namta.org

March 19, 2012

Katy Myers

10923 Magnolia Dr.

Apt. B,

Cleveland, OH 44106.

Dear Katy,

Montessori Development Partnerships and the North American Montessori

Teachers' Association have authorized a cash grant of $3000.00 in start-up

funds to be used primarily for Montessori consultancy and services from

Project 2012. Services in kind constitute an additional $5000 in honoraria

donated from David Kahn and Laurie Ewert-Kroeker (and others) in providing

on-site programming and materials for the project. The $3000.00 will be

disbursed in June.

We have elected your program for sponsorship because of our faith in your

history of making Montessori secondary programs work, especially

demonstrated in the viability and authenticity of Compass Montessori School

located in Golden, Colorado. Having had contact with Montessori High

School at University Circle and Hershey Montessori School Farm Program,

we are hoping you adopt some of our successful curriculum design and

orientation creating a unique blend of school cultures that will inevitably lead

the country in Adolescent work.

With best wishes for Denver Public Montessori Secondary School.

Si 0 k:t..._ David Kahn Executive Director, NAMTA

Executive Director, MDP

ein affiliation with the Association Montessori In temarionale-Amsterdam, Netherlands



http://www.montessori-namta.org/



From Katy Mattis, incoming Principal of Denison Montessori.

Montessori Secondary Program

Mattis, Kathryn <[email protected]>

Thu, Mar 1, 2012 at 1:05 PM

To: "[email protected]" <[email protected]>, "Fowler, John"

<[email protected]>, "[email protected]" <[email protected]>,

"Vincent, Frank" <[email protected]>, "Reina-Ayadi, Yamile"

<[email protected]>, "[email protected]"

<[email protected]>

Hi Everyone,

I apologize for not replying sooner, I have been in my own whirlwind of

interviewing to be Denison’s next principal, hopefully, I will know soon if this

dream is to become a reality.

I just wanted to give my feedback on a DPS secondary program and on why Katy

Myers is the perfect person to take this on. As a DPS upper elementary teacher

(Denison--2002-2007) and a Peer Observer (currently), I have seen a very

strong commitment to Montessori within DPS. The size of the program

continues to increase and the Montessori programs that currently exist are

constantly striving to provide authentic Montessori experiences to Denver’s

diverse students.

As an upper elementary teacher, my classroom was significantly impacted

by the loss of 6th graders to middle school

programs with competitive enrollment processes that start in 6th grade. I know

this continues to be a struggle and 2

DPS Montessori schools deal with it by not having 6th graders. Since everyone

in this e-mail is a Montessorian, I will not dive into the challenges that this

presents to authentic Montessori except to say one of my trainers once

described Montessori as creating many dangling ribbons that are neatly tied in

a bow in the 6th grade.

I am so excited about the prospect of there being a true Montessori

secondary program in DPS and I can’t say strongly enough that Katy Myers is

THE person to take on the process of making this happen. I had the pleasure

of working with Katy at Compass Montessori School, a Jeffco charter that serves

students from age 3-18. Katy is a founding parent of Compass and has vast

experience with taking a Montessori school from its infancy through maturity.

This “growing up” was most profound at the Secondary level, largely because

when she was taking this challenge on, there were no public secondary

Montessori programs. Compass is a world leader in both public and private

Secondary Montessori Education.












In the years that I was at Compass, I watched the farm school grow into a

program that truly supports Montessori’s vision of an Erdkinder. Katy was

fundamental in this growth. The current program has the students engaged in

authentic occupations with the work on the farm being a vital part of the

students’ learning. The middle school students prepare (the most delicious)

lunch for ALL of the students and staff every day! (I strongly encourage all of

you to visit Compass—Golden and make sure you get a lunch invitation!) This

authentic, purposeful work creates middle school students who are passionate

and focused. I would love if DPS could provide this continuation to its students.

Katy’s knowledge of the successes and (possibly more importantly) the

mistakes that Compass made in creating an occupation based, high achieving,

Erdkinder is what makes her the best person to get this program started in DPS.

Katy has not worked in DPS so will need the support of DPS’s Montessorians.

Unfortunately, Katy isn’t in Colorado, and can’t convene a meeting with all of us

to tell us her vision in person. Katy is in Cleveland working closely with

David Kahn. Katy and David have worked together for many years and has the

support of one of the experts on Montessori secondary education (and public

Montessori education.)

As a leader, Katy is an inspiration. I consider myself lucky to have worked with

her. She has a way of creating a vision and then making it happen, she is not

someone who backs down from a challenge, nothing is impossible! (As I think

we can all see by her willingness to take this on with such a short turn around

time!) Most admirable is her ability to gather her staff around her to create a

common vision. I have spoken to Katy about this project and she is as

passionate about making this happen as I have ever heard her. She has my

support 100%.

Lastly, when I was in the classroom, I had several students go to Compass, even

though it was miles from their homes. I am convinced that if there is a

Montessori middle school offered within DPS, students and parents will leap at

the opportunity. I look forward to working with Katy and you on this project.

Sincerely,

Katy Mattis


Spearman, Janice <[email protected]>

Sun, Mar 4, 2012 at 6:22 PM

To: Katy Myers <[email protected]>, "[email protected]"

<[email protected]>, "Trujillo-Hays, JoAnn" <JoAnn_Trujillo-

[email protected]>, "Fowler, John" <[email protected]>, "Vincent, Paul"

<[email protected]>, "Hamilton, Beth"

<[email protected]>, Kathryn Mattis <[email protected]>,

"Escalante, Alonso" <[email protected]>, "Vincent, Frank"















<[email protected]>, Laurie Ewert-Krocker

<[email protected]>, "Reina-Ayadi, Yamile" <YAMILE_REINA-

[email protected]>

Cc: David Kahn <[email protected]>, "Hairston-Brown, Tunisha"

<[email protected]>

Hi Katy,

Tunisha Hairston-Brown is one of our Primary teachers and she has wonderful

things to say about you and your work at Compass Montessori. Based on her

information about you to our staff, I believe that our Montessori teachers will be

happy to support your efforts. I also offer my support.

Janice

Janice Spearman

Principal Lincoln Elementary School

Secondary Program

Vincent, Frank <[email protected]>

Thu, Mar 1, 2012 at 2:27 PM

To: Katy Myers <[email protected]>, "[email protected]"

<[email protected]>, "Fowler, John" <[email protected]>, Kathryn

Mattis <[email protected]>, "Reina-Ayadi, Yamile" <YAMILE_REINA-

[email protected]>

Cc: David Kahn <[email protected]>

Katy and all,

I just finished our State of Colorado Review and Interview in preparation for our

Federal Audit coming up soon. TINFL as you know, so we have to have paper

documentation for everything going back two years. That stack took many

hours, is several inches high, and still is not quite complete. Therefore, I have

not been answering all my email lately. We have TCAP testing starting next

week as well, and with all the accommodations it is a scheduling nightmare. I

issued an edict and a prayer that no one is sick next week, child or adult. We’ll

see if that works.

High school could be a strong draw for students and parents who want an

alternative to current offerings, and to those who are concerned about their

child’s continuance in the Montessori program. I am a little concerned

about the potential effect on the 6th grade possibilities at both Gilpin and

Lincoln. Maybe we could transition it backwards in the future and get our 6th

grades that way. In any case, I can’t do anything about it this year. So we

support your work, and are willing to do whatever we can to help.

















(I don’t have a trainer just yet, but am still working on it.)

Frank A. Vincent,

Principal Gilpin Montessori Public School


Trujillo-Hays, JoAnn <[email protected]>

Tue, Feb 21, 2012 at 12:33 PM

To: Katy Myers <[email protected]>

While I applaud your efforts, this is not something in which I am able to be

involved. I am retiring at the end of this school year and then working next

school year to assist with the transition to new leadership. My time will be very

limited and I am not willing to take on a new endeavor at this point in my

career. I do wish you the best.

From Dr. Martha Urioste, founding principal of Mitchell (now Denison) Montessori School.


[email protected] <[email protected]>

Sat, Mar 3, 2012 at 10:57 AM Reply-To: [email protected]

To: Katy Myers <[email protected]>, [email protected],

[email protected], Paul Vincent <[email protected]>,

[email protected], Kathryn Mattis <[email protected]>,

[email protected], Frank Vincent <[email protected]>,

[email protected], Laurie Ewert-Krocker

<[email protected]>, "Reina-Ayadi, Yamile" <yamile_reina-

[email protected]>

Cc: David Kahn <[email protected]>, Deb Silvas <[email protected]>,

Ellie Nichols <[email protected]>

Dear Katy, your positive vision is so encouraging and refreshing! I have been

contacted by AMI Virginia McCue to assist with Colorado Advocacy so it may be

a good idea to include her in the information sharing. Also, monthly, AMI

teachers meet and I gave and ESF presentation there in December-can include

Ellie Nichols-who is leader and with information sharing and meetings-etc. . . I

agree with JoAnn about "dual-language" . (Second language program). Adding

Deb Silvis-Family Star Montessori Coordinator will also work. Shared leadership

and positive vision and action works! Our students will benefit from a holistic

alternative and your efforts-along with David Kahn's support reminds is so

appreciated because it has the potential of greatness of Maria Montessori

vision!

Thank you!

Martha

























Escalante, Alonso <[email protected]>

Mon, Feb 20, 2012 at 8:59 PM


Hi Katy, I believe this is an exciting possibility for our kids. However, at this

time I cannot help out on the committee. I will forward your email to the two

Montessori peer observers who might want to participate on the committee.

Thanks, Alonso

Montessori Secondary Program [email protected]

<[email protected]> Wed, Mar 7, 2012 at 9:04

AM


Hi Katy, My name is Ellie Willis. About 3.5 years ago,I began a Colorado AMI

support group for all AMI diploma holders. We usually meet about 9-10 times a

year. Some of the meetings are closed to AMI diploma holders and others are

open (most often when we have a tour of a school) for any educator who is

interested in Dr. Montessori's method.

I had heard about your incredible school from a few members of the group

(Lara and Katy) and was fortunate to see some of Compass a little over a year

ago.

I am really excited about your new direction in creating another public

Montessori school for the older "grades" and having it be coupled with the arts.

I have a small start up school in Boulder and would love the opportunity to

meet with you, at any time in the coming year, to ask you some questions

about expanding my school from an IC to also include a Primary. Please

continue to send me information about what you are creating in Denver, I am

happy to pass it along to the members of the support group and would also be

delighted to help in any way possible.

Have a wonderful day,

Ellie

303-882-5468 www.rosemontessori.com


Reina-Ayadi, Yamile <[email protected]>

Sat, Mar 3, 2012 at 1:19 PM


Dear Katy,







http://www.rosemontessori.com/




Congratulations on this first step! I will look at data: State and District School

Performance Frameworks, CSAP (TCAP) and enrollment numbers. Also I don’t

know if it would be appropriate I could talk to parents for example at Denison

that have older children (UE) to feel out some key parent engagement from

Denver. Let me know.

Yamile Reina

School Improvement Partner (cell- 720-939-7583) Region 1 - Northwest

Elementary Education Division

From Virginia McHugh, Executive Director of AMI / USA


Virginia McHugh <[email protected]>


Dear Katy, How exciting! Thanks for keeping me in the loop!

Virginia

Association Montessori International/USA

410 Alexander Street Rochester, NY 14607

[email protected] www.montessori-ami.org www.amiusa.org

585.461.5920

From Judith Orion, Director of Training, The Montessori Institute Denver

M. secondary school

Judith Orion <[email protected]>

Sun, Mar 4, 2012 at 2:35 AM

To: [email protected]

Dear Katy,

Though I am not on your email contact list, I heartily support your efforts. I am

out of the country most of the academic year, and training full-on during the

summer at The Montessori Institute (0-3 training). I just wanted to offer my

support though I am unavailable to be actively supportive.

I would love to be on your email list just to remain in touch with what is

happening. I am part of a team that is actively working with DPS to bring AMI

3-6 training to Denver beginning in the summer of 2012 or 2013 (more likely).

Enjoy the remainder of your elementary training. Regards to Greg.

Judi Orion





http://www.amiusa.org/






Hairston-Brown, Tunisha <[email protected]>

Tue, Mar 6, 2012 at 4:47 PM

To: "[email protected]" <[email protected]>

Hello Katy!

I was thrilled to see your email and interest in starting a Secondary Montessori

Progam in DPS!! It was an easy decision to endorse and offer 100 % support for

your efforts. I sent my colleagues an email describing my excitement at the

prospect of an Montessori Secondary Program in DPS, and also expressed my

full confidence in your leadership in this venture. Thank you for stepping up

to this challenge. If I can help in anyway please let me know. I would love to be

added to your distribution list regarding the application process.

Thanks, Tunisha


Kraft, Debra <[email protected]>

Tue, Apr 3, 2012 at 10:20 AM


Thank you for your tireless efforts Katy. It is most certainly a huge work and

very much appreciated by all of us. Although I have been extremely busy (I am

in school at night), I am happy to serve the process in the areas of my expertise

and would make myself available to you should you need me. I just finished one

large part of my night school training, so I am a bit more available now if you

should want to request anything from me... Please do not hesitate. My direct

line is listed below and my cell phone is 303-968-9304.

Debra Lucero Kraft Administrative Assistant

Gilpin Montessori Public School







Appendix G


Job Descriptions and Self-Governance Model

School Principal Job Description

Qualifications

Montessori Training (AMI or AMS)

Adolescent orientation or Training

Masters Degree in Education Administration and Supervision

Key Responsibilities:

1. Promote School Mission:

•Design, implement and evaluate school-wide policies, programs and

practices, which are consistent with Montessori philosophy

•Create and foster a culture of high expectations regarding behavior and

academic achievement

•Create clear lines of communication and levels of involvement with

committees, staff, students, parents and community members

•Create and foster a welcoming environment

2. Provide Leadership and Long Range Planning:

•Promote a unifying vision

•Establish clear and achievable goals and objectives and evaluate progress

towards goals on a regular basis through a participatory, long range planning

process

•Provide leadership with the School Accountability Committee, teachers, staff,

students, parents, and community members

3. Coordinate and Direct Curriculum and Assessments

•Ensure Authentic Montessori curriculum is established and maintained

•Ensure Denver Public School and Colorado Academic Standards are met and/

or exceeded

•Create, implement and evaluate the use of appropriate classroom, school-

wide, district and state assessments



•Work closely with school-wide committees, School Accountability Committee,

district and state on issues related to curriculum and assessments

•Review data on an ongoing basis. Create data based monthly reports on

academic progress, achievements and challenges for School Accountability

Committee.

•Create transparency regarding school achievement and mechanisms to

communicate the school’s academic progress, achievements and challenges to

all stakeholders.

4. Develop and Implement Policies

•Develop, implement and evaluate school-wide policies

•Implement District policies and state legal requirements

•Create school policies for any district and state policies and laws that have

been waived.

5. Supervision of Employees

•Ensure that all staff hired are qualified and have appropriate training /

licensure for their position.

•Create and evaluate high quality staff professional development.

•Provide regular, on-going written, evaluations to all professional teachers

that includes monthly observations and is based no less than 50% on

measurable data.

•Provide regular, on-going evaluations to paraprofessional staff

•Ensure clear lines of communication concerning job expectations and

individual performance

•Provide opportunities for professional growth and renewal

6. Manage Financial and Facility Operations

•Develop and maintain an accurate budget and reporting mechanism for the

SAC and School District

•Ensure expenditures are appropriately approved and prioritized

•Maximize revenue sources without compromising policies, programs and

general school wide vision

•Provide leadership and coordination of school facility improvements and

expansions

•Ensure facility maintenance services are arranged


Program Director (Junior or Senior High)

Qualifications

Montessori Training (AMI or AMS)

Adolescent orientation or Training

Coursework in Master’s Level Education Leadership Program

Responsibilities Overview

Able to strategize with team members and principal on evolution of program.

Create and maintain strong relationships with all members of the self governing

team. Cultivate and maintain the collaborative relationships between the

various school departments and programs. Maintain consistent strong

relationships with parents and students in order to actively manage issues of

behavior and discipline before the point of escalation. Support and develop

governance and autonomous learning of team including discussion with

principal and meetings regarding all aspects of the program.

Support for guides and learning environments

• Teacher Development

• Self Assessment

• Peer Evaluation

• Defining and developing the role of the adult in this Montessori

environment

• Aware of the flow in the schedule and building

• Assessment support

• Consultation with parents on transitions

• Monitor effectiveness of parent communication with team

• Support and mediation for Guides with escalated parents

• Address student discipline outside of advising

• Initiate parent follow-up on behavioral issues

Working with the School Principal

• Communicate all aspects of the program including vision and

sustainability

• Observe and understand other Montessori secondary program design and

development

• Report to principal on discipline

• Referral to principal of all Code of Conduct violations

Actively communicate with and support team members in their work of:

• Curriculum Development

• Prepared Environment

• Community Expectations



• School Culture

• High academic expectations

• Local overnight trips

• Aware of flow in schedule and building

• Student Assessment

• Staff reflection and accountability

Actively support advisors in

• Portfolio use and development

• Consultation for transition

• Parent communication on classroom and advisory issues



Self Governance Model

DPMSS will instill a leadership model centered on self-governing teams, program

directors and the school principal. The intention is to allow leadership to manifest from

“the ground up” versus “top down”. This specific model was developed at Compass

Montessori school using best practices from other teacher centered leadership models.

Success of this model depends on creating healthy balance and regular communication

between self-governing teams and the head of school along with utilizing the program

directors to keep our self-governing teams evolving.

Self governing teams always operate in an open welcoming forum. If other staff members

or the principal chooses to join the self governing meeting, they should be able to do so

easily. Our visual on this concept is the perforated circle versus a closed circle. Our proven

experience is that closed circles build walls that become very difficult to tear down.

Perforated circles foster open communication and healthy organization.

Program Director Role:

• Insure meetings are happening

weekly

• Set Agenda with input from team

Send notes to principal or insure notes are

sent to principal

Keep meeting on track

• Take notes or insure notes are being Insure four focus points are being regularly

taken addressed by the self governing teams:

Accountability, Logistics, Montessori

Theory, Problem Solving.

Freedoms:

• To set your own schedule and yearly events

• To solve problems that are occurring within your level

• To explore Montessori theory as it applies to your level

• To determine how to hold each other and students accountable.

• To participate in the hiring of any new team members.



Limits:

• Our core value is creating an

authentic Montessori program. Any

Montessori theory should be a central,

consistent part of every self- governing

decision making must have this core meeting.

value at its center.

• Self-governing teams need to meet

at a minimum of once a week in

order to fully realize the benefits of

this type of school leadership.

• Any scheduling or events that affect

other teams have to include

discussion with the other teams and

the program directors / head of

school. Scheduling that involves

hiring people must involve the

Principal early on to see if this

makes sense from a budget and

school wide perspective.

• Any problem solving that could

escalate should include program

directors / principal so that we are

informed and prepared to support

you.

DPMSS’ school wide accountability system

is the foundation of student accountability.

This includes our Student Outcomes,

Student at a Glance Cards, Farm School

Portfolio, H.S. Albums, and Sub-plane Exit

Outcomes.

Holding each other accountable to creating

authentic Montessori classrooms along with

high expectations of students, ourselves and

each other is a core part of the self-

governing team. The team needs to

determine early in the school year how best

to bring up sensitive topics and address

concerns.


Appendix H

Resume

Curriculum Vitae

Katy Myers

1900 East St. Golden, CO 80401 303.431.2385 Cell

Professional Summary

• Visionary with excellent strategic planning abilities and who can create and execute tactics that result in success

• Demonstrated Leadership

• Strong Communication Skills – both written and verbal • Excellent Financial Management Skills

Experience Head of School, 2005 - 2011

Compass Montessori School; Pre-K through 12th Grade Public Montessori Charter School

Wheat Ridge and Golden CO Assistant Head of School and Business Manager, 2001 – 2005

Compass Montessori School Founding Parent and Chairperson of Steering Committee, 1997-1998

Compass Montessori School

Significant Achievements

· Head of School for public Montessori charter school comprised of two campuses (Wheat Ridge and Golden), Preschool -12th grade, 80 staff and 600 students

· Evolved start up to a stellar Montessori program that meets or exceeds Colorado

State Education Standards.

· Obtained $7.5 million in CECFA facility bond financing and managed the purchase,

design and build of the Golden Campus, which includes a farm, commercial kitchen and was the first public school facility specifically designed for a Montessori secondary program. Managed two school expansions including the design, financing and build process.



· Replaced head of school at the Wheat Ridge campus mid-year 2008 due to financial

upheaval and staff turnover. Within two years improved staff and student retention rates to 95% and significantly improved the campus’ financial stability.

· Grew Compass Montessori Secondary program from 80 students to 200 students.

Compass High School is currently rated high performing and earned the Governor’s

Award for schools with the highest 2009-2010 academic growth rates in Colorado.

· Led staff in the design of an outcomes based Montessori pre-k through 12th grade

education accountability system.

· Created a self-governance leadership model that allows for team decision-making

while maintaining strong partnership and reporting to head of school.

· Successfully renewed charters at both campuses.

· Led the Steering Committee responsible for writing the Compass charter, purchasing

the original school facility, hiring founding staff and principal, enrolling 150 founding students and creating the first year operating budget.

· Manage finances for both campuses totaling over $4.5 million revenue.

Presentations Myers, Katy (2010). The Holistic Montessori Environment. NAMTA Adolescent Conference “The Adolescent and Technology: Find the True Balance in the Montessori Prepared Environment”, Keynote presented April 17, 2010.

Myers, Katy (2009). Maintaining Adolescent Montessori Programs in the Public Sector, Montessori Quality and Sustainability – 2009 AMI/USA Public School Forum, November 14, 2009.

Consultations National Association of Charter School Authorizers – Team Lead Evaluator for the State of New Jersey 2011 Charter School application evaluation process and for the Louisiana Department of Education 2011 Charter School application evaluation process. Evaluator for the State of Florida 2008 Charter school application evaluation process.

Colorado Department of Education Charter School Leadership Mentor Program, 2010-2011.

Great River Montessori High School, Minneapolis, MN, 2005

Education Masters of Education, Education Administration and Supervision, Arizona State University,

2005

Concentration: Leadership in Entrepreneurial Education

Thesis: Implementing the Montessori Science Curriculum “Occupations” in a Public

Montessori School; Proactive Action Research Study


Elementary (6-12), Association Montessori Internationale, Montessori Training Center of

New England, Trainer Greg MacDonald.

90% Complete – projected certification date is May, 2012. A Montessori Orientation to Adolescent Studies, North American Montessori Teachers

Association, 2003 B.S, Speech, Northwestern University, Evanston, IL 1986, Majors: Theatre and Economics

Business Experience Qwest Communications, 1999-2001. Real Estate Manager

· Managed a team of twelve real estate acquisition specialists to lease and zone sites

for wireless communication towers within the Mountain Division.

· Worked closely with the construction and engineering teams in order to insure each

project flowed seamlessly from identification to installation

· Managed the real estate accounting and property management employees to insure

that all lease payments were paid on time and accurately, and that all lease

requirements were met in order to prevent any default situations.

· During the years I managed this team, we were the highest performing Qwest real

estate acquisition team across the United States, as measured by established

company performance metrics. Beveled Designs, 1992 – 1999

Owner

· Handled the accounting, sales, accounts receivable, accounts payable, payroll, sales

and employment taxes for this stained glass manufacturing company that I co-owned with my husband.

· Grew company from our garage to an established showroom and manufacturing

facility with annual revenues of $300,000. MCI Telecommunications, 1987 - 1992

Real Estate Manager

· Managed the acquisition, build out and move in of all MCI sales offices and technical

facilities for the Western Division.

· Negotiated commercial leases.

· Audited and managed triple net lease expenses, including calculating CPI increases,

for real estate inventory totaling over $1.5 million.

· Won Excellence in Service award which recognized the top 2% of employees based

on performance.

References Tracy McIlrath, Past Board President and Interim Head of School, Compass Montessori

School; [email protected]

Pat Ludick, Montessori Consultant; [email protected] William Haft, Vice President of Authorizer Development, National Association of Charter

School Authorizers; [email protected].







Appendix I

School Organization Chart

Denver Public

Schools

School

Accountability

Committee

Program

Director

Principal

Office Staff

Program

Director

Junior High

Teachers

Senior High

Teachers

Instructional

Support Staff


Exhibit J


Staff Roster

Year 0

Principal 1

Administrative Assistant 0.5

Year 1 - 50 Students, 6th and 7th grade

Principal 0.5


Teacher who is also ELA-T qualified 1

Teacher who is HQ Spanish and ELA -E qualified 1

Teacher (who is also the Principal) 0.5

Special Education Teacher 0.25

Psychologist / Social Worker 0.2

Nurse 0.1

Farmer (para professional) 300 hours

Wednesday Afternoon Tutors 228 hours

Year 2 - 65 Students, 6th, 7th and 8th grade

Principal 0.5


Teacher who is also ELA-E qualified 1

Teacher who is HQ Spanish and ELA endorsed 1




Nurse 0.1



Year 3 - 105 Students, 7th, 8th and 9th grade

Principal 0.75


Teacher who is also ELA-E qualified 3

Teacher who is HQ Spanish and ELA endorsed 1






Nurse 0.1



Para professional (micro-economy) 315 hours

Year 4 - 140 Students, 7th - 10th grade.

Principal 0.75


Teacher who is also ELA-T qualified 4.5

Teacher who is HQ Spanish and ELA -E 1




Nurse 0.2





Principal 0.75

Administrative Assistant 1


Teacher who is HQ Spanish and ELA-E 1.5




Nurse 0.3





Principal 1


Teacher who is also ELA-T qualified 7.5

Teacher who is HQ Spanish and ELA-E 1.5

Special Education Teacher 1


Nurse 0.3






Principal 1



Teacher who is HQ Spanish and ELA-E 2

Special Education Teacher 1


Nurse 0.3






Exhibit K

Scope and Sequence

This section is excerpted from A National Montessori Curriculum Report

as published by the NAMTA Journal, Volume 37, Number 1, Winter 2012 and

then adapted to meet the DPMSS programmatic requirements.

Because Montessori education is designed in three year cycles, this scope

and sequence represents 7th - 9th grade science and is not broken out by

grade. All students will be expected to complete all the required benchmarks in

all subject areas as spelled out in the Junior and Senior High portfolio. Ninth

grade students work will be judged against high school standards, and only the

work ninth grade students complete during their ninth grade year will be

counted towards their graduation requirements. In order to comply with the 15

page limit, this document will only show detailed scope and sequence for

Science. Scope and sequence for Language Arts, Math, History and Creative

Expression are available upon request. The high school (10th, 11th and 12th)

will not open until 2016. Prior to opening, a complete scope and sequence

based on college preparatory curriculum will be submitted to DPS for approval.

Science Curriculum for Adolescents Aged from Twelve to Fifteen/Sixteen

Science is significantly embedded in the Occupations, or the work of the

adolescent community, which includes:

• practical daily life tasks, including maintenance of the community

environment

• working on and being stewards of the land, including, for example, care

of the natural environment, horticulture, agriculture and animal

husbandry

• contributing to the micro-enterprises of the community

The concept of embeddedness, sometimes referred to as ‘embodiment’, has

some very specific implications both for the preparation of the teacher and for

the design of Occupations. Each Occupation sets up environmental components

around the activities that are tied to related scientific concepts. Water, plants,

animals, botany, rocks, geology, watershed, thermal dynamics and the

transmission of energy, etc. are all embodied in the Occupation and are

inseparable from it. The work of the Occupation, like the Montessori material of

the classroom, limits the scientific investigations to the task parameters of the

Occupation. One does not exceed the task parameters of the Occupation in

order to make sure the learning of science is precisely reinforced by the work

the Occupation requires. For example the limits or task parameters of a ‘Pig


Occupation’ include the care of the animal, its vital functions, and its

physical characteristics, making this predominantly a biological study. However,

the market value of the pig invites an economic study. The pig’s habitat

necessitates a study in space and co-habitation. The nature of the task

determines the nature of the study.

The Occupation is holistic, but two main extensions emerge: One is abstract

scientific knowledge usually discussed before and after the task at hand, and

second is the social life of the community. The work of the Occupation is

undertaken collaboratively. The adult working side by side the adolescent is an

exercise in intergenerational cooperation. From the Montessori point of view,

work of this type does not hinder a student’s study; instead, it enhances the

quality of the study as students have the opportunity to apply their knowledge to

solve problems and to contribute to the community. The Occupations enable

students to build independence to the point where they experience what it means

to be economically independent in society. They also learn that collaboration

between humans ‘results in … a happy social life that will facilitate individual

progress’ (Montessori 1976 [1948]: 113). While working collaboratively on

Occupations that contribute to the life of the community, students are also

learning to discipline themselves and to work toward shared goals.



Occupation Concept Lessons - Delivered over a three year cycle

Scientific Method/Lab Skills Scientific research and the scientific method Using a dichotomous key Using a compound microscope Using the metric system/unit conversion

Basic Biology

Metabolism Cell structure: organelles Plant cells Animal cells Types of cells: nerve cell, blood cell, muscle cell, skin cell, bone

cell Cell division: mitosis/meiosis Microbiology: yeasts, molds, bacteria Food chains and food webs

Chemistry

Atoms and molecules Chemical structure and function of carbohydrates, proteins,

and fats

Physical Science

Solar radiation and electromagnetic waves Earth’s rotation and tilt Radiation and matter: reflection, transmission, and absorption Thermal mass Water cycle and basic weather principles Motion, acceleration, and force Newton’s Laws of Motion Simple machines: level, pulley, wheal, axle, inclined plane,

wedge, and screw Work, power, and simple machines Energy and transformation of energy

Economics Economic models Economic math Supply and demand Budgeting and forecasting Profit and feasibility studies Business ethics

Zoology

Characteristics of mammals Characteristics of birds Systems of mammals: digestive, respiratory, nervous,

reproductive, circulatory, skeletal/muscular (pig, cow, human) Human digestive system Systems of birds: digestive, respiratory, nervous, reproductive,

circulatory, skeletal/muscular (chicken) Classification of mammals: cow, chicken The evolution of mammals: cow, chicken Genetics: role of chromosomes, dominant and recessive traits,

probability of inheritance, Punnett Square Botany

Parts of the plant: leaf, stem, fruit, flower, seed, root Plant processes: photosynthesis, transpiration, translocation Plant classification Genetically modified organisms Hydroponics Archeology/Local History

The history of Huntsburg and Sylvester Clapp Genealogy of Huntsburg families Archeological excavation Handling, identifying, cataloguing, and displaying historical

artifacts Scientists and Scientific Contributions

Louis Pasteur cell biology, pasteurization, disproving spontaneous generation Science and Culture

The cow in history and mythology Factory farms: mass production of meat animals World hunger Food and body image Healthy diets History of greenhouses The biosphere and environmental issues: acid rain, nuclear

waste Tools and humanity: the history of tools and the nature of

humans

! In the Montessori view, adolescents learn by doing. Learning by doing is a

feature of the Montessori Science curriculum. Much of the curriculum is aligned

with the Occupations of the Montessori adolescent community. Occupations are

projects, tasks, and courses of study that arise out of needs of the adolescent

community and local environment. They provide real, meaningful work that aims

at developing a sense of worth in the students because their contributions to the

community are real.

Occupations might be understood as a project. Each project is initiated by

a problem that needs a solution. For example, if the class initiates a micro-

enterprise based on keeping poultry, the need to learn about the biology and


needs of poultry is real. This generates meaningful engagement in the process

of scientific inquiry, in which students identify and investigate key questions

and gather and collate evidence-based conclusions. While each project might

be grounded in one area of the curriculum more than others, opportunities for

interdisciplinary studies are also valued. While the main disciplinary focus of a

project might be on science and mathematics, students might also engage with

knowledge and skills related to language, art, history or geography. As the

projects unfold, students have the opportunity to contact scientists working in

relevant fields, as a source of expertise and as a model for how to conduct

scientific enquiry.

While working on projects, students are able to explore particular topics in

depth. Early in the project students participate in main lessons which outline the

key science concepts needed to engage with the project productively. Students

then work to develop their knowledge, skill and understanding to the level

required to complete the project successfully. While engaged on a project,

students are free to explore areas of science and to develop scientific capabilities

that they find relevant and interesting. In addition, because the projects are

undertaken in real life settings to meet real life challenges, the students also

explore ethical issues relevant to the project. For example, if the students are

working on a project that involves keeping poultry, they might apply their

knowledge of poultry biology and behaviour to debate and explore issues relating

to the relative merits of cage-laid, barn laid, free range and/or organic eggs.

As the project unfolds, students have the opportunity take on different

roles. For example, students whose project involves keeping poultry might take

on the roles relating to farming, using video to keep records or bookkeeping. In

this way, students learn to cooperate to achieve goals shared with others, to

experiment with different Occupations and to demonstrate to themselves and

others that they are able to contribute to meaningful and real life ventures. In

addition, they learn to think about the ethics of science and progress and develop

the ability to make informed decisions about issues that relate to the health and

well-being of themselves, their community and their environment.

The project-based approach allows students to develop science

understanding, and inquiry skills because, in order to complete each project,

students must engage in research and experimentation. The project-based

approach also enables students to understand science as human endeavour. For

example, students are encouraged to explore the genesis of scientific

knowledge and understandings by researching the biographies of great

scientists, past and present, as well as the history of scientific concepts and

ideas. As the projects unfold, students engage in seminars, debates and

discussions about not only scientific knowledge, understandings and skills, but

also the cultural and social issues that need to be taken into consideration

when decisions and problem solving involve science.



As part of the Montessori Science Curriculum for adolescents, students

take part in field trips to observe and collect data and to become familiar with

the ecology of their region. They learn to identify local plants and animals,

whether native, feral or domesticated, and study the ecological systems of the

region, including relations between organic and inorganic elements. Students

also review their knowledge of the systems for organising knowledge in science

and make note of how the knowledge, and terms used are kept current. For

example, they consolidate their knowledge of scientific taxonomies and their

organising principles, as well as features, such as features of anatomy and

physiology, which determine where organisms are placed in a classification

system. Students also use their research skills to track how knowledge about

evolution, and systems such as climate and ecology, is changing and

expanding, and what this might mean for decision makers and humanity in

general.

The aims of the Montessori science curriculum for adolescents aged from

twelve to fifteen/sixteen years include the following:

Science inquiry skills

· to work with scientific data (primary and secondary), including gathering,

recording, storing, collating, interpreting, and repeating investigations

· to represent findings in a variety of forms, including graphs, tables and

diagrams

· to seek elaboration and justification of data and ideas and reflect on

alternative interpretation

· to use principles that will validate and demonstrate personal understanding

of science

· to work collaboratively to undertake laboratory or field science around

reality based activities

· to follow scientific and mathematical procedures to observe, hypothesise,

predict and test in an area of scientific investigation of their own choice.

· to identify potential hazard and design an appropriate investigation to

observe, collect data and present findings

Earth and space sciences

· to create maps and drawings of land-based data (topographical maps).

· to collect, display and interpret data on the geologic and mineral content of

the local soil and through chemical analysis, composition studies and

testing, explaining the historical development of various components

Biological sciences

· to explore and represent patterns and cycles in the natural world

· to create and read biological scale drawings

· to investigate the role of organisms within a variety of ecosystems

· to investigate the local flora and fauna that make up the natural local habitat


· to compare and contrast various ecosystems and their associated functions

in the succession of habitats

· to collect data and track the trends and variability in behaviour of local and

domesticated animals.

Physical sciences

· to investigate physics in the total environment: the Universe, the earth, the

forces that shape the earth, the structure of matter, the transformation of

energy, the motion of things, the forces of nature

· to select and utilise various mechanical devices while testing the models and

patterns of certain scientific laws e.g. conservation of energy

Contemporary sciences

· to design and use apparatus and tools appropriate to meet occupational

challenges

· to maintain small common electrical and mechanical systems, identifying

and eliminating possible causes of malfunctions

· to compare and contrast the design, functionality and structural integrity of

self-designed structures and make appropriate recommendations for

improvement

Science (Occupations) Curriculum for the Adolescent Aged Twelve to

Fifteen/Sixteen Years



Content Strand

Knowledge, Skills and Understandings

Activities and Resources


The study of Earth and living things Earth and space sciences:

- cosmology

- astronomy

- geology and

physical

geography

Build knowledge of the stars, galaxies and the universe. Study the histor y of the exploration of the universe

through visual obser vation, telescopes, unmanned and

manned space exploration

Study the structure of the Ear th and geological histor y

- the composition of the Ear th

- three states of matter

- different ways of combining

- attraction and gravity

- geology

Study plate tectonics and geological phenomena such as

the formation of mountains Study the Sun and the Ear th

- rotation of the Ear th and its consequences

- Ear th as a sphere

- tilt of the axis

- seasons

- time zones Study the Work of Air

- protection of the atmosphere

- rains

- winds

- land and sea breezes

- seasons and the winds

- ocean currents

- the wind as sculptor Study the Work of Water

- the river

- rain

- ocean waves

- ice

- the water cycle

- water and vegetation Study of Human Geography

- zones on the Ear th

- interdependencies

- economic geography

Activities include: - making models

- reading and making maps

- creating timelines of

cosmological and

geological eras

- conducting experiments

- interdisciplinar y projects

related to weather and

climate e.g. projects that

integrate scientific,

statistical and historical

knowledge

Resources include:

- globes

- telescope

- char ts

- maps

- experiment supplies

- non-toxic supplies for

experiments

- almanac


materials (paper-based,

digital, web-based,

multimedia)


Biological

sciences:

- botany

- zoology

- physiology/

anatomy

- health sciences

Classify living things according to the Linnaean taxonomy Study and use different classification systems in use today

Study and compare the morphology, or structural features

of living things

Study the cell as the basic unit of life

- the structure of the cell

- cell respiration

- cell division/reproduction, meiosis

- photosynthesis

- biochemistr y of the cell

- DNA/RNA, mitosis, protein synthesis

Introduce and extend knowledge of genetics:

- Mendel

- dominance/recessiveness

- probability

- aberration Review and extend knowledge of natural cycles:

- water

- nitrogen

- carbon Review and extend knowledge of the vital functions of

living things plants and animals:

- body coverings

- circulation

- respiration

- digestion

- movement

- reproduction Introduce and extend knowledge of biochemistr y

Activities will include:

- investigating the life forms

in pond water and their

relations

- identifying, recording and

classifying activities in the

school environment,

including both domestic

and natural species

- creating diagrams, charts,

models, visual data displays

and multimedia

representations e.g. of

cells, cell processes, DNA

populations and

relationships in

ecosystems, genetic

patterning, natural cycles,

biological processes etc

- projects relating to

inherited traits in families

e.g. colour blindness

- creating timelines to

illustrate evolutionar y

time

- dissection

- projects that enable

students to apply

knowledge of human

physiology to own health

and well-being Resources will include:

- microscopes and other

research equipment

- resources for record-

keeping and displaying

Review and extend knowledge of human physiology, findings

including body functions, hormones and nutrients

Explore the interdependency of life

Investigate ecosystems, including populations, interactions

and biodiversity within ecosystems

Investigate the extinction of species

Investigate the development of genetic engineering

- reference and research materials (paper-based,

digital, web-based,

multimedia)

- animals

- garden plants

- natural outdoor

environment

Investigate animal behaviour :

- reflex



The study of human progress and civilisation Physical sciences:

- physics

- chemistr y

Understand foundation concepts in physics related to forces and motion, including velocity, acceleration,

iner tia, force, mass and weight, friction, work, power,

effor t, Newton’s three laws of motion, energy

transformation, mechanical advantage, efficiency

Investigate simple machines, including, lever, inclined

plane, wheel and axle, pulleys, gears

Review and extend knowledge of electricity and

magnetism

Investigate forms of energy and energy transfers

Investigate the nature of matter, including atoms and

their structure, par ticle theor y, molecular structure,

ionisation

Review and extend knowledge of elements,

compounds, chemical reactions, acids and bases, salts,

oxidation, valences, the carbon compounds of organic

chemistr y

Identify and use of the periodic table

Compare and contrast metals and non-metals

Understand and describe the carbon, oxygen and

nitrogen cycles

Under take experiments under laborator y conditions

Extend and apply research skills

Reference sources effectively

Activities include: - experiments, investigations,

project work

- working with models

Resources include:

- science laborator y



digital, web-based,

multimedia)

Contemporary sciences

- mechanics

- engineering

- histor y of science

and technology

Use and care for basic mechanics tools

Repair and maintain the systems of a combustion engine

Understand systems for cooling and heating

Understand electrical systems

Build knowledge of the mechanical and sub-atomic

proper ties of machines that allow them to work

Resources include: - museum of machines

- workshop

- tools and equipment


Synthesising and Integrating Scientific Knowledge and Understanding:

Systems of Interdependency

Scientific understanding and knowledge is synthesised and integrated in the

following ‘learning by doing’ studies of systems of interdependency.

Systems of interdependency Content Strand

Knowledge, Skills and Understandings Activities and Resources


Soil Through a study of

soil, students are

introduced to both

geological and

biological studies.

Investigate the composition of soil Relate soil chemistr y to the study of animal and plant

life Apply knowledge of the carbon, oxygen and nitrogen

cycles Understand the role of soil in photosynthesis Recognize soil types, their origins and their suitability

for specific plants Understand the geological impact of glaciers Describe the causes and effects of erosion

Activities include testing, grading and mapping soil types

Resources include:

- soil test kit

- mineral sample kit

- range of soil types

- access to internet, e.g.

Google Ear th, GIS

- plants, fer tilizers, potting

mix, plant pots



digital, web-based,

multimedia)

Water Water is integral to

the origin of life

and to the Ear th’s

histor y. It is studied

for its physical and

chemical

proper ties.

Appreciate the physical proper ties of water Identify water forms on ear th Describe the role of water in photosynthesis Identify water as the universal solvent

Recall the molecular structure of water

Understand water ionization

Understand the water cycle

Test water quality, by obser ving, measuring and

comparing features such as:

- pH

- biological indicators

- turbidity

Comprehend the concept of watershed

Discuss the ethical implications of water use and

management

Resources include: - water test kit

- chemistr y glassware for

separation of soluble and

insoluble substances.

- conductivity meter

- pH meter



digital, web-based,

multimedia)

- local water sources



Air Air is studied for its

role in ear th’s

climate and in plant

and animal life

cycles

Investigate the chemistr y of the air Define meteorology

Comprehend the transfer of heat energy Relate

movement of air to climatic patterns Understand

the role of convection in heating and

cooling Discuss the implications of degrading air quality and the

relation between air quality and climate change

Activities include testing and analysing air quality

Resources and equipment

include:

- Bunsen burners

- access to Internet e.g.

Bureau of Meteorology,

Seabreeze

- Airwatch

- air monitor box


materials (paper-based, digital,


Energy Energy is studied as

a comprehensive

force that

originated with the

Big Bang and has

global implications

as a universal

human commodity

and need.

Describe and explain and non-renewable energy sources including solar power, fossil fuels, geothermal

energy, nuclear energy Understand energy uses, including work and machines

Appreciate the nature of energy Explore

alternative energy systems Understand the

role of technology in energy

production and conser vation Discuss the ethical implications of energy use

Resources and equipment include:

- bicycles

- timing devices, e.g. video

timers, light gates

- solar panels

- electronics kits



digital, web-based,

multimedia)

Animals and Plants

Animals and plants

are studied in

terms of their role

in natural

ecosystems and in

agricultural science,

as well as for their

anatomical and vital

functions.

Investigate the characteristics of living things Understand animal and plant habitats and their

distribution Study photosynthesis Har vest plant and animal products Understand the process photosynthesis and its

impor tance in ecosystems Understand energy flow in food webs and chains Understand the concept of genetics Understand the role of biodiversity in an ecosystem Study evolution and the diversity of living things

Describe the role of adaptation in evolution

Understand the concept of homeostasis.

Resources and equipment: - microscope kit

- anatomical models

- live animals

- plants, fer tilizers, potting

mix, plant pots



digital, web-based,

multimedia)


The Human

Organism

The human

organism is studied

in terms of the life

cycle, and for its

relation with the

natural world.

Research the origins of humans

Understand the role of humans in animal

domestication

Explore the use of genetics for science, medicine and

agriculture and debate the ethics behind this use

Explore the ethics of the uses of natural resources

Discuss the various systems for food procurement,

processing and distribution.

Resources and equipment

include:

- anatomical models

- medical meters, e.g.

sphygmomanometer,

stethoscope, thermometer



digital, web-based,

multimedia)

The sample project below exemplifies how all areas of the curriculum might be

synthesised and integrated in the Occupations of the Montessori adolescent

community.

Science (Occupations) Project: Poultry Farming

The project is initiated by a group of students with an adult guide and the input

of other specialists as needed.

Goals

Engagement - Students apply scientific knowledge and skills to situations outside of the classroom. - Students show interest in new or unusual situations.

Key Concepts/

Mastery

- Students understand their biology and that of other living things, and recognise the interdependence of life.

- Students understand the structure and function of organisms, from the organisational

level of cells to systems.

- Students understand the need for reproduction in maintaining a species and a

community.

Skills - Students plan adequate control of variables in a simple experiment. - Students design a simple controlled experiment to test the effects of one variable.

- Students form inferences based on obser vation.

- Students interpret data in a graphical form.

- Students use correct procedure for handling apparatus.

Work Management

- Students follow procedures. - Students work cooperatively in a group.

- Students make neat and accurate obser vations.

Methodology

The methodology used to support project-based learning is derived from the

three-period lesson, a lesson structure that is applied at all levels of Montessori

education, from early childhood to teacher education.



First Period of the Project

In this period students participate in introductory activities that open up the topic

and key concept lessons.

The first period of the poultry farming project might include introductory activities

such as the following:

· a story that demonstrates the interdependence of humans and domesticated

animals and plants

· a reading from the section on ‘domesticates’ from Guns, Germs and Steel by

Jarrad Diamond

· the story of the pavlova

· In 1935, the chef of the Hotel Esplanade in Perth, Western Australia, Herbert

Sachse, created the pavlova to celebrate the visit of the great Russian

ballerina, Anna Pavlova. The dish is based on meringue made from egg

whites. Whilst it has been suggested this dessert was created in New

Zealand, it has become recognized as a popular Australian dish.

· a cooking lesson: how to make pavlova

· a ‘how to’ dissection lesson: dissecting an animal heart

· a ‘how to’ lesson: using a microscope

· an art lesson: painting microscope observation

Students then pose one or more key questions. The key question for the poultry

farming project might be:

What do we need to know to successfully operate a chicken egg farm?

The answer to this question determines the key concept lessons to follow.

Below are a series of key concept lessons that might be presented in the first

period of the poultry farming project. These lessons focus on students

understanding of:

· their own biology and that of other living things

· the interdependence of life

· the structure and function of organisms, from the organisational level of

cells to systems

· need for reproduction in maintaining a species and a community.

Lesson Title

Lesson 1 Classification of animal kingdom, and the classes of ver tebrate

Lesson 2 Food chains and decomposers

Lesson 3 Circulator y system

Lesson 4 Respirator y system


Lesson 5 Digestive system

Lesson 6 Structure of egg

Students might also participate in a seminar in which the following question is

researched and discussed:

How do our actions on a farm affect the balance of nature?

Students will be provided with a range of resources to explore the key concepts

and the discussion question further. These will include a range of reference and

research materials (paper-based, digital, web-based, multimedia).

During the first period of the project students build a shared specialised

vocabulary to talk about the topic. This vocabulary might include:

· Kingdom, Phylum, Class, Order, Family, Genus, Species

· autotroph, heterotroph, producer, consumer, decomposer

· poultry, fowl, hen, rooster, chicken, hatchlings

· free range, battery

· mould, fungus, bacteria, compost

· food chain, food web

· reproduction system: egg, sperm, mitosis, penis, vagina

· circulatory system: heart, blood, artery, vein

· respiratory system: lungs, diaphragm, intercostal muscles, bronchi,

bronchioles, alveoli

· digestive system: mouth, oesophagus, stomach, small intestine, large

intestine, anus

Second Period of the Project

The second period of the project includes whole group and individual,

explorations, and activities in which students actively explore, research,

experiment, discuss, and take part in hands-on practical tasks relevant to the

project. In the context of the poultry farming project these, explorations and

activities might focus on the students developing the following knowledge,

skills and understandings:

· Plan adequate control of variables in a simple experiment

· Design a simple controlled experiment to test the effects of one variable

· Follow a procedure

· Work cooperatively in a group

· Make neat and accurate observations

· Use correct procedure for handling apparatus

· Understand the structure and function of organisms, from the organisational

level of cells to systems



Whole group lessons and activities might include the following:

Lesson Title

Lesson 1 Investigating the needs of poultr y

Lesson 2 Making a chicken coop

Lesson 3 Setting up a bread mould experiment

Lesson 4 Setting up a compost decomposition experiment

Lesson 5 Creating photo identification cards of school plants and animals

Lesson 6 Conducting a hear t dissection

Lesson 7 Conducting step test for fitness

Lesson 8 Calculating lung volume

Lesson 9 Creating ar t work based on microscope obser vations of tissues

The students then undertake individual research tasks related to the project. In

the context of the poultry farming project these might include the following:

· growth of poultry

· business policy and guidelines for poultry farming

· ethical rearing of poultry

· avian diseases

· uses of poultry products: meat, eggs, feathers

· history of poultry and poultry farming

Third Period of the Project

In the third period of the project students complete a variety of tasks for

assessment, including spoken and written presentations and creative

expression. A spoken presentation might be used to present results of

observations and experiments and a written assignment or report might be

used to present research findings. Students might also be quizzed or tested on

the knowledge, skills and understandings they have gained. Students would

also present creative work, such as illustrations based on microscope

observations.


Appendix L

School Calendar and School Day Schedule

These dates are estimated and will be adjusted once the official DPS 2013/2014

School Calendar is Released.

August 8,9 Walk in registration

August 5-16 Planning / Professional Days (no class for students)*

August 19 First Day of School

September 2 Labor Day Holiday - No School

September 20 Assessment Day - No Classes

October 18 Quarter progress reports sent home

October 21 - 25 Parent / Student / Teacher conferences held after

school

October 28 - Nov. 1 Fall Break - No School

November 11 Planning / Professional Day (no class for students)

November 27-29 Thanksgiving Holiday - No School

December 20 Assessment Day - No Classes, Semester progress

reports sent home.

December 23 -

January 3 Winter Holiday - No School

January 6 Planning / Professional Day (no class for students)

January 20 Martin Luther King Holiday - No School

February 17 President Day Holiday - No School

February 18 Planning / Professional Days (no class for students)

March 14 Quarter Progress reports sent home

March 17 - 21 Parent / Student / Teacher conferences held after

school

March 24 - April 3 Spring Break Holiday - No School

April 4 Planning / Professional Days (no class for students)

May 9 Planning / Professional Days (no class for students)

May 23 Assessment Day - No Classes

May 26 Memorial Day Holiday - No Classes

June 10 Last Day of School

June 11 Planning / Professional Day; Final semester reports

sent home

June 12,13 Planning / Professional Day

Student Report Days: 171 Total Days Teacher Report Days: 191 Total Days

*The first year we will have 10 planning/professional days prior to the first day of school.

Subsequent years we will have 5 planning/professional days prior to the first day of school with

Teacher Report Days at 186.



DPMSS Junior High Daily Schedule

Monday , Tuesday, Thursday, Friday Wednesday

8:00 –

8:30

Morning Meeting, advisor check in, daily schedule

check, announcements

Community Meeting

8:30 –

11:30

Academic Work Time; small group lessons in math,

Spanish, ELL, key lessons for Occupations including

reading, writing, history, civics, and science. Students

are doing independent and small group work when not

in lessons. There will also be time for art and micro-

economy.

Academic Work Time.

11:30-

12:30

Lunch / Outdoor recreation time Lunch / Outdoor

recreation time.

12:30 –

1:15

Reading and Journal time. Advisors are conducting

portfolio checks and having one on one advising time.

Reading and Journal

time, ending with

restoration of

environment

1:15 –

3:10

Academic Work Time; small group lessons in math,

Spanish, ELL, key lessons for Occupations including

reading, writing, history, civics and science. Students

are doing independent and small group work when not

in lessons. There will also be time for art and micro-

economy.

1:30 – Students are

released to leave or

attend supervised

study hall.

3:10 –

3:30

Advisement Check-In and restoration of environment.


DPMSS High School Schedule

Monday Tuesday Wednesday Thursday Friday

8:00 –

11:40

Core Class

Lessons &

Work

Core Class

Lessons &

Work

Community

Meeting

Advising

Often other

follow up

meetings: SIP,

Intl. Trip, ACT

Prep, etc.

Core Class

Lessons &

Work

Core Class

Lessons &

Work

11:40 –

12:25

Lunch Lunch A.W.O.L Lunch Lunch

12:30-

1:30

1:35

-2:35

Elective

Classes

Elective

Classes

A.W.O.L Elective

Classes

Elective

Classes

2:40 –

3:30

Practice time

for Athletics,

performance.

Advisors

available for

tutoring

Practice time

for Athletics,

performance.

Advisors

available for

tutoring

A.W.O.L. Practice time

for Athletics,

performance.

Advisors

available for

tutoring

Practice time

for Athletics,

performance.

Advisors

available for

tutoring

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