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Alternate Assessment Curriculum FrameworkIntroduction

The D75 Alternate Assessment Curriculum Framework was developed in response to schools’

requests for instructional expectations connected to the Common Core Learning Standards

(CCLS) for students in Alternate Assessment classes. Groups of teachers, administrators, and

district content area coaches gathered for four weeks during the summer of 2013, and

participated in a collaborative process to create an Alternate Assessment Curriculum

Framework. The process included a workshop at the beginning of each week to train the group

in the leveled learner concept (Levels B, C, and D), resources available (developmental math

skills progressions, Webb’s Depth of Knowledge, Common Core Essential Elements and

Alternate Achievement Descriptors for Mathematics from the State Members of the Dynamic

Learning Maps Alternate Assessment Consortium and Edvantia, Inc.), and final product

expectations. Subsequently, small groups collaborated to develop the leveled learning plans

and activities, culminating performance tasks, and the introductory contexts for the different

modules.

The structure of the framework provides four modules in ELA, Math, Science, and Social

Studies created in grade bands (K-2, 3-5, 6-8, and High School). Four math modules have been

developed as grade specific modules for K-8, while High School modules reflect specific

conceptual categories.

Each module consists of:

a context overview

culminating performance tasks for each level

Common Core Learning Standards connections

Career Development and Occupational Studies (CDOS) standards connections

Content standards connections

essential questions

key vocabulary

lesson strands with leveled learning plans and activities for each

Resources list

materials lists

D75 Alternate Assessment Curriculum Framework 2nd Grade Math Module 2: Geometry

Underlying the development of the activities included in this document is the profound belief

that students with significant intellectual disabilities need high standards that are reasonable and

achievable given sufficient and appropriate opportunities to learn. All students who participate

in Alternate Assessment classes are expected to be provided with access and exposure to the

content learning expectations of their general education peers at a reduced depth, breath and

complexity. The presented tasks, while not reflecting the degree of higher order skills and

comprehensiveness of expectations established for students participating in the general

assessment system, do reflect reasonable and achievable expectations for students with

significant intellectual disabilities. In addition, they maintain a necessarily broad connection

with the Common Core Standards through a concentrated focus on salient features of specific

Standards. These content area sample learning plans and activities are designed not only to elicit

performances of content area thinking skills/behaviors but also to provide opportunities for

students to engage with, read and/or use content understandings that are imbedded within the

tasks.

The sample learning plans and activities for each strand have been divided into three distinct

levels of student expectations based on cognitive abilities: Level D, Level C, and Level B.

Level D learning plans and activities are reflective of students who experience the most

significant cognitive disabilities within our district. These students are typically working at the

engagement level. Instruction is typically focused on developing the accessing skills that a

student needs to possess. It is understood that for additional information processing to take place,

engagement is a necessary first step. (Please refer to the Essential Thinking Skills and

Behaviors Explanatory Notes document for further information regarding the concept of

Engagement).

Level C learning plans and activities are reflective of students who demonstrate the

essential thinking skill of conceptualization. These students can form mental representations of

a concept and apply this knowledge. They exhibit intentional behavior in response to situations.

They rely heavily on objects, picture cues, a print rich environment, and an exposure to content

in multiple and modified formats to facilitate learning. These students typically work within

Level one and two in Webb’s Depth of Knowledge. (Please refer to the Essential Thinking

Skills and Behaviors Explanatory Notes document for further information regarding the

concept of conceptualization, and Webb’s Depth of Knowledge).


Level B learning plans and activities are reflective of students who demonstrate skill

abilities closest to meeting the CCLS and content standards expectations as they are

written. These are typically students who may participate in inclusion settings and students who

may return to community based instruction programs. These students would be expected to work

in all levels of Webb’s Depth of Knowledge.

The Revision of ModulesThe Alternate Assessment Curriculum Framework was developed to serve as a guide for schools.

It is expected to be modified and adjusted in order to meet school-specific instructional goals and

objectives.

To assist schools with understanding what the revision process entails, the district gathered a

small group of teachers and administrators during the summer of 2014 to revise Math module 2

for third grade, sixth grade, and High School. These modules serve as guiding examples for

schools to refer to as they consider revisions to the additional modules in all content areas.

Along with these examples, a general revision protocol and a sample reflections document from

the summer revision group regarding the revision process can be found at the end of this

introduction.

Each revised Math module 2 (grades 3, 6, and HS) now consists of:

a context overview

culminating performance tasks for each level

sample rubric designs for the performance task at the varied levels

An IEP goal tracking rubric format

Common Core Learning Standards connections

Career Development and Occupational Studies (CDOS) standards connections

Content standards connections

essential questions

key vocabulary

Sequenced lesson strands with leveled learning plans and sequenced activities

Resources list

materials lists

A sample lesson written related to one activity in one strand


It is hoped that the D75 Alternate Assessment Curriculum Framework provides teachers and

schools with a resource to better understand how students can be provided with opportunities to

develop targeted skills through content-based instructional experiences that are also applied in

the context of functional activity experiences.

Revision Protocol

The following is a step-by-step process that schools can reference when they begin

the process of revising a module for their own use. These are generic expectations

in the order they should occur to ensure an efficient and effective revision of a

module. This is by no means the only way in which a module can be revised, but

is intended to provide the essence of what the revision process should include and

be focused around.

1. Understand the standards for the learners in your class/school.

2. Ensure the connection between the standards, the learning strands and the

performance task.

3. Ensure that the learning strands and activities within the activities are

sequenced correctly for your students.

4. Ensure that the learning activities are appropriate for each level (B, C, and

D).

5. Determine and agree upon the specific considerations that must be

accounted for when creating a rubric against the performance task for Level

B, C, and D.


A reflection Sample on “How to” Revise an Alternate Assessment

Curricular Framework Module of Study (AACF) based on the guiding

protocol. 1. How do you ‘unpack’ or understand the standards for the learners in your class?Read the standards listed in the module and isolated the key nouns and verbs. Determined what the standard asking the students to know and do. Came to consensus regarding what the performance of these standards would look like for the students in alternate classes. Finally, the group translated the standard into actionable skills for the learners.2. How do you ensure connection between the standards, the learning strands and the performance task?One method the participants used was to use color-coding to ensure a connection. First, the group members color-coded each standard. Second, they looked at each learning strand and checked off, using the color system, where elements of each standard were contained in the strand. Last, they looked at the performance task, and highlighted or checked, using the color system, where elements of each standard were contained in the task. (These key elements were translated into actionable skills accessed in the rubric. See #5)If connections were not achieved, group members made a decision to reorganize, omit, add, condense or adjust as needed. 3. How do you ensure that the learning strands and activities within the activities are sequenced correctly for your students?Several resources were used, such as the CCLS Skills Progression at a Glance, Wisconsin Early Learning Skills, Equals chapter/skills sequencing, etc. (Note: please remember that the use of available resources such as language skills progressions, other content curricular models from various states, reading skills checklists, etc. should be referenced when revising other content area modules)4. How do you ensure that the learning activities are appropriate for each level (B, C, and D)?Participants referred back to Piaget’s Cognitive Levels of Development, their own students IEPs, as well as, keeping the individual needs of the learners in alternate assessment classes at the forefront of their minds When developing the learning activities for all levels.5. What should you consider for creating a rubric against the performance task for Level B, C, and D?Isolated key skills were identified in the standards and translated to actionable learning targets for the students when developing the Level C and B rubrics. Content expectations played a significant role in establishing the rubrics. Aspects of the rubric quantified skills for the B and C level learners and included a simple rating system (4-1, 3-1, etc.).It was determined by the revision group that a specific rubric that could be used across the modules for the level D student would provide teachers with the ability to track skills related to engagement. This was determined to be the best approach to tracking progress for student who are cognitively young and require mastery of those skills related to engagement before any further content knowledge acquisition could be expected.


District 75 Alternate Assessment Curriculum Framework 2nd Grade Math Module 3

GEOMETRY

CONTEXTUNIT TOPIC: Geometry

Students begin developing shape recognition and learn geometry in a variety of ways in K-2.

The third module of Grades K-2 math is connected to geometry and properties of geometric

figures. Students are to be exposed to and taught these mathematical concepts with hands-on

instruction and with concrete manipulative. Blocks and shape manipulative of varying sizes and

color are vital for this module.

In Kindergarten students learn to basic shape identification regardless of color and/or size.

Students begin seeing that: all triangles have 3 sides; rectangles can be different sizes and still

be a rectangle, etc. In 1st grade, these concepts are expanded as students put shapes together

and break apart complex shapes into more familiar rectangles, triangles, squares, etc. There is

exposure to fractions in that students begin breaking down rectangles and circles into halves

and quarters. This concept is continued in the 2nd grade where students are asked to explain

what halves and quarters represent. Also, second grade introduces a wider variety of 2D and 3D

shapes, such as: cones, cylinder, hexagon, and octagon. Students begin composing more

complex shapes by combining 2D and 3D geometric figures.

The sample activities outlined are designed to elicit performances of mathematical thinking and

behaviors, but also provide opportunities for students to get a concrete understanding of

geometry and properties of figures. Teachers should emphasize concrete examples and regular

repeated practice using manipulative and visualizations. Regular morning meeting review of

shapes is another strategy that can be done all year long.


The activities in this module should be reinforced with varying concrete manipulative, and

repeated practice. Having students compare shapes throughout the day is a good form of

fluency building. Besides asking what shape it is, have students explain how they know. (e.g: “all

of the sides of a square are the same”)


ASSESSMENT

FORMATIVE ASSESSMENT EVIDENCE: Teacher observations

checklists completed by students

student work

pre and post assessment activities

PERFORMANCE BASED ASSESSMENT TASK

Students will act as bakery workers helping prepare items to sell for the public. There will be

brownies and pies that will need to be divided and packaged. Students can use cut-outs,

concrete manipulatives, play-dough, or real-world representations of brownies and pies.

Level D: Students will engage* by demonstrating a voluntary and sustained or repeated

attention to the dividing of a representation of, or a real pie/tray of brownies into halves.

Level C: Students will participate in simple problem solving activity that requires the student

to figure out how to share a pie or a tray of brownies equally for a specified number of people

by dividing a pie/tray of brownies into halves, fourths, sixths.

Level B: Students will divide equally a pie/ tray of brownies into a specified requested

amount from a customer. Student will be required to divide brownies into equal parts: halves,

fourths, and sixths, etc. Students at this level would be challenged to do more complex

fractional divisions.

*See explanatory notes of “engagement” in The Essential Thinking Skills and

Behaviors Document.


STANDARDS

MATH COMMON CORE ANCHOR STANDARDS:2.G.A.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided)

versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes that

possess defining attributes.

2.G.A.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-

circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right

circular cones, and right circular cylinders) to create a composite shape, and compose new

shapes from the composite shape.8

2. G.A.3 Partition circles and rectangles into two and four equal shares, describe the shares

using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and

quarter of. Describe the whole as two of, or four of the shares. Understand for these examples

that decomposing into more equal shares creates smaller shares.

MATH KEY IDEAS

Reason with shapes and their attributes.

Decompose shapes into equal parts.

CAREER DEVELOPMENT AND OCCUPATIONAL STANDARDS

Standard 2-Integrated Learning: Students will demonstrate how academic knowledge and skills

are applied in the workplace and other settings. Identify academic knowledge and skills that are

required in specific occupations. Demonstrate the difference between the knowledge of a skill

and the ability to use the skill

Standard 3a.7 Universal Foundation Skills: Using resources includes the application of financial

and human factors, and the elements of time and materials to successfully carry out a planned

activity. Managing Resources, Performance Indicator: plan a two-week activity that requires


tasks to be divided among students or coworkers, including determining priorities and following

timelines

ESSENTIAL QUESTIONS

1. How can comparing shapes differences and similarities help us identify them?

2. How do we decompose shapes into equal parts?

VOCABULARY

1. Circle

2. Cube

3. Divide

4. Divided

5. Equal

6. Fifth

7. Fourth

8. Group

9. Half

10. Hexagon

11. Part

12. Pentagon

13. Polygon

14. Quadrilateral

15. Quarter

16. Rectangle

17. Row Sides

18. Square

19. Third

20. Triangle

21. Whole

LESSON STRANDS OVERVIEW1. Recognize a shape with specified attributes such as number of angles or a given number of

equal sides. i.e. [label, identify, match]

2. Identify triangles, quadrilaterals, pentagons, hexagons and/or cubes.

3. Divide a rectangle into rows and/or Columns of same size and count the total number.

4. Divide circles and rectangles into two, three or four equal parts. Describe the result either

as two halves, three thirds, and four-fourths to recognize that equal parts that make the

whole do not need to be the same shape as the original shape.


LEARNING PLANS AND ACTIVITIES

NOTE: Preferred Mode of Communication (PMC) should be considered for all

students in all activities across all levels.

Lesson Strand 1: Recognize a shape with specified attributes such as number of angles or a

given number of equal sides. i.e. [label, identify, match]

LEARNING PLANS AND ACTIVITIES LEVEL D: Engage and explore shapes and angles using the senses.

Shape Riddle: Student will react to geo-board when presented through moving eyes,

looking, or touching the shape made on the geo-board.

Comparing Shapes: Engage and explore with two shapes, using the senses. React to

shapes when presented in lesson. Identify at least one shape.

Tile Shapes: Engage with tiles through exploration. (Touch, Sight)

Skeletal Model: Using toothpicks and play-doh, allow students to engage within the

activity through exploration of the materials presented, and shapes created by the

group.

Smartboard game: Shapes Adventure: students choose from a menu of four options

including matching, recognizing and filling in the missing shapes, as well as identifying

the attributes of shapes.

Kinesthetic Shape Matching: Student will engage and explore by sitting in the circle

with other students. Engagement also includes touching the picture/word they are

responsible for, holding it up, or looking at the picture/word.

LEARNING PLANS AND ACTIVITIES LEVEL C:D75 Alternate Assessment Curriculum Framework 2nd Grade Math Module 2: Geometry

Construct, classify and compare shapes and their properties.

Shape Riddle: Use a geo-board to make a shape. Write, draw or dictate one clue

about the shape you made. Have another student guess what the shape is. When

guessed, reveal your geo-board.

Comparing Shapes: Make two shapes on a geo-board. Draw the shapes on paper.

Write two properties of each. Give one reason why they are different.

Tile Shapes: Use small square tiles (picture cue cards of pre-made designs if

necessary) to create as many shapes as you can, recording each shape by drawing

them on a piece of paper.

Skeletal Model: Using toothpicks and play-doh, create a shape. Name the shape you

made.

Smartboard game: Shapes Adventure: students choose from a menu of four options

including matching, recognizing and filling in the missing shapes, as well as

identifying the attributes of shapes.

Kinesthetic Shape Matching: Student whose turn it is takes a card (either written in

word form or represented in picture form) and stands in the middle of a circle of

students. The other students hold different shapes (either in word or picture form as

well) and hold it up for the student in the middle to see. The student in the middle

walks over and matches their picture/word to the student with the corresponding

picture/word. It is now the student who had the corresponding picture/words turn

to be in the middle.

LEARNING PLANS AND ACTIVITIES LEVEL B: Construct, investigate and compare shapes and their properties.

Shape Riddle: Use a geo-board to make a shape. Write or dictate two clues about the

shape you made. Have the other student’s guess what the shape is; when guessed

reveal your geo-board.


Comparing Shapes: Make two shapes on a geo-board. Tell or write the properties of

each. Compare the two to see how they are the same, and how they are different.

Tile Shapes: Use small square tiles to create as many shapes as you can following the

rule that at least on full side of one tile must touch one full side of another tile every

time. Create as many shapes as you can following this rule

Skeletal Model: Using toothpicks and play-doh, create a shape. Explain how you know

what shape you created by listing its properties.

Kinesthetic Shape Matching: Student whose turn it is takes a card (either written in

word form or represented in picture form) and stands in the middle of a circle of

students. The other students hold different shapes (either in word or picture form as

well) and hold it up for the student in the middle to see. The student in the middle

walks over and matches their picture/word to the student with the corresponding

picture/word. It is now the student who had the corresponding picture/words turn to

be in the middle.

Smart board game: Shapes Adventure: students choose from a menu of four options

including matching, recognizing and filling in the missing shapes, as well as identifying

the attributes of shapes.


Lesson Strand 2: Identify triangles, quadrilaterals, pentagons, hexagons and/or cubes.

LEARNING PLANS AND ACTIVITIES LEVEL D: Engage and explore shapes and angles using the senses.

Shape Riddle: Read the book If you were a polygon, by Molly Blaisdel. Identify the

differences between the different polygons showing the shapes and giving the children

a chance to explore their properties. Student will react to geo-board when presented

through moving eyes, looking, or touching the shape made on the geo-board.

Guess that Polygon! Encourage students to engage and explore with each polygon.

Comparing Shapes: Engage and explore with two shapes, using the senses. React to

shapes when presented in lesson. Identify at least one shape.

Musical Shapes: Engage and Explore shapes that are taped onto the floor by listening

to the music, looking at the shapes or walking around and in the shapes area.

Tile Shapes: Engage with tiles through exploration. (Touch, Sight)

Skeletal Model: Using toothpicks and play-doh, allow students to engage within the

activity through exploration of the materials presented, and shapes created by the

group when directed.

LEARNING PLANS AND ACTIVITIES LEVEL C: Construct, classify and compare shapes and their properties.


differences between the different polygons. Use a geo-board to make a shape.

Write, draw or dictate one clue about the shape you made. Have another student

guess what the shape is. When guessed, reveal your geo-board. Guess that

Polygon! On separate sheets, draw different polygons. Describe one or two

properties of the polygon you choose, you can use pictures as a visual to help

students guess the shape.

Comparing Shapes: Make two shapes on a geo-board. Draw the shapes on paper.

Write two properties of each. Give one reason why they are different.


Tile Shapes: Use small square tiles (picture cue cards of pre-made designs if

necessary) to create as many shapes as you can, recording each shape by drawing

them on a piece of paper.

Musical Shapes: Tape different shapes onto the floor. Put on soft music while the

children explore the shapes you have created. One student at a time will have a turn

to explore a shape they identify. They can explore the shape to music while

counting its sides, jumping inside, jumping outside, reaching down and touching the

shape, etc…

Geometry Scavenger Hunt: Give students a sheet with clues on it, encouraging them

to find those shapes within the classroom that coincide with the clues given (ex: Find

a three sides polygon; Find a shape with four equal sides)

Skeletal Model: Using toothpicks and play-doh, create an assigned shape. Name the

shape you have made.

LEARNING PLANS AND ACTIVITIES LEVEL B: Construct, investigate and compare shapes and their properties.


differences between the different polygons. Use a geo-board to make a shape.

Write or dictate two clues about the shape you made. Have the other student’s

guess what the shape is; when guessed, reveal your geo-board. Guess that Polygon!

Draw different polygons on separate sheets. Keep them to the side as you reveal

properties of one polygon. Have the students guess the polygon by writing, drawing

or verbalizing the shape you are describing. Allow the students to take a turn

describing.

Comparing Shapes: Make two shapes on a geo-board. Tell or write the properties of

each. Compare the two to see how they are the same, and how they are different.


Geometry Scavenger Hunt: Give students a sheet with clues on it, encouraging them

to find objects that represent those shapes within the classroom that coincide with

the clues given (ex: Find a three sides polygon; Find a shape with four equal sides)

Musical Shapes: Students will create their own shapes on the floor using masking

tape. Put on soft music while the children explore the shapes you have created.

Every student will get a chance to identify and explore each shape another peer has

made on the floor. They can explore the shape to music while counting its sides,

jumping inside, jumping outside, reaching down and touching the shape, etc…

Tile Shapes: Use small square tiles to create as many shapes as you can following the

rule that at least on full side of one tile must touch one full side of another tile every

time. Create as many shapes as you can following this rule

Skeletal Model: Using toothpicks and play-doh, create a shape. Explain how you

know what shape you created by listing its properties. Use Magna shapes to create

a polygon figure, using the different properties and angles of the shapes to create a

3D image.


Lesson Strand 3: Divide a rectangle into rows and/or columns of same size and count the

total number.

LEARNING PLANS AND ACTIVITIES LEVEL D: Engage and Explore with color tiles.

Rectangle Tiles: Hand out a bag of different sized rectangles and a bag of color tiles.

Watch for reaction to presented materials through eye gazing. Engaged students

may look at the materials, and may even touch and begin to explore materials on

the table.

Make a Rectangle: Give out 12 color tiles. Allow student to interact and explore the

shapes of the smaller color tiles.

If I were a quadrilateral: For these activities, connect understanding of

quadrilaterals with the book If I were a quadrilateral, by Molly Blaisdel. Have

students engage and explore rectangles.

The Greedy Triangle: Engage and Explore using the book and coinciding materials.

To Half or not to half: Use a spinner with ½, one-third, and ¼ labeled. Take turns

spinning, and cutting a “pizza” according to the fraction spun. Students will engage

and explore with materials by sitting, looking, or touching materials.

LEARNING PLANS AND ACTIVITIES LEVEL C: Construct and Compare rectangles through the use of color tiles. Look at sizes and

number of tiles used to draw possible conclusions about rectangles.

Rectangle Tiles: Hand out a bag of different sized rectangles as well as a bag of color

tiles. Have students put tiles into rows to cover the tiles. Record how many tiles

were needed to fill in the rectangle (writing, pointing, and marking off a checklist.

Make a Rectangle: Give out 12 color tiles. Ask students to create their own

rectangles in all different sizes. If necessary use pre cut rectangles to show the skill.




students look at squares and rectangles most specifically. What is different? What is

the same? Use blocks to fill in squares and rectangles to connect the difference

between them.

The Greedy Triangle: Explore dividing rectangles using triangles by using a pattern

board, or paper with pre-drawn rectangles and lines for triangles. Allow students to

use pattern blocks to fill in the rectangle with “greedy” triangles. Try for other

shapes as well

To Half or not to half: Need a laminated paper circle, and a dry erase marker; (or a

paper circle that can be divided into different equal pieces; three different circles

representative of each fraction piece so the student can choose the correct one after

they spin) play individually, in a small group, or larger group. Use a spinner with ½,

one-third, and ¼ labeled. Take turns spinning the spinner. Whatever number the

spinner lands on is the way you must divide up the paper pizza in the middle of the

circle.

LEARNING PLANS AND ACTIVITIES LEVEL B: Create Construct and Distinguish between the different sizes of rectangles.

Rectangle Tiles: Students draw two different sized rectangles. Using a bag of color

tiles, explore the size of the drawn rectangles by filling them in with color tiles.

Count the color tiles and record how many tile’s you needed as well as ho, many

rows of tiles you had for that rectangle. Make your own addition problem for your

rectangle (ex: One rectangle was filled in by 16 color tiles; each row had four tiles in

it; I had four rows of tiles; I can make my own addition problem 4+4+4+4=16).

Make a Rectangle: Give out 12 color tiles. Have students create their own

rectangles using 12 tiles or less. How many combinations can they come up with?

Record the number of creations you came up with, including how many tile’s you

used.




students look at rectangles and tell you what their properties are. Show how they

can divide a rectangle and count to create an addition problem.

The Greedy Triangle: Explore dividing rectangles using triangles. Allow students to

create their own rectangles from triangles. Allow them to explore the possibilities of

making other shapes with triangles.

To Half or not to half: Use a spinner with ½, one-third, and ¼ labeled. Take turns

spinning, and cutting a “pizza” according to the fraction spun.


Lesson Strand 4: Divide circles and rectangles into two, three or four equal parts. Describe

the result either as two halves, three thirds, and four fourths to recognize that equal parts that

make the whole do not need to be the same shape as the original shape.

LEARNING PLANS AND ACTIVITIES LEVEL D: Explore and engage in the differences between circles and rectangles.

Geo Board Rectangles: using a geo-board, make a rectangle. Allow student to use

senses to explore the rectangle on the Geo Board. Divide the rectangle into half,

third and quarter sections. Allow students to engage using sight and touch.

Geometry Hunt: Point out circles and rectangles to students and encourage

exploration and engagement in activity.

Making Pizza: Create a rectangular and circular pizza with the students. Allow them

to explore the pizza and engage in the steps to create and divide the pizza using

their senses.

Paper Rectangle Play: Use a piece of 8.5x11 papers (shaped like a rectangle) fold it

in half and cut down the middle. Explore what shape the two halves made. Let the

students explore the whole piece of paper, and then the paper divided into sections

LEARNING PLANS AND ACTIVITIES LEVEL C: Compare, estimate and construct rectangles and circles in order to establish an

understanding of equal parts.

Paper Rectangle Play: Use a piece of 8.5x11 paper (shaped like a rectangle) Fold it in

half and cut down the middle. Explore what shape the two halves made. Show how

putting them together creates one shape, while taking them apart creates another.

Follow the same instructions with thirds and fourths. Compare shapes.

Geoboard Rectangles: using a geo-board, make a rectangle. Work with student to

divide the rectangle into two different parts. Work to divide rectangle into four

different parts. Use paper, pencils and rulers if necessary to divide rectangle into


equal parts. After splitting the shape into equal parts, ask the kids what shapes they

make.

Geometry Hunt: Take a walk around the classroom and find rectangles and circles.

Work with a partner to divide these items into halves, thirds, and fourths.

Making Pizza: Follow pizza making steps to create both a rectangular and circular

pizza with the kids. Ask them how they would divide it into halves, thirds, fourths.

Enjoy your pizza! Make individualized pizzas for the children to practice on.

LEARNING PLANS AND ACTIVITIES LEVEL B: Investigate, compare and construct using different activities to understand the

relationship between a shape and its parts.

Geo Board Rectangles: using a geo-board, make a rectangle. Record how many

ways you can divide the rectangle into two equal parts. Then record how many

ways you can divide your rectangle into three different parts, then four.

Geometry Hunt: Take a walk around the outside of the school, with a camera. Look

for rectangles and circles. When found take the circles and rectangles and

demonstrate how to divide them in half, thirds and fourths. Take a picture.

Making Pizza: Follow pizza making steps to create both a rectangular and circular

pizza with the kids. Ask them how they would divide it into halves, thirds, fourths.

Enjoy your pizza!

Paper Rectangle Play: Use a piece of 8.5x11 paper (shaped like a rectangle) Give

children instructions to fold the paper in half, thirds, and fourths. Ask them what

they notice about each shape and how it has changed as they create more parts.


MATERIALS/ RESOURCES www.k-5mathteachingresources.com

www.lakeshorelearningstore.com

www.mathwords.com

www.adaptedmind.com

www.kidsmathgamesonline.com

www.exchange.smarttech.com

www.softschools.com (identifying geometric shapes)

www.pbs.org

BOOKS If I were a Quadrilateral , by Molly Blaisdel

If I were a Polygon , by Molly Blasidel


http://www.pbs.org/

http://www.softschools.com/

http://www.exchange.smarttech.com/

http://www.kidsmathgamesonline.com/

http://www.adaptedmind.com/

http://www.mathwords.com/

http://www.lakeshorelearningstore.com/

http://www.k-5mathteachingresources.com/

Essential Thinking Skills and Behaviors: Definitions and Explanatory Notes

EngagementEngagement is a behavior involving the focusing of the mental process upon someone or something. It is commonly demonstrated by a voluntary and sustained or repeated attention to stimuli. Engagement may be expressed through a wide variety of sensory, motor and/or speech, communication and language forms. Student’s physical, emotional, cognitive, social and cultural development impact significantly on the nature of the attention they are able, or choose, to demonstrate. Therefore, individual modes of student engagement need to be identified, taught, developed, refined, and/or expanded upon. These modes may include, but not limited to: exploration through touching, listening, looking, smelling, and/or tasting; and increase/decrease or initiation/cessation of body movement; and vocalizations/verbalizations. Without engagement, additional information processing cannot take place.

Explanatory Notes: When providing students with opportunities for engagement it is critical that the same

opportunities be presented daily over time. Variation in the means of story presentation, along with increased familiarity with expectations, should serve to sustain student motivation and interest. In addition, the presentation of materials should be supplemented with ongoing, direct instruction to facilitate targeted skills and behaviors specific to the content area.

Emphasis should be placed on relating meaningful activities/materials to student’s prior knowledge and experience.

Extensive efforts should be placed on involving, to the greatest extent possible, a student’s family in providing opportunities for student engagement. Such efforts might include: planning instructional materials; inviting family members to read stories in class; planning family related fairs; encourage family members to learn about and visit public and other community resources; and responding to educational needs as expressed by a student’s family.

Each student should possess a public library card, and be a member of other community organizations when appropriate and feasible.


Environmental Differentiation

Environmental Differentiation is the recognition of differences in the attributes of things/places with which, and individuals with whom, one comes in contact and includes recognition of self as a distinct entity. It is usually demonstrated by distinct patterns of exploration or reaction to different stimuli and may be evidenced through various modes of student response. Environmental Differentiation may, but does not necessarily, include knowledge of the names/functions of the materials/places/individuals involved.

Explanatory Notes: The purpose for having students learn to differentiate is to help them develop a basis

from which they will be able to use materials functionally, make informed choices and develop concepts related to materials. However, instruction related to Environmental Differentiation should not preclude instruction toward other essential skills or behaviors (e.g. Functional Use of Objects; Self Regulation).

When various content area materials are being functionally used by a student, the student is already demonstrating environmental differentiation.

For a student with a limited response repertoire (i.e. a student with additional significant physical/sensory impairments), differentiation may be evidenced through the engagement with different stimuli. For example, a student might demonstrate differentiation simply by focusing on or maintaining hand contact with one stimulus for a significantly longer period of time than another stimulus.

For a student who is not environmentally differentiating, an implication for instruction is that the student may need to be provided with increased opportunities for sensory exploration of/interaction with the materials and for using the materials functionally. In providing these increased opportunities, it is essential to insure that a student’s safety and dignity are maintained, especially with regard to social context and age appropriateness.


Conceptualization

Conceptualization is the formation of mental representations or ideas for categorizing information or mental connections to prior experiences. As children develop, new concepts about objects, people, places and the relationship between them are continually being learned. Conceptualization may be demonstrated through a range of initiated utterances/actions or responses to questions, comments, or directions. Individual communication modes may vary, and need to be identified, taught, developed, refined and/or expanded upon.

Explanatory Notes: In identifying a concept that a student is expected to learn, it is important to make known

to instructors and students the intended definition of that concept.

It is important that incidental displays of knowledge of identified concepts/meanings are noted/documented as they occur throughout the day.

In order for a student to demonstrate the knowledge of a concept/meaning, it is necessary for the student to exhibit a behavior that is intentional. For instance, a student who might typically sit without movement would not be considered to demonstrate knowledge of “wait” by remaining in a motionless position. Rather, the student would need to initiate a movement at the proper turn-taking time in order to have displayed knowledge of what “waiting” means.

Learning environments should be picture cue/object cue/print rich, so as to facilitate the learning of the concepts.

In expecting demonstration of knowledge of specific concepts, it is important that the other concepts/meanings used contextually by the instructor are known by the student or made clear (e.g. through demonstration) to the student. This is especially important with regards to concepts/meanings that define an expected mode of performance (e.g. touch, press, look).

Beyond the concepts/meanings that are found in this curriculum frameworks, which is based on the ELA and Math Common Core Learning Standards and Science and Social Studies NYS/NYC Scope and Sequence for grade level instructional content, there are other NYS standards based concepts that may be important to explicitly address in relation to each content area. For example, in Career Development and Occupational Studies, these may include: work; start/begin; end/finish; put away/put back; more/enough; and no. In Health, these may include; privacy, danger, emergency, clean, stranger, helper, friend, “feeling uncomfortable”, sick/hurt, exercise, medicine, and choice. These other concepts can identified by referring to New York State’s Learning Standards for Family and Consumer Sciences, Health, Phys. Ed., Career Development


and Occupational Studies, The Arts, as well as, the NYSAA Alternate Grade Level Indicators for Science and Social Studies, and the grade level Extensions for English Language Arts and Math.

In addition to basic key concepts related to a content area, it is critical that students learn concepts needed for them to use their individual system of communication during assessment and instructional situations (e.g. point, touch, look, press, pick-up, give, tell, me/say).


Functional Use of Objects

Functional Use of Objects is the appropriate utilization of materials in alignment with the purpose(s) for which they exist in a given culture. It may be applied to the use of an object that has undergone modifications. Students unable to utilize materials functionally due to a physical impairment may achieve this standard by communicating the purpose of the materials.

Explanatory Notes: Emphasis should be placed on involving family members in encouraging a student to use

content related materials during functional daily activities. For example, in the area of English Language Arts/Native Language Arts, some activities might include: giving a greeting card to a relative or friend; bringing a shopping list, with accompanying tangible symbols, to the supermarket; marking important dates on a calendar; labeling household items; and engaging with books and magazines.


Problem SolvingProblem solving is the directing of one’s actions towards achieving a goal that presents uncertainty or difficulty. It presupposes an awareness of the existence of a problem. It generally involves taking into account factors related to a problem, and trying or considering more than one way to solve a problem. Resolution of a problem may be unattainable even though problem solving behaviors have been applied. Explanatory Notes:

When considering problem solving, an emphasis should be placed on a student’s involvement in the process of solving a problem rather than on a student’s resolution of a problem.

A student’s performance of Problem Solving may take the form of a variety of actions/response modes.

An implication for instruction is a recognition of the need to provide students with adequate time and opportunities “to try” or consider more than one way of solving a problem before intervening in the process.

Problem Solving may be accomplished through the completion of tasks formulated with the intent of providing opportunities for students to demonstrate specific problem solving behaviors. It may be accomplished, however, within a broader framework of general content area assignments, which naturally include a variety of problem solving situations.

A distinction involves the student’s completion of the task that the student has previously demonstrated an ability to do readily, while problem solving involves an element of uncertainly or difficulty for the student.

When a student secures needed help, instructors should not simply complete an action for the student. Rather, the student should be guided through the problem solving process, with help provided only to the extent actually needed by the student. In this way, a student hopefully will begin to approach future problem solving situations by trying another way before securing help.


Self-Regulation

Self-regulation is an ongoing monitoring of ones’ own sensory/physical/social/cognitive conditions, and an adjusting of these conditions to maintain a desired and comfortable internal state. Self-regulation involves knowing and applying a repertoire of behaviors to diverse settings, making informed choices, and acting upon or indicating a desire or need for change.Explanatory Notes: (Self-Regulation, General) The following conditions may necessitate self-regulation

o Sensory, including sensitivities to light, sound texture taste, smell and surrounding physical space.

o Physical, including pain, pleasure, hunger, thirst, discomfort, fatigue, hyperactivity, illness, and a need to use the bathroom.

o Emotional, including distress, loneliness, need for solitude, anger, aggressiveness, withdrawal, sadness, frustration, disappointment, elation, fear, anxiety, and stress.

o Social, including segregation, lack of privacy, and numbers/appearance/behaviors of individuals in the environment

o Cognitive, including level of subject content (either too high or too low), nature of subject matter presentation, and lack of appropriate means for accessing/expressing information.

Students may exhibit behaviors that are self-regulatory in nature but fail to meet the standard for self-regulation (as they are not desired behaviors). These include:

o Behaviors which are unsafe (e.g. abuse to self or others; object destruction)o Behaviors which interfere with one’s own learning or the learning of others (e.g.

replacing attention to task with stereotypic response; continuous noise production)o Behaviors which interfere with positive social interactions (e.g. grabbing belongings

of others; public disrobing).

Recognition should be given to the fact that most individuals engage in some common mannerisms or behaviors (e.g. finger-tapping; shaking of a glass with ice cubes; nail biting) through which they express their internal state. These behaviors, for the most part, are accepted by other individuals and do not seem to interfere in the development and maintenance of social relationships. Although the behavior of a student may differ in nature from these more common expressions, there is an expectation that such student behaviors, if exhibited in a safe and healthy manner, should be understood and accepted by others as an inherent part of “who” the student is. In fact, it may be precisely through such a particular behavior that a student is self-regulating.

In order to maintain internal control for self-regulating, students may need to be provided with positive behavioral support systems, including attention to communication and/or sensory needs and abilities.


Explanatory Notes: (Self-Regulation, Informed Choice-Making) An informed choice refers to a student’s selection (within a single activity) of one of two

(or possibly more) objects, activities, or environments for which opportunities for exploration/acquisition of knowledge have been provided. The informed nature of the choice may be demonstrated through a consistent response to an initial presentation (e.g. verbal; tangible; pictorial) and then to a second presentation with order/position altered**. If any doubt about a student’s selection still exists, a final presentation in either order/position can be made. Informed choice may be demonstrated in a different manner by a student who clearly has a demonstrated knowledge of the concept “yes” or “no”. Such a student needs only to reaffirm his/her choice by responding “yes” or “no” when asked if this choice is what he/she wants. Informed choice may also be demonstrated through independent indication of a choice different from the objects, activities, or environments offered.

An informed choice also assumes that a student possesses an equal opportunity to choose either of the sections available. This is especially important to consider when the student has limited motor and/or sensory abilities.

Given the concept of informed choice, various implications for instruction are evident, and include consideration of the placement of materials, the communicative means utilized by students to make choices, and steps taken to familiarize students with materials/activities/ environments available as choices.

Instructional efforts to increase a student’s opportunities to make informed choices will increase the probability of a student’s demonstration of general self-regulatory behavior, decision-making and awareness of the consequences of one’s decisions. Therefore, instructional provision for facilitating informed choice-making should be ongoing throughout a students’ day.

**It is recognized that repeatedly presenting choices in a different order/position may result in frustration on the part of students. Therefore, this type of procedure for insuring informed choice is designed primarily for the purpose of occasional assessment rather than for the purpose of ongoing instruction.


Social Interaction

Social Interaction is reciprocal in nature and involves the use of communication for a variety of purposes. These may include having one’s desires or needs realized, or becoming involved in personal relationships. Such relationships may vary and may include being a one-time partner on a project, a member of a frequently meeting group, a helper, or a friend. Social interaction presupposes self-recognition, that is, the perception of self as a separate being, distinct form people/objects in the surrounding world. Explanatory Notes:

In general, communication refers to a process through which individuals receive from, transmit to, or exchange with others information, feelings or thoughts.

In order to help a student to learn how to socially interact, it is imperative that a student be assessed in a comprehensive and ongoing manner to determine which modes of communication are most appropriate for that student. Individual communication modes may vary and need to be identified, taught, refined, and /or expanded upon. Some students may even need to have meaning assigned to some of their naturally occurring behaviors (e.g. movements; facial expressions; vocalizations) so that they might begin intentionally to use these behaviors to communicate. Such a process should result in a student having ongoing access to and use of an effective system of communication.

In interactions with a student, it is critical to be aware of and respond immediately and consistently to any form of communication exhibited by the student, especially one of a subtle nature. In so doing, one is helping the student understand and come to expect that a communication causes others to act or respond. If such student communications are not attended to, the student most likely will discontinue communication since his/her communicative intent is not being realized.

It is beneficial to use a variety of communicative means (e.g. pictures, speech, gestures) when the student is engaged in receptive communication, even if some of these means appear to be of a nature that is beyond a student’s present cognitive level. However, a student should be taught and then have access to a means of communicating expressively that is consistent with that student’s present cognitive level.

It is critical that a student’s requests/directives and rejections/protests be addressed. Even if it is determined that the student’s attempt to control the environment cannot be accommodated, the attempt should at least be acknowledged.

To maximize a student’s social interactions, emphasis needs to be placed on providing a student with an opportunity to communicate in the context of authentic situations and environments.


A student’s alternative/augmentative communication system (e.g. a device, board, and/or set of tangible symbols) needs to be accessible to the student throughout the day - at home, at school, and in community settings.

Significant emphasis should be placed on encouraging a student’s communication partners to accept and respond to alternate/augmentative forms of communication.

In order to interpret a student’s utterance or other communication as a request, it is subsequently necessary for the student to accept/interact with the referred to object/action/person. Otherwise, it may be that the student is merely recognizing the existence of an object/action/person.

To the greatest extent possible, and certainly to the degree mandated by a student’s IEP and by applicable educational regulations, a student should be learning to socially interact with students receiving general education services.

Certainly there is value in social interactions that occur between students and adults. Adults are able to provide appropriate models of communication and to respond readily to student initiations of communications. However, a significant emphasis also needs to be placed on providing opportunities for students to interact with peers (those receiving general and special education services).

When teaching a student to use a communication system expressively, it is critical that an instructor consistently model the use of the system in communications with the student.

The District 75 Office of Technology Solutions provides resources to students, staff,

administrators, and parents in the areas of instructional, informational, and assistive

technologies.


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