common%core%(%math%6th!grade!7!pre7algebra 7th!grade!7!pre7algebra 7th!grade!7!algebrai...

ì Common Core -‐ Math DRAFT Math Progressions

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2013-‐14 PMS Math Progressions 13-‐14

5th Grade

6th Grade Math

6th Grade -‐ Pre-‐Algebra

7th Grade -‐ Pre-‐Algebra

7th Grade -‐ Algebra I


8th Grade -‐ Intro to Algebra

8th Grade -‐ Geometry

13-‐14


9th Grade -‐ Geometry

9th Grade – Algebra II

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Transitions Over Three Years

ì  The new CCSS will be implemented in phases over the next several years.

ì  Many decisions have yet to be made, including: ì  how and when to phase the implementaLon; ì  development of curriculum and selecLon of course materials and texts; ì  whether to follow a “tradiLonal” or “integrated” model for teaching

math concepts at the high school level; ì  how to support learners who require either addiLonal challenge or

addiLonal support; ì  how and when to offer pathways to accelerate and pathways to allow

more Lme for mastery of content

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Part 1

ì  Common Core Math at Piedmont Middle School

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Common Core 6 Math 13-‐14 14-‐15

5th Grade Math è 6th Grade – CC6 Math

Staff reflecLons as they apply to Piedmont Students: How is CC-‐6 Math different from our current Math 6? The 1997 6th grade standards addressed: 1) Number Sense; 2) Algebra & FuncLons; 3) Measurement & Geometry; 4) StaLsLcs & Data Analysis. The new CC Standards address: 1) RaLo & ProporLon; 2) Number System; 3) Expressions and EquaLons; 4) Geometry; 5) StaLsLcs & Probability. The new CC Standards in CC6 Math also include brand new topics: Absolute Value (Algebra 1); Greatest Common Factor; Variability & Sampling; and seven addiLonal standards currently found in 7th grade math (Pre-‐Algebra) : Ra*o & Propor*on Number System Expressions & Equa*ons Geometry Sta*s*cs & Probability Units Graphs & Tables Exponents Triangles DistribuLons

Greatest Common InequaliLes Pythagorean Factor Theorem Absolute Value Perimeter & Area

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1997 CA Math Standards vs. Common Core Math Standards – 6th Grade

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Heterogeneous CC 6 Math 13-‐14 14-‐15


Staff reflecLons as they apply to Piedmont Students: Why change to a heterogeneous Common Core Math 6? A fundamental principle of the CCSS is that a mastery of algebra is essenLal to a student’s success and conLnued interest and engagement in mathemaLcs. •  Under CC, math standards are changing in 5th, 6th and 7th grade, eliminaLng

repeLLon. It was this repeLLon that made it possible for some students to “skip” 6th Grade Math.

•  CC6 Math will be more challenging than 6th Grade Math. A full year will be needed to establish a solid base of knowledge for the CC courses that follow.

•  CC math curriculum lends itself to differenLaLon. Students who master the material quickly can achieve greater depth in the subject area. Students who require more Lme can be successful at their level and engage in more depth when appropriate.

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Heterogeneous CC 6 Math 13-‐14 14-‐15


Staff reflecLons as they apply to Piedmont Students: Why change to a heterogeneous Common Core Math 6? •  The end of fich grade is too early to make a decision on most of our students’ math

pathways. It is more appropriate to make decisions about compression when student logic and mathemaLcal reasoning is more developed.

•  With that said, previous STAR Exam and AP Exam results show that most 6th grade students who have advanced to Pre-‐Algebra (under 1997 standards) performed well in these assessments.

•  Next fall’s 6th graders though, will have new CC challenges in all subject areas. At this point, it appears to be “too much” to add math compression to these challenges. Delaying math compression is expected to reduce student stress.

•  The District needs to develop pracLcal experience with the new curriculum standards and assess how students respond to the new challenges before considering pathways for compression.

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6th Grade -‐ Math 6 è 7th Grade – CC7 Math

Staff reflecLons as they apply to Piedmont Students: How is CC-‐7 Math different from our current Pre-‐Algebra? The 1997 -‐ 7th grade standards addressed: 1) Number Sense; 2) Algebra & FuncLons; 3) Measurement & Geometry; 4) StaLsLcs & Data Analysis. The new CC Standards address: 1) RaLo & ProporLon; 2) Number System; 3) Expressions and EquaLons; 4) Geometry; 5) StaLsLcs & Probability. The new CC Standards in CC7 Math also include Algebra topics: Absolute Value; Graphing InequaliLes; and 11 brand new standards: Ra*o & Propor*on Number System Expressions & Equa*ons Geometry Sta*s*cs & Probability MulL-‐step real RaLonal number Percentage-‐variable Scaling Visual overlap world problems line operaLons addiLon relaLonships drawings Variability inferences Construct equaLons 2D to 3D Probability models

transformaLons Area of a circle Solid shape models

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1997 CA Math Standards vs. Common Core Math Standards – 7th Grade

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6th Grade -‐ Pre-‐Algebra è 7th Grade – CC8 Math


Staff reflecLons as they apply to Piedmont Students: 6th & 7th grade students currently in Pre-‐Algebra are on track to take AP Calculus. By progressing into CC8 Math, these students will receive a stronger math foundaLon because of their exposure to 11 new content standards leading into Algebra I. AddiLonally, by progressing into CC8 Math rather than CC Algebra I, teachers will bridge the wide curriculum gap between our current Pre-‐Algebra course and CC Algebra I.

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1997 CA Math Standards (Pre-‐Algebra) vs. Common Core Math Standards – 8th/Algebra I

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1997 CA Math Standards vs. Common Core Math Standards – 8th/Algebra I

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Algebra I & Geometry Students 13-‐14 14-‐15





7th Grade -‐ Algebra I è 8th Grade – Geometry

8th Grade -‐ Algebra I è 9th Grade – Geometry

8th Grade -‐ Intro to Algebra è 9th Grade – Algebra I

8th Grade -‐ Geometry è 9th Grade – Algebra II

Staff reflecLons as they apply to Piedmont Students: All students currently enrolled in Algebra I or above will conLnue in their current sequencing the following year. In order to prepare students for the new State assessments, teachers will embed mulLple CC Standards in Algebra I, Geometry, and Algebra II during the 14-‐15 school year and beyond.

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Decision Point: Middle School Compression

5th grade 6th Grade 7th Grade 8th Grade

5th Grade Math è CC-‐6 Math è CC-‐7 Math CC-‐8 Math

î CC-‐7/CC-‐8 (compressed) CC-‐8/CC-‐Alg 1 (compressed)

During the 14-‐15 school year, invesLgate possible compression beginning in 15-‐16 or 16-‐17. Comparable school districts offer varying middle school compression paths.

Staff reflecLons as they apply to Piedmont Students: Teachers will use the 14-‐15 school year to assess student performance in CC6 Math, CC7 Math, and CC8 Math in order to determine the readiness of students for a possible compressed course at the middle school level. If student readiness indicates the need for a compressed course, teachers will use their experience of teaching CC6 Math, CC7 Math, and CC8 Math during the 14-‐15 school year to create a fully developed compression course for 15-‐16. A compressed CC7/CC8/CC Alg 1 is the equivalent of 3 years of course material compressed over two years in the 7th and 8th grades.

5th Grade 6th Grade 7th Grade 8th Grade

5th Grade Math è CC-‐6 Math è CC-‐7 Math è CC-‐8 Math

î CC-‐8/CC-‐Alg 1

Example #2

Example #3

5th grade 6th Grade 7th Grade 8th Grade

5th Grade Math è CC-‐6 Math è CC-‐7 Math CC-‐8 Math

î CC-‐6/CC-‐7 (compressed) è CC-‐7/CC-‐8 (compressed) CC-‐Alg 1

Example #1

Decision points: PHS Compression & Integrated Math

6th Grade -‐ Pre-‐Algebra è 7th Grade – CC8 Math è 8th Grade – CC Algebra I

7th Grade -‐ Pre-‐Algebra è 8th Grade – CC8 Math è 9th Grade – CC Algebra I

7th Grade -‐ Algebra I è 8th Grade – Geometry è 9th Grade – Algebra II

8th Grade -‐ Algebra I è 9th Grade – Geometry è 10th Grade – Algebra II

8th Grade -‐ Intro to Alg è 9th Grade – Algebra I è 10th Grade -‐ Geometry

During the 14-‐15 school year, invesLgate possible transiLon to Integrated Math beginning in 15-‐16. Also determine appropriate HS Course compression opLon (e.g. Alg2/Math Analysis).

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Decision points: Pathway Examples for “Phase-‐In” – Traditional Model

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Current 5th Grade Students

*The tradiLonal method of math course progression is used in this example to help simply the charts. There is sLll a decision to be made around conLnuing with a tradiLonal model or migraLng to the integrated math model. **This chart provides an example of high school compression occurring in CCAlg2/Math Analysis. It is just that … an example. We have not yet determined where compression will occur at the high school level. That decision will coincide with the tradiLonal/integrated math decision. Once we decide whether to stay tradiLonal or move to integrated, then we can decide when to offer compression at the high school level.

Decision points: Pathway Examples for “Phase-‐In”

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Current 6th Grade Math Students

*The tradiLonal method of math course progression is used in this example to help simply the charts. There is sLll a decision to be made around conLnuing with a tradiLonal model or migraLng to the integrated math model. **This chart provides an example of high school compression occurring in CCAlg2/Math Analysis. It is just that … an example. We have not yet determined where compression will occur at the high school level. That decision will coincide with the tradiLonal/integrated math decision. Once we decide whether to stay tradiLonal or move to integrated, then we can decide when to offer compression at the high school level.


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Current 6th Grade Pre-‐Algebra Students

*The tradiLonal method of math course progression is used in these examples to help simply the charts. There is sLll a decision to be made around conLnuing with a tradiLonal model or migraLng to the integrated math model. **This chart provides an example of high school compression occurring in CCAlg2/Math Analysis. It is just that … an example. We have not yet determined where compression will occur at the high school level. That decision will coincide with the tradiLonal/integrated math decision. Once we decide whether to stay tradiLonal or move to integrated, then we can decide when to offer compression at the high school level.


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Current 7th Grade Pre-‐Algebra Students



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Current 7th Grade Algebra I Students

All students currently enrolled in Algebra I or above will conLnue in their current sequencing the following year. In order to prepare students for the new State assessments, teachers will embed mulLple CC Standards in Algebra I, Geometry, and Algebra II during the 14-‐15 school year and beyond.


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Part 2

ì  With new standards come new assessments.

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CST vs. CAASPP Assessment 5th Grade Math

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CST vs. CAASPP Assessment 7th Grade Math

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CST vs. CAASPP Assessment Algebra I

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From Standards to … Curriculum/Instruction/Assessment

ì  2013/14 Professional Development has focused on: ì  Introducing the Common Core Standards ì  Understanding the Shics in ELA/Math ì  ImplicaLons of Common Core Standards on:

ì  Course Sequencing ì  Assessments ì  Curriculum Development

ì  2014/15 and beyond Professional Development will focus on: ì  ImplicaLons of Common Core Standards on:

ì  Curriculum Development ì  InstrucLonal PracLce ì  Student Performance/Assessments ì  InstrucLonal Materials

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ì Silicon Valley Math Initiative (SVMI) A Math Curriculum/InstrucLon/Assessment Partnership

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Q&A ì  Common Core Math

Upcoming opportuniLes for community engagement: •  4/1 – Tri-‐School Site Council •  4/2 – Incoming 6th Grade Parent InformaLon Night •  4/2 – Elementary CPT – Including Secondary Math Teachers – Silicon Valley

Math IniLaLve PresentaLon (SVMI) •  4/2 – MHS Site Council •  4/3 – PHS Site Council •  4/8 – PMS Site Council

•  4/9 – PUSD Board of EducaLon MeeLng •  4/24 – PUSD Curriculum Forum MeeLng •  5/6 – Tri-‐School Site Council •  5/7 – MHS Site Council •  5/7 – Parent EducaLon Night •  5/8 – PHS Site Council •  5/13 – PMS Site Council •  5/14 – PUSD Board of EducaLon MeeLng •  5/28 – PUSD Board of EducaLon MeeLng

Visit our updated Common Core Math FAQ: hmp://www.piedmont.k12.ca.us/wp-‐content/uploads/2014/03/CCMathFAQ.pdf

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