Massachusetts Curriculum Framework



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Massachusetts

Curriculum Framework

for

Mathematics

Grades Pre-Kindergarten to 12

Changes to 2011 Framework Highlighted or Tracked
DRAFT FOR PUBLIC COMMENT

November 29, 2016

ese logo

ese logo

This document was prepared by the

Massachusetts Department of Elementary and Secondary Education

Mitchell D. Chester, Ed. D., Commissioner



Board of Elementary and Secondary Education Members

Mr. Paul Sagan, Chair, Cambridge

Mr. James Morton, Vice Chair, Boston

Ms. Katherine Craven, Brookline

Dr. Edward Doherty, Hyde Park

Dr. Roland Fryer, Concord

Ms. Margaret McKenna, Boston

Mr. Michael Moriarty, Holyoke

Dr. Pendred Noyce, Boston

Mr. James Peyser, Secretary of Education, Milton

Ms. Mary Ann Stewart, Lexington

Mr. Nathan Moore, Chair, Student Advisory Council, Scituate

Mitchell D. Chester, Ed.D., Commissioner and Secretary to the Board

The Massachusetts Department of Elementary and Secondary Education, an affirmative action employer, is committed to ensuring that all of its programs and facilities are accessible to all members of the public.

We do not discriminate on the basis of age, color, disability, national origin, race, religion, sex, or sexual orientation.

Inquiries regarding the Department’s compliance with Title IX and other civil rights laws may be directed to the

Human Resources Director, 75 Pleasant St., Malden, MA, 02148, 781-338-6105.


© 2011 Massachusetts Department of Elementary and Secondary Education

Permission is hereby granted to copy any or all parts of this document for non-commercial educational purposes. Please credit the “Massachusetts Department of Elementary and Secondary Education.”

This document printed on recycled paper
Massachusetts Department of Elementary and Secondary Education

75 Pleasant Street, Malden, MA 02148-4906

Phone 781-338-3000 TTY: N.E.T. Relay 800-439-2370

www.doe.mass.edu



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Commissioner’s Letter ii

Acknowledgements iii
Introduction 1
Guiding Principles for Mathematics Programs in Massachusetts 8
The Standards for Mathematical Practice 14
Pre-Kindergarten–Grade 8

Introduction 18

Pre-Kindergarten 21

Kindergarten 25

Grade 1 28

Grade 2 32

Grade 3 36

Grade 4 41

Grade 5 46

Grade 6 51

Grade 7 57

Grade 8 63



High School

Conceptual Categories

Introduction 68

Number and Quantity 72

Algebra 76

Functions 83

Modeling 90

Geometry 92

Statistics and Probability 100



High School Model Pathways and Model Courses

Introduction 106



Model Traditional Pathway

Model Algebra I 111

Model Geometry 119

Model Algebra II 126



Model Integrated Pathway

Model Mathematics I 132

Model Mathematics II 140

Model Mathematics III 150



Model Advanced Courses

Model Precalculus 158



Model Advanced Quantitative Reasoning 164

Making Decisions about Course Sequences and the Model Algebra I Course….………… ..169

Standards for Mathematical Practice Grade Span Descriptions …………………………173

Application of Standards for English Language Learners and Students with Disabilities…….. 182

Glossary: Mathematical Terms and Illustrations 186

Tables and Illustrations of Key Mathematical Properties, Rules, and Number Sets 195

Sample of Works Consulted 199

Massachusetts Department ofmassachusetts state seal

Elementary and Secondary Education

75 Pleasant Street, Malden, Massachusetts 02148-4906 Telephone: (781) 338-3000

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