Massachusetts
Curriculum Framework
for
Mathematics
Grades Pre-Kindergarten to 12
Changes to 2011 Framework Highlighted or Tracked
DRAFT FOR PUBLIC COMMENT
November 29, 2016
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
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 of
Elementary and Secondary Education
75 Pleasant Street, Malden, Massachusetts 02148-4906 Telephone: (781) 338-3000
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