Massachusetts Mathematics Curriculum Framework — 2017
MATHEMATICS
Grades Pre-Kindergarten to 12
i
Massachusetts
Curriculum
Framework ¨C
2017
This document was prepared by the Massachusetts Department of Elementary and Secondary Education
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, Cambridge
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.
? 2017 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.¡±
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
doe.mass.edu
Massachusetts Department of
Elementary and Secondary Education
75 Pleasant Street, Malden, Massachusetts 02148-4906
Dear Colleagues,
I am pleased to present to you the Massachusetts Curriculum Framework for Mathematics adopted by the Board of
Elementary and Secondary Education in March 2017. This Framework builds upon the foundation of the 2010
Massachusetts Curriculum Framework for Mathematics as well as versions of the Massachusetts Mathematics Framework
published since 1995.
The current Framework incorporates improvements suggested by Massachusetts educators after six years of experience in
implementing the 2010 standards in their classrooms. These revised pre-kindergarten to grade 12 standards are based on
research and effective practice, and will enable teachers and administrators to strengthen curriculum, instruction, and
assessment.
The 2017 standards draw from the best of prior Massachusetts standards, and represent the input of hundreds of the
Commonwealth¡¯s K¨C12 and higher education faculty. The 2017 standards present the Commonwealth¡¯s commitment to
providing all students with a world-class education.
This revision of the Framework retains the strengths of previous frameworks and includes these improved features:
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Increased coherence across the grades and improved clarity of mathematical terms and language to describe
expectations for students.
Clear expectations for student mastery of basic addition, subtraction, multiplication, and division facts.
An enhanced high school section that includes: 1) clearer model course standards; and 2) guidance on making
decisions for course sequences and the model Algebra I course, along with options for various course-taking
pathways.
Guidance for moving students into an Algebra I course by grade 8 and through Calculus in high school; and
More detailed descriptions about rigor and aspirations for students with a stronger emphasis on how the content
standards, the standards for mathematical practice, and the guiding principles prepare students for college,
careers, and civic participation.
In the course of revising these standards, the Department received many valuable comments and suggestions. I want to
thank everyone who contributed their suggestions and ideas to make these revised standards useful for educators,
students, families, and the community. In particular, I am grateful to the members of the Mathematics Standards Review
Panel and our Content Advisors for giving their time generously to the project to improve the learning standards for
Massachusetts students. I am proud of the work that has been accomplished.
We will continue to collaborate with educators to implement the 2017 Massachusetts Curriculum Framework for
Mathematics.
Thank you again for your ongoing support and for your commitment to achieving the goal of improved student
achievement for all our students.
Sincerely,
Mitchell D. Chester, Ed. D.
Commissioner of Elementary and Secondary Education
Table of Contents
Acknowledgments ......................................................................................................................................................5
Introduction ................................................................................................................................................................8
Guiding Principles for Mathematics Programs in Massachusetts........................................................................ 14
The Standards for Mathematical Practice ........................................................................................................... 16
Standards for Mathematical Content Pre-Kindergarten¨CGrade 8 ................................ 19
Organization of the Pre-Kindergarten to Grade 8 Content Standards ................................................................ 20
Pre-Kindergarten ......................................................................................................................................... 22
Introduction ......................................................................................................................................................... 22
Pre-Kindergarten Overview ................................................................................................................................. 23
Pre-Kindergarten Content Standards .................................................................................................................. 24
Kindergarten ................................................................................................................................................... 25
Introduction ......................................................................................................................................................... 25
Kindergarten Overview ........................................................................................................................................ 26
Kindergarten Content Standards ......................................................................................................................... 27
Grade 1 ................................................................................................................................................................ 29
Introduction ......................................................................................................................................................... 29
Grade 1 Overview ................................................................................................................................................ 30
Grade 1 Content Standards ................................................................................................................................. 31
Grade 2 ............................................................................................................................................................... 33
Introduction ......................................................................................................................................................... 33
Grade 2 Overview ................................................................................................................................................ 34
Grade 2 Content Standards ................................................................................................................................. 35
Grade 3 ............................................................................................................................................................... 37
Introduction ......................................................................................................................................................... 37
Grade 3 Overview ................................................................................................................................................ 38
Grade 3 Content Standards ................................................................................................................................. 39
Grade 4 ............................................................................................................................................................... 42
Introduction ......................................................................................................................................................... 42
Grade 4 Overview ................................................................................................................................................ 43
Grade 4 Content Standards ................................................................................................................................. 44
Grade 5................................................................................................................................................................ 48
Massachusetts Curriculum Framework for Mathematics
1
Introduction ......................................................................................................................................................... 48
Grade 5 Overview ................................................................................................................................................ 49
Grade 5 Content Standards ................................................................................................................................. 50
Grade 6 ............................................................................................................................................................... 54
Introduction ......................................................................................................................................................... 54
Grade 6 Overview ................................................................................................................................................ 56
Grade 6 Content Standards ................................................................................................................................. 57
Grade 7 ................................................................................................................................................................ 61
Introduction ......................................................................................................................................................... 61
Grade 7 Overview ................................................................................................................................................ 62
Grade 7 Content Standards ................................................................................................................................. 63
Grade 8 ............................................................................................................................................................... 67
Introduction ......................................................................................................................................................... 67
Grade 8 Overview ................................................................................................................................................ 68
Grade 8 Content Standards ................................................................................................................................. 69
The High School Standards for Mathematical Content ......................................................... 72
Introduction ......................................................................................................................................................... 73
High School Content Standards by Conceptual Categories ................................................................................. 76
Conceptual Category: Number and Quantity [N] ....................................................................... 77
Introduction ......................................................................................................................................................... 77
Conceptual Category: Number and Quantity Overview [N] ................................................................................ 78
Conceptual Category: Number and Quantity Content Standards [N] ................................................................. 79
Conceptual Category: Algebra [A] ...................................................................................................... 81
Introduction ......................................................................................................................................................... 81
Conceptual Category: Algebra Overview [A] ....................................................................................................... 83
Conceptual Category: Algebra Content Standards [A] ........................................................................................ 84
Conceptual Category: Functions [F] .................................................................................................. 87
Introduction ......................................................................................................................................................... 87
Conceptual Category: Functions Overview [F] .................................................................................................... 88
Conceptual Category: Functions Content Standards [F]...................................................................................... 89
Conceptual Category: Modeling [?] .................................................................................................. 92
Introduction ......................................................................................................................................................... 92
Conceptual Category: Geometry [G] ................................................................................................. 94
Massachusetts Curriculum Framework for Mathematics
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