Massachusetts Mathematics Curriculum Framework — 2017

1 I This document was prepared by the Massachusetts Department of Elementary and Secondary Education Board of Elementary and Secondary Education MembersMr. 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.

2 Chester, , 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.

3 , 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: Relay 800-439-2370 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.

4 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.

5 The 2017 standards draw from the best of prior Massachusetts standards, and represent the input of hundreds of the Commonwealth s K 12 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: 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.

6 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.

7 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.

8 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 Massachusetts Department of Elementary and Secondary Education 75 Pleasant Street, Malden, Massachusetts 02148-4906 Massachusetts Curriculum Framework for Mathematics 1 Table of Contents Acknowledgments.

9 5 Introduction ..8 Guiding Principles for Mathematics Programs in 14 The Standards for Mathematical Practice .. 16 Standards for Mathematical Content Pre-Kindergarten Grade 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.

10 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 48 Massachusetts Curriculum Framework for Mathematics 2 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.