BESE March 2017: Curriculum Framework for Math DRAFT

Massachusetts

Curriculum Framework

for

Mathematics

Grades Pre-Kindergarten to 12

March 2017

FOR BOARD APPROVAL

(to be copyedited upon approval)

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 Departments 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.

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.

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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

Commissioners Letterii

Acknowledgementsiii

Introduction1

Guiding Principles for Mathematics Programs in Massachusetts9

The Standards for Mathematical Practice12

The Standards for Mathematics Content

Pre-KindergartenGrade 8

Introduction17

Pre-Kindergarten19

Kindergarten22

Grade 126

Grade 230

Grade 334

Grade 439

Grade 544

Grade 649

Grade 756

Grade 862

High School

Introduction.............................. 67

Content Standards by Conceptual Categories71

Number and Quantity74

Algebra...78

Functions.84

Modeling89

Geometry91

Statistics and Probability97

Content Standards by Model Courses and Model Pathways102

Model Traditional Pathway

Model Algebra I Course105

Model Geometry Course112

Model Algebra II Course118

Model Integrated Pathway

Model Mathematics I Course124

Model Mathematics II Course131

Model Mathematics III Course138

Model Advanced Courses

Model Precalculus144

Model Advanced Quantitative Reasoning150

Making Decisions about

High School Course Sequences and Algebra I in Grade 8155

Appendix I: Application of Standards for English Language Learners and Students with Disabilities159

Appendix II: Standards for Mathematical Practice Grade-Span Descriptions (PreK-5, 6-8, 9-12)164

Appendix III: Conceptual Category Tables: Distribution of Content Standards Across Model Course175

Glossary: Mathematical Terms and Illustrations187

Tables and Illustrations of Key Mathematical Properties, Rules, and Number Sets198

Bibliography202

Table of Contents

Massachusetts Curriculum Framework for Mathematics, FOR BESE APPROVAL (to be copyedited upon approval) iii

Massachusetts Department of

Elementary and Secondary Education

75 Pleasant Street, Malden, Massachusetts 02148-4906 Telephone: (781) 338-3000 TTY: N.E.T. Relay 1-800-439-2370

Mitchell D. Chester, Ed. D., Commissioner

April 2017

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 Commonwealths K-12 and higher education faculty. The 2017 standards present the Commonwealths commitment to providing all students with a world-class education.

This revision of the Framework retains the strengths of earlier 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;

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 eight 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 Panels and our Content Advisors for giving their time generously to the project of improving 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

iv FOR BESE APPROVAL (to be copyedited upon approval) Massachusetts Curriculum Framework for Mathematics,

The 2017 Massachusetts Curriculum Framework for Mathematics is the result of the contributions of many educators across the state. The Department of Elementary and Secondary Education wishes to thank all of the Massachusetts groups that contributed to the development of these mathematics standards.

Massachusetts Curriculum Framework for Mathematics and

English Language Arts and Literacy Review Panel, 20162017

Rachel Barlage, Lead English Teacher, Chelsea High School, Chelsea Public Schools

Jennifer Berg, Mathematics Professor, Fitchburg State

Tara Brandt, Mathematics Supervisor, K12, Westfield Public Schools

Jennifer Camara-Pomfret, English Teacher, Seekonk High School, Seekonk Public Schools

Tricia Clifford, Principal, Mary Lee Burbank School, Belmont Public Schools

Linda Crockett, Literacy Coach, Grades 68, Westfield South Middle School, Westfield Public Schools

Linda Dart-Kathios, Mathematics Department Chairperson, Middlesex Community College

Linda Davenport, Director of K12 Mathematics, Boston Public Schools

Beth Delaney, Mathematics Coach, Revere Public Schools

Lisa Dion, Manager of Curriculum, Data and Assessment, New Bedford Public Schools

Tom Fortmann, Community Representative, Lexington

Oneida Fox Roye, Director of English Language Arts and Literacy, K12, Boston Public Schools

Andrea Gobbi, Supervisor of Secondary Curriculum, Lawrence High School, Lawrence Public Schools

Donna Goldstein, Literacy Coach, Coelho Middle School, Attleboro Public Schools

Andrea Griswold, Grade 8 English Teacher, Mohawk Train Regional Middle and High School, Mohawk Trail/Hawlemont Regional School District

Susan Hehir, Grade 3 Teacher, Forest Avenue Elementary School, Hudson Public Schools

Anna Hill, Grade 6 English Language Arts Teacher, Charlton Middle School, Charlton Public Schools

Sarah Hopson, K4 Math Coach, Agawam Elementary Schools, Agawam Public Schools

Nancy Johnson, 712 Mathematics Teacher and Department Head, Hopedale Jr.-Sr. High School, Hopedale Public Schools; President, Association of Teachers of Mathematics in Massachusetts

Patty Juranovits, Supervisor of Mathematics, K12, Haverhill Public Schools

Elizabeth Kadra, Grades 7 & 8 Mathematics Teacher, Miscoe Hill Middle