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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.
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
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