Common Core Essential Elements for Mathematics

Common Core Essential Elements for Mathematics

From the State Members of the

Dynamic Learning Maps Alternate Assessment Consortium

and Edvantia, Inc.

March 7, 2012

The present publication was developed under grant 84.373X100001 from the U.S. Department of Education, Office of Special Education Programs. The views expressed herein are solely those of the author(s), and no official endorsement by the U.S. Department should be inferred.

Common Core Essential Elements and for Mathematics

Table of Contents

ACKNOWLEDGEMENTS ...................................................................................................................iv INTRODUCTION............................................................................................................................... 1 NCLB GUIDANCE.............................................................................................................................. 2 ACCESS TO INSTRUCTION AND ASSESSMENT................................................................................. 3 ACCESSING THE GENERAL CURRICULUM ....................................................................................... 4 GUIDANCE AND SUPPORT .............................................................................................................. 4 RELATIONSHIP TO THE DYNAMIC LEARNING MAPS ASSESSMENT................................................. 5 SYSTEM ALIGNMENT....................................................................................................................... 6

Levels of Performance................................................................................................................ 6 DOCUMENT ORGANIZATION .......................................................................................................... 8

Directions for Interpreting Essential Elements .......................................................................... 8 COMMON CORE ESSENTIAL ELEMENTS

Kindergarten Mathematics Standards Counting and Cardinality .................................................................................................... 9 Operations and Algebraic Thinking................................................................................... 11 Number and Operations in Base Ten................................................................................ 12 Measurement and Data .................................................................................................... 13 Geometry .......................................................................................................................... 14

First Grade Mathematics Standards Operations and Algebraic Thinking................................................................................... 15 Number and Operations in Base Ten................................................................................ 18 Measurement and Data .................................................................................................... 20 Geometry .......................................................................................................................... 22

Second Grade Mathematics Standards: Operations and Algebraic Thinking................................................................................... 23 Number and Operations in Base Ten................................................................................ 25 Measurement and Data .................................................................................................... 27 Geometry .......................................................................................................................... 29

Third Grade Mathematics Standards: Operations and Algebraic Thinking................................................................................... 30 Number and Operations in Base Ten................................................................................ 33

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Number and Operations--Fractions.................................................................................. 34 Measurement and Data .................................................................................................... 36 Geometry .......................................................................................................................... 39

Fourth Grade Mathematics Standards: Operations and Algebraic Thinking................................................................................... 40 Numbers and Operations in Base Ten .............................................................................. 42 Number and Operations--Fractions.................................................................................. 44 Measurement and Data .................................................................................................... 47 Geometry .......................................................................................................................... 50

Fifth Grade Mathematics Standards: Operation and Algebraic Thinking .................................................................................... 51 Number and Operations in Base Ten................................................................................ 53 Number and Operations--Fractions.................................................................................. 55 Measurement and Data .................................................................................................... 59 Geometry .......................................................................................................................... 61

Sixth Grade Mathematics Standards: Ratios and Proportional Relationships ............................................................................. 62 The Number System.......................................................................................................... 64 Expressions and Equations ............................................................................................... 68 Geometry .......................................................................................................................... 71 Statistics and Probability................................................................................................... 72

Seventh Grade Mathematics Standards: Ratios and Proportional Relationships ............................................................................. 74 The Number System.......................................................................................................... 76 Expressions and Equations ............................................................................................... 78 Geometry .......................................................................................................................... 80 Statistics and Probability................................................................................................... 82

Eighth Grade Mathematics Standards: The Number System.......................................................................................................... 85 Expressions and Equations ............................................................................................... 86 Functions........................................................................................................................... 89 Geometry .......................................................................................................................... 91 Statistics and Probability................................................................................................... 93

High School Mathematics Standards: Number and Quantity The Real Number System.................................................................................................. 95 Quantities.......................................................................................................................... 96 The Complex Number System .......................................................................................... 97

High School Mathematics Standards: Algebra Seeing Structure in Expressions ........................................................................................ 98 Arithmetic with Polynomials and Rational Expressions ................................................. 100 Creating Equations.......................................................................................................... 101

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Reasoning with Equations and Inequalities.................................................................... 102 High School Mathematics Standards: Functions

Interpreting Functions .................................................................................................... 105 Building Functions........................................................................................................... 108 Linear, Quadratic, and Exponential Models ................................................................... 110 Trigonometric Functions................................................................................................. 112 High School Mathematics Standards: Geometry Congruence ..................................................................................................................... 113 Similarity, Right Triangles, and Trigonometry ................................................................ 117 Circles .............................................................................................................................. 119 Expressing Geometric Properties with Equations .......................................................... 120 Geometric Measurement and Dimension ...................................................................... 122 Modeling with Geometry................................................................................................ 123 High School Mathematics Standards: Statistics and Probability Interpreting Categorical and Quantitative Data ............................................................. 124 Making Inferences and Justifying Conclusions ............................................................... 126 Conditional Probability and the Rules of Probability...........................................................128 GLOSSARY AND EXAMPLES OF MATHEMATICS TERMS.............................................................. 130 GLOSSARY OF SPECIAL EDUCATION TERMS ............................................................................... 137 BIBLIOGRAPHY OF DEVELOPMENT PROCESS.............................................................................. 141 BIBLIOGRAPHY FOR MATHEMATICS CONTENT ......................... Error! Bookmark not defined.143

APPENDIX A: SEA/STAKEHOLDER DEMOGRAPHICS

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ACKNOWLEDGEMENTS

*For stakeholder demographics, See Appendix A.

Edvantia Facilitators

Jan Sheinker, Sheinker Educational Services, Inc. Beth Judy, Director, Assessment, Alignment, and Accountability Services

Nathan Davis, Information Technology Specialist Kristen Deitrick, Corporate Communications Specialist

Linda Jones, Executive Assistant

Dynamic Learning Maps (DLM) Staff and Consultants

Neal Kingston, Project Director Alan Sheinker, Associate Project Director

Laura Kramer, Test Development Lead Karthick Palaniswamy, Technology Development Lead Kelli Thomas, Mathematics Learning Map Team Lead Carrie Mark, English Language Arts Learning Map Team Lead

Patti Whetstone, Research Associate Sue Bechard, Consultant Karen Erickson, Consultant Chris Cain, Consultant

Dynamic Learning Maps (DLM) Consortia States

Iowa Kansas Michigan Mississippi Missouri New Jersey North Carolina Oklahoma Utah Virginia Washington West Virginia Wisconsin

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