DYNAMIC LEARNING MAPS ESSENTIAL ELEMENTS FOR Mathematics Version 41 Published 2013. Revision Date: May 1, 2014 2013. Copyright University of Kansas Center for Research. All rights reserved. 1 Version 4 improves the formatting and readability. No changes to content have been made. The Dynamic Learning Maps Essential Elements are copyrighted by the University of Kansas Center for Research. They are based substantially on an earlier version that was copyrighted by Edvantia. The Essential Elements may be reprinted or used, with appropriate citation, in part or entirety by anyone in the DLM Consortium states. However, no text in the document may be modified. Comments, explanations, or other additional materials may be interspersed as long as they clearly indicate that they are not part of the Essential Elements and are not the opinions of the DLM Consortium or the University of Kansas Center for Research. Others may use the contents with written permission from the Center for Educational Testing and Evaluation. Appropriate citations follow. Dynamic Learning Maps Consortium. (2013). Dynamic Learning Maps Essential Elements for English language arts. Lawrence, KS: University of Kansas. and Dynamic Learning Maps Consortium. (2013). Dynamic Learning Maps Essential Elements for mathematics. Lawrence, KS: University of Kansas. Page 2 of 120 TABLE OF CONTENTS BACKGROUND ON THE DYNAMIC LEARNING MAPS ESSENTIAL ELEMENTS ......................................................... 5 ALIGNMENT OF THE DLM EES TO THE DLM LEARNING MAPS ............................................................................. 6 THE ALIGNMENT PROCESS ..................................................................................................................................... 6 CLAIMS AND CONCEPTUAL AREAS ......................................................................................................................... 7 RESULTING CHANGES TO THE DLM ESSENTIAL ELEMENTS ............................................................................... 10 ACCESS TO INSTRUCTION AND ASSESSMENT ...................................................................................................... 11 GUIDANCE AND SUPPORT ..................................................................................................................................... 13 CONCLUSION .......................................................................................................................................................... 14 APPENDIX ............................................................................................................................................................ 15 DYNAMIC LEARNING MAPS ESSENTIAL ELEMENTS FOR KINDERGARTEN .................................... 17 KINDERGARTEN MATHEMATICS DOMAIN: COUNTING AND CARDINALITY ........................................................... 17 KINDERGARTEN MATHEMATICS DOMAIN: OPERATIONS AND ALGEBRAIC THINKING ......................................... 19 KINDERGARTEN MATHEMATICS DOMAIN: NUMBER AND OPERATIONS IN BASE TEN ........................................ 19 KINDERGARTEN MATHEMATICS DOMAIN: MEASUREMENT AND DATA ................................................................ 21 KINDERGARTEN MATHEMATICS DOMAIN: GEOMETRY ......................................................................................... 22 DYNAMIC LEARNING MAPS ESSENTIAL ELEMENTS FOR FIRST GRADE ......................................... 23 FIRST GRADE MATHEMATICS DOMAIN: OPERATIONS AND ALGEBRAIC THINKING ............................................. 23 FIRST GRADE MATHEMATICS DOMAIN: NUMBER AND OPERATIONS IN BASE TEN ............................................ 25 FIRST GRADE MATHEMATICS DOMAIN: MEASUREMENT AND DATA ................................................................... 27 FIRST GRADE MATHEMATICS DOMAIN: GEOMETRY ............................................................................................ 28 DYNAMIC LEARNING MAPS ESSENTIAL ELEMENTS FOR SECOND GRADE .................................... 29 SECOND GRADE MATHEMATICS DOMAIN: OPERATIONS AND ALGEBRAIC THINKING ........................................ 29 SECOND GRADE MATHEMATICS: NUMBER AND OPERATIONS IN BASE TEN ...................................................... 30 SECOND GRADE MATHEMATICS DOMAIN: MEASUREMENT AND DATA ............................................................... 32 SECOND GRADE MATHEMATICS DOMAIN: GEOMETRY ....................................................................................... 34 DYNAMIC LEARNING MAPS ESSENTIAL ELEMENTS FOR THIRD GRADE ........................................ 35 THIRD GRADE MATHEMATICS DOMAIN: OPERATIONS AND ALGEBRAIC THINKING ............................................ 35 THIRD GRADE MATHEMATICS DOMAIN: NUMBER AND OPERATIONS IN BASE TEN ........................................... 37 THIRD GRADE MATHEMATICS DOMAIN: NUMBER AND OPERATIONS—FRACTIONS .......................................... 38 THIRD GRADE MATHEMATICS DOMAIN: MEASUREMENT AND DATA ................................................................... 40 THIRD GRADE MATHEMATICS DOMAIN: GEOMETRY ........................................................................................... 42 DYNAMIC LEARNING MAPS ESSENTIAL ELEMENTS FOR FOURTH GRADE .................................... 43 FOURTH GRADE MATHEMATICS DOMAIN: OPERATIONS AND ALGEBRAIC THINKING ........................................ 43 FOURTH GRADE MATHEMATICS DOMAIN: NUMBERS AND OPERATIONS IN BASE TEN ..................................... 45 FOURTH GRADE MATHEMATICS DOMAIN: NUMBER AND OPERATIONS—FRACTIONS....................................... 46 FOURTH GRADE MATHEMATICS DOMAIN: MEASUREMENT AND DATA ............................................................... 49 FOURTH GRADE MATHEMATICS DOMAIN: GEOMETRY ........................................................................................ 51 DYNAMIC LEARNING MAPS ESSENTIAL ELEMENTS FOR FIFTH GRADE ......................................... 52 FIFTH GRADE MATHEMATICS DOMAIN: OPERATIONS AND ALGEBRAIC THINKING ............................................. 52 FIFTH GRADE MATHEMATICS DOMAIN: NUMBER AND OPERATIONS IN BASE TEN ............................................ 53 FIFTH GRADE MATHEMATICS DOMAIN: NUMBER AND OPERATIONS—FRACTIONS ........................................... 55 FIFTH GRADE MATHEMATICS DOMAIN: MEASUREMENT AND DATA .................................................................... 58 FIFTH GRADE MATHEMATICS DOMAIN: GEOMETRY ............................................................................................ 60 Page 3 of 120 DYNAMIC LEARNING MAPS ESSENTIAL ELEMENTS FOR SIXTH GRADE......................................... 61 SIXTH GRADE MATHEMATICS DOMAIN: RATIOS AND PROPORTIONAL RELATIONSHIPS .................................... 61 SIXTH GRADE MATHEMATICS DOMAIN: THE NUMBER SYSTEM .......................................................................... 63 SIXTH GRADE MATHEMATICS DOMAIN: EXPRESSIONS AND EQUATIONS ........................................................... 66 SIXTH GRADE MATHEMATICS DOMAIN: GEOMETRY ............................................................................................ 68 SIXTH GRADE MATHEMATICS DOMAIN: STATISTICS AND PROBABILITY ............................................................. 69 DYNAMIC LEARNING MAPS ESSENTIAL ELEMENTS FOR SEVENTH GRADE .................................. 70 SEVENTH GRADE MATHEMATICS DOMAIN: RATIOS AND PROPORTIONAL RELATIONSHIPS .............................. 70 SEVENTH GRADE MATHEMATICS DOMAIN: THE NUMBER SYSTEM .................................................................... 71 SEVENTH GRADE MATHEMATICS DOMAIN: EXPRESSIONS AND EQUATIONS ..................................................... 73 SEVENTH GRADE MATHEMATICS DOMAIN: GEOMETRY ...................................................................................... 75 SEVENTH GRADE MATHEMATICS DOMAIN: STATISTICS AND PROBABILITY ....................................................... 76 DYNAMIC LEARNING MAPS ESSENTIAL ELEMENTS FOR EIGHTH GRADE ..................................... 79 EIGHTH GRADE MATHEMATICS DOMAIN: THE NUMBER SYSTEM ....................................................................... 79 EIGHTH GRADE MATHEMATICS DOMAIN: EXPRESSIONS AND EQUATIONS ........................................................ 80 EIGHTH GRADE MATHEMATICS DOMAIN: FUNCTIONS ......................................................................................... 82 EIGHTH GRADE MATHEMATICS DOMAIN: GEOMETRY ......................................................................................... 84 EIGHTH GRADE MATHEMATICS DOMAIN: STATISTICS AND PROBABILITY .......................................................... 86 DYNAMIC LEARNING MAPS ESSENTIAL ELEMENTS FOR HIGH SCHOOL ........................................ 87 HIGH SCHOOL MATHEMATICS DOMAIN: NUMBER AND QUANTITY—THE REAL NUMBER SYSTEM ................... 87 HIGH SCHOOL MATHEMATICS DOMAIN: NUMBER AND QUANTITY—QUANTITIES ............................................ 88 HIGH SCHOOL MATHEMATICS DOMAIN: NUMBER AND QUANTITY—THE COMPLEX NUMBER SYSTEM ........... 89 HIGH SCHOOL MATHEMATICS DOMAIN: NUMBER AND QUANTITY – VECTOR AND MATRIX QUANTITIES ......... 91 HIGH SCHOOL MATHEMATICS DOMAIN: ALGEBRA—SEEING STRUCTURE IN EXPRESSIONS ........................... 93 HIGH SCHOOL MATHEMATICS DOMAIN: ALGEBRA—ARITHMETIC WITH POLYNOMIALS AND RATIONAL EXPRESSIONS .......................................................................................................................................................