Transcription of DYNAMIC LEARNING MAPS ESSENTIAL ELEMENTS
1 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. Page 2 of 121 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.
2 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 3 of 121 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.
3 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 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 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.
4 35 THIRD GRADE MATHEMATICS DOMAIN: OPERATIONS AND ALGEBRAIC THINKING .. 35 THIRD GRADE MATHEMATICS DOMAIN: NUMBER AND OPERATIONS IN BASE TEN .. 38 THIRD GRADE MATHEMATICS DOMAIN: NUMBER AND OPERATIONS FRACTIONS .. 39 THIRD GRADE MATHEMATICS DOMAIN: MEASUREMENT AND DATA .. 41 THIRD GRADE MATHEMATICS DOMAIN: GEOMETRY .. 43 DYNAMIC LEARNING MAPS ESSENTIAL ELEMENTS FOR FOURTH GRADE .. 44 FOURTH GRADE MATHEMATICS DOMAIN: OPERATIONS AND ALGEBRAIC THINKING .. 44 FOURTH GRADE MATHEMATICS DOMAIN: NUMBERS AND OPERATIONS IN BASE TEN .. 46 FOURTH GRADE MATHEMATICS DOMAIN: NUMBER AND OPERATIONS FRACTIONS .. 47 FOURTH GRADE MATHEMATICS DOMAIN: MEASUREMENT AND DATA .. 50 FOURTH GRADE MATHEMATICS DOMAIN: GEOMETRY .. 52 DYNAMIC LEARNING MAPS ESSENTIAL ELEMENTS FOR FIFTH GRADE .. 53 FIFTH GRADE MATHEMATICS DOMAIN: OPERATIONS AND ALGEBRAIC THINKING .. 53 FIFTH GRADE MATHEMATICS DOMAIN: NUMBER AND OPERATIONS IN BASE TEN.
5 54 FIFTH GRADE MATHEMATICS DOMAIN: NUMBER AND OPERATIONS FRACTIONS .. 56 FIFTH GRADE MATHEMATICS DOMAIN: MEASUREMENT AND 59 FIFTH GRADE MATHEMATICS DOMAIN: GEOMETRY .. 61 Page 4 of 121 DYNAMIC LEARNING MAPS ESSENTIAL ELEMENTS FOR SIXTH GRADE .. 62 SIXTH GRADE MATHEMATICS DOMAIN: RATIOS AND PROPORTIONAL RELATIONSHIPS .. 62 SIXTH GRADE MATHEMATICS DOMAIN: THE NUMBER SYSTEM .. 64 SIXTH GRADE MATHEMATICS DOMAIN: EXPRESSIONS AND EQUATIONS .. 67 SIXTH GRADE MATHEMATICS DOMAIN: GEOMETRY .. 69 SIXTH GRADE MATHEMATICS DOMAIN: STATISTICS AND PROBABILITY .. 70 DYNAMIC LEARNING MAPS ESSENTIAL ELEMENTS FOR SEVENTH GRADE .. 71 SEVENTH GRADE MATHEMATICS DOMAIN: RATIOS AND PROPORTIONAL RELATIONSHIPS .. 71 SEVENTH GRADE MATHEMATICS DOMAIN: THE NUMBER SYSTEM .. 72 SEVENTH GRADE MATHEMATICS DOMAIN: EXPRESSIONS AND EQUATIONS .. 74 SEVENTH GRADE MATHEMATICS DOMAIN: GEOMETRY .. 76 SEVENTH GRADE MATHEMATICS DOMAIN: STATISTICS AND PROBABILITY.
6 77 DYNAMIC LEARNING MAPS ESSENTIAL ELEMENTS FOR EIGHTH GRADE .. 80 EIGHTH GRADE MATHEMATICS DOMAIN: THE NUMBER SYSTEM .. 80 EIGHTH GRADE MATHEMATICS DOMAIN: EXPRESSIONS AND EQUATIONS .. 81 EIGHTH GRADE MATHEMATICS DOMAIN: FUNCTIONS .. 83 EIGHTH GRADE MATHEMATICS DOMAIN: GEOMETRY .. 85 EIGHTH GRADE MATHEMATICS DOMAIN: STATISTICS AND PROBABILITY .. 87 DYNAMIC LEARNING MAPS ESSENTIAL ELEMENTS FOR HIGH SCHOOL .. 88 HIGH SCHOOL MATHEMATICS DOMAIN: NUMBER AND QUANTITY THE REAL NUMBER SYSTEM .. 88 HIGH SCHOOL MATHEMATICS DOMAIN: NUMBER AND QUANTITY QUANTITIES .. 89 HIGH SCHOOL MATHEMATICS DOMAIN: NUMBER AND QUANTITY THE COMPLEX NUMBER SYSTEM .. 90 HIGH SCHOOL MATHEMATICS DOMAIN: NUMBER AND QUANTITY VECTOR AND MATRIX QUANTITIES .. 92 HIGH SCHOOL MATHEMATICS DOMAIN: ALGEBRA SEEING STRUCTURE IN EXPRESSIONS .. 94 HIGH SCHOOL MATHEMATICS DOMAIN: ALGEBRA ARITHMETIC WITH POLYNOMIALS AND RATIONAL EXPRESSIONS.
7 95 HIGH SCHOOL MATHEMATICS DOMAIN: ALGEBRA CREATING EQUATIONS .. 97 HIGH SCHOOL MATHEMATICS DOMAIN: ALGEBRA REASONING WITH EQUATIONS AND INEQUALITIES .. 98 HIGH SCHOOL MATHEMATICS DOMAIN: FUNCTIONS INTERPRETING FUNCTIONS .. 100 HIGH SCHOOL MATHEMATICS DOMAIN: FUNCTIONS BUILDING FUNCTIONS .. 102 HIGH SCHOOL MATHEMATICS DOMAIN: FUNCTIONS LINEAR, QUADRATIC, AND EXPONENTIAL MODELS 104 HIGH SCHOOL MATHEMATICS DOMAIN: FUNCTIONS TRIGONOMETRIC FUNCTIONS .. 105 HIGH SCHOOL MATHEMATICS DOMAIN: GEOMETRY CONGRUENCE .. 107 HIGH SCHOOL MATHEMATICS DOMAIN: GEOMETRY SIMILARITY, RIGHT TRIANGLES, AND TRIGONOMETRY .. 109 HIGH SCHOOL MATHEMATICS DOMAIN: GEOMETRY CIRCLES .. 111 HIGH SCHOOL MATHEMATICS DOMAIN: GEOMETRY EXPRESSING GEOMETRIC PROPERTIES WITH EQUATIONS .. 112 HIGH SCHOOL MATHEMATICS DOMAIN: GEOMETRY GEOMETRIC MEASUREMENT AND DIMENSION .. 113 HIGH SCHOOL MATHEMATICS DOMAIN: GEOMETRY MODELING WITH GEOMETRY.
8 114 HIGH SCHOOL MATHEMATICS DOMAIN: STATISTICS AND PROBABILITY INTERPRETING CATEGORICAL AND QUANTITATIVE DATA .. 115 HIGH SCHOOL MATHEMATICS DOMAIN: STATISTICS AND PROBABILITY MAKING INFERENCES AND JUSTIFYING CONCLUSIONS .. 117 HIGH SCHOOL MATHEMATICS DOMAIN: STATISTICS AND PROBABILITY USING PROBABILITY TO MAKE DECISIONS .. 120 Page 5 of 121 Background on the DYNAMIC LEARNING Maps ESSENTIAL ELEMENTS The DYNAMIC LEARNING Maps ESSENTIAL ELEMENTS are specific statements of knowledge and skills linked to the grade-level expectations identified in the Common Core State Standards. The purpose of the DYNAMIC LEARNING Maps ESSENTIAL ELEMENTS is to build a bridge from the content in the Common Core State Standards to academic expectations for students with the most significant cognitive disabilities. The initial draft of the DYNAMIC LEARNING Maps ESSENTIAL ELEMENTS (then called the Common Core ESSENTIAL ELEMENTS ) was released in the spring of 2012.
9 The initial version of the DYNAMIC LEARNING Maps ESSENTIAL ELEMENTS (DLM EEs) was developed by a group of educators and content specialists from the 12 member states of the DYNAMIC LEARNING Maps Alternate Assessment Consortium (DLM) in the spring of 2011. Led by Edvantia, Inc., a sub-contractor of DLM, representatives from each state education agency and the educators and content specialists they selected developed the original DLM EEs draft. Experts in mathematics and English language arts, as well as individuals with expertise in instruction for students with significant cognitive disabilities reviewed the draft documents. Edvantia then compiled the information into the version released in the spring of 2012. Concurrent with the development of the DLM EEs, the DLM consortium was actively engaged in building LEARNING maps in mathematics and English language arts.
10 The DLM LEARNING maps are highly connected representations of how academic skills are acquired, as reflected in research literature. In the case of the DLM project, the Common Core State Standards helped to specify academic targets, while the surrounding map content clarified how students could reach the specified standard. LEARNING maps of this size had not been previously developed, and as a Page 6 of 121 result, alignment between the DLM EEs and the LEARNING maps was not possible until the fall of 2012, when an initial draft of the LEARNING maps was available for review. Alignment of the DLM EEs to the DLM LEARNING Maps Teams of content experts worked together to revise the initial version of the DLM EEs and the LEARNING maps to ensure appropriate alignment of these two critical ELEMENTS of the project. Alignment involved horizontal alignment of the DLM EEs with the Common Core State Standards and vertical alignment of the DLM EEs with meaningful progressions in the LEARNING maps.
