ESSENTIAL ELEMENTS AND ALTERNATE ACHIEVEMENT DESCRIPTORS FOR Mathematics Wisconsin Department of Public Instruction ESSENTIAL ELEMENTS Mathematics Wisconsin Department of Public Instruction Tony Evers, PhD, State Superintendent Madison, Wisconsin This publication is available from: Wisconsin Department of Public Instruction 125 South Webster Street Madison, WI 53703 (608) 266-8960 http://dpi.wi.gov/sped/assmt-ccee.html Bulletin No. 14099 © April 2014 Wisconsin Department of Public Instruction The Department of Public Instruction does not discriminate on the basis of sex, race, color, religion, creed, age, national origin, ancestry, pregnancy, marital status or parental status, sexual orientation or disability. Printed on recycled paper Table of Contents Section 1: Wisconsin’s Approach to Academic Standards IV Foreword V Acknowledgements VI Purpose of the Document VII Aligning for Student Success VIII Guiding Principles for Teaching and Learning X Reaching Every Student; Reaching Every Discipline XI Section 2: Wisconsin’s Approach to Mathematics XVII Section 3: Common Core Essential Elements for Mathematics 1 - 105 Section 4: Wisconsin’s Approach to Literacy in all Subjects XXVII Section 5: Wisconsin Research and Resources Research Briefs for Guiding Principles for Teaching and Learning XXXVII COMMON CORE ESSENTIAL ELEMENTS for MATHEMATICS III SECTION 1 Wisconsin’s Approach to Academic Standards Foreword In June 2010, Wisconsin adopted the Common Core State Standards in English Language Arts and Mathematics. These K-12 academic standards are aligned with college and work expectations, include rigorous content and application, and are internationally benchmarked. Additionally, the Common Core State Standards emphasize literacy in all of the disciplines. For all students to be career and college ready, including students with significant cognitive disabilities, educators should include both the content and the reading and writing skills that students need to demonstrate learning in the other disciplinary areas. All students, including students with significant cognitive disabilities, deserve and have a right to a quality educational experience. This right includes, to the maximum extent possible, the opportunity to be involved in and meet the same challenging expectations that have been established for all students. Wisconsin educators collaborated with educators from 12 other states to create alternate achievement standards aligned to the Common Core State Standards. These alternate achievement standards are called the Wisconsin Common Core Essential Elements (CCEEs) in English Language Arts and Mathematics. The CCEEs satisfy the requirement of the U.S. Department of Education that Wisconsin have alternate achievement standards for its students with significant cognitive disabilities that are clearly linked to grade-level academic content standards, promote access to the general curriculum and reflect professional judgment of the highest expectation possible. This document is a guide for parents, educators, school personnel, and other community members to support their work in teaching students with significant cognitive disabilities the academic skills necessary to succeed in life after graduation. Tony Evers, PhD State Superintendent COMMON CORE ESSENTIAL ELEMENTS for MATHEMATICS V AcknowledgementsAcknowledgments The Wisconsin Common Core Essential Elements for Mathmatics would not have been possible without the efforts of many people. These educators provided their time and expertise in contributing to the development of these alternate achievement standards. In addition, their employing agencies generously granted them time to work on this initiative. Amber Eckes Mary Richards Erin Faasuamalie Special Education Teacher Mathematics Instructional Coach Cognitive Disabilities/Assessment Consultant Verona Area School District New London School District Special Education Team Astrid Fossum Jeff Ziegler Diana Kasbaum Mathematics Teaching Specialist Teacher Leader Mathematics Consultant Milwaukee Public Schools Madison Metropolitan School District Content and Learning Team Rosemary Gardner Department of Public Instruction Staff Eva Kubinski Educational Programmer Improvement Indicators/Assessment Consultant Lakeland School of Walworth County Sandy Berndt Special Education Team Cognitive Disabilities/Assessment Consultant, Retired Crystal Hintzman Special Education Team Brian Johnson Mathematics Instructional Coach Autism/Assessment Consultant Superior School District Kristen Burton Special Education Team Education Consultant Mary Mooney Office of Educational Accountability Math Teaching Specialist Milwaukee Public Schools Thanks to the Dynamic Learning Maps consortium for organizing and leading the multi‐state initiative in the development of new alternate achievement standards and assessments aligned to the Common Core State Standards. A special thanks to Edvantia, Inc. Copyrighted Materials Every effort has been made to ascertain proper ownership on copyrighted materials and to obtain permission for this use. Any omission is unintentional. COMMON CORE ESSENTIAL ELEMENTS for MATHEMATICS VI Acknowledgements (cont’d) Purpose of the Document A special thanks to the Council of Chief State School Officers and the Sections I, 2 and 4 of this document were developed by Wisconsin National Governors Association for having the vision to undertake the educators to provide the vision and principles that support Wisconsin’s massive state-led project, the Common Core State Standards. Approach to Academic Standards. These principles, although initially developed for the CCSS, can be applied to the CCEEs and instructional Thanks to Great Lakes West Comprehensive Center and Director Linda practices of educators of students with significant cognitive disabilities. Miller for the generous support of Wisconsin’s standards projects, and to Rachel Trimble and Beth Ratway for their guidance during the last year. To assist Wisconsin education stakeholders in understanding and imple- Thanks also to the CESA Statewide Network and Commissioner Jesse menting the , Wisconsin Harness for partnering to keep the CCSS message consistent statewide, Common Core State Standards (CCSS) and to the CESA School Improvement Specialists Network for their Department of Public Instruction (DPI) has developed guidance to be role in producing and providing high quality professional development used along with the CCSS. These materials are intended to provide statewide. further direction and should not be viewed as administrative rule. This publication provides a vision for student success, guiding principles for Also thanks to the many staff members across divisions and teams at teaching and learning, and locates the standards within a multi-level sys- DPI who have collaboratively contributed their time and talent to this tem of support where high quality instruction, balanced assessment, and project. collaboration function together for student learning. Information on the design and content of the CCSS is included, as is a guide to assist with Finally, a special thanks to Wisconsin educators and citizens who facilitating local conversations about these internationally-benchmarked provided public comment and feedback to drafts of the Common Core standards and how they impact instruction. State Standards, served on statewide standards leadership groups, and supported implementation of standards. COMMON CORE ESSENTIAL ELEMENTS for MATHEMATICS VII Aligning for Student Success To build and sustain schools that support every student in achieving initiatives, each of them is connected to a larger vision of every child success, educators must work together with families, community graduating college and career ready. The graphic below illustrates how members, and business partners to connect the most promising practices these initiatives function together for a common purpose. Here, the in the most meaningful contexts. Major statewide initiatives focus on vision and set of guiding principles form the foundation for building high school graduation, Response to Intervention (RtI), and the Common a supportive process for teaching and learning rigorous and relevant Core State Standards for English Language Arts, Disciplinary Literacy, and content. The following sections articulate this integrated approach to Mathematics. While these are often viewed as separate efforts or increasing student success in Wisconsin schools and communities. A Vision: Every Child a Graduate In Wisconsin, we are committed to ensuring every child is a graduate who has successfully completed a rigorous, meaningful, 21st century education that will prepare him or her for careers, college and citizenship. Though our public education system continues to earn nation-leading graduation rates, a fact we can be proud of, one in ten students drop out of school, achievement gaps are too large, and overall achievement could be even higher. This vision for every child a graduate guides our beliefs and approaches to education in Wisconsin. Guided By Principles All educational initiatives are guided and impacted by important and often unstated attitudes or principles for teaching and learning. The Guiding Principles for Teaching and Learning emerge from research and provide the touchstone for practices that truly affect the vision of every child a graduate prepared for college and career. When made transparent, these principles inform what happens in the classroom, the implementation and evaluation of programs, and