Next Generation Math Standards

1. Math Tools for Unpacking & Addressing the West Virginia Next Generation Math Standards Elementary School Version West Virginia RESAs 3 and 7Charleston and Morgantown, WV April, 2013 1

2. Essential Workshop Questions • What is the relationship between the Common Core Standards an the Next Generation Math Standards, and why were they developed? • How are the Next Generation Math Standards organized? • What are the Six Instructional Shifts and the Eight Mathematical Practices; What are their role in the Next Generation Standards? • What processes are useful for unpacking the standards? • What are the implications of the Standards on the way we approach the teaching and learning of mathematics? 2

3. VKR Math Vocabulary Activity • Assess your Vocabulary Knowledge Rating (VKR) of personal knowledge of these important workshop words. • Consider each word and check the appropriate column. Check #4 column, if you could explain and teach others. Check #3 column if you know the term well, but would not want to teach others. Check #2 column if you have heard of the term. Check #1 column if the word is new to you.

4. VKR Math Vocabulary Activity 1 2 3 4 Common Core StandardsNext Generation StandardsStandardClusterObjectiveTeaching StrategyStudent Engagement ActivityFive Stages of T&L MathSix Instructional Shifts Eight Mathematical Practices

5. What’s the connection between the Common Core Standards and the Next Generation Standards, and why were these standards developed? 5

6. What are the Common Core Standards? The Common Core Standards are a product of a U.S. education initiative that seeks to bring diverse state curricula into alignment with each other by following the principles of standards-based education reform. The initiative is sponsored by the National Governors Association (NGA) and the Council of Chief State School Officers (CCSSO). At this time, 45 U.S. States are committed to implementing the Common Core Standards.

7. What are the Next Generation Standards? The Next Generation Standards are West Virginia’s education standards. These standards parallel the Common Core Standards, and contain modifications that meet the specific needs of West Virginia. The Next Generation Standards represent the next logical step in the progression of the statewide movement called EducateWV: Enhancing Learning. For Now. For the Future.

8. Why were the new Standards developed? The Next Generation Standards were developed to:• provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them.• be robust and relevant to the real world• reflect the knowledge and skills that our young people need for success in college and careers

9. Why were the new Standards developed? The Next Generation Standards were developed to:• be sure that American students are fully prepared for success in the global economy • help teachers zero in on the most important knowledge and skills • establish shared goals among students, parents, and teachers

10. Why were the new Standards developed? The Next Generation Standards were developed to:• help states and districts assess the effectiveness of schools and classrooms and give all students an equal opportunity for high achievement • help solve the problem of discrepancies between State’s test results and International test results • replace the discrepant array of curriculums that existed across the country

11. How are the Next Generation Standards organized? 11

12. Common Core and Next Generation Organization Terminology Common Core Standards (CCS) Next Generation Standards (NGS) Domain (CCS only) Standards (CCS and NGS) Cluster (CCS and NGS) Objective (NGS only)

13. Common Core Organization/Terminology In the Common Core Standards, the terms domain, standard, and cluster have the following meanings. domain: used for the broad math strand or category name standard: more specific math category name (next level beyond domain) cluster: group of specific learning objectives that connect with the standard

14. Common Core Standards for Math;Example of how they are organized Grade 5 Standard: Operations and Algebraic Thinking Write and interpret numerical expressionsM.5.OA.1Use parentheses, brackets or braces in numerical expressions, and evaluate expressions with these symbols. M.5.OA.2 Write simple expressions that record calculations with numbers. Domain Standard Cluster

15. Next Generation Organization/Terminology In the Next Generation Standards, the terms standard, cluster, and objective have the following meanings. standard: used for the broad math strand or category name (replaces the CC word domain) cluster: more specific math category name (next level beyond standard, replaces the CC word standard) objectives: specific things that students should learn and be able to do (listed in each cluster)

16. How are the Next GenerationMath Standards organized? Grade 5 Standard: Operations and Algebraic Thinking Write and interpret numerical expressionsM.5.OA.1Use parentheses, brackets or braces in numerical expressions, and evaluate expressions with these symbols. M.5.OA.2 Write simple expressions that record calculations with numbers. Standard Cluster Objectives

17. The Next Generation Math Standards for Grades K-5 The next five slides show the standards (broad math categories or strands) for grades K-5. Note the similarities and differences among the grade levels.

18. The Next Generation Math Standards for Grades K-5 Kindergarten Standards Counting and CardinalityQuestions and Algebraic ThinkingNumbers and Operations in Base TenMeasurement and DataGeometry

19. The Next Generation Math Standards for Grades K-5 First Grade Standards Operations and Algebraic ThinkingNumbers and Operations in Base TenMeasurement and DataGeometry

20. The Next Generation Math Standards for Grades K-5 Second Grade Standards Operations and Algebraic ThinkingNumbers and Operations in Base TenMeasurement and DataGeometry

21. The Next Generation Math Standards for Grades K-5 Third Grade Standards Operations and Algebraic ThinkingNumbers and Operations in Base TenNumbers and Operations with FractionsMeasurement and DataGeometry

22. The Next Generation Math Standards for Grades K-5 Fourth Grade Standards Operations and Algebraic ThinkingNumbers and Operations in Base TenNumbers and Operations with FractionsMeasurement and DataGeometry

23. The Next Generation Math Standards for Grades K-5 Fifth Grade Standards Operations and Algebraic ThinkingNumbers and Operations in Base TenNumbers and Operations with FractionsMeasurement and DataGeometry

24. The Next Generation Math Standards for Grades K-5 The next five slides show the breakdown of the common Operations and Algebraic Thinking (Questions and Algebraic Thinking for Kindergarten) standard for grades K-5. Each slide shows the clusters for the standard, and the number of objectives associated with each cluster.

25. The Next Generation Math Standards for Grades K-5 Take note of the standard, cluster, and number of objectives for each cluster. Work with a partner from your grade level, and see if you can guess what the objectives are for your grade-level clusters.

26. How are the Next Generation Math Standards organized? Kindergarten Standard and Cluster Questions and Algebraic Thinking•Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from (5 objectives)

27. How are the Next Generation Math Standards organized? First Grade Standard and Cluster Operations and Algebraic Thinking•Represent and Solve Problems Involving Addition and Subtraction-(2 objectives)• Understand and Apply Properties of Operations and the Relationship between Addition and Subtraction- (2 objectives)• Add and Subtract within 20- (2 objectives)• Work with Addition and Subtraction Equations- (2 objectives)

28. How are the Next Generation Math Standards organized? Second Grade Standard and Cluster Operations and Algebraic Thinking• Represent and Solve Problems Involving Addition and Subtraction-(1 objective)• Add and Subtract within 20- (1 objective)• Work with Equal Groups of Objects to Gain Foundations for Multiplication- (2 objectives)

29. How are the Next Generation Math Standards organized? Third Grade Standard and Cluster Operations and Algebraic Thinking• Represent and Solve Problems Involving Multiplication and Division-(4 objectives)• Understand Properties of Multiplication and the Relationship between Multiplication and Division- (2 objectives)• Multiply and Divide within 100- (1 objective)• Solve Problems Involving the Four Operations and Identify and Explain Patterns in Arithmetic- (2 objectives)

30. How are the Next Generation Math Standards organized? Fourth Grade Standard and Cluster Operations and Algebraic Thinking• Use the Four Operations with Whole Numbers to Solve Problems-(3 objectives)• Gain Familiarity with Factors and Multiples- (1 objective)• Generate and Analyze- (1 objective)

31. How are the Next Generation Math Standards organized? Fifth Grade Standard and Cluster Operations and Algebraic Thinking• Write and Interpret Numerical Expressions- (2 objectives)• Analyze Patterns and Relationships- (1 objective)

32. The Next Generation Math Standards for Grades K-5 After guessing what the objectives are for each cluster, work in grade-level teams and read the objectives for each cluster identified in this activity. For each objective, work together to create a math problem that captures the essence of the objective. The standard, clusters, objectives and sample problems will be share with the entire group to provide a K-5 vertical view of the teaching and learning progressions associated with the K-5 math program.

33. Six Instructional Shifts Associated with West Virginia’s Next Generation Math Standards 33

34. Six Instructional Shifts in Math Focus Coherence Fluency Understanding Applications Dual Intensity New Points of Emphasis for Teaching the Next Generation Standards

35. Instructional Shifts • Instructional Shifts within the common core are needed for students to attain the standards. Kelly L. Watts, RESA 3

36. 6 Shifts in Mathematics • Focus • Coherence • Fluency • Deep Understanding • Applications • Dual Intensity Kelly L. Watts, RESA 3

37. Focus • In reference to the TIMMS study, there is power of the eraser and a gift of time. The Core is asking us to prioritize student and teacher time, to excise out much of what is currently being taught so that we can put an end to the mile wide, inch deep phenomenon that is American Math education and create opportunities for students to dive deeply into the central and critical math concepts. We are asking teachers to focus their time and energy so that the students are able to do the same. Kelly L. Watts, RESA 3

38. Focus • Teachers • Make conscious decisions about what to excise from the curriculum and what to focus on • Pay more attention to high leverage content and invest the appropriate time for all students to learn before moving onto the next topic • Think about how the concepts connect to one another • Build knowledge, fluency, and understanding of why and how we do certain math concepts. • Students • Spend more time thinking and working on fewer concepts • Being able to understand concepts as well as processes. (algorithms) Kelly L. Watts, RESA 3

39. Coherence • We need to ask ourselves – • How does the work I’m doing affect work at the next grade level? • Coherence is about the scope and sequence of those priority standards across grade bands. • How does multiplication get addressed across grades 3-5? • How do linear equations get handled between 8 and 9? • What must students know when they arrive, what will they know when they leave a certain grade level? Kelly L. Watts, RESA 3

40. Coherence • Students • Build on knowledge from year to year, in a coherent learning progression • Teachers • Connect the threads of math focus areas across grade levels • Think deeply about what you’re focusing on and the ways in which those focus areas connect to the way it was taught the year before and the years after Kelly L. Watts, RESA 3

41. Fluency • Fluency is the quick mathematical content; what you should quickly know. It should be recalled very quickly. It allows students to get to application much faster and get to deeper understanding. We need to create contests in our schools around these fluencies. This can be a fun project. Deeper understanding is a result of fluency. Students are able to articulate their mathematical reasoning, they are able to access their answers through a couple of different vantage points; it’s not just getting the answer but knowing why. Students and teachers need to have a very deep understanding of the priority math concepts in order to manipulate them, articulate them, and come at them from different directions. Kelly L. Watts, RESA 3

42. Fluency • Students • Spend time practicing, with intensity, skills (in high volume) • Teacher • Push students to know basic skills at a greater level of fluency • Focus on the listed fluencies by grade level • Create high quality worksheets, problem sets, in high volume Kelly L. Watts, RESA 3

43. Deep Understanding • The Common Core is built on the assumption that only through deep conceptual understanding can students build their math skills over time and arrive at college and career readiness by the time they leave high school. The assumption here is that students who have deep conceptual understanding can: • Find “answers” through a number of different routes • Articulate their mathematical reasoning • Be fluent in the necessary baseline functions in math, so that they are able to spend their thinking and processing time unpacking mathematical facts and make meaning out of them. • Rely on their teachers’ deep conceptual understanding and intimacy with the math concepts Kelly L. Watts, RESA 3

44. Deep Understanding • Students • Show, through numerous ways, mastery of material at a deep level • Use mathematical practices to demonstrate understanding of different material and concepts • Teacher • Ask yourself what mastery/proficiency really looks like and means • Plan for progressions of levels of understanding • Spend the time to gain the depth of the understanding • Become flexible and comfortable in own depth of content knowledge Kelly L. Watts, RESA 3

45. Applications • The Common Core demands that all students engage in real world application of math concepts. Through applications, teachers teach and measure students’ ability to determine which math is appropriate and how their reasoning should be used to solve complex problems. In college and career, students will need to solve math problems on a regular basis without being prompted to do so. Kelly L. Watts, RESA 3

46. Applications • Students • Apply math in other content areas and situations, as relevant • Choose the right math concept to solve a problem when not necessarily prompted to do so • Teachers • Apply math in areas where its not directly required (i.e. science) • Provide students with real world experiences and opportunities to apply what they have learned Kelly L. Watts, RESA 3

47. Dual Intensity • This is an end to the false dichotomy of the “math wars.” It is really about dual intensity; the need to be able to practice and do the application. Both things are critical. Kelly L. Watts, RESA 3

48. Dual Intensity • Students • Practice math skills with a intensity that results in fluency • Practice math concepts with an intensity that forces application in novel situations • Teacher • Find the dual intensity between understanding and practice within different periods or different units • Be ambitious in demands for fluency and practices, as well as the range of application Kelly L. Watts, RESA 3

49. The Next Generation Math Standards for Grades K-5 The next six slides show the six instructional shifts and short instructional scenarios that each connect with one of the shifts. Read each scenario and determine the instructional shift that it represents.

50. Six Instructional Shifts in Math Focus Coherence Understanding Applications Dual Intensity Fluency Mrs. Johnson, a fifth-grade teacher, delivered two informational lessons on the concept of parentheses, brackets, braces, and numeric expressions. After two days of paper/pencil practice, she decided to teach her students the 550 Game (demonstrated in the Corwin/Silver Strong workshop) and to let them compete in pairs. Her goal was to help her 5th graders to sharpen their proficiency with numeric expressions and math symbols, and to mentally process numbers faster.