Unwrapping the Common Core State Standards for Administrators

1. Unwrapping the Common Core State Standards for Administrators

2. Objectives Increase participant’s knowledge of the CCSS for Mathematics Increase participant’s knowledge of the shifts of the CCSS for Mathematics Increase participant’s ability to unpack content and mathematical practice standards

3. Outcomes Knowledge to lead implementation of the Common Core State Standards. Vision to integrate the implementation of the Common Core State Standards into broad education improvement efforts. Metrics to clearly describe what successful progress in implementation looks like and facilitates a flexible cycle of change. Build capacity so that all members of the education landscape are learning together.

4. Rationale for the CCSS Declining US competitiveness with other developed countries NAEP performance that is largely flat over the past 40 years in 8th grade • Slight improvement at the 4th grade level • Slight decline at the high school level High rates of college remediation

5. Principles of the CCSS Aligned to requirements for college and career readiness Based on evidence Honest about time

6. Digging into the Common Core Activity

13. Common Core State Standards for Mathematics: Key Shifts

14. Mathematics: 3 Shifts Focus: Focus strongly where the standards focus.

15. Shift #1: Focus Strongly where the Standards Focus Significantly narrow the scope of content and deepen how time and energy is spent in the math classroom. Focus deeply on what is emphasized in the standards, so that students gain strong foundations.

16. Traditional U.S. Approach

17. Focusing Attention Within Number and Operations

18. Engaging with the shift: What do you think belongs in the major work of each grade?

19. Key Areas of Focus in Mathematics

20. Mathematics: 3 Shifts Focus: Focus strongly where the standards focus. Coherence: Think across grades, and link to major topics

21. Shift #2: Coherence: Think Across Grades, and Link to Major Topics Within Grades Carefully connect the learning within and across grades so that students can build new understanding on foundations built in previous years. Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.

22. Coherence Activity

23. Coherence: Link to Major Topics Within Grades Example: Data Representation Standard MACC.3.MD.2.3

24. Coherence: Link to Major Topics Within Grades Example: Geometric Measurement MACC.3.MD.3 (cluster)

25. CCSS 4.NF.4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Grade 4 5.NF.4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5.NF.7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Grade 5 6.NS. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.6.NS.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Grade 6 Informing Grades 1-6 Mathematics Standards Development: What Can Be Learned from High-Performing Hong Kong, Singapore, and Korea? American Institutes for Research (2009, p. 13)

26. Alignment in Context: Neighboring Grades and Progressions One of several staircases to algebra designed in the OA domain. 26

27. Mathematics: 3 Shifts Focus: Focus strongly where the standards focus. Coherence: Think across grades, and link to major topics Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, andapplication

28. Shift #3: Rigor: In Major Topics, Pursue Conceptual Understanding, Procedural Skill and Fluency, and Application The CCSSM require a balance of: • Solid conceptual understanding • Procedural skill and fluency • Application of skills in problem solving situations Pursuit of all three requires equal intensity in time, activities, and resources.

29. Solid Conceptual Understanding Teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives Students are able to see math as more than a set of mnemonics or discrete procedures Conceptual understanding supports the other aspects of rigor (fluency and application)

32. Fluency The standards require speed and accuracy in calculation. Teachers structure class time and/or homework time for students to practice core functions such as single-digit multiplication so that they are more able to understand and manipulate more complex concepts

33. Required Fluencies in K-6

34. Fluency in High School

35. Application Students can use appropriate concepts and procedures for application even when not prompted to do so. Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in K-5, 6-8, and HS. Teachers in content areas outside of math, particularly science, ensure that students are using grade-level-appropriate math to make meaning of and access science content.

36. Engaging with the shift: Making a True Statement This shift requires a balance of three discrete components in math instruction. This is not a pedagogical option, but is required by the standards. Using grade __ as a sample, find and copy the standards which specifically set expectations for each component. Rigor = ______ + ________ + _______

37. Discussion Have you observed any of these shifts in your schools with the implementation of NGSSS? What have you seen?

38. Common Core in Action? Observe Mr. McKinney’s class. Do you see the shifts of CCSS incorporated into his teaching? Teaching the Pythagorean Theorem

39. Reflecting on the Shifts for Mathematics Activity

40. Structure of CCSS Standards for Mathematical Practice Grade level or High School conceptual category Domain Cluster Standard

41. Standards for Mathematical Practice

42. Standards of Mathematical Practice Activity

43. Metrics: What it Looks Like Everyone in the system needs clarity around the goals – what it will look like when implemented. Metrics let us know what progress we are making in meeting goals. The system must be set up to collect progress data, and also monitor and adjust.

44. Unpacking Practice Standards Activity

45. Unpacking Content Standards Activity

46. Unpacking Content Standards Answers 2 questions: “What does that mean?” “What should I do to help my students demonstrate that?” Product Clear explanations, definitions, and background research Ideas for tasks Guides differentiation and planning

47. Unpacking Process

48. Essential Element of Unpacking Process Read the standard. Identify and discuss the technical meaning of important words in the language of the standard. Explore research pertaining to the content in the standard, including common misconceptions related to the topic. Determine what the standard calls for students to know and be able to do. Determine how the standard relates to learning progressions, standards progressions, and big ideas. Determine how students will demonstrate proficiency.

49. MACC.6.RP.1.3a MACC.6.RP.1.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations MACC.6.RP.1.3a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

50. MACC.6.RP.1.3a MACC.6.RP.1.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations MACC.6.RP.1.3a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.