November 26, 2012

1. If you have not downloaded and/or viewed the materials that will be discussed during this webinar, you may access them at the MDE CCSS SharePoint site. • Visit https://districtaccess.mde.k12.ms.us/commoncore/ 2. In the left pane, click on Training Materials. 3. Select the folder “The Common Core State Standards Trilogy”. 4. Download and/or print materials as needed.

2. The Common Core State Standards Trilogy: Revisiting the PARCC Model Content Frameworks, the Progression Documents, and the Standards for Mathematical Practice Office of Curriculum and Instruction Marla Davis Office Director for Mathematics November 26, 2012

3. Pre-Assessment(Mix-n-Match) Set C: The Progression Documents Standards for Mathematical Practice PARCC Model Content Frameworks Set A: Focus Coherence Rigor Set B:

4. Agenda Key Shifts in the Common Core State Standards for Mathematics (CCSSM) Focusing on the PARCC Model Content Frameworks Focusing on the Progression Documents Focusing on the Standards for Mathematical Practice Bridging the Gap Between the CCSSM Trilogy and Instruction 6. Resources

5. Key Shifts in the CCSSM

6. Key Shifts in the CCSSM Focus:Focus instruction where the standards place emphasis. Coherence:Think across grades, and link to major topics. Rigor:Pursue conceptual understanding, procedural skill, fluency, and application.

7. Think-Pair-Share At your school site, discuss the following statement: “Why focus? There’s so much math that students need to learn. Why limit them to just a few things?”

8. Traditional U.S. Approach to Mathematics(Shift #1: Focus)

9. Focus: The Standards call for a greater focus in mathematics. Rather than racing to cover topics, the CCSSM significantly narrows and deepens the way time and energy are spent in the math classroom. They focus deeply on the major work of each grade so that students can gain strong foundations. Adapted from : www.achievethecore.org

10. Key Shifts in the CCSSM(Shift #1: Focus)

11. Key Shifts in the CCSSM(Shift #1: Focus) Operations and Algebraic Thinking Expressions and Equations Algebra F1 F2 F3 Number and Operations- Base Ten The Number System Number and Operations-Fractions K 1 2 3 4 5 6 7 8 High School

12. Key Shifts in the CCSSM(Shift #1: Focus) Question: What does focus look like for the student? Answer: spend more time thinking and working on priority concepts understand concepts and their connections to processes (algorithms)

13. Key Shifts in the CCSSM(Shift #1: Focus) Question: What does focus look like for the teacher? Answer: build understanding of how andwhy certain mathematics concepts are done facilitate the learning process by identifying specific concepts and standards that connect to one another pay more attention to priority content and invest the appropriate time for all students to learn before moving onto the next topic

14. Think-Pair-Share At your school site, discuss the following statement: “Why should I be concerned about coherence between the grades? I have enough to teach at my own grade level!”

15. Traditional U.S. Approach to Mathematics(Shift #2: Coherence) We gave them: and we expected them to: but our students were often: This forced them to:

16. Coherence: The Standards are designed around coherent progressions from grade to grade. Teachers should carefully connect the learning across grades to enable students to build new understanding onto foundations built in previous years. Every standard, every domain, and every cluster should be viewed as an extension of previous learning, not as a separate or new event. Adapted from : www.achievethecore.org

17. Key Shifts in the CCSSM(Shift #2: Coherence)

18. Key Shifts in the CCSSM(Shift #2: Coherence) Question: What does coherence look like for the student? Answer: make connections between what was taught in a previous grade (or unit) and new information apply previous skills to new skill sets transfer knowledge and skills within and across domains and adapt when necessary

19. Key Shifts in the CCSSM(Shift #2: Coherence) Question: What does coherence look like for the teacher? Answer: intentionally develop lessons and units that scaffold student learning and experiences from previous grades create opportunities for students to communicate their understanding create a safe environment where student misconceptions can be evaluated

20. Think-Pair-Share At your school site, discuss the following statement: “Just call me Mr. Rigor! I assigned all the Word Problems for homework last night!”

21. Traditional U.S. Approach to Mathematics(Shift #3: Rigor)

22. Rigor: The Standards require that mathematics instruction provide rich opportunities for students to pursue conceptual understanding, procedural skill, fluency and application with equal intensity. Adapted from : www.achievethecore.org

23. Key Shifts in the CCSSM(Shift #3: Rigor) Question: What does rigor look like for the student? Answer: involved in meaningful, relevant, rich mathematical tasks that require conceptual understanding engaged with challenging concepts and skills that require fluency, critical thinking and application

24. Key Shifts in the CCSSM(Shift #3: Rigor) Question: What does rigor look like for the teacher? Answer: provide opportunities for students to apply mathematical concepts in thought-provoking real-world situations strategically arrange activities that allows students to “struggle” with the math select mathematical tasks that require a balance of mathematical procedure and deep conceptual understanding

25. Out of the need for FOCUS came the PARCC Model Content Frameworks. Out of the need for COHERENCE came the Progression Documents. Out of the need for RIGOR came the Standards for Mathematical Practice.

26. A Grecian Urn You have just purchased an expensive Grecian urn and asked the dealer to ship it to your house. He picks up a hammer, shatters it into pieces, and explains that he will send one piece in an envelope each day for the next year. You object; he says “Don’t worry, I’ll make sure that you get every single piece. The markings are clear, so you’ll be able to glue itall back together. I’ve got this covered. I do this for a living!”

27. Focusing on the PARCC Model Content Frameworks ** PARCC Model Content Frameworks (Version 3.0) was released on November 19, 2012**

28. PARCC Model Content Frameworks Structure: Examples of Key Advances from Previous Grades Fluency Expectations or Examples of Culminating Standards Examples of Major Within-Grade Dependencies Examples of Opportunities for Connections Among Standards, Clusters, or Domains Examples of Opportunities for In-depth Focus Examples of Opportunities for Connecting Mathematical Content and Mathematical Practices Content Emphases by Cluster

29. PARCC Model Content Frameworks Purpose: To inform development of item specifications To support implementation of the CCSSM To provide detailed information about standards, fluencies, connections and content emphases

30. PARCC Model Content Frameworks 7.G.1 7.G.2(part 1 only) 7.G.4 7.G.5 7.G.6 Directions: Locate Handout #1: CCSSM Grade 7. Locate Handout #2: The Roman Mosaic. Identify the 7th Grade Standard(s) that are likely connected to this task.

31. PARCC Model Content Frameworks The facilitator will discuss and model the online (search) capabilities of the PARCC Model Content Frameworks for Mathematics for the standards just indicated.

32. Focusing on the Progression Documents

33. CCSSM Progression Documents Draft K–6 Progression on Geometry Draft K–5 Progression on Measurement and Data (measurement part) Draft K–5 Progression on Measurement and Data (data part) Draft K–5 Progression on Number and Operations in Base Ten Draft K–5 Progression on Counting and Cardinality and Operations and Algebraic Thinking Draft 3–5 Progression on Number and Operations—Fractions Draft 6–8 Progression on Statistics and Probability Draft 6–8 Progression on Expressions and Equations Draft 6–7 Progression on Ratios and Proportional Relationships Draft High School Progression on Statistics and Probability

34. CCSSM Progression Documents Purpose: To show the progression of skills, concepts, and fluency between the standards, and from grade to grade. To provide evidence linking the Grades K-8 domains to the High School Conceptual Categories. To provide vocabulary that is indirectly included in individual standards. To explain things that the Standards themselves cannot (e.g. sequencing, cognitive difficulties and pedagogical solutions).

35. CCSSM Progression Documents Directions: Locate Handout #3: K-6 Geometry Progression. Locate (and highlight) the answer to the following questions.

36. CCSSM Progression Documents What are the four levels of Geometric Thinking? (page 3) At the end of Kindergarten, students should not only be able to discuss shape and orientation, but what else? (page 7) According to 1.G.1 students should be able to distinguish between what two types of attributes? (page 8) 4. What useful instructional activity is offered for 2nd graders to assist in spatial structuring? (page 11) In Grade 4, what eight vocabulary words do students develop an explicit awareness of? (page 14) What 5th grade standard introduces students to the coordinate system? (page 16) Sixth grade students can draw polygons in the coordinate plane if they are given what characteristics? (page 19) As students enter high school, recognizing the significance of an existing line in a figure is part of which mathematical practice? (page 20)

37. Think-Pair-Share Based on key evidence we just reviewed in the Progression Document, discuss as a team the sophisticated, grade appropriate response expected of a 7th grader responding to the Roman Mosaic Task?

38. Focusing on the Standards for Mathematical Practice

39. Standards forMathematical Practice • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

40. Standards for Mathematical Practice Purpose: To describe the variety of expertise that mathematics educators should seek to develop in their students. To identify the level of engagement, ways of thinking, and behaviors necessary for rigorous classroom instruction and discourse.

41. Standards for Mathematical Practice Question: Do the Standards for Mathematical Practice describe student behaviors or teacher behaviors? Answer: Both!!The Standards for Mathematical Practice will only become a part of our students’ everyday “math behavior” if teachers effectively and consistently model what is expected by each Practice.

42. Standards forMathematical Practice

43. Think-Pair-Share As a team, create a list of instructional strategies, activities, or questions you can ask students to ensure the Mathematical Practices are incorporated as students complete the Roman Mosaic Task.

44. “We were purposeful in calling the Mathematical Practices standards because then they won’t be ignored.” Dr. William (Bill) McCallum Lead Writer for the CCSSM & the CCSSM Progression Documents

45. Post-Assessment(Mix-n-Match) Set C: The Progression Documents Standards for Mathematical Practice PARCC Model Content Frameworks Set A: Focus Coherence Rigor Set B:

46. Bridging the Gap Between the CCSSM Trilogy and Instruction

47. Tri-State Quality Review Rubric Directions: Locate Handout #4: Tri-State Quality Review Rubric.

48. Tri-State Quality Review Rubric Purpose: To provide clear, descriptive criteria for CCSS lessons/units To provide meaningful, constructive feedback to developers of lessons/units To identify lessons/units that can serve as models To guide collegial review and juryingprocesses Source: EQuiP Collaborative in conjunction with Achieve

49. Tri-State Quality Review Rubric Question: Can the Tri-State Quality Review Rubric be used in the planning stage of a lesson (or unit)? Answer: Absolutely!! The Tri-State Quality Review Rubric should be used as you develop your lesson plans; and should be used after a lesson plan (or unit) has been carried out.