Math Common Core Standards

1. Math Common Core Standards Jennie Winters Lake County ROE jwinters@lake.k12.il.us

2. Focus for Today • 3 types of change • Standards for Mathematical Practice • Focus, Coherence & Rigor • Assessment • Curriculum: Quality Units/Lessons • Q & A

3. Instructional Change • Curricular Change • Assessment Change • Common Core Implementation

4. Practice Standards 1. Makesenseof problems and persevere in solving them.

5. Practice Standards 2. Reason abstractly and quantitatively.

6. Practice Standards 3. Construct viable argumentsandcritiquethe reasoning of others.

7. Practice Standards 4.Modelwith mathematics.

8. Practice Standards 5. Use appropriate toolsstrategically.

9. Practice Standards 6. Attend to precision.

10. Practice Standards 7. Look for and make use ofstructure.

11. Practice Standards 8. Look for and express regularity in repeated reasoning.

12. Modes of Representation(Lesh, Post, & Behr, 1987) Manipulative Models Real-world Situations Pictures Written Symbols Oral/Written Language

13. Modes of Representation • Manipulative/ Tools • Real-Life Situations • Picture/Graph • Table/Chart • Oral & Written Language • Symbols (Equations, etc.)

14. The CCSS Requires Three Shifts in Mathematics Focus: Focus strongly where the standards focus. Coherence: Think across grades, and linkto major topics Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency,andapplication

15. Rigor The CCSSM require a balance of: • Solid conceptual understanding • Procedural skill and fluency • Application of skills in problem solving situations Pursuit of all threes requires equal intensity in time, activities, and resources.

16. 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)

17. 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

18. Required Fluencies in K-6

19. 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.

20. Assessment • Conceptual Assessment • Includes Observational Tools

21. 2nd Grade Example Students each create their own paper airplane and take turns flying them. They use a tape measure to find the distance each has flown to the nearest foot. What concepts are being assessed?

23. Assessment • Conceptual Assessment • Includes Observational Tools • Procedural Skill & Fluency Assessment • Includes Extended Response

25. Assessment • Conceptual Assessment • Includes Observational Tools • Procedural Skill & Fluency Assessment • Includes Extended Response • Application • Includes Rich Tasks

27. Curriculum • Sequence of units (Coherence) • Prioritization • Sequence within units: • Conceptual before procedural • Application throughout

28. The Tri-State Quality Review Rubric Criteria

29. 4 Dimensions • Alignment to the Rigor of the CCSS • Key Areas of Focus in the CCSS • Instructional Supports • Assessment

30. 1 – Alignment to the Rigor of the CCSS The unit aligns with the letter and spirit of the CCSS: • Targets a set of grade level mathematics standard(s) at the level of rigor in the CCSS for teaching & learning

32. 1 – Alignment to the Rigor of the CCSS The unit aligns with the letter and spirit of the CCSS: • Standards for Mathematical Practice that are central to the unit are identified, handled in a grade-appropriate way, and well connected to the content being addressed.

34. 1 – Alignment to the Rigor of the CCSS The unit aligns with the letter and spirit of the CCSS: • Presents a balance of mathematical procedures and deeper conceptual understanding inherent in the CCSS

35. 2-Key Areas of Focus in the CCSS The unit reflects evidence of key shifts that are reflected in the CCSS. • Focus Centers on the concepts, foundational knowledge and level of rigor that are prioritized in the standards.

36. 2-Key Areas of Focus in the CCSS The unit reflects evidence of key shifts that are reflected in the CCSS. • Coherence Makes connections and provides opportunities for students to transfer knowledge and skills within and across domains and learning progressions.

38. 2-Key Areas of Focus in the CCSS The unit reflects evidence of key shifts that are reflected in the CCSS. • Rigor Requires students to engage with an demonstrate challenging mathematics in the following ways:

39. 2-Key Areas of Focus in the CCSS • Conceptual Understanding Requires students to demonstrate conceptual understanding through complex problem solving, in addition to writing and speaking about their understanding.

40. 2-Key Areas of Focus in the CCSS • Procedural Skill & Fluency Expects, supports and provides guidelines for procedural skill and fluency with core calculations, mathematical procedures and strategies (when called for in the standards for the grade) to be performed quickly and accurately.

41. 2-Key Areas of Focus in the CCSS • Application Provides opportunities for students to independently apply mathematical concepts in real-world situations and problem solve with persistence, choosing and applying an appropriate model or strategy to new situations.

42. 3 – Instructional Supports The unit is responsive to varied student needs: • Includes clear and sufficient guidance to support teaching and learning of the targeted standards, including, when appropriate, the use of technology and media.

43. 3 – Instructional Supports The unit is responsive to varied student needs: • Uses and encourages precise and accurate mathematics, academic language, terminology, and concrete or abstract representations (e.g. pictures, symbols, expressions, equations, graphics, models) in the discipline.

45. 3 – Instructional Supports The unit is responsive to varied student needs: • Engages students in productive struggle through relevant, thought-provoking questions, problems, and tasks that stimulate interest and elicit mathematical thinking.

46. 3 – Instructional Supports The unit is responsive to varied student needs: • Addresses instructional expectations and is easy to understand and use.

47. 3 – Instructional Supports Provides appropriate level and type of scaffolding, differentiation, intervention, and support for a broad range of learners: • Supports diverse cultural and linguistic backgrounds, interests and styles.

49. 3 – Instructional Supports Provides appropriate level and type of scaffolding, differentiation, intervention, and support for a broad range of learners: • Provides extra supports for students working below grade level.

50. 3 – Instructional Supports Provides appropriate level and type of scaffolding, differentiation, intervention, and support for a broad range of learners: • Provides extensions for students with high interest or working above grade level.