Targeted Professional Development 2: Relating Instruction and CCSSM – On the Road to Curriculum Revision

1. Targeted Professional Development 2: Relating Instruction and CCSSM – On the Road to Curriculum Revision

2. Session Goal Developing a clear picture of the Common Core State Standards by: • Using rich problems to understand the Standards for Mathematical Practice • Digging into the content standards through the Critical Areas of Focus in order to create instruction based upon the CCSSM and develop a foundation for curriculum revision.

3. Session Overview • Review of the Standards for Mathematical Practices • Incorporating Literacy Standards and 21st Century Skills • Using Rich Problems • Utilizing the Model Curriculum • Next Steps

4. A Look Inside the CCSS for Mathematics

5. MP + CAF + Standards = Instruction In order to design instruction that meets the rigor and expectations of the CCSSM, understanding the Mathematical Practices and Critical Areas of Focus are essential.

6. Standards for Mathematical PracticeMathematical ‘Habits of Mind’

7. Grade Level Introduction

8. Grade Level Overview Grade 8 Overview The Number System Know that there are numbers that are not rational, and approximate them by rational numbers. Expressions and Equations Work with radicals and integer exponents. Understand the connections between proportional relationships, lines, and linear equations. Analyze and solve linear equations and pairs of simultaneous linear equations. Functions Define, evaluate, and compare functions. Use functions to model relationships between quantities. Geometry Understand congruence and similarity using physical models, transparencies, or geometry software. Understand and apply Pythagorean Theorem. Solve real-world and mathematical problems involving volume of cylinders, cones and spheres. Statistics and Probability Investigate patterns of association in bivariate data. Mathematical Practices • 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 • Look for and express regularity in repeated reasoning

9. Format of K-8 Standards Grade Level Domain Standard Cluster

10. CCSS for High School Mathematics • Organized in “Conceptual Categories” • Number and Quantity • Algebra • Functions • Modeling • Geometry • Statistics and Probability • Conceptual categories are not courses • Additional mathematics for advanced courses indicated by (+) • Standards with connections to modeling indicated by (★)

11. Conceptual Category Introduction

12. Conceptual Category Overview Domain Cluster

13. Format of High School Standards Domain Cluster Standard Advanced

14. Two Main Pathways

15. Pathway Overview

16. Course Overview: Critical Areas (units)

17. Course Detail by Unit (critical area)

19. 21st Century Skills • Creativity and innovation • Critical thinking and problem solving • Communication and collaboration • Information, media and technology literacy • Personal management • Productivity and accountability • Leadership and responsibility • Interdisciplinary and project-based learning

20. Reading Literacy StandardsGrades 6-8

21. Writing Literacy StandardsGrades 6-8

22. What does literacy look like in the mathematics classroom? • Learning to read mathematical text • Communicating using correct mathematical terminology • Reading, discussing and applying the mathematics found in literature • Researching mathematics topics or related problems • Reading appropriate text providing explanations for mathematical concepts, reasoning or procedures • Applying readings as citing for mathematical reasoning • Listening and critiquing peer explanations • Justifying orally and in writing mathematical reasoning • Representing and interpreting data

24. Digging Deeper into the CCSS

25. CCSS Mathematical Practices • 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 • Look for and express regularity in repeated reasoning

26. CCSS Mathematical Practices • 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 • Look for and express regularity in repeated reasoning

27. Activity 1:Task Analysis with the Standards for Mathematical Practice • Individually work MARS task #1 • Identify Standards for Mathematical Practice • Individually work MARS task #3 • Identify Standards for Mathematical Practice • Share with a partner: • Solution(s) • Determine, support 1-2 Mathematical Practices http://map.mathshell.org/materials/tasks.php

28. Activity 1: Analysis Template

29. CCSS Mathematical Practices • 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 • Look for and express regularity in repeated reasoning

30. Critical Areas of Focus Critical Areas of Focus inform instruction by describing the mathematical connections and relationships students develop in the progression at this point.

31. Concepts,Skills and Procedures Concepts • Big ideas • Understandings or meanings • Strategies • Relationships Understanding concepts underlies the development and usage of skills and procedures and leads to connections and transfer. Skills and Procedures • Rules • Routines • Algorithms Skills and procedures evolve from the understanding and usage of concepts.

32. Concepts,Skills and Procedures Understand ratio concepts and use ratio reasoning to solve problems. • Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. • Understand the concept of a unit rate a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship. • 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. • 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. • Solve unit rate problems including those involving unit pricing and constant speed. • Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. • Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

33. Concepts,Skills and Procedures Understand ratio concepts and use ratio reasoning to solve problems. • Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. • Understand the concept of a unit rate a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship. • 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. • 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. • Solve unit rate problems including those involving unit pricing and constant speed. • Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. • Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

34. Activity 2:Task Analysis with CCSSM • Individually work the assigned problem (Adapted from Mathematics in Context) • With a partner share your solution then: • Identify the Mathematical Practices • Identify grade level and Critical Area of Focus • Identify the related Clusters and Standards

35. Activity 2:Task Analysis with CCSSM Share and discuss: • the Solution strategies • the Mathematical Practices • aligned grades, Critical Areas of Focus • the Clusters and Standards What evidence is needed to demonstrate understanding at your grade level? Adapted from Mathematics in Context

36. CCSS Mathematical Practices • 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 • Look for and express regularity in repeated reasoning

37. Rich Tasks: A Wealth of Benefits

38. Quick Write: What do you know about rich problems?

39. Adapted from Collins “Writing Across the Curriculum”

40. Quick Write: What do you know about rich problems?

41. What Makes a Problem Rich? • Significant mathematics • Mathematical Practices • Multiple layers of complexity • Multiple entry points • Multiple solutions and/or strategies • Leads to discussion or other questions • Students are the workers and the decision makers

42. Is it Rich? • What are essential characteristics of rich problems?

43. A Problem or an Exercise? Problem Exercise Computation “problem” Solution process is recognizable Routine Contextual but not engaging • The answer is not immediately known • Requires persistence • Engaging • Feasible • Valued

44. Incorporating Rich Problems in Instruction NOW

45. How would you enrich these? • Brian ran a 5 km run in 18.4 minutes. How fast did he run? • Factor the trinomial 21x² – 50x – 16 • Multiply 14 times 2.5. • The angles of a quadrilateral have measures 90°, 90°, 100° and n°. Find the value of n.

46. Create Your Own Rich Problem • Significant mathematics • Mathematical Practices • Multiple layers of complexity • Multiple entry points • Multiple solutions and/or strategies • Provides an opportunity to connect and relate mathematics • Leads to discussion or other questions

47. Model Curriculum

48. Model Curriculum:Instructional Strategies and Resources

49. Model Curriculum:Instructional Resources and Tools

50. Rich Task Sources Ohio Resource Center • www.OhioRC.org Inside Mathematics • http://www.insidemathematics.org Balanced Assessment (MARS tasks) • http://balancedassessment.concord.org NCTM Illuminations • http://illuminations.nctm.org/