1. Vacaville USD October 30, 2014

2. AGENDA Problem Solving, Patterns, Expressions and Equations Math Practice Standards and High Leverage Instructional Practices Number Talks –Computation Strategies Multiplication and Division

3. Expectations We are each responsible for our own learning and for the learning of the group. We respect each others learning styles and work together to make this time successful for everyone. We value the opinions and knowledge of all participants.

4. Cubes in a Line How many faces (face units) are there when: 6 cubes are put together? 10 cubes are put together? 100 cubes are put together? n cubes are put together?

5. Questions? What do I mean by a “face unit”? Do I count the faces I can’t see?

6. Cubes in a Line How many faces (face units) are there when: 6 cubes are put together? 10 cubes are put together? 100 cubes are put together? n cubes are put together?

7. Cubes in a Line

12. We found several different number sentences that represent this problem. What has to be true about all of these number sentences?

13. Math Practice Standards Remember the 8 Standards for Mathematical Practice Which of those standards would be addressed by using a problem such as this?

14. CCSS Mathematical Practices OVERARCHING HABITS OF MIND 1.Make sense of problems and persevere in solving them 6.Attend to precision REASONING AND EXPLAINING 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others MODELING AND USING TOOLS 4.Model with mathematics 5.Use appropriate tools strategically SEEING STRUCTURE AND GENERALIZING 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

15. High Leverage Instructional Practices

16. High-Leverage Mathematics Instructional Practices An instructional emphasis that approaches mathematics learning as problem solving

17. CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

18. CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

19. An instructional emphasis on cognitively demanding conceptual tasks that encourages all students to remain engaged in the task without watering down the expectation level (maintaining cognitive demand)

20. CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

21. CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

22. Instruction that places the highest value on student understanding

23. CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

24. CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

25. Instruction that emphasizes the discussion of alternative strategies

26. CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

27. CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

28. Instruction that includes extensive mathematics discussion (math talk) generated through effective teacher questioning

29. CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

30. CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

31. Teacher and student explanations to support strategies and conjectures

32. CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

33. CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

34. The use of multiple representations

35. CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

36. CCSS Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

37. Number Talks

38. What is a Number Talk? Also called Math Talks A strategy for helping students develop a deeper understanding of mathematics –Learn to reason quantitatively –Develop number sense –Check for reasonableness –Number Talks by Sherry Parrish

39. What is Math Talk? A pivotal vehicle for developing efficient, flexible, and accurate computation strategies that build upon key foundational ideas of mathematics such as –Composition and decomposition of numbers –Our system of tens –The application of properties

40. Key Components Classroom environment/community Classroom discussions Teacher’s role Mental math Purposeful computation problems

41. Classroom Discussions What are the benefits of sharing and discussing computation strategies?

42. Students have the opportunity to: –Clarify their own thinking –Consider and test other strategies to see if they are mathematically logical –Investigate and apply mathematical relationships –Build a repertoire of efficient strategies –Make decisions about choosing efficient strategies for specific problems

43. 5 Goals for Math Classrooms Number sense Place Value Fluency Properties Connecting mathematical ideas

44. Clip 5.6 – 5 th Grade Subtraction: 1000 – 674 Before we watch the clip, talk at your tables –What possible student strategies might you see? –How might you record them?

45. What evidence is there that the students understand place value? How do the students’ strategies exhibit number sense? How does fluency with smaller numbers connect to the students’ strategies? How are accuracy, flexibility, and efficiency interwoven in the students’ strategies?

46. Clip 3.7 – 3 rd Grade Array Discussion: 8 x 25 Before we watch the clip, talk at your tables –What possible student strategies might you see? –How might you record them?

47. How does the array model support the student strategies? How does breaking the factors into friendly numbers promote the goals of efficiency and flexibility? How do the teacher’s questions foster an understanding of multiplication? What math understandings and misunderstandings are addressed with this model?

48. Clip 5.5 – 5 th Grade Division String: 496 ÷ 8 Before we watch the clip, talk at your tables –What possible student strategies might you see? –How might you record them?

49. What evidence is there that students understand place value? How do students build upon their understanding of multiplication to divide? How does the teacher connect math ideas throughout the number talk?

50. Solving Word Problems

51. 3 Benefits of Real Life Contents Engages students in mathematics that is relevant to them Attaches meaning to numbers Helps students access the mathematics.

52. Hannah has $500. She buys a camera for $435 and 4 other items for $9 each. Now Hannah wants to buy speakers for $50. Does she have enough money to buy the speakers?

53. The Lane family took a road trip. During the first week, they drove 907 miles. The second week they drove 297 miles more than the first week. How many miles did they drive during the two weeks?

54. Katrina spent $500 on her new tablet. Her father spent 4 times as much to buy his new computer. How much more did her father spend?

55. Multiplication

56. Strategies for Multiplication Repeated Addition Skip Counting Equal Groups Arrays and Area Models Partial Products Traditional US Algorithm

57. Multiplication 67 x 3 Solve using at least 3 different strategies

58. C – R – A Concrete Representational Abstract

59. Multiplication 467 x 35 Solve using at least 3 different strategies Did your choice of strategies change as the numbers got larger?

60. Division

61. Strategies for Division Repeated Subtraction Skip Counting Equal Groups Arrays and Area Models Partial Quotients Traditional US Algorithm

62. Division Measurement vs Fair Share? 47  3 Strategy 1: Representational Measurement Strategy 2: Representational Fair Share

63. Concrete Use base 10 chips and recording sheet 437  3