1. Vacaville USD December 5, 2014

2. AGENDA Problem Solving and Patterns Math Practice Standards and High Leverage Instructional Practices Number Talks –Computation Strategies Word Problems Addition and Subtraction Strategies –Facts –Double digit plus single digit

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 face units can you see when cubes are put together?

5. Cubes in a Row How many face units do you see on 1 cube?

6. Cubes in a Row How many face units do you see on 2 cubes? How can you keep track of what sides you have counted?

7. Cubes in a Row You are going to be given 2 strips of paper like this: _____________ number of cubes number of face units 7

8. Cubes in a Row What patterns do you see? How could those patterns help you figure out how many face units there would be?

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

10. 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

11. High Leverage Instructional Practices

12. High-Leverage Mathematics Instructional Practices An instructional emphasis that approaches mathematics learning as problem solving. 1.Make sense of problems and persevere in solving them.

13. 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) 1.Make sense of problems and persevere in solving them.

14. Instruction that places the highest value on student understanding 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively

15. Instruction that emphasizes the discussion of alternative strategies 3.Construct viable arguments and critique the reasoning of others

16. Instruction that includes extensive mathematics discussion (math talk) generated through effective teacher questioning 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

17. Teacher and student explanations to support strategies and conjectures 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others

18. The use of multiple representations 1.Make sense of problems and persevere in solving them. 4.Model with mathematics 5.Use appropriate tools strategically

19. Number Talks

20. 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

21. What is Number 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

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

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

24. 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

25. 4 Goals for K-2 Classrooms Developing number sense Developing fluency with small numbers Subitizing Making tens

26. K.1 – Kindergarten Number Talk using ten frames and dot cards Think about the following questions as you watch.

27. How does the teacher build students’ fluency with small numbers? What questions does the teacher pose to build understanding? What strategies are the students using to build meaning of the numbers? How does the teacher support student communication during the number talk?

28. K.2 – Kindergarten Number Talk Using Rekenreks Think about the following questions as you watch.

29. What instructional strategies does the teacher use to engage the students? How does the teacher use rekenreks as a tool to build fluency with small numbers? What role does the game “Can You Guess My Way?” play on the number talk? What mathematical understandings and misconceptions are being addressed?

30. Clip 2.1 – 2 nd Grade Addition: 8 + 6 (using 10-frames) Before we watch the clip, talk at your tables –What possible student strategies might you see? –How might you record them?

31. What role do the 10-frames play in developing fluency with small numbers? What questions does the teacher use to build understanding about composing and decomposing numbers? How does the use of double 10-frames support the goal of K-2 number talks?

32. Solving Word Problems

33. 3 Benefits of Real Life Contents Engages students in mathematics that is relevant to them Attaches meaning to numbers Helps students access the mathematics.

34. Word Problems Concrete –ACT IT OUT!!! Representational –Draw a model 1 to 1 representation Bar or scaled representation Abstract –Write a number sentence –Use a strategy

35. Word Problems Practice problems

36. Math Facts Tools Ten frames Rekenreks Number lines Ten sticks / counters

37. Math Facts Strategies Counting all / Counting On Doubles / Doubles +/- 1 Making tens Using known facts

38. Developing Strategies We are going to give you a series of problems (number talks) designed to promote specific strategies With a partner –Solve each problems using all of the tools –Decide which tool or tools best support students in understanding and developing that strategy

39. 1 st Grade Number Talks Start with visuals and move to symbolic

40. Counting All / Counting On A

41. Counting All / Counting On B

42. Counting All / Counting On C

43. Counting All / Counting On 6 + 3 6 + 5 6 + 7

44. Doubles/Near Doubles

45. Doubles/Near Doubles A

46. Doubles/Near Doubles B

47. Doubles/Near Doubles C

48. Doubles/Near Doubles 4 + 4 4 + 3 3 + 3 3 + 4

49. Making Tens

50. Making Tens A

51. Making Tens B

52. Making Tens C

53. Making Tens A 9 + 1 9 + 3 + 1 9 + 5 + 1

54. Making Tens B 8 + 2 8 + 2 + 4 8 + 6

55. Making Tens C 7 + 3 7 + 5 7 + 8

56. Making Friendly Numbers A 8 + 2 8 + 6 8 + 5

57. Making Friendly Numbers B 6 + 6 9 + 6 9 + 8

58. Additional Tools Hundreds Chart

59. Extending Friendly Numbers A 4 + 3 14 + 3 34 + 3

60. Extending Friendly Numbers B 6 + 8 26 + 8 56 + 8

61. Extending Friendly Numbers C 4 + 5 40 + 50 46 + 50

62. Extending Friendly Numbers D 6 + 2 60 + 20 63 + 20