1. Vacaville USD October 28, 2014

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

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 “fat 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. Cubes in a Line Let’s agree to use the simplest form of the equation: F = 4n + 2 What does F stand for? What does n stand for?

14. Cubes in a Line F = 4n + 2 Suppose I have 250 cubes. How many faces will that be? John says he has 602 face units. How many cubes does he have? Kris says he has 528 faces units. How many cubes does he have?

15. Equivalent Expressions Which of the following expressions are equivalent? Why? 2(x + 4) 8 + 2x 2x + 4 3(x + 4) − (4 + x) x + 4

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

17. Math Content Standards Look at your 6 th Grade Content Standards – Expressions and Equations Which standards would be addressed by using problems such as these?

18. 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

19. High Leverage Instructional Practices

20. High-Leverage Mathematics Instructional Practices An instructional emphasis that approaches mathematics learning as problem solving –Mathematical Practice 1

21. 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) –Mathematical Practice 1

22. Instruction that places the highest value on student understanding –Mathematical Practices 1 and 2

23. Instruction that emphasizes the discussion of alternative strategies –Mathematical Practice 3

24. Instruction that includes extensive mathematics discussion (math talk) generated through effective teacher questioning –Mathematical Practices 2, 3, 6, 7, and 8

25. Teacher and student explanations to support strategies and conjectures –Mathematical Practices 2 and 3

26. The use of multiple representations –Mathematical Practices 4 and 5

27. Number Talks

28. 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

29. 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

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

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

32. 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

33. 5 Goals for Math Classrooms Number sense Place Value Fluency Properties Connecting mathematical ideas

34. 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?

35. 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?

36. Clip 5.4 – 5 th Grade Division: 150 ÷ 15; 300 ÷ 15 Before we watch the clip, talk at your tables –What possible student strategies might you see? –How might you record them?

37. What mathematical relationships are being built upon during the class discussion? How do the students’ strategies exhibit number sense? What understandings and misconceptions does the area model help the students confront? What understandings and misconceptions do students have about the area model?

38. Number Talks Illustrative Mathematics Task Reasoning about Multiplication and Division and Place Value, Part 1 How could you use problems like these as part of a number talk to see what students understanding about multiplication, division and place value?

39. Solving Word Problems

40. 3 Benefits of Real Life Contents Engages students in mathematics that is relevant to them Attaches meaning to numbers Helps students access the mathematics.

41. Expressions and Equations 6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

42. Integers

43. Integers What are negative numbers?

45. - 5 - 4 - 3 - 2 - 1

46. Integers How are negative numbers used and why are they important?

47. Integers What are opposites? How are they shown on a number line?

48. - 5 - 4 - 3 - 2 - 1

49. Integers What is the absolute value of a number?

50. - 5 - 4 - 3 - 2 - 1

51. Integers How do we use positive and negative numbers to represent quantities in real- world contexts?

52. Finish labeling all of the points on the number line. Locate - 3 on the number line What is the opposite of - 3? –Where is it located on the number line? What is the absolute value of - 3? –Where do you see that on the number line? How far is it from - 3 to 5? –How can you use the number line to solve this?

53. - 5 - 4 - 3 - 2 - 1

54. Integers and the Real World Comparing Temperatures Absolute Value and Ordering 1

55. Coordinate Grid

57. Naming Points – Secret Message

58. Coordinate Grid