1. Vacaville USD November 4, 2014
FIFTH GRADE Session 2
Vacaville USD
November 4, 2014

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

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

8. Cubes in a Line

9. Cubes in a Line

10. Cubes in a Line

11. Cubes in a Line

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

13. 5.OA.2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × ( ) is three times as large as , without having to calculate the indicated sum or product.

14. 5. OA. 3 Generate two numerical patterns using two given rules
5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

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

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

17. High Leverage Instructional Practices

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

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)
Make sense of problems and persevere in solving them.

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

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

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

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

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

25. Number Talks

26. 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

27. 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

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

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

30. 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

31. 5 Goals for Math Classrooms
Number sense
Place Value
Fluency
Properties
Connecting mathematical ideas

32. Clip 5.6 – 5th 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?

33. 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?

34. Clip 5.1 – 5th Grade Multiplication: 12 x 15
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 students understand place value?
How do student strategies exhibit number sense?
How do the teacher and students connect math ideas?
What questions does the teacher use to facilitate student thinking about big ideas?

36. Clip 5.5 – 5th 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?

37. 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?

38. Solving Word Problems

39. 3 Benefits of Real Life Contents
Engages students in mathematics that is relevant to them
Attaches meaning to numbers
Helps students access the mathematics.

40. A crane operator unloaded the following cargo:
5 pallets of lumber. Each pallet weighs 7.3 tons.
9 pallets of concrete. Each pallet weighs 4.8 tons.
How many pounds of cargo were unloaded?
Which load of cargo was heavier, the lumber or the concrete? How many pounds heavier?

41. Ava is saving for a new computer that costs $1,218
Ava is saving for a new computer that costs $1,218. She has already saved half of the money. Ava earns $14.00 per hour. How many hours must Ava work in order to save the rest of the money?

42. Mrs. Onusko made 60 cookies for a bake sale
Mrs. Onusko made 60 cookies for a bake sale. She sold 2/3 of them and gave 3/4 of the remaining cookies to the students working at the sale. How many cookies did she have left?

43. Equivalent Fractions

44. 5th Grade
Use equivalent fractions as a strategy to add and subtract fractions.

45. CaCCSS
Fractions are equivalent (equal) if they are the same size or they name the same point on the number line.

46. Fraction Families

47. Equivalent Fractions Fraction Family Activity
Equivalent Fraction Activity

48. 5th Grade CCSS-M
5.F.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/ /12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

49. Adding Fractions

50. 1
Add 1 2

51. 2

55. 3

59. Subtracting Fractions

60. Subtracting Fractions
Possible sequence of instruction
Subtracting 2 fractions less than 1

61. Subtracting Fractions
Subtracting when 1 fraction is between 1 and 2 and 1 fraction is less than 1

62. Subtracting Fractions
Subtracting mixed numbers

63. Subtracting Fractions
Strategies: Change to improper fractions

64. Subtracting Fractions
Strategies: Borrow

65. Subtracting Fractions
Strategies: Shift (Compensate)

66. Multiplying Fractions

67. 5.F.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

68. 5.F.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side