1. Vacaville USD September 5, 2014

2. AGENDA Problem Solving and Patterns Math Practice Standards and Effective Questions Word Problems Ratios and Proportions Rates Making Sense of Percents Percents, Fractions, and Decimals

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. Regina’s Logo How many tiles are needed to make a Size 5? What about a Size 10? a Size 20? A Size 100?

5. Regina’s Logo What is a strategy that will let you quickly and easily figure out how many tiles you will need for any given size?

6. Regina’s Logo Recursive Add 3 each time SIZE# OF TILES 15 28 311 414 517

7. Regina’s Logo 3n + 2

8. Regina’s Logo 3n + 2

9. Regina’s Logo 2(n + 1) + n

10. Regina’s Logo 2n + (n + 2)

11. Standards What 6 th grade standards, or parts of standards do tasks like this address?

12. The Use of Effective Questions

13. Questioning plays a critical role in the way teachers –Guide the class –Engage students in the content –Encourage participation –Foster understanding

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. SMP’s So how does the use of effective questioning relate to the Standards for Mathematical Practice?

16. SMP’s and Questions Your group will receive 16 cards –8 SMP’s –8 lists of questions related to the SMP’s Your job is to match each SMP with the questions designed to support that SMP.

17. Asking Effective Questions Pick 2 colors... 1.Use one color to highlight questions that you are already asking. 2.Use the 2nd color to highlight questions that you would like to ask this year.

18. Additional Resources Effective Questions – PBS

19. Solving Word Problems

20. 1.Read the entire problem, “visualizing” the problem conceptually 2.Determine who and/or what the problem is about 3.Rewrite the question in sentence form leaving a space for the answer.

21. 4.Draw the unit bars that you’ll eventually adjust as you construct the visual image of the problem 5.Chunk the problem, adjust the unit bars to reflect the information in the problem, and fill in the question mark.

22. 6.Correctly compute and solve the problem (show all work!) 7.Write the answer in the sentence and make sure the answer makes sense.

23. Standards Where do you see “word problems”, “problems in context” or “real world problems” in your standards?

24. Standards RP 1, 2, 3 NS 1, 5, 7b, 7c, 7d, 8, 9 EE 2c, 6, 7, 8, 9 G 1, 2, 3, 4 –6 th Grade Word Problems

25. Ratios and Proportions

26. Ratios Talk at your tables What is a ratio? How is a ratio similar to a fraction? How is a ratio different from a fraction?

27. Ratios Mr. Hill noticed that when he split his class into groups of 5, each group had exactly 3 boys and 2 girls What ratios could you write to describe Mr. Hill’s class?

28. Ratios Mr. Hill noticed that when he split his class into groups of 5, each group had exactly 3 boys and 2 girls Does this mean that there are exactly 3 boys and 2 girls in Mr. Hill’s class?

29. 3 boys : 2 girls BBBGGBBBGG BBBGGBBBGG BBBGGBBBGG BBBGGBBBGG BBBGGBBBGG BBBGGBBBGG 3 : 2 6 : 4 9 : 6 12 : 8 15 : 10 10 : 12

30. Replicating

31. Mrs. Field did the same thing for all the 6 th grade students as Bay View Elementary School. She discovered that in order to have the same number of boys in each group and the same number of girls in each group, she need to make groups of 7. How many boys and how many girls might be in each group?

32. Mrs. Field did the same thing for all the 6 th grade students as Bay View Elementary School. Each group had 4 boys and 3 girls. How many 6 th grade students do you think are at Bay View Elementary Schoo? Be prepared to justify your answer!

33. 4 boys : 3 girls Suppose there are 72 6 th grade boys. How many girls would there be? Suppose there are 72 6 th grade girls. How many boys would there be? Suppose I know that there are 119 students. How many boys and how many girls are there?

34. What is a Proportion? A proportion is a name we give to a statement that two ratios are equal. It can be written in two ways: two equal fractions, or, using a colon, a:b = c:d

35. Proportions Find the missing number.

36. Proportions But what if it doesn’t work out nicely?

37. Fraction Equivalence Let’s go back for a minute and review equivalent fractions. Suppose I want to see if the following is true?

38. Cross Multiply Why does it work? (mathematically)

39. Comparing Fractions Finding a common denominator If I don’t care about finding the least common denominator, what is a quick way to find a common denominator?

40. True or False!

41. Equivalent Ratios Write 2 ratios that you know are equivalent Prove they are equivalent by finding a common denominator What do you notice about the numerators?

42. Cross Multiply 8  9 = 6  12

43. Cross Multiply d  a = c  b

44. Cross Multiply ad = cb

45. Standards Read the 6 th Grade Standards for Ratios and Proportional Relationships Similar to previous standards: –1, 2, 3b, 3c Different: –3a, 3d

46. ENY Lesson 10

48. Supplemental Lessons Engage NY Module 1 Lessons 10-23

49. Sense Making And Percents

50. Percents So what does “percent” mean? Percent means "out of 100."

51. Why Percents? What is the relationship between Fractions Decimals Percents

52. Percent So if percent means “out of 100” what is another way to think of 50%? 25% 10%

53. Mental Math 80 36 30 25 50% 40 18 15 12.5 25% 20 9 7.5 6.25 75% 60 27 22.5 18.75

54. Mental Math 80 36 30 25 10% 8 3.6 3 2.5 5% 4 1.8 1.5 1.25 15% 12 5.4 4.5 3.75

55. Model Drawing And Percents

56. There are 240 students in the fifth grade. If 60% of them are girls, how many girls are in the fifth grade? 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 240 24 48 72 96 120 144 0

57. At the fair, 65% of the visitors went on the Ferris Wheel. If 634 visitors went on the Ferris Wheel, how many people attended the fair? 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% x 0 65 100 634 x =

58. At the bake sale, there were 24 cupcakes left over. If there were 120 cupcakes to start with, what percent of the cupcakes were left over? 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 120 0 x 100 24 120 24 =

59. Practice Percent Problems

60. 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 1010 Percents Fractions Decimals