Teaching Priority Concepts in Math Grade 6

1. Teaching Priority Concepts in Math Grade 6 Kim Louttit September 26, 2013

2. Updates • Annotated 2013 assessment questions • Modules • As per a phone call, Ken Slentz said that a quarter to half of the modules will be out by the end of this month…

3. Content emphasis by cluster

4. Let’s do some math!! • Go to www.infuselearning.com • Choose STUDENT LOGIN • Enter Room ID: 69506 • Enter your first name • Click Submit

5. websites • Learnzillion.com • http://learnzillion.com/lessons/1181-divide-a-whole-number-by-a-unit-fraction

6. Tape Diagrams • If you have any tape diagramming experience, try to solve this problem using tape diagrams. If not, solve it algebraically. • Two pears and a pineapple cost $2. Two pears and three pineapples cost $4.50. Find the cost of a pineapple.

7. Using tape diagrams • Promote perseverance in reasoning through problems. • Develop students’ independence in asking themselves: • “Can I draw something?” • “What can I label?” • “What do I see?” • “What can I learn from my drawing?”

8. Forms of the tape diagram Part-Whole Model Comparison Model

9. Foundations for tape diagrams in Pk-1 • Sara has 2 apples. Jon has 5 apples. How many apples do they have altogether? How many more apples does Jon have than Sara?

10. Tape Diagram Problems • Example 1: Sara has 5 stamps. Mark brings her • 4 more stamps. How many stamps does Sara • have now?

11. Tape Diagram Problems • Example 2: Sara has 16 stamps. Mark brings • her 4 more stamps. How many stamps does • Sara have now?

12. Tape Diagram Problems • Example 3: Sara brought 4 apples to school. After Mark brings her some more apples, she has 9 apples altogether. How many apples did Mark bring her?

13. Tape Diagram Problems • Example 4: Matteo has 5 toy cars. Josiah has 2 more than Matteo. How many toy cars do Matteo and Josiah have altogether?

14. Tape Diagram Problems • Example 5: Jasmine had 328 gumballs. Then, she gave 132 gumballs to her friend. How many gumballs does Jasmine have now?

15. Tape Diagram Problems • Example 6: Jose has 4 paper clips. Harry has twice as many paper clips as Jose. How many paper clips does Harry have?

16. Tape Diagram Problems • Example 7: Jose has 4 paper clips. Harry has twice as many paper clips as Jose. How many paper clips do they have altogether?

17. Tape Diagram Problems • Example 8: William’s weight is 40 kg. He is 4 times as heavy as his youngest brother Sean. What is Sean’s weight?

18. Tape Diagram Problems • Example 9: Jamal has 8 more marbles than Thomas. They have 20 marbles altogether. How many marbles does Thomas have?

19. Tape Diagram Problems • Example 10: The total weight of a football and 10 tennis balls is 1 kg. If the weight of each tennis ball is 60 g, find the weight of the football.

20. Tape Diagram Problems • Example 11: David spent 2/5 of his money on a storybook. The storybook cost $20 how much did he have at first?

21. Tape Diagram Problems • Example 12: Alex bought some chairs. One third of them were red and one fourth of them were blue. The remaining chairs were yellow. What fraction of the chairs were yellow?

22. Tape Diagram Problems • Example 13: Jim had 360 stamps. He sold 1/3 of them on Monday and ¼ of the remainder on Tuesday. How many stamps did he sell on Tuesday?

23. Tape Diagram Problems • Example 14: Max spent 3/5 of his money in a shop and ¼ of the remainder in another shop. What fraction of his money was left? If he had $90 left, how much did he have at first?

24. Tape Diagram Problems • Example 15: Henry bought 280 blue and red paper cups. He used 1/3 of the blue ones and 1/2 of the red ones at a party. If he had an equal number of blue cups and red cups left, how many cups did he use altogether?

25. Tape Diagram Problems • Example 16: A club had 600 members. 60% of them were males. When 200 new members joined the club, the percentage of male members was reduced to 50%. How many of the new members were males?

26. Tape Diagram Problems • Example 17: Meagan had $1780 and Lisa had $1910. Lisa gave some money to Meagan. In the end Meagan had twice as much money as Lisa. How much money did Lisa give to Meagan?

27. Tape Diagram Problems • Example 18: The ratio of the length of Tom’s rope to the length of Jan’s rope was 3:1. The ratio of the length of Maxwell’s rope to the length of Jan’s rope was 4:1. If Tom, Maxwell and Jan have 80 feet of rope altogether, how many feet of rope does Tom have?

28. Tape Diagram Problems • Example 19: Lena finds two boxes of printer paper in the teacher supply room. The ratio of the packs of paper in Box A to the packs of paper in Box B is 4:3. If half of the paper in Box A is moved to Box B, what is the new ratio of packs of paper in Box A to Box B?

29. Tape Diagram Problems • Example 20: Sana and Amy collect bottle caps. The ratio of the number of bottle caps Sana has to the number Amy has is 2:3. The ratio became 5:6 when Sana added 8 more bottle caps to her collection. How many bottle caps does Amy have?

30. Tape Diagram Problems • Example 21: The ratio of songs on Jessa’s phone to songs on Tessie’s phone is 2 to 3. Tessie deletes half of her songs and now has 60 fewer songs than Jessa. How many songs does Jessa have?

31. Tape Diagram Problems • Example 22: Of the kids taking swimming lessons at City Pool this summer, 36 of them, or 45%, are girls. How many kids are taking swimming lessons?

32. Tape Diagram Problems • Example 23: A digital picture frame was on sale at Circuit City for $78. If this reflects a discount of 35%, what was the original price of the picture frame?

33. Key points • When building proficiency in tape diagraming skills start with simple accessible situations and add complexities one at a time. • Develop habits of mind in students to reflect on the size of bars relative to one another. • Part-whole models are more helpful when modeling situations where:_____________________________ • Compare to models are best when: ____________________________________

34. Ratio Tables & Double number lines

35. Ratio Tables & equations

36. Coordinate plane

37. Dividing fractions (Begins in grade 5)

38. Dividing fractions

39. What does division mean? • Interpret quotients of whole numbers as the number of objects in each share when _____ objects are partitioned into equal shares of _____ objects each • ½ ÷ 3 means what? • 3 ÷ ½ means what?

40. Dividing Fractions • Maura cuts a piece of rectangular clay in half. She then divides one half into 3 equal parts. What fraction of the whole piece of clay is each of the 3 parts?

41. Dividing Fractions • A roll of wire 3/5 long is cut into 6 equal pieces. How long is each piece?

42. Dividing Fractions • A 4/5 pound cantaloupe is cut into 2 equal pieces. What is the weight of each piece of cantaloupe?

43. Dividing Fractions • Mia walks a 2 mile trail. She stops to exercise every 1/5 mile. How many times does Mia stop to exercise?

44. Dividing Fractions • The serving size for a toddler’s daily vitamin C is ¾ cup of orange juice. If there are 2 cups of orange juice, how many servings of vitamin C are there for a toddler?

45. Dividing Fractions • What is ? • Create a model to support your answer.

46. Dividing Fractions • What is ? • Create a model to support your answer.

47. Dividing Fractions • How many cup servings are in cup of yogurt?

48. Relationship between fraction models and equations

49. Relationship between fraction models and equations

50. Dividing with fractions • Why do we multiply by the reciprocal when dividing fractions? • If you were to divide 2 by 3… • Is that the same as 2 × 1/3? • When you are dividing number (whole and fractions) you can always write the fraction as a product of two numbers.