1. Grade 6 Module 1 Lesson 11

2. Example 1 Create four equivalent ratios (2 by scaling up and 2 by scaling down) using the ratio 30 to 80.

3. Example 1 Create four equivalent ratios (2 by scaling up and 2 by scaling down) using the ratio 30 to 80. Example of Scaling up: 30 to 80 is equivalent to 60 to 160 Example of Scaling down: 30 to 80 is equivalent to 3 to 8

4. Example 1 Create four equivalent ratios (2 by scaling up and 2 by scaling down) using the ratio 30 to 80. Scaling up: 30:80 90:240, 120:320, 150: 400, 180:480

5. Example 1 Create four equivalent ratios (2 by scaling up and 2 by scaling down) using the ratio 30 to 80. Scaling up: 30:80 90:240, 120:320, 150: 400, 180, 480 Scaling down: 30:80 6:16, 9:24, 12:32, 15:40, 18:48, 21:56

6. Example 1 Write a ratio to describe the relationship shown in the table. Hours# of Pizzas Sold 216 540 648 1080

7. Example 1 Write a ratio to describe the relationship shown in the table. The ratio used to create the table is 1:8, which means that there are 8 pizzas being sold every hour. Hours# of Pizzas Sold 216 540 648 1080

8. Exercise 1 The following tables show how many words each person can text in a given amount of time. Compare the rates of texting for each person using the ratio table. Michaela Minutes3579 Words150250350450 Minutes2468 Words90180270360 Jenna Minutes36912 Words120240360480 Maria

9. Exercise 1 How can we compare the texting rates?

10. Exercise 1 How can we compare the texting rates? Which girl has the fastest texting rate and which has the slowest?

11. Exercise 1 How can we compare the texting rates? Which girl has the fastest texting rate and which has the slowest? If you used ratios to compare, what do the ratios mean in the context of this problem?

12. Exercise 1 How can we compare the texting rates? Which girl has the fastest texting rate and which has the slowest? If you used ratios to compare, what do the ratios mean in the context of this problem? How can we use the ratios to help us compare the texting rates of the three girls?

13. Exercise 1 How can we compare the texting rates? Which girl has the fastest texting rate and which has the slowest? If you used ratios to compare, what do the ratios mean in the context of this problem? How can we use the ratios to help us compare the texting rates of the three girls? Why can’t I just pick the student that has the largest number of words at the end of the table?

14. Exercise 1 If there were a fourth person, Max, who can text 55 words per minute, how could we create a table to show his texting speed? Complete the table so that it shows Max has a texting rate of 55 words per minute. Minutes Words Max

15. Exercise 1 If there were a fourth person, Max, who can text 55 words per minute, how could we create a table to show his texting speed? Complete the table so that it shows Max has a texting rate of 55 words per minute. Minutes1 Words55 Max

16. Exercise 1 If there were a fourth person, Max, who can text 55 words per minute, how could we create a table to show his texting speed? Complete the table so that it shows Max has a texting rate of 55 words per minute. Minutes12 Words55110 Max

17. Exercise 1 If there were a fourth person, Max, who can text 55 words per minute, how could we create a table to show his texting speed? Complete the table so that it shows Max has a texting rate of 55 words per minute. Minutes123 Words55110165 Max

18. Exercise 1 If there were a fourth person, Max, who can text 55 words per minute, how could we create a table to show his texting speed? Complete the table so that it shows Max has a texting rate of 55 words per minute. Minutes1234 Words55110165220 Max

19. Exercise 2 The tables show the comparison of the amount of water to the amount of juice concentrate (JC) in grape juice made by three different people. Whose juice has the greatest water-to-juice concentrate ratio, and whose juice would taste strongest? Be sure to justify your answer.

20. Exercise 2 Work with your partner to answer question 2a.

21. Exercise 2 Franca’s juice has the greatest amount of water in comparison to juice concentrate (5:1), followed by Milton (4:1) and then Laredo (3:1). Because Laredo’s juice has the least amount of water in comparison to juice concentrate, his juice would taste the strongest.

22. Exercise 2 Put the juice in order from the juice containing the most water to the juice containing the least water.

23. Exercise 2 Put the juice in order from the juice containing the most water to the juice containing the least water. Franca, Milton, Laredo

24. Exercise 2 Put the juice in order from the juice containing the most water to the juice containing the least water. Answer: Franca, Milton, Laredo Explain how you used the values in the table to determine the order.

25. Exercise 2 Explain how you used the values in the table to determine the order. Laredo makes his juice by combining 3 cups of water for every cup of juice concentrate. Franca makes her juice by combining 5 cups of water for every cup of juice concentrate. Milton makes his juice by combining 4 cups of water for every cup of juice concentrate.

26. Exercise 2 What ratio was used to create each table?

27. Exercise 2 What ratio was used to create each table? Loredo 3:1 Franca 5:1 Milton 4:1 Explain how the ratio could help you compare the juices.

28. Exercise 2(b) The next day, each of the three people made juice again, but this time they were making apple juice. Whose juice has the greatest water- to-juice concentrate ratio, and whose juice would taste the strongest? Be sure to justify your answer.

29. Exercise 2b 6:112:218:3 5:215:6 8:316:6

30. Exercise 2(b) The next day, each of the three people made juice again, but this time they were making apple juice. Whose juice has the greatest water- to-juice concentrate ratio, and who juice would taste the strongest? Be sure to justify your answer. Laredo: 6:1Franca: 5:2Milton: 8:3 (How do we compare these three ratios?)

31. Exercise 2(b) Laredo: 6:1Franca: 5:2Milton: 8:3 (How do we compare these three ratios?) Laredo: 6:1 is equivalent to 12:2 and 18:3. When comparing Laredo to Franca (5:2) and Milton (8:3), you can see that more cups of water was added to Laredo. This tells us that Laredo’s juice has the weakest apple taste.

32. Exercise 2(b) Laredo: 6:1Franca: 5:2Milton: 8:3 How do we compare the other two ratios? (They currently do not have the same number of cups of water or cups of juice.) We would need to either make the cups of water equal or cups of juice equal.

33. Exercise 2(b) Laredo: 6:1Franca: 5:2Milton: 8:3 (How do we compare the other two ratios?) Franca: 5:2 --  5 × 8: 2 × 8 ---  40:16 Milton: 8:3 --  8 × 5: 3 × 5 ---  40:15 Now we can compare and see that Franca’s juice has more juice concentrate compared to water than Milton’s juice.

34. Exercise 2(b) Laredo: 6:1Franca: 5:2Milton: 8:3 (How do we compare the other two ratios?) Franca: 15/6 Milton: 16/6 Franca’s juice is the stronger of the two because it has 1 less cup of water per 6 cups of juice in comparison to Milton’s juice.

35. Exercise 2(b) Laredo: 6:1Franca: 5:2Milton: 8:3 Put the juices in order from the strongest apple taste to the weakest apple taste.

36. Exercise 2(b) Laredo: 6:1Franca: 5:2Milton: 8:3 Put the juices in order from the strongest apple taste to the weakest apple taste. Franca, Milton, Laredo Explain how you used the values in the table to determine the order.

37. Exercise 2(b) What ratio was used to create each table? Laredo_________ Franca__________ Milton_________

38. Exercise 2(b) What ratio was used to create each table? Laredo: 6:1 Franca: 5:2 Milton: 8:3 Explain how the ratio could help you compare the juices.

39. Exercise 2(b) What ratio was used to create each table? Laredo: 6:1 Franca: 5:2 Milton: 8:3 Explain how the ratio could help you compare the juices. How was this problem different than the grape questions?

40. Exercise 2(c) JC Water Max JC Water Sheila

41. Exercise 2(d) Strawberries other #1 Strawberries other #2

42. Exercise 2(c) JC4812 Water153045 Max Sheila JC36912 Water8162432

43. Exercise 2(d) Strawberries246 other71421 #1 Strawberries369 other91827 #2

44. Closing Today we used ratio tables to compare two ratios that were not equivalent and answered questions about which situation would reach a given level first. Can anyone think of another way to compare two different ratios?

45. Closing Today we used ratio tables to compare two ratios that were not equivalent and answered questions about which situation would reach a given level first. Can anyone think of another way to compare two different ratios? The value of a ratio might be useful because then we could determine which ratio had the larger or smaller value.