1. Grade 6 Module 1 Lesson 16

2. Example 1: Introduction to Rates and Unit Rates Diet cola was on sale last week; it cost $10 for every 4 packs of diet cola. a.How much do 2 packs of diet cola cost? Packs of Cola Total Cost

3. Example 1: Introduction to Rates and Unit Rates Diet cola was on sale last week; it cost $10 for every 4 packs of diet cola. a.How much do 2 packs of diet cola cost? Packs of Cola4 Total Cost10

4. Example 1: Introduction to Rates and Unit Rates Diet cola was on sale last week; it cost $10 for every 4 packs of diet cola. a.How much do 2 packs of diet cola cost? Packs of Cola42 Total Cost105

5. Example 1: Introduction to Rates and Unit Rates Diet cola was on sale last week; it cost $10 for every 4 packs of diet cola. b. How much does 1 pack of diet cola cost? Packs of Cola Total Cost

6. Example 1: Introduction to Rates and Unit Rates Diet cola was on sale last week; it cost $10 for every 4 packs of diet cola. b. How much does 1 pack of diet cola cost? Packs of Cola2 Total Cost5

7. Example 1: Introduction to Rates and Unit Rates Diet cola was on sale last week; it cost $10 for every 4 packs of diet cola. b. How much does 1 pack of diet cola cost? Packs of Cola21 Total Cost52.50

8. Example 1: Introduction to Rates and Unit Rates Rate - $10 for every 4 packs of diet cola is a rate because it is a ratio of two quantities (money : soda)

9. Example 1: Introduction to Rates and Unit Rates Rate - $10 for every 4 packs of diet cola is a rate because it is a ratio of two quantities (money : soda) Unit Rate – The unit rate is 2.5 because it is the value of the ratio.

10. Example 1: Introduction to Rates and Unit Rates Rate - $10 for every 4 packs of diet cola is a rate because it is a ratio of two quantities (money : soda) Unit Rate – The unit rate is 2.5 because it is the value of the ratio. Rate Unit – The rate unit is dollar/packs of cola because it costs $2.50 for every 1 pack of cola.

11. Exploration Challenge Teagan went to Gamer Realm to buy new video games. Gamer Realm was having a sale: $65 for 4 video games. He bought 3 games for himself and one game for his friend, Diego, but Teagan does not know how much Diego owes him for the one game. What is the unit price of the video game? What is the rate unit?

12. Exploration Challenge Teagan went to Gamer Realm to buy new video games. Gamer Realm was having a sale: $65 for 4 video games. He bought 3 games for himself and one game for his friend, Diego, but Teagan does not know how much Diego owes him for the one game. What is the unit price of the video game? What is the rate unit? $65 ÷ 4 = ___

13. Exploration Challenge Teagan went to Gamer Realm to buy new video games. Gamer Realm was having a sale: $65 for 4 video games. He bought 3 games for himself and one game for his friend, Diego, but Teagan does not know how much Diego owes him for the one game. What is the unit price of the video game? What is the rate unit? $65 ÷ 4 = ___ (The unit price is $16.25)

14. Exploration Challenge Teagan went to Gamer Realm to buy new video games. Gamer Realm was having a sale: $65 for 4 video games. He bought 3 games for himself and one game for his friend, Diego, but Teagan does not know how much Diego owes him for the one game. What is the unit price of the video game? What is the rate unit? $65 ÷ 4 = ___ (The unit price is $16.25) The rate unit is dollars/video games.

15. Exploration Challenge Four football fans took turns driving the distance from New York to Oklahoma to see a big game. Each driver set the cruise control during his leg of the trip, enabling him to travel at a constant speed. The men changed drivers each time they stopped for gas and recorded their driving times and distances in the table below.

16. Exploration Challenge FanDistance (mi)Time (hr) Andre2084 Matteo4568 Janaye3006 Greyson2655 Use the given to answer the following questions. a. What two quantities are being compared?

17. Exploration Challenge FanDistance (mi)Time (hr) Andre2084 Matteo4568 Janaye3006 Greyson2655 Use the given to answer the following questions. a.What two quantities are being compared? miles and hours

18. Exploration Challenge FanDistance (mi)Time (hr) Andre2084 Matteo4568 Janaye3006 Greyson2655 Use the given to answer the following questions. b.What is the ratio of the two quantities for Andre’s car? What is the associated rate?

19. Exploration Challenge FanDistance (mi)Time (hr) Andre2084 Matteo4568 Janaye3006 Greyson2655 Use the given to answer the following questions. b.What is the ratio of the two quantities for Andre’s car? What is the associated rate? Andre’s ratio: 208:4

20. Exploration Challenge FanDistance (mi)Time (hr) Andre2084 Matteo4568 Janaye3006 Greyson2655 Use the given to answer the following questions. b.What is the ratio of the two quantities for Andre’s car? What is the associated rate? Andre’s ratio: 208:4 Andre’s rate: 52 miles per hour

21. Exploration Challenge FanDistance (mi)Time (hr) Andre2084 Matteo4568 Janaye3006 Greyson2655 Use the given to answer the following questions. c.Answer the same two questions in part (b) for the other three drivers.

22. Exploration Challenge FanDistance (mi)Time (hr) Andre2084 Matteo4568 Janaye3006 Greyson2655 Use the given to answer the following questions. c.Answer the same two questions in part (b) for the other three drivers. Matteo’s ratio: 456:8 Matteo’s rate: 57 miles per hour

23. Exploration Challenge FanDistance (mi)Time (hr) Andre2084 Matteo4568 Janaye3006 Greyson2655 Use the given to answer the following questions. c.Answer the same two questions in part (b) for the other three drivers. Janaye’s ratio: 300:6 Janaye’s rate: 50 miles per hour

24. Exploration Challenge FanDistance (mi)Time (hr) Andre2084 Matteo4568 Janaye3006 Greyson2655 Use the given to answer the following questions. c.Answer the same two questions in part (b) for the other three drivers. Greyson’s ratio: 265:5 Greyson’s rate: 53 miles per hour

25. Exploration Challenge FanDistance (mi)Time (hr) Andre2084 Matteo4568 Janaye3006 Greyson2655 Use the given to answer the following questions d.For each driver, circle the unit rate and put a box around the rate unit.

26. Exploration Challenge FanDistance (mi)Time (hr) Andre2084 Matteo4568 Janaye3006 Greyson2655 Use the given to answer the following questions. b.What is the ratio of the two quantities for Andre’s car? What is the associated rate? Andre’s ratio: 208:4 Andre’s rate: 52 miles per hour

27. Exploration Challenge FanDistance (mi)Time (hr) Andre2084 Matteo4568 Janaye3006 Greyson2655 Use the given to answer the following questions. c.Answer the same two questions in part (b) for the other three drivers. Matteo’s ratio: 456:8 Matteo’s rate: 57 miles per hour

28. Exploration Challenge FanDistance (mi)Time (hr) Andre2084 Matteo4568 Janaye3006 Greyson2655 Use the given to answer the following questions. c.Answer the same two questions in part (b) for the other three drivers. Janaye’s ratio: 300:6 Janaye’s rate: 50 miles per hour

29. Exploration Challenge FanDistance (mi)Time (hr) Andre2084 Matteo4568 Janaye3006 Greyson2655 Use the given to answer the following questions. c.Answer the same two questions in part (b) for the other three drivers. Greyson’s ratio: 265:5 Greyson’s rate: 53 miles per hour

30. Exploration Challenge 3. A publishing company is looking for new employees to type novels that will soon be published. The publishing company wants to find someone who can type at least 45 words per minute. Dominique discovered she can type at a constant rate of 704 words in 16 minutes. Does Dominique type at a fast enough rate to qualify for the job? Explain why or why not.

31. Exploration Challenge 3. Minutes16 Words704

32. Exploration Challenge 3. Minutes816 Words352704

33. Exploration Challenge 3. Minutes4816 Words176352704

34. Exploration Challenge 3. Minutes24816 Words88176352704

35. Exploration Challenge 3. Minutes124816 Words4488176352704

36. Exploration Challenge 3. Minutes124816 Words4488176352704 Dominique does not type at a fast enough rate because she only types 44 words per minute.

37. Exploration Challenge 3. Minutes1 Words45 How many words does Dominique need to type in 20 minutes in order to be able to qualify for this job?

38. Exploration Challenge 3. Minutes110 Words45450 How many words does Dominique need to type in 20 minutes in order to be able to qualify for this job?

39. Exploration Challenge 3. Minutes11020 Words45450 900 How many words does Dominique need to type in 20 minutes in order to be able to qualify for this job? Dominique would need to type 900 words in 20 minutes in order to be able to qualify for this job.

40. Closing Lesson Summary: A ratio of two quantities, such as 5 miles per 2 hours, can be written as another quantity called a rate. The numerical part of the rate is called the unit rate and is simply the value of the ratio, in this case 2.5. This means that in 1 hour, the car travels 2.5 miles. The unit for the rate is miles/hour, read “miles per hour”.