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Page 1: Grade 6 Module 1 Lesson 16

Grade 6 Module 1 Lesson 16

Page 2: Grade 6 Module 1 Lesson 16

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 ColaTotal Cost

Page 3: Grade 6 Module 1 Lesson 16

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 4Total Cost 10

Page 4: Grade 6 Module 1 Lesson 16

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 4 2Total Cost 10 5

Page 5: Grade 6 Module 1 Lesson 16

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

Page 6: Grade 6 Module 1 Lesson 16

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 2 Total Cost 5

Page 7: Grade 6 Module 1 Lesson 16

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 2 1 Total Cost 5 2.50

Page 8: Grade 6 Module 1 Lesson 16

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)

Page 9: Grade 6 Module 1 Lesson 16

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.

Page 10: Grade 6 Module 1 Lesson 16

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.

Page 11: Grade 6 Module 1 Lesson 16

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?

Page 12: Grade 6 Module 1 Lesson 16

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 = ___

Page 13: Grade 6 Module 1 Lesson 16

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)

Page 14: Grade 6 Module 1 Lesson 16

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.

Page 15: Grade 6 Module 1 Lesson 16

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.

Page 16: Grade 6 Module 1 Lesson 16

Exploration Challenge

Fan Distance (mi) Time (hr)

Andre 208 4Matteo 456 8Janaye 300 6

Greyson 265 5

Use the given to answer the following questions.a. What two quantities are being compared?

Page 17: Grade 6 Module 1 Lesson 16

Exploration Challenge

Fan Distance (mi) Time (hr)

Andre 208 4Matteo 456 8Janaye 300 6

Greyson 265 5

Use the given to answer the following questions.a. What two quantities are being compared?

miles and hours

Page 18: Grade 6 Module 1 Lesson 16

Exploration Challenge

Fan Distance (mi) Time (hr)

Andre 208 4Matteo 456 8Janaye 300 6

Greyson 265 5

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?

Page 19: Grade 6 Module 1 Lesson 16

Exploration Challenge

Fan Distance (mi) Time (hr)

Andre 208 4Matteo 456 8Janaye 300 6

Greyson 265 5

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

Page 20: Grade 6 Module 1 Lesson 16

Exploration Challenge

Fan Distance (mi) Time (hr)

Andre 208 4Matteo 456 8Janaye 300 6

Greyson 265 5

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

Page 21: Grade 6 Module 1 Lesson 16

Exploration Challenge

Fan Distance (mi) Time (hr)

Andre 208 4Matteo 456 8Janaye 300 6

Greyson 265 5

Use the given to answer the following questions.c. Answer the same two questions in part (b) for

the other three drivers.

Page 22: Grade 6 Module 1 Lesson 16

Exploration Challenge

Fan Distance (mi) Time (hr)

Andre 208 4Matteo 456 8Janaye 300 6

Greyson 265 5

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

Page 23: Grade 6 Module 1 Lesson 16

Exploration Challenge

Fan Distance (mi) Time (hr)

Andre 208 4Matteo 456 8Janaye 300 6

Greyson 265 5

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

Page 24: Grade 6 Module 1 Lesson 16

Exploration Challenge

Fan Distance (mi) Time (hr)

Andre 208 4Matteo 456 8Janaye 300 6

Greyson 265 5

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

Page 25: Grade 6 Module 1 Lesson 16

Exploration Challenge

Fan Distance (mi) Time (hr)

Andre 208 4Matteo 456 8Janaye 300 6

Greyson 265 5

Use the given to answer the following questionsd. For each driver, circle the unit rate and put a box around the rate unit.

Page 26: Grade 6 Module 1 Lesson 16

Exploration Challenge

Fan Distance (mi) Time (hr)

Andre 208 4Matteo 456 8Janaye 300 6

Greyson 265 5

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

Page 27: Grade 6 Module 1 Lesson 16

Exploration Challenge

Fan Distance (mi) Time (hr)

Andre 208 4Matteo 456 8Janaye 300 6

Greyson 265 5

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

Page 28: Grade 6 Module 1 Lesson 16

Exploration Challenge

Fan Distance (mi) Time (hr)

Andre 208 4Matteo 456 8Janaye 300 6

Greyson 265 5

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

Page 29: Grade 6 Module 1 Lesson 16

Exploration Challenge

Fan Distance (mi) Time (hr)

Andre 208 4Matteo 456 8Janaye 300 6

Greyson 265 5

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

Page 30: Grade 6 Module 1 Lesson 16

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.

Page 31: Grade 6 Module 1 Lesson 16

Exploration Challenge

3. Minutes 16Words 704

Page 32: Grade 6 Module 1 Lesson 16

Exploration Challenge

3. Minutes 8 16Words 352 704

Page 33: Grade 6 Module 1 Lesson 16

Exploration Challenge

3. Minutes 4 8 16Words 176 352 704

Page 34: Grade 6 Module 1 Lesson 16

Exploration Challenge

3. Minutes 2 4 8 16Words 88 176 352 704

Page 35: Grade 6 Module 1 Lesson 16

Exploration Challenge

3. Minutes 1 2 4 8 16Words 44 88 176 352 704

Page 36: Grade 6 Module 1 Lesson 16

Exploration Challenge

3. Minutes 1 2 4 8 16Words 44 88 176 352 704

Dominique does not type at a fast enough rate because she only types 44 words per minute.

Page 37: Grade 6 Module 1 Lesson 16

Exploration Challenge

3. Minutes 1 Words 45

How many words does Dominique need to typein 20 minutes in order to be able to qualify forthis job?

Page 38: Grade 6 Module 1 Lesson 16

Exploration Challenge

3. Minutes 1 10 Words 45 450

How many words does Dominique need to typein 20 minutes in order to be able to qualify forthis job?

Page 39: Grade 6 Module 1 Lesson 16

Exploration Challenge

3. Minutes 1 10 20 Words 45 450 900

How many words does Dominique need to typein 20 minutes in order to be able to qualify forthis job?Dominique would need to type 900 words in20 minutes in order to be able to qualify forthis job.

Page 40: Grade 6 Module 1 Lesson 16

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”.


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