Eureka Lesson for 6th Grade Unit THREE
Unit Rates
These 2 lessons can be taught in 2 class periods – Or 3 with struggling learners.
Challenges: None that I see. These 2 lessons are very good, but please familiarize
yourselves with the lessons before using them.
Page 2-3 Overview
Pages 4-6 Lesson 16 From Ratios to Rates - Teachers’ Detailed Instructions
Pages 7-8 Exit Ticket w/ solutions for Lesson 16
Page 9-12 Student pages for Lesson 16
Pages 13-16 Lesson 17 From Rates to Ratios - Teachers’ Detailed Instructions
Pages 17-18 Exit Ticket w/ solutions for Lesson 17
Pages 19-23 Student pages for Lesson 17
A STORY OF RATIOS
6
Mathematics Curriculum
GRADE
GRADE 6 • MODULE 1
Topic C:
Unit Rates
6.RP.A.2, 6.RP.A.3b, 6.RP.A.3d
Focus Standard:
6.RP.A.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠
0, and use rate language in the context of a ratio relationship. For example,
“This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup
of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a
rate of $5 per hamburger.”
6.RP.A.3b
Use ratio and rate reasoning to solve real-world and mathematical problems,
e.g., by reasoning about tables of equivalent ratios, tape diagrams, double
number line diagrams, or equations.
6.RP.A.3d
Instructional Days:
b.
Solve unit rate problems including those involving unit pricing and
constant speed. For example, if it took 7 hours to mow 4 lawns, then at
that rate, how many lawns could be mowed in 35 hours? At what rate
were lawns being mowed?
d.
Use ratio reasoning to convert measurement units; manipulate and
transform units appropriately when multiplying or dividing quantities.
8
Lesson 16: From Ratios to Rates (E) 1
Lesson 17: From Rates to Ratios (S)
Lesson 18: Finding a Rate by Dividing Two Quantities (M)
Lessons 19–20: Comparison Shopping—Unit Price and Related Measurement Conversions (E, P)
Lessons 21–22: Getting the Job Done—Speed, Work, and Measurement Units (P, E)
Lesson 23: Problem Solving Using Rates, Unit Rates, and Conversions (S)
In Topic C, students apply their understanding of ratios and the value of a ratio as they come to understand
that a ratio relationship of 5 miles to 2 hours corresponds to a rate of 2.5 miles per hour, where the unit rate
is the numerical part of the rate, 2.5, and miles per hour is the newly formed unit of measurement of the rate
(6.RP.A.2). Throughout Topic C, students continue to make use of the representations and diagrams of Topics
1
Lesson Structure Key: P-Problem Set Lesson, M-Modeling Cycle Lesson, E-Exploration Lesson, S-Socratic Lesson
Topic C:
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Unit Rates
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Topic C
A STORY OF RATIOS
6•1
A and B as they investigate the concepts of this topic within the context of real-world rate problems. In
Lesson 16, students develop their vocabulary and conceptual understanding of rate as they work through and
discuss problems that require expressing simple ratios as rates using the phrases such as ‘per’, ‘for each’ and
‘for every’. In Lesson 17, students reinforce their understanding as they see problems for the first time where
the ratio relationship is expressed in rate form. Students are asked to verbalize and depict the underlying
ratio relationship as a collection of equivalent ratios.
In Lesson 18, students generalize the process for finding a rate and define the term unit rate relating it to the
value of a ratio. In the remaining lessons of Topic C, students solve unit rate problems involving unit pricing,
constant speed, and constant rates of work (6.RP.A.3b). They combine their new understanding of rate to
connect and revisit concepts of converting among different-sized standard measurement units (5.MD.A.1).
They then expand upon this background as they learn to manipulate and transform units when multiplying
and dividing quantities (6.RP.A.3d). In Lessons 19–20, students are conscientious consumers, and
comparison shop by comparing unit prices and converting measurement units as needed. For instance, when
comparing a 10-ounce bag of salad that sells for $2.25 to a 1-pound bag of salad that retails for $3.50,
students recognize that in addition to finding a unit price, they must convert pounds to ounces for an
accurate comparison.
In Lessons 21–22, students conduct real-world simulations that generate rates related to speed and work. In
doing so, students begin to view math as a tool for solving real-life problems. Topic C concludes with Lesson
23, in which students draw upon their experiences in previous modeling lessons to demonstrate their ability
to problem-solve using rates, unit rates, and conversions.
Topic C:
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Unit Rates
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Lesson 16
A STORY OF RATIOS
6•1
Lesson 16: From Ratios to Rates
Student Outcomes


Students recognize that they can associate a ratio of two quantities, such as the ratio of miles per hour is 5: 2,
to another quantity called the rate.
Given a ratio, students precisely identify the associated rate. They identify the unit rate and the rate unit.
Classwork
Ratios can be transformed to rates and unit rates.
Example 1 (5 minutes): Introduction to Rates and Unit Rates
Students complete the problem individually. Encourage students to use prior knowledge of equivalent ratios. Discuss
answers and methods after a few minutes of student work time.
Example 1: Introduction to Rates and Unit Rates
Diet cola was on sale last week; it cost $𝟏𝟏𝟏𝟏 for every 𝟒𝟒 packs of diet cola.
a.
How much do 𝟐𝟐 packs of diet cola cost?
Packs of Diet Cola
Total Cost
𝟒𝟒
𝟏𝟏𝟏𝟏
𝟐𝟐 packs of diet cola cost $𝟓𝟓. 𝟎𝟎𝟎𝟎.
b.
𝟐𝟐
𝟓𝟓
How much does 𝟏𝟏 pack of diet cola cost?
Packs of Diet Cola
Total Cost
𝟐𝟐
𝟓𝟓
𝟏𝟏 pack of diet cola costs $𝟐𝟐. 𝟓𝟓𝟓𝟓.
𝟏𝟏
𝟐𝟐. 𝟓𝟓𝟓𝟓
After answers have been discussed, use this example to identify the new terms.
Rate: $10 for every 4 packs of diet cola is a rate because it is a ratio of two quantities.
Unit Rate: The unit rate is 2.5 because it is the value of the ratio.
Rate Unit: The rate unit is dollars/packs of diet cola because it costs 2.5 dollars for every 1 pack of diet cola.
Now that the new terms have been introduced, use these vocabulary words throughout the lesson.
Lesson 16:
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From Ratios to Rates
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Lesson 16
A STORY OF RATIOS
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Exploratory Challenge (25 minutes)
Students may work in pairs or small groups to be able to discuss different methods of solving examples. Encourage them
to show or explain their thinking as much as possible. Take note of different ways groups are solving problems. After
providing time for groups to solve the problems, have different groups present their findings and explain the methods
they used to solve each problem.
Exploratory Challenge
1.
2.
Teagan went to Gamer Realm to buy new video games. Gamer Realm was having a sale: $𝟔𝟔𝟔𝟔 for 𝟒𝟒 video games. He
bought 𝟑𝟑 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 games? What is the rate unit?
The unit price is $𝟏𝟏𝟏𝟏. 𝟐𝟐𝟐𝟐; the rate unit is dollars/video game.
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 or her portion of the trip, enabling him or her to travel at a constant speed. The group
changed drivers each time they stopped for gas and recorded their driving times and distances in the table below.
Fan
Andre
Matteo
Janaye
Greyson
Distance (miles)
𝟐𝟐𝟐𝟐𝟐𝟐
𝟒𝟒𝟒𝟒𝟒𝟒
𝟑𝟑𝟑𝟑𝟑𝟑
𝟐𝟐𝟐𝟐𝟐𝟐
Use the given data to answer the following questions.
a.
Time (hours)
𝟒𝟒
𝟖𝟖
𝟔𝟔
𝟓𝟓
What two quantities are being compared?
The two quantities being compared are distance and time, which are measured in
miles and hours.
b.
Andre’s rate: 𝟓𝟓𝟓𝟓 miles per hour
Answer the same two questions in part (b) for the other three drivers.
Matteo’s ratio: 𝟒𝟒𝟒𝟒𝟒𝟒: 𝟖𝟖
Matteo’s rate: 𝟓𝟓𝟓𝟓 miles per hour
Greyson’s ratio: 𝟐𝟐𝟐𝟐𝟐𝟐: 𝟓𝟓
Greyson’s rate: 𝟓𝟓𝟓𝟓 miles per hour
Janaye’s ratio: 𝟑𝟑𝟑𝟑𝟑𝟑: 𝟔𝟔
d.
3.
If one of these drivers had
been chosen to drive the entire
distance,
a.
Which driver would have
gotten them to the game
in the shortest time?
Approximately how long
would this trip have
taken?
b.
Which driver would have
gotten them to the game
in the greatest amount of
time? Approximately
how long would this trip
have taken?
What is the ratio of the two quantities for Andre’s portion of the trip? What is the
associated rate?
Andre’s ratio: 𝟐𝟐𝟐𝟐𝟐𝟐: 𝟒𝟒
c.
Scaffolding:
Janaye’s rate: 𝟓𝟓𝟓𝟓 miles per hour
For each driver in parts (b) and (c), circle the unit rate and put a box around the rate unit.
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 𝟒𝟒𝟒𝟒 words
per minute. Dominique discovered she can type at a constant rate of 𝟕𝟕𝟕𝟕𝟕𝟕 words in 𝟏𝟏𝟏𝟏
minutes. Does Dominique type at a fast enough rate to qualify for the job? Explain why or
why not.
Minutes
Words
𝟏𝟏
𝟒𝟒𝟒𝟒
𝟐𝟐
𝟖𝟖𝟖𝟖
𝟒𝟒
𝟏𝟏𝟏𝟏𝟏𝟏
𝟖𝟖
𝟑𝟑𝟑𝟑𝟑𝟑
𝟏𝟏𝟔𝟔
𝟕𝟕𝟕𝟕𝟕𝟕
Dominique does not type at a fast enough rate because she only types 𝟒𝟒𝟒𝟒 words per
minute.
Lesson 16:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
From Ratios to Rates
Scaffolding:
Question 3 could be extended
to ask students to figure out
how many words she needed
to type in the 20 minutes to be
able to qualify.
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Lesson 16
A STORY OF RATIOS
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Closing (10 minutes)
Describe additional questions:

What are some examples of rates?

What are some examples of unit rates?
Lesson Summary
A ratio of two quantities, such as 𝟓𝟓 miles per 𝟐𝟐 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 𝟐𝟐. 𝟓𝟓. This means
that in 𝟏𝟏 hour, the car travels 𝟐𝟐. 𝟓𝟓 miles. The unit for the rate (or rate unit) is miles/hour, which is read “miles per
hour”.
Exit Ticket (5 minutes)
Lesson 16:
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From Ratios to Rates
130
Lesson 16
A STORY OF RATIOS
Name ___________________________________________________
6•1
Date____________________
Lesson 16: From Ratios to Rates
Exit Ticket
Angela enjoys swimming and often swims at a steady pace to burn calories. At this pace, Angela can swim 1,700 meters
in 40 minutes.
a.
What is Angela’s unit rate?
b.
What is the rate unit?
Lesson 16:
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From Ratios to Rates
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Lesson 16
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6•1
Exit Ticket Sample Solutions
Angela enjoys swimming and often swims at a steady pace to burn calories. At this pace, Angela can swim 𝟏𝟏, 𝟕𝟕𝟕𝟕𝟕𝟕 meters
in 𝟒𝟒𝟒𝟒 minutes.
a.
What is Angela’s unit rate?
𝟒𝟒𝟒𝟒. 𝟓𝟓
b.
What is the rate unit?
Meters per minute
Problem Set Sample Solutions
The Scott family is trying to save as much money as possible. One way to cut back on the money they spend is by finding
deals while grocery shopping; however, the Scott family needs help determining which stores have the better deals.
1.
At Grocery Mart, strawberries cost $𝟐𝟐. 𝟗𝟗𝟗𝟗 for 𝟐𝟐 lb., and at Baldwin Hills Market strawberries are $𝟑𝟑. 𝟗𝟗𝟗𝟗 for 𝟑𝟑 lb.
a.
What is the unit price of strawberries at each grocery store? If necessary, round to the nearest penny.
Grocery Mart: $𝟏𝟏. 𝟓𝟓𝟓𝟓 per pound (𝟏𝟏. 𝟒𝟒𝟒𝟒𝟒𝟒 rounded to nearest penny)
Baldwin Hills Market: $𝟏𝟏. 𝟑𝟑𝟑𝟑 per pound
b.
If the Scott family wanted to save money, where should they go to buy strawberries? Why?
Possible Answer: The Scott family should got to Baldwin Hills Market because the strawberries cost less
money there than at Grocery Mart.
2.
Potatoes are on sale at both Grocery Mart and Baldwin Hills Market. At Grocery Mart, a 𝟓𝟓 lb. bag of potatoes cost
$𝟐𝟐. 𝟖𝟖𝟖𝟖, and at Baldwin Hills Market a 𝟕𝟕 lb. bag of potatoes costs $𝟒𝟒. 𝟐𝟐𝟐𝟐. Which store offers the best deal on
potatoes? How do you know? How much better is the deal?
Grocery Mart: $𝟎𝟎. 𝟓𝟓𝟓𝟓 per pound
Baldwin Hills Market: $𝟎𝟎. 𝟔𝟔𝟔𝟔 per pound
Grocery Mart offers the best deal on potatoes because potatoes cost $𝟎𝟎. 𝟎𝟎𝟎𝟎 less per pound at Grocery Mart when
compared to Baldwin Hills Market.
Lesson 16:
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From Ratios to Rates
132
Lesson 16
A STORY OF RATIOS
6•1
Lesson 16: From Ratios to Rates
Classwork
Ratios can be transformed to rates and unit rates.
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?
b.
How much does 1 pack of diet cola cost?
Exploratory Challenge
1.
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 games? What is the rate unit?
Lesson 16:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
From Ratios to Rates
S.65
Lesson 16
A STORY OF RATIOS
2.
6•1
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 or her portion of the trip, enabling him or her to travel at a constant speed. The group
changed drivers each time they stopped for gas and recorded their driving times and distances in the table below.
Fan
Distance (miles)
Time (hours)
Andre
208
4
300
6
Matteo
Janaye
Greyson
456
8
265
5
Use the given data to answer the following questions.
a.
What two quantities are being compared?
b.
What is the ratio of the two quantities for Andre’s portion of the trip? What is the associated rate?
Andre’s Ratio: _________________
c.
d.
Andre’s Rate: ________________
Answer the same two questions in part (b) for the other three drivers.
Matteo’s Ratio: _________________
Matteo’s Rate: _________________
Janaye’s Ratio: _________________
Janaye’s Rate: _________________
Greyson’s Ratio: _________________
Greyson’s Rate: _________________
For each driver in parts (b) and (c), circle the unit rate and put a box around the rate unit.
Lesson 16:
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From Ratios to Rates
S.66
Lesson 16
A STORY OF RATIOS
3.
6•1
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.
Lesson 16:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
From Ratios to Rates
S.67
Lesson 16
A STORY OF RATIOS
6•1
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, which is read “miles per hour”.
Problem Set
The Scott family is trying to save as much money as possible. One way to cut back on the money they spend is by finding
deals while grocery shopping; however, the Scott family needs help determining which stores have the better deals.
1.
2.
At Grocery Mart, strawberries cost $2.99 for 2 lb., and at Baldwin Hills Market strawberries are $3.99 for 3 lb.
a.
What is the unit price of strawberries at each grocery store? If necessary, round to the nearest penny.
b.
If the Scott family wanted to save money, where should they go to buy strawberries? Why?
Potatoes are on sale at both Grocery Mart and Baldwin Hills Market. At Grocery Mart, a 5 lb. bag of potatoes cost
$2.85, and at Baldwin Hills Market a 7 lb. bag of potatoes costs $4.20. Which store offers the best deal on
potatoes? How do you know? How much better is the deal?
Lesson 16:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
From Ratios to Rates
S.68
Lesson 17
A STORY OF RATIOS
6•1
Lesson 17: From Rates to Ratios
Student Outcomes

Given a rate, students find ratios associated with the rate, including a ratio where the second term is one and a
ratio where both terms are whole numbers.

Students recognize that all ratios associated to a given rate are equivalent because they have the same value.
Classwork
Given a rate, you can calculate the unit rate and associated ratios. Recognize that all ratios associated with a given rate
are equivalent because they have the same value.
Example 1 (4 minutes)
Example 1
Write each ratio as a rate.
a.
The ratio of miles to the number of hours is 𝟒𝟒𝟒𝟒𝟒𝟒
to 𝟕𝟕.
Miles to hour: 𝟒𝟒𝟒𝟒𝟒𝟒: 𝟕𝟕
Student responses:
𝟒𝟒𝟒𝟒𝟒𝟒 miles
𝟕𝟕 hours
b.
The ratio of the number of laps to the number of
minutes is 𝟓𝟓 to 𝟒𝟒.
Laps to minute: 𝟓𝟓: 𝟒𝟒
= 𝟔𝟔𝟔𝟔 miles/hour
Student responses:
𝟓𝟓 laps
𝟒𝟒 minutes
𝟓𝟓
= laps/min
𝟒𝟒
Example 2 (15 minutes)
Demonstrate how to change a ratio to a unit rate then to a rate by recalling information students learned the previous
day. Use Example 1, part (b).
Example 2
a.
Complete the model below using the ratio from Example 1, part (b).
Ratio: 𝟓𝟓: 𝟒𝟒
Lesson 17:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Unit Rate:
From Rates to Ratios
𝟓𝟓
𝟒𝟒
Rate:
𝟓𝟓
𝟒𝟒
laps/minute
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Rates to Ratios: Guide students to complete the next flow map where the rate is given, and then they move to unit rate
and then to different ratios.
b.
Complete the model below now using the rate listed below.
Ratios: Answers may vary
Unit Rate: 𝟔𝟔
𝟔𝟔: 𝟏𝟏, 𝟔𝟔𝟔𝟔: 𝟏𝟏𝟏𝟏, 𝟏𝟏𝟏𝟏: 𝟐𝟐, etc.
Discussion

Will everyone have the same exact ratio to represent the given rate? Why or why not?
Possible Answer: Not everyone’s ratios will be exactly the same because there are many different
equivalent ratios that could be used to represent the same rate.


What are some different examples that could be represented in the ratio box?
Answers will vary: All representations represent the same rate: 12: 2, 18: 3, 24: 4.


Will everyone have the same exact unit rate to represent the given rate? Why or why not?
Possible Answer: Everyone will have the same unit rate for two reasons. First, the unit rate is the value
of the ratio, and each ratio only has one value. Second, the second quantity of the unit rate is always 1,
so the rate will be the same for everyone.


Will everyone have the same exact rate when given a unit rate? Why or why not?
Possible Answer: No, a unit rate can represent more than one rate. A rate of

unit rate of 6 feet/second.
18
3
feet/second has a
Examples 3–6 (20 minutes)
Students work on one problem at a time. Have students share their reasoning. Provide opportunities for students to
share different methods on how to solve each problem.
Examples 3–6
3.
Dave can clean pools at a constant rate of
a.
𝟑𝟑
𝟓𝟓
pools/hour.
What is the ratio of the number of pools to the number of hours?
𝟑𝟑: 𝟓𝟓
Lesson 17:
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Lesson 17
A STORY OF RATIOS
b.
How many pools can Dave clean in 𝟏𝟏𝟏𝟏 hours?
Pools
Hours
𝟐𝟐
𝟐𝟐
𝟐𝟐
= 𝟔𝟔 pools
𝟐𝟐
𝟐𝟐
𝟐𝟐
𝟐𝟐
𝟐𝟐
Dave can clean 𝟔𝟔 pools in 𝟏𝟏𝟏𝟏 hours.
c.
6•1
= 𝟏𝟏𝟏𝟏 hours
How long does it take Dave to clean 𝟏𝟏𝟏𝟏 pools?
Pools
Hours
𝟓𝟓
𝟓𝟓
𝟓𝟓
𝟓𝟓
𝟓𝟓
𝟓𝟓
𝟓𝟓
= 𝟏𝟏𝟏𝟏 pools
= 𝟐𝟐𝟐𝟐 hours
𝟓𝟓
It will take Dave 𝟐𝟐𝟐𝟐 hours to clean 𝟏𝟏𝟏𝟏 pools.
4.
𝟏𝟏
𝟒𝟒
Emeline can type at a constant rate of pages/minute.
a.
What is the ratio of the number of pages to the number of minutes?
𝟏𝟏: 𝟒𝟒
b.
Emeline has to type a 𝟓𝟓-page article but only has 𝟏𝟏𝟏𝟏 minutes until she reaches the deadline. Does Emeline
have enough time to type the article? Why or why not?
𝟏𝟏
𝟐𝟐
𝟑𝟑
𝟒𝟒
𝟖𝟖
𝟏𝟏𝟏𝟏 𝟏𝟏𝟏𝟏
Pages
𝟒𝟒
𝟓𝟓
Minutes
𝟐𝟐𝟐𝟐
No, Emeline will not have enough time because it will take her 𝟐𝟐𝟐𝟐 minutes to type a 𝟓𝟓-page article.
c.
Emeline has to type a 𝟕𝟕-page article. How much time will it take her?
Pages
𝟓𝟓
𝟔𝟔
𝟕𝟕
Minutes
𝟐𝟐𝟐𝟐
𝟐𝟐𝟐𝟐 𝟐𝟐𝟐𝟐
It will take Emeline 𝟐𝟐𝟐𝟐 minutes to type a 𝟕𝟕-page article.
5.
𝟓𝟓
Xavier can swim at a constant speed of meters/second.
a.
𝟑𝟑
What is the ratio of the number of meters to the number of seconds?
𝟓𝟓: 𝟑𝟑
Lesson 17:
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Lesson 17
A STORY OF RATIOS
b.
6•1
Xavier is trying to qualify for the National Swim Meet. To qualify, he must complete a 𝟏𝟏𝟏𝟏𝟏𝟏 meter race in 𝟓𝟓𝟓𝟓
seconds. Will Xavier be able to qualify? Why or why not?
Meters
Seconds
𝟓𝟓
𝟑𝟑
𝟏𝟏𝟏𝟏𝟏𝟏
𝟔𝟔𝟔𝟔
𝟏𝟏𝟏𝟏
𝟔𝟔
Xavier will not qualify for the meet because he would complete the race in 𝟔𝟔𝟔𝟔 seconds.
c.
Xavier is also attempting to qualify for the same meet in the 𝟐𝟐𝟐𝟐𝟐𝟐 meter event. To qualify, Xavier would have
to complete the race in 𝟏𝟏𝟏𝟏𝟏𝟏 seconds. Will Xavier be able to qualify in this race? Why or why not?
Meters
Seconds
𝟏𝟏𝟏𝟏𝟏𝟏
𝟔𝟔𝟔𝟔
𝟐𝟐𝟐𝟐𝟐𝟐
𝟏𝟏𝟏𝟏𝟏𝟏
Xavier will qualify for the meet in the 𝟐𝟐𝟐𝟐𝟐𝟐 meter race because he would complete the race in 𝟏𝟏𝟏𝟏𝟏𝟏 seconds.
6.
The corner store sells apples at a rate of 𝟏𝟏. 𝟐𝟐𝟐𝟐 dollars per apple.
a.
What is the ratio of the amount in dollars to the number of apples?
𝟏𝟏. 𝟐𝟐𝟐𝟐: 𝟏𝟏
b.
Akia is only able to spend $𝟏𝟏𝟏𝟏 on apples. How many apples can she buy?
𝟖𝟖 apples
c.
Christian has $𝟔𝟔 in his wallet and wants to spend it on apples. How many apples can Christian buy?
Christian can buy 𝟒𝟒 apples and would spend $𝟓𝟓. 𝟎𝟎𝟎𝟎. Christian cannot buy a 𝟓𝟓th apple because it would cost
$𝟔𝟔. 𝟐𝟐𝟐𝟐 for 𝟓𝟓 apples, and he only has $𝟔𝟔. 𝟎𝟎𝟎𝟎.
Closing (2 minutes)

Explain the similarities and differences between rate, unit rate, rate unit, and ratio.
Lesson Summary
𝟐𝟐
𝟐𝟐
A rate of gal/min corresponds to the unit rate of and also corresponds to the ratio 𝟐𝟐: 𝟑𝟑.
𝟑𝟑
𝟑𝟑
All ratios associated with a given rate are equivalent because they have the same value.
Exit Ticket (4 minutes)
Lesson 17:
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From Rates to Ratios
136
Lesson 17
A STORY OF RATIOS
Name ___________________________________________________
6•1
Date____________________
Lesson 17: From Rates to Ratios
Exit Ticket
Tiffany is filling her daughter’s pool with water from a hose. She can fill the pool at a rate of
1
10
gallons/second.
Create at least three equivalent ratios that are associated with the rate. Use a double number line to show your work.
Lesson 17:
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From Rates to Ratios
137
Lesson 17
A STORY OF RATIOS
6•1
Exit Ticket Sample Solutions
Tiffany is filling her daughter’s pool with water from a hose. She can fill the pool at a rate of
𝟏𝟏
𝟏𝟏𝟏𝟏
gallons/second.
Create at least three equivalent ratios that are associated with the rate. Use a double number line to show your work.
Answers will vary.
Problem Set Sample Solutions
1.
Once a commercial plane reaches the desired altitude, the pilot often travels at a cruising speed. On average, the
cruising speed is 𝟓𝟓𝟓𝟓𝟓𝟓 miles/hour. If a plane travels at this cruising speed for 𝟕𝟕 hours, how far does the plane travel
while cruising at this speed?
𝟑𝟑, 𝟗𝟗𝟗𝟗𝟗𝟗 miles
2.
Denver, Colorado often experiences snowstorms resulting in multiple inches of accumulated snow. During the last
𝟒𝟒
snow storm, the snow accumulated at inch/hour. If the snow continues at this rate for 𝟏𝟏𝟏𝟏 hours, how much snow
will accumulate?
𝟖𝟖 inches
Lesson 17:
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𝟓𝟓
From Rates to Ratios
138
Lesson 17
A STORY OF RATIOS
6•1
Lesson 17: From Rates to Ratios
Classwork
Given a rate, you can calculate the unit rate and associated ratios. Recognize that all ratios associated with a given rate
are equivalent because they have the same value.
Example 1
Write each ratio as a rate.
a.
The ratio of miles to the number of hours is 434
to 7.
b.
The ratio of the number of laps to the number of
minutes is 5 to 4.
Example 2
a.
Complete the model below using the ratio from Example 1, part (b).
Ratio
Unit Rate
Rate
laps/minute
Lesson 17:
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From Rates to Ratios
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Lesson 17
A STORY OF RATIOS
b.
6•1
Complete the model below now using the rate listed below.
Ratio
Unit Rate
Rate
𝟔𝟔 ft/sec
Examples 3–6
3.
Dave can clean pools at a constant rate of
3
5
pools/hour.
a.
What is the ratio of the number of pools to the number of hours?
b.
How many pools can Dave clean in 10 hours?
c.
How long does it take Dave to clean 15 pools?
Lesson 17:
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From Rates to Ratios
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Lesson 17
A STORY OF RATIOS
4.
5.
Emeline can type at a constant rate of
1
4
6•1
pages/minute.
a.
What is the ratio of the number of pages to the number of minutes?
b.
Emeline has to type a 5-page article but only has 18 minutes until she reaches the deadline. Does Emeline
have enough time to type the article? Why or why not?
c.
Emeline has to type a 7-page article. How much time will it take her?
Xavier can swim at a constant speed of
5
3
meters/second.
a.
What is the ratio of the number of meters to the number of seconds?
b.
Xavier is trying to qualify for the National Swim Meet. To qualify, he must complete a 100 meter race in 55
seconds. Will Xavier be able to qualify? Why or why not?
c.
Xavier is also attempting to qualify for the same meet in the 200 meter event. To qualify, Xavier would have
to complete the race in 130 seconds. Will Xavier be able to qualify in this race? Why or why not?
Lesson 17:
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From Rates to Ratios
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Lesson 17
A STORY OF RATIOS
6.
6•1
The corner store sells apples at a rate of 1.25 dollars per apple.
a.
What is the ratio of the amount in dollars to the number of apples?
b.
Akia is only able to spend $10 on apples. How many apples can she buy?
c.
Christian has $6 in his wallet and wants to spend it on apples. How many apples can Christian buy?
Lesson 17:
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From Rates to Ratios
S.72
Lesson 17
A STORY OF RATIOS
6•1
Lesson Summary
A rate of
2
3
gal/min corresponds to the unit rate of
2
3
and also corresponds to the ratio 2: 3.
All ratios associated with a given rate are equivalent because they have the same value.
Problem Set
1.
Once a commercial plane reaches the desired altitude, the pilot often travels at a cruising speed. On average, the
cruising speed is 570 miles/hour. If a plane travels at this cruising speed for 7 hours, how far does the plane travel
while cruising at this speed?
2.
Denver, Colorado often experiences snowstorms resulting in multiple inches of accumulated snow. During the last
snow storm, the snow accumulated at
snow will accumulate?
Lesson 17:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
4
5
inch/hour. If the snow continues at this rate for 10 hours, how much
From Rates to Ratios
S.73