Lesson Plan: 6.RP.A.2 Unit Rate
(This lesson should be adapted, including instructional time, to meet the needs of your students.)
Content/Grade Level
Background Information
Ratios and Proportional Relationships/Grade 6
Unit/Cluster
Understand ratio concepts and use ratio reasoning to solve problems.
Lesson Topic
Using ratio and rate reasoning to solve real-world and mathematical problems.
Essential Questions
Essential Questions &
Enduring Understandings  How are rates and unit rates used in the real world?
Addressed in the Lesson
 How is a unit rate similar to and different from a ratio?
Enduring Understandings
 A unit rate is a special ratio with a denominator of one that compares different types of measures.
FOCUS
𝑎
6.RP.A.2: Understand the concept of a unit rate 𝑏 associated with a ratio a:b with b ≠ 0, and use rate language
in the context of a ratio relationship. (Major Standard)
It is critical that the Standards for Mathematical Practices are incorporated in ALL lesson activities throughout
the unit as appropriate. It is not the expectation that all eight Mathematical Practices will be evident in every
lesson. The Standards for Mathematical Practices make an excellent framework on which to plan your
instruction. Look for the infusion of the Mathematical Practices throughout this unit.
COHERENCE
Across-Grade Coherence: Content Knowledge from Earlier Grades
𝑎
(𝑛 × 𝑎)
4.NF.A.1: Explain why a fraction 𝑏 is equivalent to a fraction (𝑛 × 𝑏) by using visual fraction models, with
attention to how the number and size of the parts differ even though the two fractions themselves are the same
size. Use this principle to recognize and generate equivalent fractions.
5.NF.B.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number
by a fraction.
Within-Grade Coherence: Content from Other Standards in the Same Grade that Provide Reinforcement
6.RP.A.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two
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quantities.
RIGOR

Procedural Skill
As students have the opportunity to practice multiplication and division of whole numbers, fractions and
decimals while working real world problems.

Conceptual Understanding
 Students have the opportunity to develop for themselves the meaning of ratio, rate and unit rate by using
their skills to solve real world problems.
Modeling/Application
 Students have the opportunity to work with models their thinking about ratios as they work real world
problems using equations.
Student Outcomes


Students will be able to determine a unit rate given a ratio.
Students will solve real-world mathematical problems by finding unit rates.
Learning Experience
Component
Method for determining
student readiness for the
lesson
Details

Which Standards for
Mathematical Practice(s)
does this address? How
is the Practice used to
help students develop
proficiency?
In the warm up, students will explain what a ratio is and how the parts of the ratio
relate to one another. Teachers will determine how in depth they need to review based
upon the student responses.
o Ask: What is a ratio? Have students talk to a partner and share thinking.
A ratio is a comparison between two numbers of the same kind (e.g., objects,
persons, students, spoonfuls, units of whatever identical dimension), usually
expressed as "a to b" or a:b, sometimes expressed arithmetically as a quotient of
𝑎
the two 𝑏. The comparison between two measures, expressed as the number of
times one is bigger or smaller than the other.
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Learning Experience
Component
Details
Which Standards for
Mathematical Practice(s)
does this address? How
is the Practice used to
help students develop
proficiency?
o Teachers will select a few students to share responses.
Explain that in prior lesson(s), they learned about comparing same types of measures
(part/part and part/whole ratios). Show students one of the graphics (or a different one that
you think would be of special interest to your own students). Ask them to identify as many
part/part and part/whole ratios as they can by grouping and comparing objects in the
graphic presented to them.
Graphic A
Graphic B
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Learning Experience
Component
Details
Which Standards for
Mathematical Practice(s)
does this address? How
is the Practice used to
help students develop
proficiency?
Graphic C
Motivation/Warm Up

Activity 1
UDL Components:
 Principle I: Representation is present in the activity.
Prior knowledge is activated about ratio as they sort their cards. Students have a
chance to use mathematical vocabulary as they work in groups.
 Principle II: Expression is present in the activity.
UDL Components
 Multiple Means of
Representation
Ask: What are some examples of ratios in the lives of your students?
o In pairs, have students record responses on sticky notes, and post them on a white
board/chalk board/ wall/door/etc. After Activity 1, students will revisit their sticky
notes to classify as part/part, part/whole, or unit rate.
Make sense of types of
ratios by planning a
solution pathway instead
of jumping to a solution
while sorting cards into
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Learning Experience
Component
Details

Multiple Means for
Action and
Expression
 Multiple Means for
Engagement
Key Questions
Formative Assessment
Summary

The students begin by working in groups and sorting cards of ratios and rates.
Scaffolding is gradually released as they work through their sorting.
Principle III: Engagement is present in the activity
This task allows for activity participation as they explore the meaning of ratio and rate.
It allows time for evaluation of their work.
Ratio/Rate Cards Sort – Put students in groups of two or three. Ask students to sort
cards (Attachment #1) into categories (do not give them any guidance, such as titles,
amount of categories, etc.)
(SMP#1)

Have students explain their categorization.
o Is there evidence of knowledge of part-part, part-whole, and “other”?
(SMP#3)

Discuss this chart:
Which Standards for
Mathematical Practice(s)
does this address? How
is the Practice used to
help students develop
proficiency?
categories and explain
their reasoning.
(SMP#1)
The students can
construct viable
arguments and critique
the reasoning of others by
justifying conclusions as
they sort the cards.
(SMP# 3)
Attend to precision is
done in this activity as
the students communicate
with others and try to use
clear mathematical
language when
discussing their
reasoning. .
(SMP#6)
Reference: Adapted from Van de Walle, Teaching Student Centered Mathematics, grades
5-8, volume 3, pg. 155
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Learning Experience
Component
Details
Which Standards for
Mathematical Practice(s)
does this address? How
is the Practice used to
help students develop
proficiency?

Ask:
o Would you change the arrangement of your card sort given this new information?
Why or why not?
o What do you notice about the rate cards?
Possible answer: They use different types of measures.
 What other real life examples of rates can you give?
(SMP#6)



Invite student volunteers to explain the definition of unit rate, and guide student
responses into a broader discussion:
 A unit rate represents a rate with a denominator of 1 in fraction form. Rates are
usually expressed in per unit form. Examples include: miles per hour, pizza slices
per person, inches per foot, heartbeats per minute, cost per pound, etc.
Return to the card sort. Which rate cards are rates and which are unit rates?
Review your original sticky notes and classify (or re-classify, if necessary) students’
authentic life examples.
(SMPs #1, #3, #6)
Activity 2
UDL Components
 Multiple Means
of
Representation
 Multiple Means
for Action and
Expression
UDL Components:
 Principle I: Representation is present in the activity.
Students will use this activity as an opportunity to access prior skill from earlier grades
and practice with a new idea for finding unit rates.
 Principle II: Expression is present in the activity.
The gallery walk allows students movement as they solve the problems around the
room.
 Principle III: Engagement is present in the activity
Make sense of problems
and persevere in solving
them on the gallery walk
as they monitor their own
progress and change their
approach if necessary.
(SMP#1)
The students model with
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Learning Experience
Component

Multiple Means
for Engagement
Key Questions
Formative Assessment
Summary
Details
The gallery walk fosters discussion, collaboration and community in order to compare
their prices.
Finding the unit rate using equivalent ratios.
 Show two examples:
Example #1:
15 hamburgers for $75. How much per hamburger? (Note to teacher: Make
sure students are solving using equivalent ratios.)
$75
15
=
𝑥
$75 ÷15
1
15÷15
=
$5
1
Which Standards for
Mathematical Practice(s)
does this address? How
is the Practice used to
help students develop
proficiency?
mathematics as they
apply the mathematics
they know to solve
everyday problems.
(SMP# 4)
The students are
attending to precision as
they communicate
precisely with others on
the gallery walk.
(SMP# 6)
What is the unit rate?
Answer: $5 per hamburger
Example #2:
Four movie tickets cost $52. How much does it cost for each ticket?
$52
4
=
𝑥
$52 ÷4
1
4÷4
=
$13
1
What is the unit rate?
Answer: $13 per movie ticket
(SMP#4)
Use this video to show an example of comparing prices.
www.BrainPop.com/math/dataanalysis/comparingprices/
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Learning Experience
Component
Which Standards for
Mathematical Practice(s)
does this address? How
is the Practice used to
help students develop
proficiency?
Details

Which is the better buy? (Rate application)
 Compare the prices for various sizes of popcorn sold at the local movie theater.
Mega Bag
$10.24 for 32 oz.
Giant Bag
$6.00 for 24 oz.
Medium Bag $4.48 for 16 oz.
Kid’s Bag
$2.40 for 8 oz.

What is the unit price per ounce for each bag of popcorn? Show your equivalent
ratios.
10.24
?
10.24  32
.32
=
=
32
1
32  32
1
6.00
24
4.48
16
2.40
8
?
6.00  24
1
24  24
?
4.48  16
1
16  16
=
=
=
?
2.40  8
1
88
=
=
=
.25
1
.28
1
.30
1

What size popcorn is the best buy? Explain your reasoning. Answer: The giant
bag the best buy because it cost less than the other three kinds.
(SMP#4)

Have the students work in two’s and try the eight problems posted around the room
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Learning Experience
Component
Details
Which Standards for
Mathematical Practice(s)
does this address? How
is the Practice used to
help students develop
proficiency?
(Attachment #2). Have students go to at least 4 problems to find the unit rate or best
buy. Provide a capture sheet for each student (Attachment #3).
(SMP# 1, #6)
Closure
Interventions/Enrichments
 Students with
Disabilities/Struggling
Learners
 ELL
 Gifted and Talented
Students will need to determine which scenario is correct and justify their reasoning.
 Put 2 pictures of grocery ads of two brands of the same thing side by side on the
document camera. Have the students individually determine which brand is the better
buy.
(SMP#1)
Supporting Information
Students with Disabilities/Struggling Learners
 Provide calculator for students who need it.
 When you work in groups make sure you pair these students with someone who can help them.
ELL
 Front load vocabulary (ratio, rate, unit rate)
Gifted and Talented
 Have the students play this game.
www.mathsisfun.com/measure/unit-price-game.html
 Have students look for misleading adds based on unit pricing.
Materials


White boards (optional)
Post-it Notes
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Technology



Resources
www.BrainPop.com/math/dataanalysis/comparingprices/
www.mathsisfun.com/measure/unit-price-game.html
Websites in the Enrichment section
Calculator
Document camera
Van de Walle, Teaching Student Centered Mathematics, grades 5-8, volume 3
Carnegie Learning Math Series – Volume 1
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Attachment #1: Graphics for Part/Part and Part/Whole Ratios
Graphic A
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Attachment #1: Graphics for Part/Part and Part/Whole Ratios
Graphic B
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Attachment #1: Graphics for Part/Part and Part/Whole Ratios
Graphic C
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Attachment #2: Ratio/Rate Card Sort
Number of red
Number of red
Number of roses
Number of
Number of
roses to number roses to number
per bouquet
baseballs to
footballs to
of flowers in
of yellow roses
number of bats
number of
bouquet
12 to 1
in supply room
soccer balls
6
25
6 to 18
5 to 8
24
11
Number of
Number of
Number of
Number of
Probability of
footballs per
points earned
points earned to points earned to
getting a head
class
per pupil
number of
number of points
with one coin
5:5
possible points
not earned
toss
1
1140
76
80
or
or
1:1
80 : 20
2
15
1
100
Probability of
Number of heads Number of green Number of miles
Cost of cereal
getting a head
in 10 tosses
M&Ms to total
per gallon
per ounce
with one coin
candies in bag
23
5
. 27
toss
6 to 10
1 to 2
1
1
23
Number of heart Number of pizza Number of boys
Number of girls
Cost of bananas
beats per minute slices per person
to number of
to total number
per pound
girls in same
students in class
67 : 1
3:1
class
13 : 24
$1.20 : 1
11 to 13
Number of
Number of blue Number of miles
Number of
Number of songs
apples to
socks to total
per hour
gallons in 4
to cost of songs
number of
number of socks
minutes
oranges
in the drawer
67 : 1
12 : 4
20 : $5.00
5:7
6 to 14
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Attachment #2: Ratio/Rate Card Sort - Answer Sheet
Number of red
roses to number
of flowers in
bouquet
Number of red
roses to number
of yellow roses
6
6 to 18
ratio
24
Number of
footballs per
class
5:5
or
unit rate
1:1
Number of tails
with one coin
toss
1 to 2
ratio
Number of heart
beats per minute
67 : 1
unit rate
Number of
apples to
number of
oranges
ratio
5:7
Number of roses
per bouquet
12 to 1
ratio
1140
15
unit rate
or
rate
unit rate
Number of
points earned
per pupil
76
Number of
points earned to
number of
possible points
80
1
ratio
100
Number of heads Number of green
in 10 tosses
M&Ms to
number candies
6 to 10
in bag
ratio
ratio
Number of
baseballs to
number of bats
in supply room
5
25
11
Number of
footballs to
number of
soccer balls
5 to 8
ratio
Number of
Number of heads
points earned to
with one coin
number of points
toss
1
not earned
2
80 : 20
ratio
Number of miles
per gallon
23
1
unit rate
ratio
Cost of cereal
per ounce
. 27
1
unit rate
23
Number of pizza
slices per person
3:1
Number of boys
in class to
number of girls
ratio in class
unit rate
11 to 13
Number of blue Number of miles
socks to total
per hour
number of socks
67 : 1
in the drawer
unit rate
ratio 6 to 14
Number of girls
to total number
students in class
13 : 24
Cost of bananas
per pound
ratio
unit rate
Number of
gallons in 4
minutes
12 : 4
rate
$1.20 : 1
Number of songs
to cost of songs
20 : $5.00
ratio
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Attachment #3: Number 1
Which is the Better Buy?
2 liters of Juice at $3.80
or
1.5 liters of Juice at $2.70
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Attachment #3: Number 2
Which is the Better Buy?
10 pencils for $4.00
or
6 pencils for $2.70
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Attachment #2: Number 3
Which is the Better Buy?
10 fl.oz. of shampoo at $3.60, or
20 fl.oz. of shampoo at $7.10, or
30 fl.oz. of shampoo at $9, or
50 fl.oz. of shampoo at $14.50
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Attachment #2: Number 4
Which is the Better Buy?
½ pint of milk at $0.52, or
1 pint of milk at $0.99, or
1 quart of milk at $2.10, or
½ gallon of milk at $4.00
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Attachment #2: Number 5
Which is the Better Buy?
500 g of minced beef at $6, or
700 g of stewing beef at $8.68, or
1 kg of beef steak at $14.50, or
1.6 kg of beef roast at $20.80
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Attachment #2: Number 6
What is the Speed?
Maria drove to her mother’s house,
which is 204 miles away. If it took
her 3 hours, what was her average
speed?
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Attachment #2: Number 7
What is the Cost?
Four gallons of gasoline cost $16.80.
What is the price per gallon?
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Attachment #2: Number 8
Which is the Better Buy?
3 cans of soda for $1.27
or
5 cans of soda for $1.79
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Attachment #4
Problems
#1
#2
#3
#4
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#5
#6
#7
#8
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Attachment #4 Answers
1. 1.5 liters at $2.70
2. 10 pencils for $4.00
3. 50 fl. oz. of shampoo at $14.50
4. 1 pt. of milk at $0.99
5. 500 g of minced beef at $6.00
6. 68 miles per hour
7. $4.20
8. 5 cans of soda for $1.79
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