Topic A: Proportional
Relationships
Lesson 1
An Experience in Relationships as
Measuring Rate
LEARNING TARGET
Lesson 1: An Experience in Relationships as Measuring Rate – Day 1
Today I can write a ratio and rate and compute a unit rate and explain their meaning in the
context of the problem.
STANDARDS
7.RP.2a Decide whether two quantities are
in a proportional relationship, e.g., by testing
for equivalent ratios in a table or graphing
on a coordinate plane and observing
whether the graph is a straight line through
the origin.
KEY VOCABULARY
Ratio
Rate
Unit rate
AGENDA
• (5 min) Review Key Vocabulary: Ratio
• (10 min) Example 1: How Fast is Our
Class?
• (5 min) MODEL: Ratio
• (10 min) Discussion
• (5 min) Review Key Vocabulary: Rate &
Unit Rate
• (5 min) MODEL: Rate
• (5 min) MODEL: Unit Rate
• (10 min) Extension
• (5 min) Exit Ticket
• (20-30 min) Online Practice
Review Key Vocabulary
A ratio is a comparison of two numbers by
division.
Example:
60
,
3
60: 3, 60 to 3
Example 1: How Fast is Our Class?
Trial
Number of
Papers
Time
(in seconds)
Ratio
Rate
Unit Rate
1
2
3
1. How will we measure our rate of passing out papers?
2. What quantities will we use to describe our rate?
MODEL: Ratio Column
• Teacher: Trial 1
• Class: Trial 2
• Partner: Trial 3
Discussion
1. What was the ratio from the first trial?
2. What was the ratio in the third trial?
3. Are these two ratios equivalent? Explain.
Review Key Vocabulary
• A rate is a ratio of different units.
Example:
60 𝑚𝑖𝑙𝑒𝑠
3 ℎ𝑜𝑢𝑟𝑠
A unit rate is a rate with a denominator of 1.
20 𝑚𝑖𝑙𝑒𝑠
Example:
1 ℎ𝑜𝑢𝑟
MODEL: Rate & Unit Rate Columns
• Teacher: Trial 1
• Class: Trial 2
• Partner: Trial 3
Extension
Let’s say that in another class period students
were able to pass 28 papers in 15 seconds. A
third class period passed 18 papers in 10
seconds. How do these compare to our fastest
unit rate?
Exit Ticket – Day 1
1. Describe the difference between the ratio
and rate in Example 1.
2. Describe how we turned the rate into a unit
rate in Example 1.
LEARNING TARGET
Lesson 1: An Experience in Relationships as Measuring Rate – Day 2
Today I can write ratios and equivalent ratios and explain their meaning in the context of the
problem.
STANDARDS
7.RP.2a Decide whether two quantities are
in a proportional relationship, e.g., by testing
for equivalent ratios in a table or graphing
on a coordinate plane and observing
whether the graph is a straight line through
the origin.
KEY VOCABULARY
Ratio
Equivalent ratios
AGENDA
• (5 min) Review Key Vocabulary: Ratio
• (20 min) Example 2: Our Class by
Gender
• (10 min) MODEL: Ratio
• (10 min) Discussion
• (5 min) Review Key Vocabulary:
Equivalent Ratios
• (10 min) Extension
• (5 min) Exit Ticket
• (20-30 min) Online Practice
Review Key Vocabulary
A ratio is a comparison of two numbers by
division.
Example:
60
,
3
60: 3, 60 to 3
Example 2: Our Class by Gender
Class
Number of boys
Number of girls
Ratio of boys to
girls
Period 1
Period 3
Period 5
All
1. What are we comparing in this example?
2. Are the units different? Explain.
3. Does it matter the order we write the ratio? Explain.
MODEL: Ratio of Boys to Girls Column
• Teacher: Period 1
• Class: Period 3
• Partner: Period 5 & All
Discussion
1. Are the ratios of boys to girls in the three classes
equivalent?
2. What could these ratios tell us?
3. What does the ratio of boys to girls in Period 1
to all classes tell us? Are they equivalent?
4. If there is a larger ratio of boys to girls in one
class than all classes, what does that mean must
be true about the boy/girl ratio in other classes?
5. How do we compare the ratios when we have
varying sizes of quantities?
Review Key Vocabulary
Equivalent ratios have different numbers but
represent the same relationship.
Example:
60
3
=
20
1
Extension
Write down two equivalent ratios comparing
boys to girls from our class. Explain your
process.
Exit Ticket – Day 2
How do the equivalent ratios compare to the
ratio of ALL boys: ALL girls? What does this
mean?
LEARNING TARGET
Lesson 1: An Experience in Relationships as Measuring Rate – Day 3
Today I can compute a unit rate and explain its meaning in the context of the problem.
STANDARDS
7.RP.2a Decide whether two quantities are
in a proportional relationship, e.g., by testing
for equivalent ratios in a table or graphing
on a coordinate plane and observing
whether the graph is a straight line through
the origin.
KEY VOCABULARY
Rate
Unit rate
AGENDA
• (5 min) Review Key Vocabulary: Rate &
Unit Rate
• (15 min) Exercise 1: Which is the Better
Buy?
• (15 min) Critique Responses
• (5 min) Lesson Summary
• (25 min) Problem Set
• (If Time) Extension
• (15-20 min) Quiz: Lesson 1
Review Key Vocabulary
• A rate is a ratio of different units.
Example:
60 𝑚𝑖𝑙𝑒𝑠
3 ℎ𝑜𝑢𝑟𝑠
A unit rate is a rate with a denominator of 1.
20 𝑚𝑖𝑙𝑒𝑠
Example:
1 ℎ𝑜𝑢𝑟
Exercise 1: Which is the Better Buy?
Value-Mart is advertising a Back-to-School sale
on pencils. A pack of 30 sells for $7.97 whereas
a 12-pack of the same brand costs $4.77. Which
is the better buy? How do you know?
Mathematical Practice: Reason abstractly and quantitatively
Critique Responses
Lesson Summary
How is finding a rate or unit rate helpful when
making comparisons between quantities?
Problem Set
1 Point
(Unsatisfactory)
2 Points
(Partially Proficient)
3 Points
(Proficient)
A correct answer
Missing or incorrect Missing or incorrect with some evidence
answer and little
answer but
of reasoning or an
evidence of
evidence of some
incorrect answer
reasoning
reasoning
with substantial
evidence
4 Points
(Advanced)
A correct answer
supported by
substantial
evidence of solid
reasoning
Extension
Watch the video clip of Tillman the English Bulldog, the Guinness
World Record holder for Fastest Dog on a Skateboard.
1.
2.
At the conclusion of the video, your classmate takes out his or her
calculator and says, “Wow that was amazing! That means the dog
went about 5 meters in 1 second!” Is your classmate correct, and
how do you know?
After seeing this video, another dog owner trained his dog,
Lightning, to try to break Tillman’s skateboarding record.
Lightning’s fastest recorded time was on a 75-meter stretch where
it took him 15.5 seconds. Based on this data, did Lightning break
Tillman’s record for fastest dog on a skateboard? Explain how you
know.
Video Link