Equations of Proportional Relationships
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Warm Up
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Equations of Proportional Relationships
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Warm Up
McGraw Hill |
Equations of Proportional Relationships
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Warm Up
McGraw Hill |
Equations of Proportional Relationships
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Warm Up
McGraw Hill |
Equations of Proportional Relationships
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
7.RP.A.2
Recognize and represent proportional relationships between quantities.
7.RP.A.2.B
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
7.RP.A.2.C
Represent proportional relationships by equations.
Standards for Mathematical Content
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Equations of Proportional Relationships
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Standards for Mathematical Practice
MP1
Make sense of problems and persevere in solving them.
MP2
Reason abstractly and quantitatively.
MP3
Construct viable arguments and critique the reasoning of others.
MP4
Model with mathematics.
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Equations of Proportional Relationships
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Standards for Mathematical Practice
MP5
Use appropriate tools strategically.
MP6
Attend to precision.
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Equations of Proportional Relationships
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Students will write equations to represent proportional relationships.
Lesson Goal
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Equations of Proportional Relationships
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Learn�Identify the Constant of Proportionality in Equations
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Equations of Proportional Relationships
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Words | Symbols |
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Example | Graph |
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Learn�Identify the Constant of Proportionality in Equations
McGraw Hill |
Equations of Proportional Relationships
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Learn�Identify the Constant of Proportionality in Equations
McGraw Hill |
Equations of Proportional Relationships
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Example 1�Identify the Constant of Proportionality in Equations
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Equations of Proportional Relationships
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Example 1�Identify the Constant of Proportionality in Equations
Think About It!
How would you begin solving the problem?
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Equations of Proportional Relationships
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Example 1�Identify the Constant of Proportionality in Equations
McGraw Hill |
Equations of Proportional Relationships
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Example 1�Identify the Constant of Proportionality in Equations
McGraw Hill |
Equations of Proportional Relationships
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Example 1�Identify the Constant of Proportionality in Equations
Talk About It!
How much would Olivia pay for 10 yogurts at this same rate?
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Equations of Proportional Relationships
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Example 1�Identify the Constant of Proportionality in Equations
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Equations of Proportional Relationships
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Example 1�Identify the Constant of Proportionality in Equations
195
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Equations of Proportional Relationships
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Example 1�Identify the Constant of Proportionality in Equations
Check
Part B What does the constant of proportionality represent in the context of the problem?
A An airplane travels 390 miles per hour.
B An airplane travels 1 mile per 4 hours.
C An airplane travels 1 mile per 585 hours.
D An airplane travels 195 miles per hour.
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Equations of Proportional Relationships
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Example 1�Identify the Constant of Proportionality in Equations
Check
Part B What does the constant of proportionality represent in the context of the problem?
A An airplane travels 390 miles per hour.
B An airplane travels 1 mile per 4 hours.
C An airplane travels 1 mile per 585 hours.
D An airplane travels 195 miles per hour. D
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Equations of Proportional Relationships
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Learn�Proportional Relationships and Equations
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Equations of Proportional Relationships
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Learn�Proportional Relationships and Equations
Write the equation.
Simplify.
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Equations of Proportional Relationships
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Learn�Proportional Relationships and Equations
Talk About It!
What is the equation for a proportional relationship where the constant of proportionality is 3.25?
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Equations of Proportional Relationships
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Example 2�Proportional Relationships and Equations
Write an equation relating the total cost y to the number of gallons of gas x if it is a proportional relationship.
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Equations of Proportional Relationships
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Example 2�Proportional Relationships and Equations
Step 1 Find the constant of proportionality between cost and gallons.
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Equations of Proportional Relationships
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Example 2�Proportional Relationships and Equations
Step 2 Write the equation.
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Equations of Proportional Relationships
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Example 2�Proportional Relationships and Equations
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Equations of Proportional Relationships
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Example 2�Proportional Relationships and Equations
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Equations of Proportional Relationships
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Example 2�Proportional Relationships and Equations
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Equations of Proportional Relationships
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Example 3�Proportional Relationships and Equations
The perimeter of a square is proportional to the length of one side. A square with 10-inch sides has a perimeter of 40 inches.
Write an equation relating the perimeter of the square to its side length. Then find the perimeter of a square with a 6-inch side.
Part A Write an equation.
Part B Use the equation to find the perimeter of a square with a side length of 6 inches.
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Equations of Proportional Relationships
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Example 3�Proportional Relationships and Equations
Part A Write an equation.
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Equations of Proportional Relationships
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Example 3�Proportional Relationships and Equations
Write the equation.
Multiply.
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Equations of Proportional Relationships
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Example 3�Proportional Relationships and Equations
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Equations of Proportional Relationships
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Check
Jack is in charge of the 120,000-gallon community swimming pool. Each spring, he drains the pool in order to clean it. When finished, he refills the pool with fresh water. Jack can fill the pool with 500 gallons of water in 5 minutes.
Example 3�Proportional Relationships and Equations
Part A
Write an equation that represents the relationship between the total number of gallons y and the number of minutes spent filling the pool x.
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Equations of Proportional Relationships
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Check
Jack is in charge of the 120,000-gallon community swimming pool. Each spring, he drains the pool in order to clean it. When finished, he refills the pool with fresh water. Jack can fill the pool with 500 gallons of water in 5 minutes.
Example 3�Proportional Relationships and Equations
Part A
Write an equation that represents the relationship between the total number of gallons y and the number of minutes spent filling the pool x.
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Equations of Proportional Relationships
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Check
Example 3�Proportional Relationships and Equations
Part B
How long will it take to become completely filled?
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Equations of Proportional Relationships
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Check
Example 3�Proportional Relationships and Equations
Part B
How long will it take to become completely filled?
1,200 minutes
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Equations of Proportional Relationships
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Apply�Running
Hugo can run 4 miles in �25 minutes. How many more miles can Hugo run in 90 minutes than in 25 minutes? Assume the relationship is proportional and he runs at a constant rate.
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Equations of Proportional Relationships
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Apply�Running
Talk About It!
Can you always assume that Hugo runs at a constant rate for any amount of time predicted? Explain your reasoning.
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Equations of Proportional Relationships
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Apply�Running
Check
Emily can ride her bike 15 kilometers in 45 minutes. How many more kilometers can she bike in two hours than in 45 minutes? Assume the relationship is proportional and she always bikes at the same rate.
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Equations of Proportional Relationships
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Apply�Running
Check
Emily can ride her bike 15 kilometers in 45 minutes. How many more kilometers can she bike in two hours than in 45 minutes? Assume the relationship is proportional and she always bikes at the same rate.
25 km
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Equations of Proportional Relationships
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Exit Ticket
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Equations of Proportional Relationships
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Exit Ticket
5; Sample answer: The constant of proportionality is the speed the elevator travels in miles per hour. So, the elevator travels at a speed of 5 miles per hour.
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Equations of Proportional Relationships
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