Constant of Proportionality (Grade 7)

These lessons, with videos, examples, and solutions, help Grade 7 students learn how to recognize and represent proportional relationships between quantities.

B. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Common Core: 7.RP.2b

Suggested Learning Targets

• I can identify a constant relationship of unit rates in tables.
• I can identify a constant relationship of unit rates in graphs.
• I can identify a constant relationship of unit rates in equations.
• I can identify a constant relationship of unit rates in diagrams.
• I can identify a constant relationship of unit rates in verbal descriptions.
  

The following diagram shows what is meant by the constant of proportionality. Scroll down the page for more examples and solutions on how to determine the constant of proportionality.

Identify the constant of proportionality (unit rate) (Common Core 7.RP.2b)

In this lesson you will learn

• How to identify the constant of proportionality in ratio tables by dividing?
• How to determine the constant of proportionality in graphs by finding the ratio of y to x?
• How to write an equation that expresses the relationship between two proportional quantities by finding the constant of proportionality?
• How to identify the constant of proportionality from a labeled diagram by writing an equation of the form y = mx and solving for m?

Ratios and Proportional Relationships
Analyze proportional relationships and use them to resolve real-world and mathematical problems.

Example:

1. Find the constant of proportionality (unit rate) from the table.
2. Find the constant of proportionality (unit rate) from the graph.
3. Find the constant of proportionality (unit rate) from the following equations.
   (a) y = 10x
   (b) y = 8x
   (c) y = 1/2 x

Unit Rate Task (CCSS Math 7.RP.2b)
This video covers a task in which students are asked to find a constant of proportionality and use it as a unit rate to find the solution. This task aligns with CCSS Math 7.RP.2b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Example:
The 4 tables represent the distance traveled by 4 objects and the time each took to travel that distance. Using a constant of proportionality or a unit rate, list the objects in order from fastest to slowest.

Constant of Proportionality (7th Grade Math)
What is the constant of proportionality?
The constant value of the ratio of two proportional quantities x and y; usually written y = kx where k is factor of proportionality.
How can we find the constant of proportionality?
A constant of proportionality does not include units.

How to use constant of proportionality to solve word problems?

Examples:

1. Wildlife conservationists are concerned that the deer population might not be constant across the National Forest. The scientists found that there were 144 deer in 16 square mile area for the forest. In another part of the forest, conservationists counted 117 deer is a 13 square mile area. Yet a third conservationist counted 24 deer in a 216 square acre plot of the forest. Do conservationists need to be worried? a) What ts the unit rate of deer per square mile?
   b) What is the constant of proportionality?
   c) What is the meaning of the constant of proportionality in this problem?
   d) Use the unit rate of deer per square mile to determine how many deer are there for every 207 square miles.
   e) Use the unit rate to determine the number of square miles in which you would find 486 deer?
2. Suzette and Margo want to prepare crepes for all the students in their French class. A recipe males 20 crepes with a certain amount of flour, milk and 2 eggs. The girls know that they already have plenty of flour and milk but need to determine the number of eggs needed to make 50 crepes because they are not sure they have enough eggs for the recipe.
   a) Considering the amount of eggs necessary to make the crepes, what is the constant of proportionality?
   b) What does the constant of proportionality mean in the context of this problem?
   c) How many eggs will be needed for 50 crepes?
   d) What is anther name for the constant that relates the measures of two quantities?
   e) How is the Constant of Proportionality related to the unit rate?

Example of constant of proportionality word problem
David is making his own strawberry yogurt. In David’s mixture, the number of strawberries is proportional to the amount of milk, in cups. David uses 4 cups of milk for every 14 strawberries in his mixture. Which equation represents the relationship between s, the number of strawberries, and m, the number of cups of milk he uses?

How to find the Constant of Proportionality in a Table
Find the constant (k) in a directly proportional relationship is nearly identical to finding unit rate. Simple division/simplifying will get the job done.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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