Proportional Relationships in Tables

Proportional Relationships in Tables

Objective: Understand what a proportional relationship is and represent the relationship using a table of vales.

Multiple Select

Select all of the examples below that show proportional relationships between two ratios:

• $$\frac{1}{2}=\frac{4}{8}$$  

• $$\frac{1}{4}=\frac{2}{5}$$  

• $$\frac{1}{3}=\frac{3}{9}$$  

• $$\frac{0}{2}=\frac{5}{10}$$  

• $$\frac{4}{9}=\frac{8}{13}$$  

Multiple Choice

Which of the following tables of data do you think represents a proportional relationship?

What is a proportional relationship?

• A proportional relationship is a relationship in which the ratio between the two quantities is equivalent for all values.

• The table to the right represents a proportional relationship...

Open Ended

What do you notice about the table?

Write down at least two things that you notice in the table.

(Click to enlarge the picture if needed)

What is important to know about proportional relationships?

• They are represented by equivalent ratios between the input and output values.

• Can be used to calculate unit rate.

Open Ended

The table represents the distance in feet that a turtle travels over a certain number of minutes. How many feet would the turtle travel in 1 minute?

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Multiple Choice

Which table shows a proportional relationship?

(Click on the picture to enlarge it, if needed.)

• A

• B

• C

• D

Constant of Proportionality

• All proportional relationships have constant ratio, which is called the unit rate.

• ​

• ​In the table to the right, the unit rate can be found by dividing the distance by the time.

Multiple Choice

The table below represents the amount of money Junior earns mowing lawns during the summer. What is the unit rate between hours and money earned?

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• $3

• $4

• $2

• $9

Multiple Choice

Is the relationship between x and y proportional?

If so, what is the unit rate?

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• Yes;

  $$\frac{1}{3}$$  

• Yes; 

  3

• Yes; 

  5

• No