Objective

I understand the terms proportional relationship and constant of proportionality.

I can use a table to reason about two quantities that are in a proportional relationship.

Online Workbook

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Lesson Summary

If the ratios between two corresponding quantities are always equivalent, the relationship between the quantities is called a proportional relationship.

This table shows different amounts of milk and chocolate syrup. The ingredients in each row, when mixed together, would make a different total amount of chocolate milk, but these mixtures would all taste the same.

Notice that each row in the table shows a ratio of tablespoons of chocolate syrup to cups of milk that is equivalent to 4:1.

About the relationship between these quantities, we could say:

tablespoons of chocolate syrup	cups of milk
4	1
6	$1 \frac{1}{2}$
8	2
$\frac{1}{2}$	18
12	3
1	14

The relationship between amount of chocolate syrup and amount of milk is proportional.
The relationship between the amount of chocolate syrup and the amount of milk is a proportional relationship.
The table represents a proportional relationship between the amount of chocolate syrup and amount of milk.
The amount of milk is proportional to the amount of chocolate syrup.

We could multiply any value in the chocolate syrup column by $\frac{1}{4}$ to get the value in the milk column. We might call $\frac{1}{4}$ a unit rate, because $\frac{1}{4}$ cups of milk are needed for 1 tablespoon of chocolate syrup. We also say that $\frac{1}{4}$ is the constant of proportionality for this relationship. It tells us how many cups of milk we would need to mix with 1 tablespoon of chocolate syrup.

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