Intro to Non-Proportional Relationships

Intro to Non-Proportional Relationships

By Alexandra Barker

​Proportional Relationships

Before we look at non-proportional relationships, let's review proportional relationships.

​Example 1

Here's our first example:

​

Mrs. Sanchez makes $22.50/hour at her work.​

Multiple Choice

Mrs. Sanchez makes $22.50 per hour. How much money will she make after 0 hours of work?

• $22.50

• $0.00

• Not enough information.

Multiple Choice

Mrs. Sanchez makes $22.50 per hour. How much money will she make after 5 hours of work?

• $22.50

• $27.50

• $112.50

• $0.00

​Example 2

Here's our next example:

​

The table describes the distance (y) traveled by a cyclist in hours riding (x). 

Multiple Choice

The table describes the distance (y) traveled by a cyclist in hours riding (x). How far will the cyclist travel after 0 hours?

• 12 miles

• 0 miles

• Not enough information.

Multiple Choice

The table describes the distance (y) traveled by a cyclist in hours riding (x). How far will the cyclist travel after 3 hours?

• 12 miles

• 0 miles

• 36 miles

• 24 miles

Multiple Choice

The table describes the distance (y) traveled by a cyclist in hours riding (x). How far will the cyclist travel after 5 hours?

• 12 miles

• 48 miles

• 36 miles

• 60 miles

Multiple Choice

The table describes the distance (y) traveled by a cyclist in hours riding (x). How fast is the cyclist travelling?

• 12 miles

• 12 hours

• 12 miles per 1 hour

• 1 mile per 12 hours

​Example 3

Here's our next example:

​

The graph describes the money Mr. Mangham earns for each hour of work.

Fill in the Blank

The graph describes the money Mr. Mangham earns for each hour of work. How much money does he earn after working 0 hours?

Fill in the Blank

The graph describes the money Mr. Mangham earns for each hour of work. How much money does he earn after working 3 hours?

Fill in the Blank

The graph describes the money Mr. Mangham earns for each hour of work. How much money does he earn after working 5 hours?

Fill in the Blank

The graph describes the money Mr. Mangham earns for each hour of work. How much is he earning each hour?

Open Ended

What makes these relationships proportional?

Going Bowling

School is out for the winter break and Sammy and his friend Tommy are going bowling.  Tommy has his own shoes and does not need to rent any, but Sammy does need to rent.

What is the initial cost for Tommy?      

What is the initial cost for Sammy?

What is the rate charged per game?​

Draw

Fill in the table. Remember, Tommy has his own shoes, Sammy rents some for $2.00 and the games are $3.00 per game.

Draw

Fill in the graphs. Remember, Tommy has his own shoes, Sammy rents some for $2.00 and the games are $3.00 per game.

​Example 1

Mr. Sanchez is given $7 each day plus  $22.50/hour at his work. 

Multiple Choice

Mrs. Sanchez is given $7 each day plus  $22.50/hour at her work. How much money will she make after 0 hours of work?

• $22.50

• $0.00

• $7.00

• $29.50

Multiple Choice

Mrs. Sanchez is given $7 each day plus  $22.50/hour at her work. How much money will she make after 5 hours of work?

• $119.50

• $147.50

• $7.00

• $29.50

​Example 2

Here's our next example:

​

The table describes the distance (y) traveled by a cyclist in hours riding (x). 

Multiple Choice

The table describes the distance (y) traveled by a cyclist in hours riding (x). How far has the cyclist travelled after 0 hours?

• 25 miles

• 0 miles

• 35 miles

Multiple Choice

The table describes the distance (y) traveled by a cyclist in hours riding (x). How far has the cyclist travelled after 3 hours?

• 55 miles

• 25 miles

• 65 miles

Multiple Choice

The table describes the distance (y) traveled by a cyclist in hours riding (x). How far has the cyclist travelled after 5 hours?

• 45 miles

• 25 miles

• 75 miles

Multiple Choice

The table describes the distance (y) traveled by a cyclist in hours riding (x). How fast is the cyclist travelling?

• 35 miles per 1 hour

• 10 miles miles per 1 hour

• 25 miles per 1 hour

• 1 mile per 10 hours

​Example 3

Here's our next example:

​

The graph describes the money Mr. Mangham earns for each hour of work.

Fill in the Blank

The graph describes the money Mr. Mangham earns for each hour of work. How much money does he earn after working 0 hours?

Fill in the Blank

The graph describes the money Mr. Mangham earns for each hour of work. How much money does he earn after working 3 hours?

Fill in the Blank

The graph describes the money Mr. Mangham earns for each hour of work. How much money does he earn after working 3 hours?

Fill in the Blank

The graph describes the money Mr. Mangham earns for each hour of work. How much is he earning each hour?

Open Ended

What makes these examples different from the first examples?