# Revisiting Proportional Relationships

Warmup

Activity #1

Find Relationship Between two Changing Quantities.

• Keep the slider at 7 and select three costs from the table.
• Divide them by their corresponding quantities. ​
• Change the slider to a different number and select three costs from the table.
• Divide them by their corresponding quantities.

(1.) What number on the slider did you choose?

(2.) What number did you get? ​

(3.) Describe the relationship between the quantity and the cost based on the “constant of proportionality. ​

(4.) Describe the relationship between the “constant of proportionality” and the graph.

Activity #2

Complete a Table of Proportional Relationships.

Tyler swims at a constant speed, 5 meters every 4 seconds.

• Record your answer in the table below to show how long it take him to swim 114 meters.

Write an equation to represent the proportional relationship above.

A factory produces 3 bottles of sparkling water for every 8 bottles of plain water.

• Complete the table below based on this information.

(1.) How many bottles of sparkling water does the company produce when it produces 600 bottles of plain water?

(2.) Write an equation to represent the proportional relationship above.

Activity #3

Exercise Questions.

A recipe calls for 1/2 cup sugar and 1 cup flour.

• Complete the table below to show how much sugar and flour to use in different numbers of batches of the recipe.

An airplane is flying from New York City to Los Angeles. The distance it travels in miles, d, is related to the time in seconds, t .. ., by the equation d = 0.15t.

(1.) How fast is it flying? Be sure to include the units.

(2.) How far will it travel in 30 seconds?

(3.) How long will it take to go 12.75 miles?

Challenge #1

Two students are solving the same problem: At a hardware store, they can cut a length of rope off of a big roll, so you can buy any length you like. The cost for 6 feet of rope is £7.50. How much would you pay for 50 feet of rope, at this rate?

Kiran knows he can solve the problem this way:

(1). What would be Kiran’s answer?

Kiran wants to know if there is a more efficient way of solving the problem. Priya says she can solve the problem with only 2 rows in the table.

(2). What do you think Priya’s method is?

Challenge #2

Different nerve signals travel at different speeds.

• Pressure and touch signals travel about 250 feet per second.
• Dull pain signals travel about 2 feet per second.

(1.) How long does it take you to feel an ant crawling on your foot?

(2.) How much longer does it take to feel a dull ache in your foot?

Challenge #3

A grocer can buy strawberries for \$1.38 per pound.

(1.) Write an equation relating c, the cost, and  p, the pounds of strawberries.

(2.) A strawberry order cost \$241.50. How many pounds did the grocer order?

Quiz Time