# ﻿Two Equations for Each Relationship

Warmup

Here are the second and fourth figures in a pattern.

(1.) What do you think the first and third figures in the pattern look like?

(2.) Describe the 10th figure in the pattern.

Activity #1

Complete a Table of Proportional Values. There are 100 centimeters (cm) in every meter (m).

• Complete the table below.

There are 100 centimeters (cm) in every meter (m).

• Complete the table below.

(1.) For each table above, find the constant of proportionality.

(2.) What is the relationship between these constants of proportionality?

(3.) For each table, write an equation for the proportional relationship. Let x represent a length measured in meters and y represent the same length measured in centimeters.

(4.) Compare the two equations you wrote for the two different tables. What do you notice?

(5.) How many cubic centimeters are there in a cubic meter?

(6.) How do you convert cubic centimeters to cubic meters?

(7.) How do you convert cubic meters to cubic centimeters?

Activity #2

Interprete a Table of Proportional Values. It took Priya 5 minutes to fill a cooler with 8 gallons of water from a faucet that was flowing at a steady rate. Let w be the number of gallons of water in the cooler after t  minutes.

(2.) What does 1.6 tell you about the situation?

(3.) What does 0.625 tell you about the situation?

(4.) Priya changed the rate at which water flowed through the faucet. Write an equation that represents the relationship of  w and t  when it takes 3 minutes to fill the cooler with 1 gallon of water.

(5.) Was the cooler filling faster before or after Priya changed the rate of water flow? Explain how you know.

Activity #3

Solve Problems on Proportional Relationships. At an aquarium, a shrimp is fed gram of food each feeding and is fed 3 times each day.

• Complete the table to show how many grams of food the shrimp is fed over different numbers of days.

(1.) What is the constant of proportionality? What does it tell us about the situation?

(2.) If we switched the columns in the table, what would be the constant of proportionality? Explainyour reasoning.

(3.) Use d  for number of days and  f for amount of food in grams that a shrimp eats to write two equations that represent the relationship between d and f.

(4.) If a tank has 10 shrimp in it, how much food is added to the tank each day?

(5.) If the aquarium manager has 300 grams of shrimp food for this tank of 10 shrimp, how many days will it last? Explain or show your reasoning.

Challenge #1

The table below represents a proportional relationship.

(1.) constant of proportionality: __________

(2.) Equation: = ________

Challenge #2

The table below represents the relationship between a length measured in meters and the same length measured in kilometers.

(1.) Complete the table.

(2.) Write an equation for converting the number of meters to kilometers. Use for number of meters and for number of kilometers.

Challenge #3

On a map of Chicago, 1 cm represents 100 m. Select all statements that express the same scale.

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