Lesson 5Two Equations for Each Relationship
Learning Goal
Let’s investigate the equations that represent proportional relationships.
Learning Targets
I can find two constants of proportionality for a proportional relationship.
I can write two equations representing a proportional relationship described by a table or story.
Lesson Terms
- constant of proportionality
- proportional relationship
Warm Up: Missing Figures
Problem 1
Here are the second and fourth figures in a pattern.
What do you think the first and third figures in the pattern look like?
Describe the 10th figure in the pattern.
Activity 1: Meters and Centimeters
Problem 1
There are 100 centimeters (cm) in every meter (m).
Complete each of the tables.
Tables:
length (m)
length (cm)
length (cm)
length (m)
For each table, find the constant of proportionality.
What is the relationship between these constants of proportionality?
For each table, write an equation for the proportional relationship. Let
represent a length measured in meters and represent the same length measured in centimeters.
Are you ready for more?
Problem 1
How many cubic centimeters are there in a cubic meter?
Problem 2
How do you convert cubic centimeters to cubic meters?
Problem 3
How do you convert the other way?
Activity 2: Filling a Water Cooler
Problem 1
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
Which of the following equations represent the relationship between
and ? Select all that apply. What does 1.6 tell you about the situation?
What does 0.625 tell you about the situation?
Priya changed the rate at which water flowed through the faucet. Write an equation that represents the relationship of
and when it takes 3 minutes to fill the cooler with 1 gallon of water. Was the cooler filling faster before or after Priya changed the rate of water flow? Explain how you know.
Activity 3: Feeding Shrimp
Problem 1
At an aquarium, a shrimp is fed
How much food does a shrimp get fed in one day?
Complete the table to show how many grams of food the shrimp is fed over different numbers of days.
number of days
food in grams
What is the constant of proportionality? What does it tell us about the situation?
If we switched the columns in the table, what would be the constant of proportionality? Explain your reasoning.
Use
for number of days and for amount of food in grams that a shrimp eats to write two equations that represent the relationship between and . If a tank has 10 shrimp in it, how much food is added to the tank each day?
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.
Lesson Summary
If Kiran rode his bike at a constant 10 miles per hour, his distance in miles,
We can rewrite the equation:
When two quantities