Lesson 3More About Constant of Proportionality
Learning Goal
Let’s solve more problems involving proportional relationships using tables.
Learning Targets
I can find missing information in a proportional relationship using a table.
I can find the constant of proportionality from information given in a table.
Lesson Terms
- constant of proportionality
- equivalent ratios
- proportional relationship
- ratio
Warm Up: Equal Measures
Problem 1
Use the numbers and units from the list to find as many equivalent measurements as you can. For example, you might write “30 minutes is
You can use the numbers and units more than once.
1
12
0.4
60
50
40
0.01
30
0.3
24
6
2
centimeter
meter
hour
feet
minute
inch
Activity 1: Centimeters and Millimeters
There is a proportional relationship between any length measured in centimeters and the same length measured in millimeters.
There are two ways of thinking about this proportional relationship.
Problem 1
If you know the length of something in centimeters, you can calculate its length in millimeters.
Complete the table.
length (cm)
length (mm)
What is the constant of proportionality?
Problem 2
If you know the length of something in millimeters, you can calculate its length in centimeters.
Complete the table.
length (mm)
length (cm)
What is the constant of proportionality?
Problem 3
How are these two constants of proportionality related to each other?
Problem 4
To convert from centimeters to millimeters, you can multiply by .
To convert from millimeters to centimeters, you can divide by or multiply by .
Are you ready for more?
Problem 1
How many square millimeters are there in a square centimeter?
Problem 2
How do you convert square centimeters to square millimeters? How do you convert the other way?
Activity 2: Pittsburgh to Phoenix
Problem 1
On its way from New York to San Diego, a plane flew over Pittsburgh, Saint Louis, Albuquerque, and Phoenix traveling at a constant speed.
Complete the table as you answer the questions. Be prepared to explain your reasoning.
segment | time | distance | speed |
---|---|---|---|
Pittsburgh to Saint Louis | |||
Saint Louis to Albuquerque | |||
Albuquerque to Phoenix |
What is the distance between Saint Louis and Albuquerque?
How many minutes did it take to fly between Albuquerque and Phoenix?
What is the proportional relationship represented by this table?
Diego says the constant of proportionality is 550. Andre says the constant of proportionality is
. Do you agree with either of them? Explain your reasoning.
Lesson Summary
When something is traveling at a constant speed, there is a proportional relationship between the time it takes and the distance traveled. The table shows the distance traveled and elapsed time for a bug crawling on a sidewalk.
We can multiply any number in the first column by
This table represents the same situation, except the columns are switched.
We can multiply any number in the first column by
Notice that