Lesson 3Revisiting Proportional Relationships
Learning Goal
Let’s use constants of proportionality to solve more problems.
Learning Targets
I can use a table with 2 rows and 2 columns to find an unknown value in a proportional relationship.
When there is a constant rate, I can identify the two quantities that are in a proportional relationship.
Lesson Terms
- percentage
- unit rate
Warm Up: Recipe Ratios
Problem 1
A recipe calls for
sugar (cups) | flour (cups) |
---|---|
Activity 1: The Price of Rope
Problem 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.
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.
length of rope (feet)
price of rope (dollars)
What do you think Priya’s method is?
Activity 2: Swimming, Manufacturing, and Painting
Problem 1
Tyler swims at a constant speed, 5 meters every 4 seconds. How long does it take him to swim 114 meters?
distance (meters) | time (seconds) |
---|---|
Problem 2
A factory produces 3 bottles of sparkling water for every 8 bottles of plain water. How many bottles of sparkling water does the company produce when it produces 600 bottles of plain water?
number of bottles | number of bottles |
---|---|
Problem 3
A certain shade of light blue paint is made by mixing
Problem 4
For each of the previous three situations, write an equation to represent the proportional relationship.
Are you ready for more?
Problem 1
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.
How long does it take you to feel an ant crawling on your foot?
How much longer does it take to feel a dull ache in your foot?
Activity 3: Finishing the Race and More Orange Juice
Problem 1
Lin runs
Problem 2
Priya mixes
Lesson Summary
If we identify two quantities in a problem and one is proportional to the other, then we can calculate the constant of proportionality and use it to answer other questions about the situation. For example, Andre runs at a constant speed, 5 meters every 2 seconds. How long does it take him to run 91 meters at this rate?
In this problem there are two quantities, time (in seconds) and distance (in meters). Since Andre is running at a constant speed, time is proportional to distance. We can make a table with distance and time as column headers and fill in the given information.
distance (meters) | time (seconds) |
---|---|
To find the value in the right column, we multiply the value in the left column by
At this rate, it would take Andre