Proportional Reasoning
Proportional Relationships
Constant of Proportionality and Equations
Context
Random
100
A punch recipe calls for 2 cups of juice and 1 cup of Ginger Ale.
How many cups of juice would you need if you use 7 cups of Ginger Ale?
14 cups of juice
100
What two things need to be true for a graph to be proportional?
Goes through the origin 0,0 and is a straight line
100
What is the constant of proportionality in the following equation? y=143x
143
100
What is Ms. Portlock's Favorite Drink to Start Her Morning?
Celsius.
100
A triangle has angles of 62° and 88°.
What is the measure of the third angle?
30°
200
You can pay $15 to ride a Lime Scooter for 4 minutes.
How much does it cost to ride a Lime Scooter for 1 minute?
$3.75
200
Is this a proportional relationship? If yes, what is the constant of proportionality? If no, why not?
No because the ratio of y to x is not constant
200
Write an equation with the constant of proportionality 3.2
y=3.2x
200
What does the point (0,20) mean in this problem?
You have to pay $20 to get into the theme park. Perhaps parking?
200
What is the constant of proportionality?
2 miles per hour
300
Are the following ratios proportional to each other?
10 boys to 12 girls in class. 25 boys to 30 girls in the school.
Yes
300
Which graph is proportional?
300
Find the constant of proportionality for the following table and use it to write an equation for the table.
y=3x
300
What does the point (4,2) represent in this problem?
For every 4 shirts sold, 2 dollars are kept as profit.
300
Is the following equation proportional? Why or why not?
y=5+3x
No, it cannot be written in the form y=kx
400
Ms. Portlock LOVES to sew. She can make 2 shirts in 15 days. How long will it take her to make 200 shirts?
1,500 days.
400
Is the following table proportional?
If not, why not?
If yes, what is the constant of proportionality?
Yes, the constant of proportionality is 1/2
400
Write an equation for this graph with m for miles and h for hours.
m=2h
OR
h=1/2m
400
Find the constant of proportionality AND write an equation for this graph.
Last - find the missing value of y.
k = 4
y = 4x
y = 4*5 = 20
400
What is the constant of proportionality of water used per minute?
5 gallons per minute
500
If 5 Mr. Beast Burgers cost $30, how much will 12 Mr. Beast Burgers cost?
$72
500
Which machine has a proportional relationship with the time in minutes and what is its constant of proportionality?
Machine Q and a constant of proportionality of 6
500
Find the constant of proportionality AND write an equation for this graph.
k = 1/2
y = 1/2x
500
Ms. Portlock eats 14 burritos every 4 minutes. Write an equation relating the burritos eaten, b, and the amount of minutes, m.
b=3.5m b=7/2m
OR
m=2/7b
500
Ms. Weber pays $10 for 12 eggs and Ms. Portlock paid $4.50 for 6 eggs. Find how much each person paid per egg and determine who got the better deal.
Ms. Weber paid $0.83 per egg and Ms. Portlock paid $0.75 per egg. Ms. Portlock got the better deal.