6th Grade: Ratio and Rate Reasoning
What is the ratio of 3 blue marbles to 5 red marbles?
3:5
How many inches are in 5 feet?
60 inches
A lemonade recipe calls for 2 cups of sugar or every 5 cups of water. How much sugar is needed for 20 cups of water?
8 cups of sugar
What is the definition of a function?
A rule that assigns exactly one output to each input.
Find the slope of the line passing through (2, 4) and (5, 10).
6/3 = 2
A cell phone plan costs $25 per month plus $0.10 per text message. Write an equation to model this relationship.
y = 0.25 + 0.10x
A car travels 120 miles in 3 hours. What is its speed in miles per hour?
40 miles per hour
Convert 3 kilograms to grams.
3,000 grams
If 6 pencils cost $4.50, how much does 1 pencil cost?
$0.75
Is the relationship y=x2y = x^2y=x2 a function? Why or why not?
Yes, because each input has exactly one output.
Write the equation of a line with a slope of 3 passing through the origin.
y = 3x
The cost to print books is $100 plus $5 per book. What is the initial cost?
$100
Complete the table of equivalent ratios for 2:3:
| 2 | 4 | ? | 10 |
| 3 | ? | 9 | 15 |
6 and 12
A recipe calls for 2 liters of water. How many millimeters is this?
2,000 millimeters
A map has a scale of 1 inch = 10 miles. How many miles does 3.5 inches represent?
35 miles
What is the graph of a function with a constant output of 5?
A horizontal line at y=5y = 5y=5.
If the slope of a line is 4 and the y-intercept is -2, what is the equation of the line?
y=4x−2
A bike rental company charges $10 to rent a bike and $5 per hour. What is the total cost for 4 hours?
$30
Two bags of sugar weigh 6 pounds. What is the unit rate per bag?
3 pounds per bag
If there are 100 centimeters in a meter, how many meters are in 450 centimeters?
4.5 meters
A car uses 3 gallons of gas to travel 90 miles. How far can it travel on 5 gallons?
150 miles
True or False: All linear equations are functions.
False (e.g., x=3x = 3x=3 is not a function).
What is the slope of a line perpendicular to a line with a slope of 2/3?
-3/2
A car’s value decreases by $2,000 every year. If the initial value is $20,000, write the function to model this.
y=20000−2000x
If the ratio of students to teachers is 10:1, how many teachers are there for 50 students?
5 teachers
Convert 5.5 hours to minutes.
330 minutes
If a class of 24 students has 6 students wearing glasses, what fraction of the class wears glasses?
1/4
Which of the following is not a function:
y = 2x + 1, y = x^3, or x^2 + y^2 = 25
x^2 + y^2 = 25
If a line passes through (0, -5) and has a slope of -3, what is its equation?
y = -3x - 5
For the function y=3x+4y = 3x + 4y=3x+4, what is the rate of change and the initial value?
Rate of change: 3; Initial value: 4