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Understanding Unit Rates: Per One and Rate Language

For every unit rate problem, include the 'per [unit]' label in your answer. Show the division you used to find the unit rate.

Grade 6·22 problems·~35 min·Common Core Math - Grade 6·standard·6-rp-a-2
Work through problems with immediate feedback
A

Recall / Warm-Up

1.

Which statement uses ratio language?

2.

A car travels 150 miles in 3 hours. Which expression gives the number of miles traveled per hour?

3.

Divide: 75 ÷ 15 = ?

B

Fluency Practice

1.

Which statement correctly uses rate language to describe the ratio 75:1575:15 (dollars to hamburgers)?

2.

Which statement uses correct rate language?

3.

A car travels 100 miles in 4 hours. What is the unit rate in miles per hour?

4.

A package of 8 granola bars costs $6. What is the price per bar?

A number line from 0 to 1 with tick marks at 0, 1/4, 1/2, 3/4, and 1, labeled with fraction values. Used as a reference scale for locating unit rates between 0 and 1.
5.

A recipe uses 3 cups of flour for every 4 cups of sugar. What is the unit rate of flour per cup of sugar?

C

Varied Practice

1.

What is the unit rate associated with the ratio 60:12 (miles:minutes)?

2.

A runner completes 5 miles in 2 hours. The unit rate is: 5÷2=___5 \div 2 = \_\_\_ miles   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   hour.

unit rate value:
rate word:
A two-row table prompting students to compare two different unit-rate questions from the same flour-to-sugar ratio.
3.

A recipe uses 3 cups of flour for 4 cups of sugar. A student says the unit rate is 43\frac{4}{3} cups of sugar per cup of flour. Another says it is 34\frac{3}{4} cups of flour per cup of sugar. Who is correct?

4.

A student says "the unit rate for 6:10 is 3:5 because I simplified the ratio." Explain the error: simplifying 6:10 to 3:5 gives a   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   , not a unit rate. The actual unit rate is 6÷10=___6 \div 10 = \_\_\_.

type of result:
unit rate value:
5.

The unit rate for distance driven is 45 miles per hour. How far does the car travel in 3 hours?

D

Word Problems

1.

Store A sells 5 oranges for $2.00. Store B sells 3 oranges for $1.29.

1.

What is the unit price (price per orange) at Store A?

2.

What is the unit price (price per orange) at Store B? Round to the nearest cent.

3.

Which store is the better deal?

2.

A recipe uses 3 cups of flour for every 4 cups of sugar. A baker wants to use 8 cups of sugar.

Complete the reasoning.
Unit rate =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   cup of flour per cup of sugar
Cups of flour needed for 8 cups of sugar =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  

unit rate:
cups of flour:
3.

A factory produces 420 items in 7 hours.

Complete the reasoning.
Unit rate =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   items per hour
Items produced in 10 hours =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  

unit rate:
items in 10 hours:
E

Error Analysis

1.

A recipe has a ratio of 3 cups of oats to 2 cups of raisins. Kai was asked: "What is the unit rate of oats per cup of raisins?" He answered: "2÷3=232 \div 3 = \frac{2}{3} cup of oats per cup of raisins."

What error did Kai make?

2.

Amara was asked to find the unit rate for the ratio 45 miles:15 minutes. She computed 45÷15=345 \div 15 = 3 and wrote: "The unit rate is 3."

What error did Amara make?

F

Challenge / Extension

1.

A recipe uses 23\frac{2}{3} cup of juice for every 45\frac{4}{5} cup of water. What is the unit rate of juice per cup of water?

2.

The ratio 3:4 has a unit rate of 34\frac{3}{4}.
Write an equivalent ratio that gives the same unit rate:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   :  ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  
Unit rate of your ratio:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  

first term:
second term:
unit rate:
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