# Using the Language of Rate

Students will use numbers, symbols, and language to describe a unit rate associated with a ratio and use rate language in the context of a ratio relationship.

## Lesson Objective

The lesson is aligned to the Common Core State Standards for Mathematics – 6.RP.2 Ratios and Proportional Relationships – Understand the concept of a unit rate *a*/*b* associated with a ratio *a*:*b* with *b not equal to *0, and use rate language in the context of a ratio relationship.

## Materials Required

- Calculator

## Lesson Procedure

**Using numbers, symbols and language to describe the relationship of the ratio between two quantities.**

Example

Oliver paid $56 for 7 pizzas.

Unit rate: The cost of one pizza was $8.

Ratio relationship: Oliver paid $6 for 7 pizzas, which was a rate of $8 per pizza.* *

* *

*1. *Brandon paid $24 for 8 drinks. What was the unit rate? Write a description of the ratio relationship.

*2. *Alison made lemonade. She used 2 cups of sugar and the juice from 6 lemons. Write a description of the ratio relationship.

3. Dylan wants to make cookies. The recipe says Dylan should use 3 cups of flour and 12 ounces of chocolate chips. Write a description of the ratio relationship.

4. Noah paid $16 for 4 hamburgers. What was the unit rate? Write a description of the ratio relationship.

## Answers

*1. The unit rate was $3 for one drink. *Brandon paid $24 for 8 drinks, which was a rate of $3 per drink.

*2. *Alison used 2 cups of sugar and the juice from 6 lemons, so she used 1/3 cup of sugar for each lemon.

3. The recipe has a ratio of 3 cups of flour to 12 ounces of chocolate chips, so there is 1 cup of flour to 4 ounces of chocolate chips.

4. The unit rate was $4 for one hamburger. Noah paid $16 for 4 hamburgers, which was a rate of $4 per hamburger.

## Individual or Group Work

Find the unit rate.

- A 16-ounce package of sausage costs $5.60. What is the cost of one ounce?
- A dozen (12) eggs cost $2.64. What is the cost of one egg?
- An 8-ounce package of cheese costs $2.96. What is the cost of one ounce?
- Four ears of corn costs $1. What is the cost of one ear of corn?
- A 6-ounce can of almonds costs $3. What is the cost of one ounce of almonds?

Use rate language to describe the ratio relationship between the two quantities.

*1. *Josh paid $28 for 4 tickets to the county fair.

*2. E*mily paid $6 for 12 tickets for rides at the county fair.

3. Jack bought 4 medium lemonades for $18.

4. Oliver paid $6 for 4 bags of popcorn.

## Answers

- The cost of one ounce of sausage is $0.35.
- The cost of one egg is $0.22.
- The cost of one ounce of cheese is $0.37.
- The cost of one ear of corn is $0.25.
- The cost of one ounce of almonds is $0.50.
- Josh paid $28 for 4 tickets to the county fair, so $7 was the cost of one ticket to the county fair.
- Emily paid $6 for 12 tickets for rides at the county fair, so $0.50 was the cost of one ticket.
- Jack bought 4 medium lemonade drinks and paid $18, so 1 lemonade drink cost $4.50.
- Oliver bought 4 bags of popcorn and paid $6, so 1 bag of popcorn cost $1.50.