# Using the Language of Ratio

Students will use numbers, symbols and language to describe the relationship of the ratio between two quantities.

## Lesson Objective

The lesson is aligned to the Common Core State Standards for Mathematics – 6.RP.1 Ratios and Proportional Relationships – Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

## Materials Required

- 12 blocks of one color
- 12 blocks of another color
- (for example, 12 red blocks and 12 blue blocks)

## Lesson Procedure

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

Example

Place 3 red blocks on your desk.

Place 6 blue blocks on your desk.

The ratio of red blocks to blue blocks is 1 : 2, because for every 1 red block on your desk there are 2 blue blocks.* *

1. Show the ratio of 5 red blocks to 2 blue blocks.*2. *Write a description and an explanation for the ratio of 5 red blocks to 2 blue blocks.

3. There are 4 red blocks and 12 blue blocks. Write a description and an explanation for this ratio.

4. Write a ratio of red blocks to blue blocks for the following description of a ratio. For every 3 red blocks there are 4 blue blocks.

## Answers

- For every 5 red blocks, students should put 2 blue blocks on their desk. Students could put 10 red blocks and 4 blue blocks on their desk.
- The ratio of red blocks to blue blocks is 5:2, because for every 5 red blocks on my desk there are 2 blue blocks.
- The ratio of red blocks to blue blocks is 1:3, because for every 1 red block there are 3 blue blocks.
- 3:4

## Individual or Group Work

Use numbers and ratio language to describe and explain a ratio relationship between the two quantities.

- One bicycle seat to two bicycle wheels.
- In the farmyard, Jack saw cows. He saw four legs for every tail.
- For every car, there are 3 passengers.
- In the school election, for every 3 votes Emily received, Rose received 2 votes.
- On the farm, there are 8 wheels for every 1 truck.

Use numbers to write a ratio for each description of a ratio relationship between the two quantities.

- Three tricycle wheels to one tricycle seat.
- In the farmyard, Oliver saw chickens. He saw two legs for every beak.
- There are 8 passengers and 2 cars.
- In the school election, for every 5 votes Jasper received, Nick received 4 votes.

On the farm, there are 4 wheels for each tractor.

## Answers

- The ratio of 1 bicycle seat to 2 bicycle wheels is 1:2, because for every 1 bicycle seat there are 2 bicycle wheels.
- The ratio of 4 legs to 1 tail in the farmyard is 4:1, because for every 4 legs there is 1 tail.
- The ratio of 1 car to 3 passengers is 1:3, because for every 1 car there are 3 passengers.
- The ratio of 3 votes to 2 votes in the school election is 3:2, because for every 3 votes Emily received, Rose received 2 votes.
- The ratio of 8 wheels to 1 truck is 8:1, because there are 8 wheels for every 1 truck.
- 3:1
- 2:1
- 8:2 or 4:1
- 5:4
- 4:1

## Concluding Statement

Students should be able to use numbers, symbols and language to describe the relationship of the ratio between two quantities.