# Ratios and Proportions / Building a Table of Ratios

Activity 3 of 15
Students generate equivalent ratios in a table, where values in each row of the table are a multiple of the values in the original ratio and that the entries in each column can be obtained by adding the original values in the ratio to the previous row.

## Planning and Resources

Objectives
Students should understand and be able to generalize strategies for finding equivalent ratios in a table. They understad the role of multiplication and addition in generating equivalent ratios.

Vocabulary
ratio
equivalent ratio

Standard:

## Lesson Snapshot

#### Understanding

Students should recognize that the rows (or columns) of a ratio table are some (positive rational) multiple of each other. This will be important when they begin to compare ratios.

### What to look for

Have students explain their strategies for solving problems involving equivalent ratios.

### Sample Assessment

If Sara used 3 cups of pancake mix to make 24 pancakes, how many cups would she need to make 40 pancakes?

Answer: 3:24 is equivalent to 1:8, which is equivalent to 5:40. So, the answer is 5 cups of pancake mix.

#### The Big Idea

Building tables of ratios illustrates that adding any two equivalent ratios produces another equivalent ratio.

### What are the students doing?

Students reason about the table of equivalent ratios by using both the visual images of the circles and squares and the numbers in the table.

### What is the teacher doing?

Remind students that to find equivalent ratios, they must multiply or divide both terms of the ratio by the same positive number.