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.