Lesson 3: Equivalent Ratios

Getting Started

In the previous lesson, you used pictures to illustrate and understand ratios. In this lesson, you're going to use diagrams to understand equivalent ratios. Visual representations such as double number lines, tape diagrams, tables, and coordinate plane graphs can be used to represent both ratios and equivalent ratios and to solve problems involving ratios.

Stuff You Need

  • Interactive Notebook

Ideas to Think About

  • Why is it helpful to be able to represent ratios in different ways?
  • What are some tools that can help us to solve problems involving ratios?

Things to Know

  • A tape diagram is a visual tool that uses equal-sized rectangles to represent the parts of a ratio.
  • A double number line diagram is a visual tool that uses two parallel number lines to show equivalent ratios.
  • Tables and graphs are useful tools for finding multiple equivalent ratios.


  • Understand the concept of a ratio
  • Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations
  • Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane; use tables to compare ratios

Introducing the Lesson

In this lesson, your child will learn how to use tape diagrams, double number lines, and tables and graphs to understand and solve problems involving ratios and equivalent ratios.