Learn on PengienVision, Mathematics, Grade 6Chapter 5: Understand and Use Ratio and Rate

Lesson 4: Represent and Graph Ratios

In this Grade 6 lesson from enVision Mathematics Chapter 5, students learn how to represent equivalent ratios using ratio tables and coordinate graphs. They practice plotting ordered pairs derived from ratio relationships, using both repeated addition and proportional reasoning to extend ratios and solve problems. Students also discover that points representing equivalent ratios always form a straight line on a coordinate plane, connecting the concept to real-world contexts like pricing and recipes.

Section 1

Additive and Multiplicative Structures of Ratios

Property

You can generate equivalent ratios using two primary methods:

Multiplication or Division: Multiply or divide both quantities in a ratio by the same non-zero number, $c$ .

a:b \rightarrow (a \cdot c) : (b \cdot c)

Repeated Addition: Add the quantities of the original ratio to the previous ratio to generate a sequence.

Section 2

Representing Ratios as Ordered Pairs

Property

A set of equivalent ratios can be organized in a ratio table. Each row in the table represents a pair of corresponding values, which can be written as an ordered pair $(x, y)$ .

Examples

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Additive and Multiplicative Structures of Ratios

Property

You can generate equivalent ratios using two primary methods:

Multiplication or Division: Multiply or divide both quantities in a ratio by the same non-zero number, $c$ .

a:b \rightarrow (a \cdot c) : (b \cdot c)

Repeated Addition: Add the quantities of the original ratio to the previous ratio to generate a sequence.

Section 2

Representing Ratios as Ordered Pairs

Property

A set of equivalent ratios can be organized in a ratio table. Each row in the table represents a pair of corresponding values, which can be written as an ordered pair $(x, y)$ .