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:

  1. Multiplication or Division: Multiply or divide both quantities in a ratio by the same non-zero number, cc.
a:b(ac):(bc)a:b \rightarrow (a \cdot c) : (b \cdot c)
  1. 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)(x, y).

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 5: Understand and Use Ratio and Rate

  1. Lesson 1

    Lesson 1: Understand Ratios

  2. Lesson 2

    Lesson 2: Generate Equivalent Ratios

  3. Lesson 3

    Lesson 3: Compare Ratios

  4. Lesson 4Current

    Lesson 4: Represent and Graph Ratios

  5. Lesson 5

    Lesson 5: Understand Rates and Unit Rates

  6. Lesson 6

    Lesson 6: Compare Unit Rates

  7. Lesson 7

    Lesson 7: Solve Unit Rate Problems

  8. Lesson 8

    Lesson 8: Ratio Reasoning: Convert Customary Units

  9. Lesson 9

    Lesson 9: Ratio Reasoning: Convert Metric Units

  10. Lesson 10

    Lesson 10: Relate Customary and Metric Units

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Additive and Multiplicative Structures of Ratios

Property

You can generate equivalent ratios using two primary methods:

  1. Multiplication or Division: Multiply or divide both quantities in a ratio by the same non-zero number, cc.
a:b(ac):(bc)a:b \rightarrow (a \cdot c) : (b \cdot c)
  1. 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)(x, y).

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 5: Understand and Use Ratio and Rate

  1. Lesson 1

    Lesson 1: Understand Ratios

  2. Lesson 2

    Lesson 2: Generate Equivalent Ratios

  3. Lesson 3

    Lesson 3: Compare Ratios

  4. Lesson 4Current

    Lesson 4: Represent and Graph Ratios

  5. Lesson 5

    Lesson 5: Understand Rates and Unit Rates

  6. Lesson 6

    Lesson 6: Compare Unit Rates

  7. Lesson 7

    Lesson 7: Solve Unit Rate Problems

  8. Lesson 8

    Lesson 8: Ratio Reasoning: Convert Customary Units

  9. Lesson 9

    Lesson 9: Ratio Reasoning: Convert Metric Units

  10. Lesson 10

    Lesson 10: Relate Customary and Metric Units