Learn on PengiReveal Math, Course 1Module 7: Relationships Between Two Variables

7-4 Multiple Representations

In this Grade 6 lesson from Reveal Math Course 1, Module 7, students learn how to identify independent and dependent variables and use them to create multiple representations of a relationship, including equations, tables, and graphs. Using real-world scenarios like a car wash fundraiser and an online store, students practice writing linear equations such as t = 7c + 150, building corresponding input-output tables, and plotting ordered pairs on a coordinate graph. The lesson emphasizes how words, equations, tables, and graphs each describe the same relationship in different ways.

Section 1

Writing an Equation from a Word Problem

Property

To translate a real-world word problem into a two-variable equation, follow these steps:

  1. Identify the two changing quantities: Determine what the independent variable (input) and dependent variable (output) are.
  2. Define Variables: Choose letters to represent these two unknown quantities.
  3. Find the Rule: Identify the mathematical operation (addition, subtraction, multiplication, or division) that connects the two variables.
  4. Write the Equation: Assemble the variables and the rule into an equation showing how the output relates to the input.

Examples

  • Problem: A streaming service charges 8 dollars per month. What is the total cost for a certain number of months?
    • Variables: Let m represent the number of months (independent) and C represent the total cost (dependent).
    • Equation: C = 8m
  • Problem: A plant is currently 5 inches tall and grows 2 inches every week.
    • Variables: Let w represent the number of weeks (independent) and h represent the total height (dependent).
    • Equation: h = 5 + 2w

Book overview

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Module 7: Relationships Between Two Variables

  1. Lesson 1

    7-1 Relationships Between Two Variables

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  2. Lesson 2

    7-2 Write Equations to Represent Relationships Represented in Tables

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  3. Lesson 3

    7-3 Graphs of Relationships

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  4. Lesson 4Current

    7-4 Multiple Representations

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Lesson overview

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Section 1

Writing an Equation from a Word Problem

Property

To translate a real-world word problem into a two-variable equation, follow these steps:

  1. Identify the two changing quantities: Determine what the independent variable (input) and dependent variable (output) are.
  2. Define Variables: Choose letters to represent these two unknown quantities.
  3. Find the Rule: Identify the mathematical operation (addition, subtraction, multiplication, or division) that connects the two variables.
  4. Write the Equation: Assemble the variables and the rule into an equation showing how the output relates to the input.

Examples

  • Problem: A streaming service charges 8 dollars per month. What is the total cost for a certain number of months?
    • Variables: Let m represent the number of months (independent) and C represent the total cost (dependent).
    • Equation: C = 8m
  • Problem: A plant is currently 5 inches tall and grows 2 inches every week.
    • Variables: Let w represent the number of weeks (independent) and h represent the total height (dependent).
    • Equation: h = 5 + 2w

Book overview

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

Continue this chapter

Module 7: Relationships Between Two Variables

  1. Lesson 1

    7-1 Relationships Between Two Variables

    LearnPractice
  2. Lesson 2

    7-2 Write Equations to Represent Relationships Represented in Tables

    LearnPractice
  3. Lesson 3

    7-3 Graphs of Relationships

    LearnPractice
  4. Lesson 4Current

    7-4 Multiple Representations

    LearnPractice