Graphing and Interpreting Graphs of Proportional Relationships

Graphing and Interpreting Graphs of Proportional Relationships
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Overview

Ever wondered how to teach proportional relationships in an engaging way to your 7th and 8th grade students?

In this lesson plan, students will learn about representing proportional relationships through graphs and equations and explore their real-life applications. Then, they will also practice interpreting graphs of proportional relationships and understanding what the points represent in the context of the problem. Through artistic and interactive guided notes, checks for understanding, practice activities including a doodle & color by number worksheet, and a maze worksheet, students will gain a comprehensive understanding of proportional relationships.

The lesson culminates with a real-life application example that explores how proportional relationships are used in a practical context. Students will learn how to apply their knowledge of proportional relationships to solve real-world problems.

Get the Lesson Materials

Represent Proportional Relationships Graphs & Equations Guided Notes w/ Doodles

Represent Proportional Relationships Graphs & Equations Guided Notes w/ Doodles

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Learning Objectives

After this lesson, students will be able to:

  • Represent proportional relationships using graphs and equations
  • Interpret graphs and equations of proportional relationships
  • Calculate the constant of proportionality from a graph or equation
  • Calculate unit rates from a graph or equation
  • Explain the meaning of a point on the graph of a proportional relationship in terms of the situation
  • Explain how graphing proportional relationships is useful in real life


Prerequisites

Before this lesson, students should be familiar with:

  • How to plot points on a coordinate plane
  • Basic algebraic skills, including operations with decimals and whole numbers


Materials

Key Vocabulary

  • Proportional relationship
  • Constant of proportionality
  • Unit rate


Procedure

Introduction

Proportional Relationships Equations, Graphs, Constant of Proportionality Guided Notes Image Introduction
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As a hook, ask students why understanding proportional relationships is important in real life. You can provide examples such as determining the amount of time it takes to complete a task, or comparing prices at the grocery store. Refer to the last page of the guided notes as well as the FAQs below for more ideas.

Use the first page of the guided notes to introduce the concept of representing proportional relationships with graphs and equations. Walk through the key points such as understanding what each point on the graph represents in terms of the situation, how to calculate the constant of proportionality & unit rate, and how to construct equations based on the constant of proportionality. You can model using the example of Charlie in space, as shown in the guided notes (page 1).

Based on student responses and understanding, reteach any concepts that students need extra help with. Then, have the students move onto the next page of guided notes (page 2) to practice constructing equations, graphing, interpreting graphs of proportional relationships. If your class has a wide range of proficiency levels, you can pull out students for reteaching, while more advanced students can work on the practice exercises independently.

Practice

Proportional Relationships Equations, Graphs, Constant of Proportionality Guided Notes Image Practice
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Have students practice graphing proportional relationships, interpreting graphs, and constructing equations using the maze activity (page 3), and color by number activity (page 4). Students will also be asked to solve for constant of proportionality in the practice. Walk around to answer student questions. You can also assign it as homework.

Real-Life Application

Proportional Relationships Equations, Graphs, Constant of Proportionality Guided Notes Image Real Life Applications
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Use the last page of the guided notes (page 5) to bring the class back together, and introduce the concept of real-world application of proportional relationships. Explain to students that proportional relationships can be found in various real-life situations. These situations involve two quantities that change together at a constant rate or ratio.

Give examples of real-world scenarios where proportional relationships can be observed, such as:

  1. Distance and Time: Discuss how the distance travelled is directly proportional to the time spent on the road.
  2. Job Wages: Explain how some jobs pay employees based on the number of hours they work. For example, if a person earns $18 per hour, the amount of money they earn is directly proportional to the number of hours they work. As the number of hours worked increases, their earnings also increase.
  3. Recipes: Share how recipes often require proportional measurements of ingredients. For example, if a recipe calls for 2 cups of flour and 1 cup of sugar, the ratio between flour and sugar remains constant even if the total amount of ingredients increases or decreases.

Ask students if they can think of any other real-life situations that involve proportional relationships. Encourage them to share their ideas with the class.

Refer to the FAQ section in the resource for more ideas on how to teach real-life applications of proportional relationships.

Extensions

Additional Self-Checking Digital Practice

If you’re looking for digital practice for Representing Proportional Relationships Graphs & Equations, try my Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun, and a powerful tool for differentiation.

Here are some activities to explore:

Additional Print Practice

A fun, no-prep way to practice Representing Proportional Relationships Graphs & Equations is Doodle Math — they’re a fresh take on color by number or color by code. It includes multiple levels levels of practice, perfect for a review day or sub plan.

Here are some activities to try:


FAQs

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