Solving Proportions & Proportional Relationships

Introduction

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As a hook, ask students why it is important to understand and solve proportions in real-life situations. Refer to the last page of the guided notes as well as the FAQs below for ideas.

Use the first page of the guided notes to introduce the concept of solving proportions using cross multiplication. Walk through the steps of cross multiplication and explain how it can be used to solve proportions. Emphasize the importance of setting up the proportion correctly and cross multiplying, then isolating the variable to find the missing value.

Based on student responses, reteach the concept of cross multiplication and solving proportions if needed. Provide additional examples and guide students through the process until they can confidently solve proportions using cross multiplication.

Practice

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Have students practice solving proportions using cross multiplication using the practice worksheets provided in the resource. Students can practice using page 2 (word problems) and page 3 (maze activity). Walk around the classroom to answer any questions students may have.

Fast finishers can dive into page 4 (color by number activity) for extra practice. You can assign it as homework for the remainder of the class.

Real-Life Application

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Use the last page of the guided notes (real life applications) to bring the class back together, and introduce the concept of real-life applications of solving proportions and proportional relationships. Explain to the students that proportions can be used to solve a variety of real-world problems, where there is a direct relationship between two quantities.

Examples of real-life applications of proportion include:

• Cooking: Proportions are frequently used in cooking to adjust recipes to make different serving sizes. For instance, if a recipe serves 4 people and you need to serve 8 people, the ingredients for the recipe can be doubled using proportion.
• Scaling: Proportions are used in scaling objects, such as maps, blueprints, or models. For example, if you have a blueprint of a house and you need to build a larger model, you can use proportions to scale up the dimensions.
• Similar Figures: Proportions are used in geometry to compare the sizes of similar figures. For instance, if you have two similar triangles and you know the measures of one pair of corresponding sides, you can set up a proportion to find the measures of the other pair of corresponding sides.

These are just a few examples of real-life applications of solving proportions and proportional relationships. Refer to the FAQ for more ideas on how to teach it!

Additional Self-Checking Digital Practice

If you’re looking for digital practice for solving proportions and proportional relationships, 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 a few activities to explore:

• Solving Proportions Digital Pixel Art | Proportional Relationships Pixel Art Google Sheets
• Constant of Proportionality Pixel Art Google Sheets

Additional Print Practice

A fun, no-prep way to practice solving proportions and proportional relationships is Doodle Math — they’re a fresh take on color by number or color by code. It includes multiple levels of practice, perfect for a review day or sub plan.

Here are a few activities to try:

• Constant of Proportionality Doodle Math [Christmas Themed]
• Constant of Proportionality Doodle Math [Thanksgiving]

Real-Life Math Project

A fun way to wrap this lesson with your students is with one of my real-life math projects. They enable students to see the application of the math in an engaging, extended project:

• Scale Drawings Scale Factors Minecraft Inspired Project

This activity is NOT AN OFFICIAL MINECRAFT PRODUCT. NOT APPROVED BY OR ASSOCIATED WITH MOJANG.