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Introduction to ratio and proportion

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📖Standard

CCSS.MATH.CONTENT.7.RP.A.1 Analyze proportional relationships and use them to solve real-world and mathematical problems.

⏰Time Required

30 minutes

📲Technology Required

Projector or smart board for in–class or access to computer or tablet for web meeting for remote learning. Presentation could be printed for students at home without computer access.

📃Lesson Summary

Students are presented with definitions of ratio and proportion along with multiple examples and ways to solve these problems.

📚Lesson

Introduce ratios and proportions

Use the Google slides presentation for definition of ratio and proportion and some practice problems.

NOTE TO TEACHER: This presentation includes multiple explanations for multiple levels of understanding. There is a solution using algebra, with cross-multiplication and an explanation of why cross-multiplication works. There is also an explanation using equivalent fractions. If you are teaching an algebra class, use the first explanation and delete the second. For a more basic math class, delete the first explanation and just use equivalent fractions.

Use ratio and proportion in real life

The end of the presentation gives a recipe for biscuits. You can delete the answer in slide 29 if you want to test their knowledge or you can leave it in for students to check themselves.

Here are three ways you can use this:

  • Have students actually bake using their recipe solution.
  • Have students simply answer the question (easiest)
  • Select one or more incorrect answers as well as the correct answer and bake yourself. Then bring the results in and have students taste them. This takes more work from the teacher but can be pretty hilarious if you feel in a baking mood or can get a volunteer to do it.

Assessment

Assessment can be done as a group, having students answer the questions posed in the presentation or students can submit answers individually.

Related lesson

Ratios as fractions is a nine-minute video that can be used to preview this material or for re-teaching for those students who are still struggling.

Rates, Ratios and Proportions with Fractions

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📖STANDARDS

CCSS.MATH.CONTENT.7.RP.A.1 Compute unit rates, including those that involve complex fractions, with like or different units.

CCSS.MATH.CONTENT.7.RP.A.2.C. Represent proportional relationships by equations

⏰Time Required

30-45 minutes

📲Technology Required

Projector and computer required to watch video in class. Alternatively, students can be assigned to watch on computer, phone or tablet at home. Google apps or PowerPoint required for slide presentation.

📃Lesson Summary

Students watch a 4-minute video giving examples of finding unit rates by simplifying fractions. They solve a problem together as a class and are given a short lecture on solving rate problems with complex fractions. Problems provided can be worked by students individually or done together in class.

📚Lesson Plan

This lesson plan assumes that your students understand simplifying complex fractions. They should know how to divide a fraction by an integer or by another fraction.

1. Watch video explaining unit rates

2. Solve a problem as a class

Using this Google slides presentation, students solve a problem together as a class. They are reminded the meaning of “reciprocal” and that in dividing one fraction by another, you multiply by the reciprocal of the fraction in the denominator. Additional slides give students instruction and tips on solving rates problems that include complex fractions.

3. Solve a variety of problems involving rates and complex fractions

The problem set is found here and the answer key with problems solved step–by-step is here. You know your class best. If you have already covered complex fractions and rate problems, these can be used as formative assessment or review. Alternatively, you may wish to either:

  • Assign the problems, have the students give these a try and then correct together as a class.
  • Select some of the problems to review together and assign the remainder as homework.
  • Assign the problems for students to complete individually, as either in-class work or homework and grade using the answer key provided.

4. Watch a video of a student applying ratio and proportion

At this point, many students will still need further clarification. In this video, Eva shows how she uses ratio and proportion to reduce a recipe for 4 dozen cookies to one for 2 dozen cookies.

Assessment

Students will be assessed based on performance on the problems provided.

State Standards

Missouri Learning Standard 7.RP.A.1

Minnesota Math Standard 7.2.2.1 – Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations.