In this lesson students are given definitions of ratio and rate and examples of computing rate and distance. Students complete a short assignment using animals observed outdoors as the data for computing ratio, rate and proportion. An alternative assignment is given for students learning at home or otherwise requiring modification. The lesson concludes with game play.
Begin with this Google slides presentation defining ratio and rate and including examples of rate and distance problems. Students learning at home can read the presentation and do the activities and problems on their own.
If your students are having difficulty understanding the problems, this video may help.
Compute rate, ratio and proportion
In this short assignment, also linked in the Google slides presentation, using animals observed outdoors as the data for computing ratio, rate and proportion.
Everyone needs to get a partner. You and your partner will go outside and each count as many different species of animals as you can. Do this for exactly 5 minutes. Two of the exact same kind of animal only count as one species.
After 5 minutes is up, find the ratio of your animals compared to your partner’s list of animals.
Next, find the rate. How many animals did you see per minute?
Lastly, your group shall compare your ratio to another group. Are they proportional or non-proportional?
An alternative assignment is given for students learning at home or otherwise unable to work outside with a partner, where students find animals in two slides.
End with a game
Students play AzTech games for 15 minutes to end the lesson. Time-rate-distance problems are included as a bonus question in AzTech: The Story Begins and are required to win the game in AzTech: Meet the Maya.
Once students have played the game, you can look in the AzTech teacher reports to see an individual students response. You will need to know your students’ usernames. To see an example of a report, enter the username “ddtester” .
Projector or smart board for in–class or access to computer or tablet for web meeting for remote learning.
Students are presented with definitions of ratio and proportion along with multiple examples and ways to solve these problems.
Watch the video Ratios and Rates below, which discusses ratios and fractions.
Yes, this lesson plan is just a video. We watched LOTS of boring videos on ratios and rates to find this one!
This video can be used before or after the lesson on Introduction to Ratio and Proportion, either as an introduction for students who need more preparation or a second look for students who could benefit from having the material presented in a different way.
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 can be done as a group, having students answer the questions posed in the presentation or students can submit answers individually.
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.
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
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.
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.
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
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.
Students will be assessed based on performance on the problems provided.
Missouri Learning Standard 7.RP.A.1
Minnesota Math Standard 22.214.171.124 – 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.