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# Lesson Plan

Algebra: Olympic Races
 Subject: Math Grade span: 6 to 8 Duration: 45 minutes (can be ongoing)
This lesson was excerpted from the Afterschool Training Toolkit under the promising practice: Finding Math

Description:

This sample lesson is one example of how you can implement the Finding Math practice. In this activity, students examine Olympic athlete profiles and use algebra skills to calculate average speed and calories burned per minute in given events.

Learning Goals:

• Understand a calorie as a unit of energy
• Use algebra skills to figure out average speed and calories burned per minute
• Understand the basic concept of a function (describe how changes in one quantity result in changes in another)
• Problem solve using a variety of strategies, approaches, and math skills

Materials:

Preparation:

Print out copies of the Athlete Profiles (PDF).

What to Do:

• Assign students to small groups of four or five, based on skill level and which students work well together.
• Introduce the activity and distribute the athlete profiles. Explain that students will use the information given about the athletes' performance to calculate average speed and calories burned per minute.
• Review a calorie as a unit of energy.
• Ask students to read the profiles and then choose one athlete per group. As a group, students should note the data or information given and come up with a strategy for calculating two averages: calories burned per minute and speed per minute. Use the guiding questions on the handout to help students figure out the formula for each answer. See the Teaching Tips for this lesson for more information.
• Move among the small groups, asking guiding questions or giving simple examples to help students come up with the formula. Avoid giving them a formula outright. Instead, see if a series of guiding questions can help students use what they know to figure out the formula as a group. Be aware that there are a number of ways they may set up formulas.
• When students have finished, ask them as a group to discuss how they found their answers, what strategies they used, and how they decided whether their answers made sense. You may also wish to ask them which events appeared to burn more calories or result in faster overall speeds, and why. Are there other differences that matter? Do you think the athletes' speeds and calories burned would vary from day to day or race to race? Why? How might we account for that in the average?

Teaching Tips:

This lesson asks students to take data about an athlete and use algebra skills to figure out more information (calories burned per minute and speed). Students should be able to work together to come up with the formulas that will lead to the answers. Rather than giving them an answer, use guiding questions and the Teaching Tips below to help students use what they know to find an effective formula. Approaches and formulas will vary from group to group. Allow students enough freedom to discover their own methods for approaching the problem, and use each group's discussion to evaluate students' understanding of the algebra skills involved. Remember that the approach students take and how they use variables are more important than the answers they come up with.

To find the calories burned per minute:
• One way to approach the problem is to present a simpler problem. If someone burns 60 calories in 60 minutes, how many calories are burned per minute? What about 120 calories in 60 minutes? What does this tell you about the formula needed to find the calories burned per minute?
• Now, let's look at the male cross-country skier who burns 2,050 calories in a 90-minute event. To find the calories burned per minute, divide 2,050 by 90.
• You may want to use a calculator to find the answer (2,050 calories/90minutes = 21.6 calories per minute).
To find the speed:
• Speed equals distance divided by time. However, rather than giving students this formula, consider the tips below to help them figure it out.
• One way to approach the problem is to ask students to estimate if the skier's speed is going to be faster or slower than 30 kilometers per hour. (We know that the skier went 30 kilometers in 90 minutes, so he must be traveling slower than 30km per hour.)
• Some students may see a way to break down the problem into parts. For example, students may figure out that 90 minutes represents three half-hours, and that the skier went a total of 30 kilometers. Then you can ask them how many kilometers the skier went per half hour (10km) and per hour (20km).
• Another way that students can find the speed is to divide the distance (30km) by the time (90 minutes), for a total of .333 kilometers per minute. They can then multiply the speed per minute (.333) by 60 to find the speed per hour (20km).
• Students may want to use a calculator to solve this problem (30/90 = .333 or a third of a kilometer per minute). They then multiply the speed per minute (.333) by 60. Note that if students do use a calculator, they will come up with an answer of 19.98, and should round up.
• To get a number that isn't rounded off, students can convert time in minutes (90) to time in hours (1.5) before doing this last calculation (30/1.5 = 20).

Evaluate (Outcomes to look for):

• Student participation and engagement
• Students working together to understand, define, and solve problems
• Answers that reflect an understanding of a calorie, data, and the information provided in the athlete profiles
• Answers that reflect an understanding of a function (how quantities affect other quantities)
• Answers that reflect an understanding of how to find an average of calories burned per minute and speed per minute
• Effective use of variables

Standards: