## Who Lost More?

• Lesson
6-8
1

In this lesson, students analyze ways for calculating weight loss. Students compare the results and choose the method they consider to be the best and most fair.

In preparation for class, you will want to choose and preview an episode of The Biggest Loser that you will show to your class. During the weigh-in, record the contestants' names, starting weights, and current weights on a master copy of the Who Lost More Activity Sheet. Then, make copies for your students.

Introduce the idea of weight loss by playing a clip from the beginning of The Biggest Loser episode you chose. Explain that the contestants are trying to lose more weight than the others. Pass out the Who Lost More activity sheet. Have students complete Question 1. Ask students to volunteer their answers. Record their choices and how they determined that the contestant lost the most on the Who Lost More? Overhead.

Students might subtract the new weight from the starting weight, find percent decrease, find the percent of the current weight, or just compare the weights of the contestants.

If no student suggests using percent change, ask, "How else can we determine who lost the most weight? Some people might say that ______ lost the most weight. Why do you think they say that?" Ask the students, "What about people who had different starting weights?"

Have students work in small groups. Let each group choose a calculation method other than percent decrease to determine the amount of weight loss for each contestant. Each group should complete Question 2.

Play a clip of the contestants weighing in at the end of the episode. As a contestant stands on a scale, the weight and percentage of weight lost that week is also displayed. Have students answer Question 3.

Ask, "How do you calculate percent decrease?" Have the students work in their groups to create a formula. Ask several students to share their formulas and list them on the board. Be sure everyone has a correct formula, equivalent to

100 × (old weight – new weight) / old weight

Have students complete Questions 4–6 by calculating the weight loss using their own method and the percent decrease.

After students complete Question 7, ask, "Which method do you think is the most fair for determining weight loss?" Allow students to vote for their preferred method and tally the votes on the board. Once the votes are tallied, ask students why they chose certain methods. Invite classroom discussion on which methods work and which don't work. Have students explain their answers.

Assessment Options

1. Students can write a letter to the producers of The Biggest Loser to explain either why their calculation method works well or why they should use a different method of calculation.
2. Have students present their opinions to the class, justifying their method using computational results. Students could use a PowerPoint presentation or make a poster. Presentations should include the method they suggest with a rationale supported by computations.

Extension

Students can create line graphs, plotting the weight loss of contestants throughout the season. With internet access, students can research the data on their own.

Questions for Students

1. What are the pros and cons of your preferred calculation method?

[Answers will vary based on the methods chosen by students. However, students should note that percent decrease is a more fair method than just determining the number of pounds lost, since participants have different initial weights.]

2. Why do you think The Biggest Loser uses percent decrease as their calculation method?
[Answers may vary, but students should come to the conclusion that percent decrease is most fair to the participants with different starting weights.]
3. How does the formula for percent decrease connect to what you already know about percents?
[Students should realize that just like in calculating percents, finding percent decrease requires dividing two values and multiplying by 100.]
4. How do you determine percent decrease?
[100 × (old weight – new weight) / old weight.]
5. Which calculation do you think is the least fair? Why?

[Answers will vary based on methods chosen by students.]

Teacher Reflection

• Were students able to work on their own to complete the worksheet?
• Were students able to determine a formula for percent of decrease on their own?
• Was the clip selection from The Biggest Loser engaging for the students?
• Were students sufficiently challenged?
• Did students achieve the learning objectives? In particular, did students provide carefully thought out answers to the short answer questions?

### Learning Objectives

Students will:

• Brainstorm methods of calculating weight loss.
• Use percent of decrease to calculate weight loss.
• Think critically about different methods of calculation.

### NCTM Standards and Expectations

• Work flexibly with fractions, decimals, and percents to solve problems.
• Compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line.

### Common Core State Standards – Mathematics

• CCSS.Math.Content.7.RP.A.3
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

• CCSS.Math.Content.7.NS.A.3
Solve real-world and mathematical problems involving the four operations with rational numbers.

• CCSS.Math.Content.7.EE.B.3
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or$2.50, for a new salary of \$27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

### Common Core State Standards – Practice

• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP7
Look for and make use of structure.