The Biggest Loser Linear Relations Project Math 10 C Situation: The Biggest Loser is a television reality show that takes morbidly obese Americans and trains them full-time on an isolated campus. You have been hired by The Biggest Loser to train the following contestants: Jared is a 43 year old male who is 6’2’’ tall and 435 pounds. Salim is a 27 year old male who is 5’6” tall and 380 pounds. Hassan is a 41 year old male who is 6’8” tall and 513 pounds. Arya is a 28 year old female who is 5’7’’ tall and 370 pounds. You will have them on campus for 10 weeks and your goal is to help them lose as much weight as possible. The winner will be the contestant who loses the greatest percentage of his/her body fat over the course of 10 weeks. Task: The producers of the show want to have an idea as to which contestant will win the show. They have asked you to make a prediction after the first 5 weeks, supported by mathematical models, so that they can prepare for the eventual winner. Track and analyze the weight loss of each contestant. Data for contestants: Jared Salim Hassan Arya Week Weight Week Weight Week Weight Week Weight 0 435 0 380 0 513 0 315 1 410 1 375 1 478 1 308 2 395 2 363 2 436 2 302 3 387 3 353 3 420 3 295 4 380 4 336 4 425 4 288 5 374 5 327 5 436 5 281 Process: 1. Using the above data, draw a graph for weeks 0 to 5 for each contestant. Put all four contestants’ data on the same graph and use a different colour for each contestant. Is it reasonable to connect the points on the graphs? Why or why not? 2. Determine the slope between weeks 0 and 5 for each contestant. Add a straight line between week 0 and week 5 to each contestant’s graph. 3. What does the slope represent? 4. What does the y-intercept represent? 5. Determine the linear equation for each contestant modeling their weight loss for weeks 0 to 5. 6. State the domain and range for each contestant for weeks 0 to 5. 7. Use your equations from #5 to predict the weight of each of the contestants at the end of the show. 8. Using all of the above information, make a mathematically-based prediction as to who will win the show. Be sure to show all your calculations and explain your prediction. Extension: 1. Whose predicted weight would be least/most accurate and why? 2. Would it be reasonable to extrapolate this data for 52 weeks? Why or why not? 3. Consider another way of comparing the overall weight loss: pounds lost per inch of height. Would this method change the winner of the show? Assessment Rubric Level Excellent Proficient Adequate Limited* Insufficient / Criteria 4 3 2 1 Blank* Performs Performs Performs Performs Performs No score is Calculations precise and focused and appropriate superficial awarded explicit accurate and generally and irrelevant because there calculations. calculations. accurate calculations. is no evidence calculations. of student performance. Presents Data Presentation of Presentation Presentation of Presentation of No data is data is of data is data is data is vague presented. insightful and logical and simplistic and and astute. credible. plausible. inaccurate. Explains Shows a Shows a Shows a Shows a No explanation Choice solution for the solution for solution for the solution for the is provided. problem; the problem; problem; problem; provides an provides a provides provides insightful logical explanations explanations explanation. explanation. that are that are complete but incomplete or vague. confusing. Communicates Develops a Develops a Develops a Develops an No findings are findings compelling and convincing predictable unclear communicated. precise and logical presentation presentation presentation presentation that partially with little that fully that mostly considers consideration considers considers purpose and of purpose and purpose and purpose and audience; uses audience; uses audience; uses audience; some inappropriate appropriate uses appropriate mathematical mathematical appropriate mathematical vocabulary, vocabulary, mathematical vocabulary, notation and notation and vocabulary, notation and symbolism. symbolism. notation and symbolism. symbolism.
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