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The Biggest Loser.doc

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									                                     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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