Choosing a Model and Naming What It Ignores · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Models answer, assumptions decide

Mathematics · Mathematical Thinking · ages 14-15
Name ______________________   Date ____________

  1. Using the gym model C equal to 20 plus 15m, where C is in pounds and m is months, what is the cost for 8 months?

    Answer: ______________

  2. A gym charges a 20 pound joining fee plus 15 pounds per month. Which formula gives the total cost C for m months?

    • C equal to 20 plus 15m
    • C equal to 15 plus 20m
    • C equal to 20m
    • C equal to 35m

  3. A gym charges a 20 pound joining fee plus 15 pounds per month. Which formula gives total cost C for m months?

    • C equals 15 plus 20m
    • C equals 20 plus 15m
    • C equals 35m

  4. Jay says a model that fitted last year perfectly is automatically safe next year. Is Jay right?

    Circle one:   True   False

  5. A sunshine model predicts 200 visitors, but a football final cuts the real count to 120. What is the right verdict?

    • The model is useless forever
    • Sunshine mattered less that day than the match; judge the model against its assumptions
    • The visitors miscounted on purpose

  6. A linear model predicts 200 weekend visitors from 40 hours of sunshine, but a football final cuts the real count to 120. What is the right verdict on the model?

    • The answer is unusable as it stands; name the event effect before trusting it further
    • The model is now disproved for every future weekend
    • The count of 120 must be wrong because the model said 200
    • Models are always right, so report 200 visitors

  7. A model predicts a town of 5000 people growing at 2 percent per year. Which assumption is the long range forecast most sensitive to?

    • The growth rate staying at 2 percent
    • The starting population being exactly 5000
    • Counting people in whole numbers
    • Measuring time in years

  8. Snow depth follows D equals 3 plus 2h. Which change would spoil predictions fastest?

    • Snow stops after one hour
    • An extra flake lands on the ruler
    • You read the depth twice

  9. Two forecasts use the same data but different growth rates, and their answers differ wildly. What does that tell you?

    • The growth rate is the sensitive assumption; test it before trusting either answer
    • Both answers are automatically wrong
    • The data was collected twice

  10. Which report of a model answer is honest?

    • The answer is 140, whatever happens
    • The answer is 140 if snow falls steadily; a thaw would spoil it
    • The answer is 140 because models are always right
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Models answer, assumptions decide W1-mt_UtK9aauJ6e-s1

  1. 140 · 15 times 8 is 120, plus the 20 pound joining fee gives 140 pounds.
  2. C equal to 20 plus 15m · The 20 pound fee is paid once so it is the starting value, and each month adds 15 pounds, giving C equal to 20 plus 15m.
  3. C equals 20 plus 15m · The 20 pound fee is paid once and each month adds 15.
  4. False · Conditions change. Past fit never guarantees future results.
  5. Sunshine mattered less that day than the match; judge the model against its assumptions · An ignored factor ruled the day. Name it before trusting the model again.
  6. The answer is unusable as it stands; name the event effect before trusting it further · The model ignores big events, and this weekend shows that assumption breaking the answer.
  7. The growth rate staying at 2 percent · A small shift in the rate compounds every year, while a small error in the starting count does not compound.
  8. Snow stops after one hour · The model assumes steady snowfall, so snow stopping breaks it.
  9. The growth rate is the sensitive assumption; test it before trusting either answer · Wild swings from one input mark it as the sensitive assumption.
  10. The answer is 140 if snow falls steadily; a thaw would spoil it · An honest report states the answer with the assumption it rests on.
Worksheet · LightMySky