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Lesson plan · Grade 11 · 50 minutes

Outbreak Model

I can solve exponential models for time with logarithms in base 2, 10 and e, read percent growth from an exponential, and explain where a pure exponential model breaks.

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Standard
F-LE.A.4 CCSS-Math
F-IF.C CCSS-Math
Shape
Explore first
Grouping
Pairs on devices, with whole-class pauses.
You need
The tool on the projector and on student devices. Calculators with ln and log.
Tool
curioclass.org/tools/outbreak-model/
  1. Hook5 min
  2. Explore15 min
  3. Make sense12 min
  4. Apply13 min
  5. Exit check5 min

Before class

  • Open Grow with Virus X in a city (10 cases, doubling every 3 days).
  • Every story is invented and labeled as a made-up example, not a real forecast.
  • Model: N(t) = a e^(kt). For Virus X, k = 0.2310, so growth is 26.0 percent a day.

Hook 5 min

  1. "Ten people have a new virus, and cases double every 3 days. When will a million people have it?" Take guesses in days.
  2. Record the guesses on the board. "Let's find out, and learn to answer exactly."

Explore 15 min

  1. Press Play and watch the Milestones list: 100, 1 thousand, 10 thousand. "How far apart are they?" (9.97 days each.)
  2. Press Log. The curve becomes a straight line. "Why?"
  3. Pairs turn on Compare steady growth. "How long would a steady line take to reach 1 million?"
  4. Pairs switch Describe growth by between doubling time, tenfold time and continuous rate. "The curve never moves. What changes?"

Make sense 12 min

  1. Switch to Ask when and press 1 million. The Solve it panel works it three ways and all land on t = 49.83 days.
  2. On the board, solve 10 × 2^(t/3) = 1,000,000 with log base 2, then base 10, then ln. "Why must they agree? Where does log 2 come from?"
  3. Compare with the class guesses. Press Check it to run the clock to that moment.

Apply 13 min

  1. Pairs turn on Guess first and solve two targets for another Story on paper before pressing Show the answer.
  2. Pairs try the Fading rumor, which halves every 5 days. "Why is 'when does it reach 2,100?' answered 'Never'? What does the negative t mean?"
  3. Switch to Hit the ceiling and pick United States. The exponential passes the population; the logistic levels off. "When do they start to disagree, and why?"

Exit check 5 min

On a card: "A post has 50 shares and the shares double every 4 hours. Write N(t) and solve for when it reaches 100,000 shares, showing the log step. What percent does it grow each hour?" Then: "Name one assumption of the model that breaks first in a real school."

Support and stretch

  • Support: start with base 2 only, counting doublings before using logs.
  • Support: use the table of whole days on either side of each answer.
  • Stretch: derive D = ln 2 / k and W = ln 10 / k from N(t) = a e^(kt).
  • Stretch: compare the Virus X ceilings for Denver, Colorado and the World. Why are they so close together in days?

Short on time

  • Grow with Log (8 min).
  • Ask when for 1 million (8 min), then the exit card (5 min).

How each button works is in the teacher notes. From Curio Class, free under CC BY 4.0: change it, print it, share it.