IM 6.2.17 Lesson: A Fermi Problem
Andre likes a hot cocoa recipe with 1 cup of milk and 3 tablespoons of cocoa. He poured 1 cup of milk but accidentally added 5 tablespoons of cocoa.
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[/img][br][br]How can you fix Andre’s mistake and make his hot cocoa taste like the recipe?
Explain how you know your adjustment will make Andre’s hot cocoa taste the same as the one in the recipe.
Record the Fermi question that your class will explore together.
Make an estimate of the answer. If making an estimate is too hard, consider writing down a number that would definitely be too low and another number that would definitely be too high.
What are some smaller sub-questions we would need to figure out to reasonably answer our bigger question?
Think about how the smaller questions above should be organized to answer the big question. Label each smaller question with a number to show the order in which they should be answered. If you notice a gap in the set of sub-questions (i.e., there is an unlisted question that would need to be answered before the next one could be tackled), write another question to fill the gap.
Brainstorm at least five Fermi problems that you want to research and solve.
If you get stuck, consider starting with “How much would it cost to . . .?” or “How long would it take to . . .?”