**Learning Targets:**

- I can apply what I have learned about ratios and rates to solve a more complicated problem.
- I can decide what information I need to know to be able to solve a real-world problem about ratios and rates.

**Related Pages**

Illustrative Math

Grade 6

Let’s solve a Fermi problem.

Illustrative Math Unit 6.2, Lesson 17 (printable worksheets)

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.

- 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.

“Fermi problems,” named after Enrico Fermi, an Italian physicist, are problems that are impossible to measure directly, but can be roughly estimated using known facts and calculations. Here are some other examples of Fermi problems:

- “How long would it take to paddle across the Pacific Ocean?”
- “How much would it cost to replace all the windows on all the buildings in the United States?”
- “How many times does your heart beat in a year?”
- “How many hours of television do you watch in a year?”
- “Some research has shown that it takes 10,000 hours of practice for a person to achieve the highest level of performance in any field—sports, music, art, chess, programming, etc. If you aspire to be a top performer in a field you love—as Michael Jordan in basketball, Tiger Woods in golf, Maya Angelou in literature, etc., how many years would it take you to meet that 10,000-hour benchmark if you start now? How old would you be?”

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

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