prologue

act one

  • 1. Guess which glass contains more soda.
  • 2. A can of Coca-Cola contains 12 ounces. Guess how much soda is in each glass right now.

act two

  • 3. What information will you need to know to solve the problem?

  • Make sure students attend to precision here. If they suggest "radius" and "height," ask them to tell you what height they want. Radius seems natural but radius requires you know where the exact center of the circle is.

  • 4. Which would be easiest to measure: the radius, the diameter, or the circumference?

  • The radius requires the exact center. The circumference is tough because wrapping a string around the glass lumps the glass in with the soda. The diameter can be found by exploiting the fact that the diameter is the longest chord in a circle.

act three

sequel

  • 5. How tall would the soda have to be so both glasses held the same amount?
  • 6. Danielle says you can just multiply the radius by the height in both glasses and compare those answers to see which has more soda. Is she right? Can you prove why or why not?