Review with students how Archimedes made his estimate for the number of grains of sand in a marble-sized sphere as described on page 150 in the Student Guide.
- Archimedes estimated that a sphere about the size of a marble would hold about 40 × 40 × 40 = 64,000 poppy seeds. How can you write that using exponents? (403 = 64,000 poppy seeds)
- How many grains of sand did Archimedes decide it would take to have the same volume as one poppy seed? (10,000 grains of sand)
- How did Archimedes estimate the number of grains of sand in a marble-sized sphere?
(64,000 × 10,000 = 640,000,000 grains of sand)
Ask students to work in pairs to solve the following problem:
- Mr. Moreno's class estimated that 4000 marbles would fit inside the aquarium in their classroom. Using Archimedes' estimate for the volume of a marble-sized sphere, about how many grains of sand will fit in their aquarium? Show or tell how you know. (Possible response: 640,000,000 × 4000 = 2,560,000,000,000 or about 2.5 trillion grains of sand.)
As students discuss these questions, encourage them to read the numbers out loud to practice reading large numbers.
