by Dan Meyer

• 1. How many pennies are there?
• 2. Guess as close as you can.
• 3. Give an answer you know is too high.
• 4. Give an answer you know is too low.

• video — building the pyramid

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

• image — the base layer of pennies — 40 pennies x 40 pennies
• image — single stack of pennies — 13 pennies per stack
• image — penny dimensions
• link — square pyramidal numbers sum

• image — answer
• image — newspaper clipping

• 6. I have $1,000,000.00 in pennies, how big of a pyramid can I make?
• 7. Each stack has 13 pennies which is a strange number to choose. Why do you think Marcelo Bezos chose it? [Hint: not out of an abundance of superstition.]
• 8. Bezos says he can tell you the number of pennies in a pyramid with this equation:
  
  
  where s is the number of pennies in a stack and b is the number of pennies on one side of the square base of the pyramid. Does this work? If so, prove it.
• 9. The Wheat and the Chessboard problem.
• 10. Give groups of students a dollar in pennies. See how fast they can assemble seven stacks of thirteen pennies. Then ask them to use that as a sample to determine how long it would take them to build the entire pyramid.
• 11. If Bezos now wanted to add more levels to the pyramid, what's the best way for him to do that?
• 12. How heavy is the pyramid?