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Information that is needed, and asked for:
Next layer is 39 x 39 -
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Basic Math solution: multiply + addition. Then demonstrate the formula and how it relates and shortens the process.
Formula:
Pennies in Pyramid =((1/3)*b³+ (1/2)*b² + (1/6)*b)*(SH)
Bezos Penny Pyramid Equation, 1982
where, b = number of pennies laid across on one side of a square based pyramid
SH = Stack Height , (number of pennies in each stack)
or
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The Math Problem as it would be presented in a Math Book:
11. A pyramid is made out of layers of stacks of pennies. Each stack contains 13 pennies. The base layer is a square with 40 stacks on each side. The next layer has 39 stacks on each side. The top layer has 1 stack. How many pennies are in the pyramid?
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Sequel
Student questions determine what other problems they can solve.
What in real life or past history has this shape? Why this shape? Pyramids, buildings(Luxor Hotel in Las Vegas), civil war cannon ball storage
- 5. What is the weight of the pyramid?
- 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?
Resources:
Three Acts - download for instructions, video, answers
http://mrmeyer.com/threeacts/pyramidofpennies/
Video of complete presentation to group of teachers
http://www.youtube.com/watch?v=YG9oqlQdVp0&feature=youtu.be&t=18m36s
http://en.wikipedia.org/wiki/Square_pyramidal_number
https://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0
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