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- I have $1,000,000.00 in pennies, how big of a pyramid can I make?
- 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.]
- 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.
Here's my burning question: is that enough? Is that skinny outline enough for you to use this in your classroom?
Check for understanding: what happens during the first, second, and third acts of a mathematical story? What are your moves? What questions do you ask your students?
Act one is about visuals, context, and perplexity. Act one hits you in the gut, not the head. Act one eagerly invites questions like, "What is that?" or "Why did he do that?" If your students are anything like the teachers who have worked with this image, you'll get a fair number of them wondering, "How heavy is that?" and "How much is that worth?" both of which tie into the most popular (by far) question, "How many pennies is that?" Have them write down a guess along with numbers they know are too high and too low. Share guesses. Stir up some competition.
Act two is about tools, information, and resources. "What do you need to know to figure out the answer to your question?" Dimensions of the base? Number of pennies in a stack? The change from one level to the next? Give them what they want.
Act three is the resolution. When groups of students start finding answers, ask them to check the answers against the bounds they set up earlier. Challenge them with one of the sequel problems while you help other students. Bring students up to explain their different solution strategies to each other. Then pay off their hard work and show them the answer.
- Teachers in my PD session love this one and, as their facilitator, so do I. They each come up with their own interesting question and yet the math doesn't change. Whether you're curious about weight, duration, quantity, or cost, we're all going to work with area and series. That's a win for every stakeholder in the room.
- I'm especially fond of this one because everyone has a place to start. You can seriously start counting the pennies one-by-one if that's the highest level of abstraction you can handle. We'll beef up your skills over the course of the problem.
- How many students will factor the number of pennies per stack, saving themselves a load of work? ie. 13*1 + 13*4 + 13*9 + … + 13*1600 vs. 13(1 + 4 + 9 + … + 1600) It's going to be fun comparing work around the room.
- A compelling visual is its own classroom management. If you put up a visual that's a) simultaneously strange and familiar, b) larger than life, and c) aesthetically clear and interesting, the class is yours. Maybe only for a moment, but that moment is yours to lose. The class has given you permission to take them somewhere interesting. I'm not sure I can say the same for a worksheet. A worksheet brings with it a very different set of bags.
- This one is courtesy of Dan Anderson. I'm drinking your milkshake here, Dan. Where were you on this story?
2011 July 8: Changed one of the sequels per David Wees' remarks in the comments.
2011 July 15: Elizabeth Bezos, wife of Marcelos, the guy who made the pyramid, stops by to say hi in the comments.