The Challenge: Explore a toppling sand pile.
Materials Needed: Paper, pencil, and probably a good eraser. You could also do this using a whiteboard or other writing surface.
Math concepts you could explore with this challenge: algebra, arithmetic, counting, fractals, functions isometric, proportions/ratios
Above is my explanation (note, I’m pretty sure I have a mistake in toppling 20)
Here is a video that Numberphile put together describing them as well:
Depending on how you use this activity, you may engage with different mathematical standards. I’ve listed possible connected math content above. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!
2.) Reason abstractly and quantitatively. Is it possible for a pile to topple differently? Does it matter if different stages appear different or is it necessary for the toppling to be consistent?
5.) Use appropriate tools strategically. How might you meld this with computer programming? Is there a less or more illuminative coloring for the sand piles? What kinds of coloring may make the sand pile structures more obvious or less?
7.) Look for and make use of structure. What would an isometric (triangular) grid toppling looks like? How about a hexagonal one?