Here is a possible way to introduce or more likely review Pascal's Triangle. (Disclaimer: I have not actually done this with students. If you try it, let me know how it turns out!)
- Have students stand in a triangular number arrangement
- Give the top student a penny.
- Give the top student another penny, and have him/her give the pennies, one each, to students in the next row
- Explain that this is what everyone will have to do: "when the time comes, give half of your pennies to each of the two students in the next row."
- Now give the top student two pennies, which get passed down to the next row, and from there to the next row, which gets us to 1 2 1
- Ask that row how many pennies they have altogether. Give that many pennies to the top student. Those should trickle down to 1 3 3 1.
- Ask that row how many they have, and give that many pennies to the top student.
You get the powers of two pattern for free.