Becoming Mathemagicians

Starting this week, my small band of math students hope to become mathemagicians, and put on a magic show

for the other math groups. This project may grow to include all sorts of math, including measurement (making our own top hats, for instance), money fluency (ticket prices?) and so on. Right now, though, our focus is on the actual "show" itself. 

We will be practicing this trick until we've got it down pat. The math involved is immediate recall of the "make ten" - so if the student does not know all of the number pairs to 10, the trick does not go as well. Each child learned this trick on Monday, and we are currently working on techniques to make our presentation of the trick look smoother and, well, trickier! You can practice at home - all you need is a standard card deck, without 10s, jacks, queens, or kings. The ace should count as a 1. You should have 36 cards in all.

Here's how you do it:

1. Hold out the shuffled deck, and ask a person to choose any three cards.
2. Ask the person to determine if any two of his cards add to ten. If so, he must return one of the two to you and choose a replacement. Repeat this until the person has three cards, no two of which add to ten. Tell the person you will determine which cards he has. The person can put these three cards aside while you perform the trick.
3. Begin the card trick by simply turning each of the remaining cards face up in front of you, one at a time. As soon as you see any two cards that add to ten, cover those two with the next two cards from the deck.
4. Continue on in this manner, covering pairs that add to ten every time you see them, until the deck is finished. If there are no such pairs, place the next card out to form a new pile. Note: if you are left with only one card in the end, simply make a new pile.
5. When the cards in your hand have all been turned over, remove the pairs of piles whose top cards add to ten.
6. There should be three remaining piles. Determine the missing cards by finding the addend that goes with the top card of each pile to make ten.