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Tuesday, December 19, 2017

Getting Tricky in Math Class

Each year, I like to teach a "magic" trick about this time of year. The math skill we are honing through this trick is "make 10". All year we have been working on mental math techniques, and being able to quickly make 10 is a big part. Children who know immediately that 9 + 1, 8 + 2, 7 + 3, 6 + 4, and 5 + 5 equal 10 have a much easier time to mentally do harder problems, like 16 + 7 (perhaps thinking, "I know 7 and 3 make 10, so I'll take 3 from 16 to do so. Then 10 plus 13 is 23.") This type of flexible thinking is crucial for fluent mathematicians, and is part of what is known as number sense.

Anyway, we are practicing this trick in our math group all week, and hope to perform it for other math groups soon after Winter Break. 

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.

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