## Wednesday, July 27, 2011

### Summy: A Math Twist on a Classic Card Game

I love the classic card game of rummy.  Whether it's because the game is so great or I'm just not very original (I prefer to believe the former), I constantly revisit rummy as a basis for creating new learning games.

My latest twist on rummy involves adding positive and negative integers.  It's called Summy (pun most certainly intended):
1. Players are dealt 7 cards.
2. Remaining cards are placed in a draw pile, with the top card turned over to be the "sum total" card and the first in the discard pile.
3. Black = positive integers, red = negative integers.  All face cards are positive or negative 10, depending on their color.
4. During their turn, each player draws one card from either the draw or discard pile, and tries to make groups of 2 cards or more that add up to the sum total.
5. Players must put down something, so they might have to keep drawing cards until they can.
6. After their turn, players should discard one card from their hand.
7. When one player has no cards left, the game is over.
As I noted when I revisited my combining like terms card game, if your students aren't familiar with the draw-play-discard structure of games like rummy, you might need to adjust or eliminate some rules.  The key here is that instead of making groups according to traditional rummy rules, players are seeking sums that match the sum total.  All other parts of the game are secondary.

Let's use the cards on the left as an example.  If my "sum total" card is (-8), I need to find 2 or more cards in my hand whose sum is (-8).  I could put down a group of 3 using either the jack of diamonds or queen of hearts as (-10):

(-10) + (-5) + 7

That wouldn't be the best play, though.  I would still have a red and black face card in my hand, worth (-10) and 10 respectively.  Since their sum is zero, I can include them in my group as well:

(-10) + (-5) + 7 + (-10) + 10

I'd be left with just the 8 and (-2).  I'd still have to draw a card, and discard one, so I would not have won quite yet, but I'd be well on my way to victory.

One of the most important lessons I learned while tutoring at Mathnasium was that children need number sense to become great at math.  With this game, they're being challenged to think of multiple ways of adding up to the same total, and as their hand changes constantly, so do the possibilities.