April 5, 2014

We’ve recently invented a game that surely already exists in some form already. But it’s been super fun to play, and we’ve been using it with kids and teachers at all grades. It’s kind of magic. We don’t have a scoring system for the game, and I don’t think it needs it in many cases, but if you have ideas for how we could convert how close you get to the target number to a score, I’d love to hear it.

One great outcome is that the game raises tangible issues about arithmetic. One amazing question that came up with a group of teachers: would 58 x 69 be greater or less than or equal to 59 x 68?

It wasn’t until a teacher suggested the partial products method of multiplying that everyone could see why we should expect these products to be different. But the insights didn’t stop there. Someone argued that the difference between a “switched product” like 28 x 79 vs 29 x 68 will always be a multiple of 10. Then someone conjectured that you could figure out exactly what the difference is based on the differences between the pairs of digits in the tens and ones places. A very cool discussion that came from an oddly compelling game.

So here’s the game:

## Horseshoes

Horseshoes is a simple game with almost limitless potential. It’s fun, quick, and can lead to differentiated practice, creative math practice, and also seed interesting conversations about math patterns.

How to Play
Horseshoes can be played with the whole class, or in small groups. Remove all face cards and tens from a deck of cards, so the only cards are from 1 to 9. The teacher/leader picks out two cards, forms a two digit number with them, and writes it on the board. This is the target number. Then the leader picks four more cards and writes those digits on the board.
The goal of the game is to create an equation using only the four digits that were drawn that equals an amount as close as possible to the target. Whoever is closest to the target wins that round. It doesn’t matter whether someone goes over or under.

Example Game
The leader draws a 3 and a 7, and writes the target number 37 on the board. Then the leader draws the four digits 2, 4, 4, and 9. After all the digits are written on the board, there are three minutes of quiet, where everyone writes their attempts and equations down on their own paper.
When the three minutes are up, the leader calls on people who say what they got, and how they got it.
Student 1: I got 43, by taking 49 – 4 – 2.
Student 2: I got 38. I took 9 x 4 to make 36, then added 4 and subtracted 2 to get 38.
Student 3: I got 37 exactly! I did 44 – 9 +2.

Variations
By taking different targets, we can encourage different kinds of arithmetic practice. For example:
Four digit Horseshoes: Pick a 4-digit number as the target. This forces multiplication. Fraction Horseshoes: Arrange the target as a fraction (i.e., 3/7 instead of 37).

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