# Math Games

When I was in the third grade my friend Alexander and I invented a math game (whereby invented I mean, “I’m unable to precisely track down the origins of this game, so I’m assuming we created it entirely on our own”). In this post I’m going to describe how to play the game, and why I think it was really a really excellent tool for teaching several skills.

## Rules

To start with, you need a deck of cards, we used some special math cards where
the number of cards with each value were *not* evenly distributed, and the
cards went 1-20 (possibly zero was included). Since most people don’t have
access to these, a deck of playing cards should work in a pinch, note that it’s
not really important to have a complete deck, or only one deck, and the faces
don’t matter, so it’s fine to mix-and-match decks from that drawer where you
accumulate partial card decks.

To start, you deal a row of 4 cards, face down in a line between the two players::

```
Player one
C C C C
Player two
```

Then, on each side of the stacks in the middle, you deal a pile of 4 cards, face down. (Meaning each player has 4 stacks of 4 cards, each of which is associated with one of the cards in the middle)::

```
Player one
4C 4C 4C 4C
C C C C
4C 4C 4C 4C
Player two
```

To start the game, each player flips two of the cards in the middle over, simultaneously.

Then players look at each of their stacks, and for each one they must find a
series of arithmetic operations which lead to the value of the corresponding
card in the middle. For example, if my target was 7, and I was dealt 2, 4, 6,
8, I might find: `(8 - 4) + (6 / 2)`

. Each number must be used exactly once,
and any binary operators are legal (at the time we only knew about addition,
subtraction, multiplication, and division, but if you can find a use for
logarithms or exponentiation be my guest).

Once a player has found a series for all 4 of their decks, they tell their opponent, and then they explain the series of operations they used for each target. If a player has forgotten one of the solutions, or made a mistake, both of them return to trying to find solutions.

If finding a solution seems impossible, a player can show their cards to their opponent and both of them can think really hard about if it’s possible.

## Why I like this

I believe this game was an important tool in developing my arithmetic skills at an early age. It teaches a few skills:

- Arithmetic: Obviously you have to be able to do computations quickly and correctly in order to do well at this game.
- Estimation: One of the tricks to quickly processing all the possible
operations you could perform is to look at the scale of numbers, for example
if I’m targeting a 2, and in my hand I have a 7 and an 8, I would never
contemplate
`7 * 8`

, because I know it will be difficult to get back down from 56. - Cooperation: While it is something of a competitive game, when a player is stuck and thinks a solution is impossible to find, the other player helps them. Further, at the end of a round, a player always explains how they found their solutions, so the other player can learn.
- While not a skill, as such, this game teaches that math is fun! There’s no doubt in my mind that this game is more fun that the memorization of multiplication tables many students are forced to do.