*[Photo by stevendepolo.]*

**Math concepts:** addition, subtraction, multiplication, division, powers and roots, factorial, mental math, multi-step thinking

**Number of players:** any number

**Equipment:** deck of math cards, pencils and scratch paper, timer (optional)

## Set Up

All players must agree on a Target Number for the game. Try to choose a number that has several factors, which means there will be a variety of ways to make it. Traditionally, I start my math club students with a target of 24.

Shuffle the deck, and deal four cards face down to each player. (For larger target numbers, such as 48 or 100, deal five or six cards to each player.) The players must leave the cards face down until everyone is ready. Set the remainder of the deck to one side.

## How to Play

- At a signal, all players pick up their hands and look at the cards. Each player tries to combine all four numbers in his hand to make the target number.
- Players may add, subtract, multiply, or divide the numbers in any order, but they may not put two cards together to make a two-digit number. With older students, allow using one card as an exponent on another. Factorials and the square root function may also help to spice up the game.
- Each card may be used only once in the calculation.

For example, if the target number was 12, and you were dealt an Ace (= 1), 7, 8, and 10, you might try:

10 + 8 + 1 – 7 = 12,

or

(10 – 8 ) × (7 – 1) = 12,

but not

(10 – 8 ) × 7 – 1 – 1 = 12,

which uses the 1 card twice.

- There is an element of chance to the deal. Some hands will not make the target number, no matter how you combine them.
- If after a few minutes, all players seem stumped, the dealer should give each player one more card. Then the players may use all five cards in their hands or choose any combination of four cards.
- On rare occasions, the dealer may have to deal another round of extra cards before any player can hit the target.

## Endgame

When you figure out a way to make the target number, lay your cards face up on the table. Explain your calculation so the other players can check it.

The first player to make the target number, using at least four cards in legal arithmetic calculations, is the winner of that hand. Play several hands, scoring one point per hand, and the first player to score six point wins the game.

## Variations

**Target Race:** To eliminate the element of chance, deal four cards face up in the middle of the table. All players use these cards, and whoever is the first to figure out how to calculate the target number wins that hand.

**Target Number with Variables:** For a faster-paced game, include the face cards in your deck, and let them work as variables. A face card in your hand may take any value that a number card might have, from 1 to 10.

**Target Dice:** Instead of cards, throw five dice on the table. All players try to combine the numbers showing on the dice to make the target number.

**Timed Target Number:** Give each player a piece of paper and a pencil or pen. Set the timer for an agreed-upon time, perhaps 10 or 15 minutes. Deal 8 cards face up on the table, and start the timer. Each player writes on a piece of paper all the ways he can combine any of these numbers to make the target number. Each card may be used only once in each calculation, but it may be reused in as many different calculations as you can think of. For example, if the target is 24, and a player wants to use the equation 3 × (4 + 4) = 24, there must be a 3 and two 4s on the table. Whoever comes up with the most (valid) ways to calculate the target number wins.

**Target Solitaire:** Play a solitaire game by dealing 8 cards face up and challenging yourself to find all the ways they can be combined to make your target number.

## Comments

Peggy Kaye (Games for Math) suggests a game like my Timed Target Number variation, but for younger students. She deals out only 5 cards and sets the target number as 10.

I have also enjoyed the commercial version of Target Number, called the 24 Game, which uses special playing cards invented by Robert Sun. The game comes in a wide range of levels, allowing students to practice topics from simple addition and subtraction to fractions, decimals, and even algebra.

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Sounds a little like Krypto. (which I just taught to a bunch of middle school math teamers this weekend…)

I can’t find a good website. Wikipedia describes “international rules” which seem unnecessarily complicated.

This is simpler: http://www.boardgamegeek.com/boardgame/7694/krypto#info

or this: http://www.math.niu.edu/~rusin/uses-math/games/krypto/

Short version: Each player gets 5 numbered cards, and all try to make a target number first. They must use all five of their cards, with just the 4 basic operations (parentheses are fine). The target changes each hand, and is determined by flipping one last card.

I hadn’t heard of Krypto before, but I’m not surprised to hear that someone else invented this game before I did.

We’ve played the Krypto variation (turning up one last card to be the target number) in my older math clubs, but it seemed that we had more hands where we had to re-deal than when I picked a target like 24. But then, this was before my kids had worked with factorials or tried the year game. With those experiences as background, perhaps we would have done better.

Interested readers can play Krypto here:

* Krypto Onlineor for younger players:

* Primary KryptoThere is a whole collection of this kind of the game. I call them “Make an Identity”. The variations include the number of terms and the target number.

Those are great puzzles!

Thanks for sharing. I really must find time to play around on your site more often. You have so many interesting pages…

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