Have you and your children been struggling to learn the math facts? The game of Math Card War is worth more than a thousand math drill worksheets, letting you build your children’s calculating speed in a no-stress, no-test way.
Math concepts: greater-than/less-than, addition, subtraction, multiplication, division, fractions, negative numbers, absolute value, and multi-step problem solving.
You will need several decks of math cards. Don’t rush to look for these at your school supply store or try to order them through your favorite website. Math cards are normal, poker-style playing cards with the jack, queen, king, and jokers removed. Make one deck of math cards per player. A math deck contains 40 cards, so a single game of Addition War lets a child work 20 problems, and he hears his opponent work 20 more—and if your children are like mine, they will rarely want to stop at just once through the deck.
As my students learn their math facts, they need extra practice on the hard-to-remember ones like 6 × 8. With a normal deck of cards, however, I find they turn up far too many problems like 1 × 9 or 2 × 7. To give a greater challenge to older children, I make each player a double deck of math cards, but I remove the aces, deuces, and tens. This gives each player a 56-card deck full of the toughest problems to calculate.
[This is an old, classic children’s game. I’ve often been amazed how such a simple thing can keep my kids occupied for hours. In our variations, because the math card decks are only 4/5 the size of a regular card deck, we give each player his own pack of cards. We don’t shuffle the decks together at the beginning, although I suppose you could—that would be more like the traditional game, which (at least in our house) is usually played with a single deck shuffled and split between the players.]
How to Play
Basic War—Each player turns one card face up. The player with the greatest number wins the skirmish, placing his own and all captured cards into his prisoner pile. Whenever there is a tie for greatest card, all the players battle: each player lays three cards face down, then a new card face up. The greatest of these new cards will capture everything on the table. Because all players join in, someone who had a low card in the initial skirmish may ultimately win the battle. If there is no greatest card this time, repeat the 3-down-1-up battle pattern until someone breaks the tie. The player who wins the battle captures all the cards played in that turn.
When the players have fought their way through the entire deck, count the prisoners. Whoever has captured the most cards wins the game. Or shuffle the prisoner piles and play on until someone collects such a huge pile of cards that the others concede.
For most variations, the basic 3-down-1-up battle pattern becomes 2-down-2-up. For advanced games, however, the battle pattern is different: in case of a tie, the cards are placed in a center pile. The next hand is played normally, with no cards turned down, and the winner of that skirmish takes the center pile as well.
Addition War—Players turn up two cards for each skirmish. The highest sum wins.
Advanced Addition War—Turn up three (or four) cards for each skirmish and add them together.
Subtraction War—Players turn up two cards and subtract the smaller number from the larger. This time, the greatest difference wins the skirmish.
Product War—Turn up two cards and multiply.
Advanced Product War—Turn up three (or four) cards and multiply.
Fraction War—Players turn up two cards and make a fraction, using the smaller card as the numerator. Greatest fraction wins the skirmish.
Improper Fraction War—Turn up two cards and make a fraction, using the larger card as the numerator. Greatest fraction wins.
Integer Addition War—Black cards are positive numbers; red cards are negative. The greatest sum wins. Remember that -2 is greater than -7.
Integer Product War—Black cards are positive numbers; red cards are negative. The greatest product wins. Remember that two negative numbers make a positive product.
Wild War—Players turn up three cards and may do whatever math manipulation they wish with the numbers. The greatest answer wins the skirmish.
Advanced Wild War—Black cards are positive numbers; red cards are negative numbers. Players turn up four cards (or five) and may do whatever math manipulation they wish with the numbers. The greatest answer wins the skirmish.
Reverse Wild War—Players turn up three cards (or four, or five) and may do whatever math manipulation they wish with the numbers. The answer with the lowest absolute value (closest to zero) wins the skirmish.
Math War Trumps
The biggest problem with Math War is that it’s really just a worksheet in disguise. Children enjoy it more than a worksheet because of the social interaction, but there’s no choice or strategy to the game.
But you can introduce strategic thinking into your number practice by playing Math War Trumps:
- Players draw two cards from their deck and look at them.
- The player whose turn it is calls the trump: which math operation to do, and whether the low or high answer takes the trick.
- Then all players reveal their cards and calculate.
For even more strategy, let players draw three cards and choose which two to reveal. Then they draw two more to replenish their hand for the next turn.
Update: Math War with Special Decks
Check out all the wonderful ways for middle and high school students to play Math War. Algebra, geometry, and trig decks created by teachers and shared free for your use!
More Ways to Play
Multi-Digit War—Turn up two or three cards and create a 2-digit or 3-digit number.
Multi-Digit Subtraction War—Turn up three cards. Make two of them into a 2-digit number, then subtract the third. Example: Suppose you turn up 3,4, and 5. Should you arrange them as 54-3 or 45-3 or 35-4 or . . . ?
Multi-Digit Product War—Turn up three cards. Make two of them into a 2-digit number, then multiply by the third. Example: Suppose you turn up 3,4, and 5. Should you arrange them as 5×43 or 4×53 or 3×54 or . . . ?
My Closest Neighbor—Instead of turning up cards at random, each player draws a hand of five cards. Then turn up a target card such as “Closest to 1/2” and try to make a fraction from two cards in your hand that will be near the target but not equal to it. Chris posted a set of printable target cards at her blog. I modified the game for regular playing cards: Fraction Game: My Closest Neighbor.
Logarithm War—Requires a special deck of cards. Download from Kate’s blog: This Game Really Is Worth 1000 Worksheets in doc or pdf format. Sadly lost to the time-monster who eats old pages on the internet.
Logs and Trig War—Jim extended Kate’s logarithm war to include trig functions. Double the cards, double the fun! Download from Jim’s blog: War: what is it good for?
Speed Racer—For two players of evenly-matched ability. Each player turns up one card, and the first player who calls out the correct sum (or difference, or product) of those two cards wins the pair.
- Can you think of another variation to share?
If you enjoyed this post, check out my Math You Can Play book series featuring math games for all ages.
Hat tips: Marni suggested the Mult-Digit variation in the comments section below, but I didn’t think to add it as an update until Mary from the Albany Area Math Circle suggested the Multi-Digit Product War variation in a comment on another post. And then her extension of the game made me think of the Multi-Digit Subtraction War variation. Math tutor and games enthusiast Nancy Rooker suggested the Trumps variation in an email. Amy suggested the Speed Racer variation.