Math is In the Cards
By Michael Naylor

In the game of "Make 10," kids deal 12 cards face up and pull out groups of cards that add up to 10.
Artwork: Laura bethel-sehn

An ordinary deck of playing cards can provide wonderful ways for children to learn number sense, practice math facts and develop spatial visualization skills. Here's a deckful of mathematical card games that will help turn your students into math aces.

More or less (Grades K-1)
Each child gets a set of cards Ace through 10 (for the numbers 1-10). One child selects a "secret card" from his or her hand and places it face down. The second child tries to guess what the number on the card is by selecting a card from his hand and placing it face up. The first child then tells whether the secret card is greater or less than the face-up card. The second child continues to make guesses until he has discovered the value of the secret card. Players then switch roles.

War (Grades K-1)
This classic game helps students recognize relative values of numbers. Players split a deck of cards and simultaneously flip over their top cards. The highest-value card wins the pair. If the cards have the same value, players deal an additional three cards face down and then place the fourth card face up. The card with the highest value wins all the cards from the round, including the face-down cards.

Make 10 (Grades K-2)
Remove the face cards from a deck. Deal 12 cards face up. Players take turns finding and removing combinations of cards that add up to 10. When both the players agree that no more tens are possible, more cards are dealt. This game helps students recognize parts of 10, an important step in learning to add and subtract base 10 numbers.

Missing addend "mind reading" (Grades 1-3)
In this game for three players, one student is the leader and the other two are the players. The two players each draw a card and, without looking at it, hold it up to their foreheads so that everyone else can see it. The leader announces the sum of the two cards. Each player must figure out which card is on his or her own forehead. When both players have figured out their cards, a new leader is chosen and the game continues. Try playing this game with four or five players for a challenge!

Missing factor "mind reading" (Grades 3-6)
This is identical to the previous game, except the leader announces the product of the cards. A nice feature is that all players get practice with products and factors in every round.

Build a number (Grades 4-8)
When playing this game with younger children, remove the face cards; with older kids, make Jacks worth 11, Queens 12 and Kings 13. If your deck has Jokers, make them worth 0.

Each group of 2-5 students selects a target number from 1-30. Five cards are then flipped face up, and the object is for students to make a number sentence using all five cards with any operations to reach the target number.

For example, suppose the target number is 20 and the cards in play are 5, 5, 6, 2, and Ace (worth 1). One winning combination is: 5 x 2 + 5 + 6 - 1 = 20. Another is (6 x 5) - (2 x 5 x 1). Also, (6 ÷ 2) x 5 + (5 x 1) works, as do many more.

The first player to find a winning combination keeps the cards and chooses the next target number. If no combination is found in about a minute, flip over another card and try to make a combination using six cards.

To keep the game fair for players of different abilities, introduce the rule that if a player hasn't made a combination in three rounds, he or she may make combinations using four of the five cards; other players must use five.

Multiplication zone (Grades 4-8)
This game for two to four players encourages the use of multiplication facts and estimation. Jacks are worth 11, Queens 12 and Kings 0 or 13. Each player is dealt 10 cards.

A card from the remaining stack is flipped face up. Its value is multiplied by 10, and players try to find a pair of cards whose product is in that "decade." For example, if the flipped card is a six, then the zone is any number in the sixties (60-69), so a winning pair would be 9 and 7 (product 63) or 12 and 5 (product 60), etc.

Any player who can make a pair removes those cards from his or her hand. Play continues until one player's hand is empty.

Memory (Grades K-8)
This classic game for two to four players builds visual memory and spatial reasoning. Arrange the cards face down, as shown below. Players take turns turning over a pair of cards. If the numbers match, the player wins the two cards and takes another turn. If the cards don't match, they're flipped face down and the next player has a turn.

Here are three variations:
Half Deck: Split a deck into two groups, one with hearts and clubs, one with spades and diamonds. Players use one of these half decks to match a red card with the black card of the same value.

Two of Four: Deal all 52 cards face down. Players try to match two cards of the same value. Since there are four cards of each value, this game moves quickly.

Full Monty: All 52 cards are used, but two cards only count as a pair if they match in value and color. This lengthy game is perfect for rainy recesses!

Michael Naylor is a professor of math education at Western Washington University, Bellingham, WA.

August/September 2004, Vol.35, No.1