How Card Games Can Develop Math Skills

In one of my favorite movies, The Gods Must Be Crazy, there were two side characters who drove the jeep in their guerrilla warfare army. Whenever there was a stop in the movement forward, they’d pull out a deck of cards and get back into whatever game they were playing. I totally relate to them. I’m happy to carry around a deck of UNO cards and keep a running game going. Card games are good for more than occupying time; they are also great for developing math skills. During this time of school closures, card games are an excellent way to continue to develop math skills at home and make use of resources likely available.

Interested in more great professional learning resources for educators? Check out this blog: Numbers are Everywhere, and They Don’t Bite!

One application of math to many card games is keeping score of a hand or the final score of a game (such as in UNO). I encourage this not for determining who won but for making students add or subtract and then compare numbers. The teacher can assign card games to develop and practice counting strategies, such as making a 10 and then counting on. For example, suppose that in an UNO game, in which it is necessary to determine the number of points remaining in a hand at the end of a round, I have the following seven cards: 5, 2, 6, 1, 0, 8, and 3. To get the total points in my hand of 25, I start by making a 10 with 2 + 8 and a 10 with 6 + 3 + 1, then put these together to get 20, and finally count on from 20 to add the 5 and 0. Total scores in UNO are determined by adding several hands together. Look at all the math I just had to do!

In basic games like War, players set down one or more cards from their share of the deck and the winner is the one who has the highest value. Many primary skills are at play from counting to comparing numbers. Many variations of the game of War change how cards are counted, the operations used, and ways to tally the final score. These variations can make the challenges appropriate for students working on different skills. Many of these variations can be found online. Below are just a few types of War games I have seen:

• Multiplication War: Each player puts down two cards at a time and multiplies the two values. The player with the greater product wins the cards.
• Fraction War: Each player puts down two cards, one as the numerator and one as the denominator. Players can follow the rule that the greater card is the denominator or that the greater card is the numerator, or they can choose which card is the numerator and which the denominator. The winner can be either the player with the greater fraction value or the player with the lesser fraction value.
• Integer War: Black cards (clubs and spades) are considered positive numbers and red cards (diamonds and hearts) are considered negative numbers. Each player puts down two cards and adds them together (or in other variations of the game, subtracts or multiplies). The player with the greater sum (or difference or product) wins the cards.

Another important skill learned with card games is strategizing, whether anticipating possible outcomes or planning the best next move. When I’m playing cards I’m often thinking about such things as playing a low card, making a pair, getting rid of a card right away, or saving it to play toward the end of the game. It may be inappropriate to play or teach poker games in school, like blackjack or five-card stud. However, there are many other variations of these games that offer enjoyment and challenge but do not train students for a gambling career! Two such games are Make 24 and Hit the Target.

• Make 24 (2–4 players): Four or five cards are turned face up for all players to see and use. Each player uses the values on the cards, with any combination of operations, to create a result of 24. Variations include allowing the use of any number of cards or requiring that all the turned-up cards be used to make 24. There are several ways to determine a winner, such as the first player to make an expression that equals 24, the player to create the most expressions that equal 24 in a set time, or the player to end up with the most points when adding a point each time each card is used to reach 24.
• Hit the Target (2–4 players or students in teams): This game is very similar to Make 24. A number is randomly chosen as the target. The value can be limited to be between 1 and 10, 1 and 20, or 1 and 1,000 based on the level of challenge appropriate for the players. A set number of cards are turned over for all players to use (for higher targets, such as above 30, it is good to turn over 6 or 7 cards). Players use the values on the cards to create expressions that equal the target number. Variations for this game are the same as those described for Make 24.

It is important to have students share ideas about the best strategies they think will work. This both broadens and deepens students’ learning. Students’ strategies may not always make sense, or may often have a more creative, imaginative bent, but by looking at those strategies, students are learning to figure out different approaches.

Like other games, card games also build problem-solving ability, perseverance, and adaptability, which are all important skills in working with mathematics. In games, often, a move you were planning to make is thwarted and you must make another plan. Or the card you thought would come up doesn’t, and again, you have to endure and make a new plan. This process teaches students to become more accepting of failures and frustrations and to move on. Plans are always falling apart, and we have to learn to adapt. This is an important part of game playing, math work, and life.

When you let students develop their own games with a deck of cards, they can also develop creativity with numbers. They can create some crazy rules, some at high levels of thinking and some that are just plain funny. Creativity is also an important part of mathematical thinking, especially with problem solving and applications.

I love card games. I love math. I love teaching and learning. So naturally, I triply love seeing all three come together!