Krypto Math Game Strengthens Basic Skills

Mathematics involves pattern identification and problem solving. In order for students to move smoothly through the problem-solving process, a strong background in mental arithmetic is an asset. Students naturally learn best when they are engaged. One way to reinforce mental math skills is to allow students to play the math card game, Krypto, invented by Daniel Yovich in 1963. I used this game in both upper elementary and middle school classes. As long as students know basic operations, it applies. It is also a perfect parallel when introducing the order of operations.

Cards
The game cards are produced by the M.P.H. Games Company and can be purchased online or at educational stores. Due to the cost factor, my students made their own sets from index cards. They enjoyed being able to take the decks home to play with their families as well.
Although there are variations, a basic set consists of 56 cards:
3 each: #1-6
4 each: # 7-10
2 each: #11-17
1 each: #18-25
The students numbered each group of cards in different colors.

Object
Six cards are dealt face up so that all group players can see them. One is the 'target' card and the other five are the 'hand'. Combine the five cards in the hand in any order using addition, subtraction, multiplication or division to end up with the solution, the target card.

Procedure
Each number is to be used once and only once. Numbers can be grouped as if they were in parentheses. In basic games, only whole, positive numbers can be used. My students broke into groups of 4 or 5 students. The rules we determined were that a player would be given 30 seconds to explain his solution once he stated he had one. If he had a correct solution, he received a point. An incorrect solution resulted in a -1 and the other players were then given a chance to correctly solve. We played ten games to determine a winner in each group.

Examples:
Hand = 6, 1, 7, 5, 3 Target Card = 8
Solution
7 - 6 = 1
1 + 5 = 6
6 + 3 = 9
9 - 1 = 8

Hand = 1, 6, 3, 5, 10 Target Card = 6
Solution
5 x 6 = 30
30 ÷ 10 = 3
3 ÷ 1 = 3
3 + 3 = 6

There are over 3 million combinations in Krypto, yet only about 1% are actually unsolvable. Click here to try your hand at playing primary Krypto.

Suggestions
When I introduce Krypto to a group of students, I begin by playing whole class games. I use an overhead device to project the 6 cards on the board. At first, several demonstrations are in order. Next, students work in pairs to determine solutions. Finally, they work individually. A student is then selected to explain her strategy to the class. At that point, they have the understanding necessary to play in small groups.

I often create a bulletin board in class entitled "Take the Krypto Challenge". Students are given a week to solve as many of the Krypto problems as possible. The week's winners receive prizes.

Strategies
Teach the students some simple tricks:
If the sum of the '5 hand cards' and the target card are both either odd or even, the solution can generally be found using addition and subtraction only.

Zero Strategy: Use the zero property of multiplication or the identity property of addition, especially if the target card is the same as one of the 5 playing cards
Example:
Hand = 7, 9, 3, 7, 20 Target Card = 20
7 - 7 = 0
0 x 9 = 0
0 x 3 = 0
0 + 20 = 20

One Strategy: Use the identity property of multiplication.
Example:
Hand = 6, 8, 5, 12, 2 Target Card = 13
12 ÷ 2 = 6
6 ÷ 6 = 1
1 x 8 = 8
8 + 5 = 13

Modifications
Lower grades should use only a primary deck of cards, numbers 1 through 10. I even begin middle school students with the primary deck. When students are ready, we add in the 11 to 25 cards. In middle school, I eventually use fractions as well.

Other math articles by this author:
Math Bulletin Board Ideas for Teachers: A Slideshow
An Interactive Approach to Adding Positive and Negative Numbers
Teaching Math: Subtracting Integers

Reference
NCTM Illuminations: Exploring Krypto