Problem-solving games

Teaching Pre K-8, Nov/Dec 1999 by May, Lola

Presenting Krypto and Baby Krypto - two games that are guaranteed to motivate your students.

A numbers game that involves the whole class can provide a wonderful opportunity to meet the challenge of problem-solving.

I'm referring specifically to the game of Krypto, a math motivator if ever there was one. What's more, since it's possible to have more than one solution, the activity (and the motivation) can continue for quite some time.

There's nothing particularly difficult about the basic rules of the game. Five numbers between 1 and 20 are chosen at random by five students. A target number between 30 and 50 is then chosen by a sixth student.

Students try to create an equation that equals the target number. They may use each of the chosen numbers only once; however, they may use any combination of the operations - addition, subtraction, multiplication and division - and they may use the operations as many times as they want.

Keeping score. Krypto is more fun if you keep score. Points can be awarded based on how many chosen numbers are used to make the target number:

Three numbers, 300 points Four numbers, 500 points Five numbers, 1000 points

To provide some excitement, the class can be divided into two or three teams.

Let's say, for example, that the five chosen numbers are 3,7,11,14 and 15, and that the target number is 32.

Two possible solutions are: (3 x 7) 11 = 32

R3 x 7) 111 x (15 - 14) = 32

The first solution earns 300 points; the second solution, 1000 points.

Keep trying. Actually, Krypto isn't all that difficult - but it certainly looks it. Who can blame students if they become discouraged and give up after only two or three minutes of unsuc-- cessfully trying to equal the target number?

There is, however, something you can do to encourage the students. Before they get started, tell them about a computer study that was carried out in California.

According to the computer, when all five random numbers are used with the four operations, the target number can be reached 86 percent of the time.

Krypto is for the upper grades, starting in the second half of fifth grade. Students who know other operations - for example, square root, squaring a number or factorial - can use them.

Baby Krypto. This is just what you think it is - an easier version of Krypto. It's suitable for third, fourth, and beginning fifth graders.

Baby Krypto is played just like regular Krypto, with students choosing five random numbers and one target number.

The scoring is the same, too: 1000 points when all five chosen numbers are used; 500 points for four numbers; and 300 points for three numbers. Students can use all four operations in any combination.

The only difference from regular Krypto is that in Baby Krypto the five chosen numbers are from 1 through 10 and the target number is from 11 through 20.

For example, five students might choose the following numbers: 2,3,4, 7 and 9. A sixth student might pick 14 as the target number.

Some solutions are: 3 4 7 =14 9-4 7 2 = 14

(4 7 9) -(2x3) = 14

The first solution is worth 300 points; the second, 500 points; and the third, 1000 points.

In grades three and four, students who need enrichment can form a small group, pick five random numbers and a target and then talk to each other about solutions.

Problem-solving requires the student to try many different ways to solve a problem. This is accomplished in Krypto and Baby Krypto.

Students learn from each other as they see and share solutions. Last but not least, students get valuable practice in computation.

Next issue: Keeping Mental Math Alive.

Lola May is a mathematics consultant, a former Math consultant for the Winnetka (IL) Public Schools and a Teaching Editor of Teaching K-8.