The 10° Computer and other Games by Gwyn Lyon Gates Elementary School Acton, Massachusetts The teaching of math to kids is traditionally divided into lecture and drill. In the re-thinking of a second grade math program, I decided to incorporate some different approaches to aspects of math computation. A game such as Input-Output can be noisily exciting, and effectively teach the relationships between sets of numbers. INPUT-OUTPUT A game for the Blackboard or Overhead Projector. Divide the acetate into two columns or make two columns on the blackboard. Place a numeral in the left or Input column. Through the function of the magic-black-box-computing-teaching machine, the number is transformed into a new number. teaching machine = ? Input 4 Output 7 Place a new number in the input column, and using the same teaching machine function, a new number appears in Output. Input 4 0 Output 7 3 answer: t.m. = +3 Continue to add numbers until a student guesses what function the teaching machine is set for. Second graders can do problems of this level of difficulty: teaching machine = ? Input 4 7 10 Output 11 17 23 answer: t.m. = 2x + 3 The game can be adapted for many types of algebraic equations: teaching machine = ? Input 9 25 4 Output 4 6 3 answer: t.m. = √x +1 As an added bonus, a child with such learning problems as would exclude him from the successful completion of a traditional worksheet can often excel in "head" games that require no written response. THE 10¢ COMPUTER The teacher must also begin to rely more on manipulative materials to move the child securely from the concrete to the abstract. Hence, the ten cent computer: Materials: a large grocery box. 1 sheet of acetate, 8" x 10". Method: Cut the box up so that you have one large sheet of cardboard, without seams, that will completely cover the stage of the overhead projector. Mine is 12" x 1l½", but measure yours to be sure. Cut four holes in the top third of your cardboard. Save the cut-outs! Tape the sheet of acetate so that it covers the holes. Then hinge the covers back over the holes with tape. A Simple Binary Game: Beginning at the left side, mark the numerals 1, 2, 4, 8 on each acetate-covered hole.* Close all the covers. Place the computer on the stage of the projector, and turn on the projector. Lift the first cover on the left. Computer now shows "1". Write on the blackboard, 1000. Close all the covers. Lift cover marked Write on blackboard, 0100, and explain that because the light is on in the "2" position, the binary notation is 0100. Close all covers. Explain that all numbers up to 15 can be shown with only the four lighted positions. How can you make 3? 7? 14? [image] Binary Numbers for the 1O¢ computer By this time, the children will have grasped the idea, and can work quite competently up to 32, using only the blackboard notations. If you want to carry on, you can make an "advanced" computer with 6 holes that can record numbers all the way up to 63! *Normal binary number notation goes right-to-left, i.e. 1 = 0001, 6 = 0110, 8 = 1000, etc. If you think your kids can grasp this, give it a try. Suggested Bibliography Ahl, David. Getting Started in Classroom Computing. Digital Equipment Corporation, Maynard, Massachusetts. Adler, Irving and Ruth. Numerals, New Dresses for Old Numbers. John Day, Company. New York, N. Y. Kenyon, Raymond. I Can Learn about Calculators and Computers. Harper and Row. New York, N. Y.