Last One Standing: Creative, Cooperative Problem Solving

By Green, David A. | Teaching Children Mathematics, November 2002 | Go to article overview
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Last One Standing: Creative, Cooperative Problem Solving


Green, David A., Teaching Children Mathematics


Eyes darted around the circle as some students just followed along and others counted ahead, trying to figure out if they would survive or not. "In," said one student. "Out," said the next, and then sat down. So the game went, around and around the circle, with every other player sitting out until only one third grader remained standing--the winner.

The Game

I had gathered my students to play a favorite counting game, in which the winner would receive an imaginary prize. After a spirited discussion, the class decided that the winner of the contest would be given his or her favorite food for lunch for the rest of the school year and would have double science time and free time, two classroom favorites. I asked the students to raise their hands if they were interested in entering the contest. Everybody raised her or his hand. "But there is a catch," I continued. "Anyone who enters the contest and loses--which is everybody except the one winner--will lose all of his or her science and free time. Who still wants to enter the contest?" Far fewer hands went up. "The goal," I concluded, "is to figure out how to win every time."

Since the beginning of the School year, I had emphasized problem solving and number sense in my mathematics curriculum, impressing on my students how vital these skills are to good mathematicians. Daily "math challenges" covering a range of content featured problems for which the method of solving was not defined. The students had encountered challenges related to our studies of place value, addition and subtraction, geometry, measurement, multiplication, and probability. Students had to figure out how to solve such challenges by drawing on a variety of problem-solving strategies and using their reasoning, logic, and mathematics skills. The activities gave us an opportunity to discuss, and reflect on, the process of doing mathematics. They also underscored the fact that there is not one "right way" to solve a problem and helped my students take risks as learners. Having spent much of the year developing their problem-solving and number sense skills, my students needed to tackle a larger challenge, one that wo uld weave together some of the mathematics strands they had already studied and would require them to collect, record, organize, and analyze data. They also needed a challenge that would require the use of not a single problem solving strategy but multiple strategies. Thus my third graders embarked on a week-long mathematics exploration that blended together problem solving and number sense, cooperative and independent learning, and a range of mathematics Content and Process Standards set forth in Principles and Standards for School Mathematics (NCTM 2000).

The game that I developed is played as follows: The contestants stand in a circle. The first person in the circle says "In." The next person says "Out," sits down and is out of the game. The next person says "In," and the next player sits down. The contest continues repeatedly around the circle, knocking every other person out until only one survivor remains. A similar activity, "King Arthur's Problem," is presented in Marilyn Burns' book Math For Smarty Pants, in which knights risk their lives vying for the princess's hand in marriage (Burns 1982).

Our game started with eleven students in the circle and the rest looking on. I identified the starting person as "Player 1" and asked students to predict who would win. Some students chose the winner randomly and others did a quick count around the circle. After everyone made a prediction, we started the elimination process until we had our winner: Player 7.

Before starting another round, I added an extra student to the circle and asked the class to make new predictions. Based on the results of the first trial, some students stuck with Player 7, while others chose a new winner. Many chose Player 8, the person following the first winner.

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