Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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Problem SolvingSession 03 Overviewtab aTab btab ctab dtab eReference
Part B

Exploring Problem Solving
  Introduction | Chairs, Stools, and Tennis Balls | Problem Reflection | Your Journal


Think about the problem and reflect on the following questions. When you've formulated an answer to each question, select "Show Answer" to see our response.

Question: How did moving the tennis balls help you decide on possible solutions?

Show Answer
Our Answer:
Grouping the tennis balls in groups of three or four lets us see different combinations of chairs and stools that use all 30 tennis balls. It also helps us find out if there is more than one possible combination. Concrete materials enable problem solvers to find a solution, to discover patterns in order to be more efficient in finding other possible solutions, and, after some experience, to become more systematic in finding all of the solutions.

Question: How does making a table help you organize your thinking?

Show Answer
Our Answer:
The table is a tool to help organize your thinking as you work through the problem. For example, if you began with one stool that uses three tennis balls, you'd then realize that you have 27 remaining tennis balls, a number that is not divisible by four. You could then continue with two, three, and four stools, using the same method. This is a more systematic approach and relies on the use of number concepts to reach a solution.

You could also use a table to organize your work in a "guess and check" approach. In this case, the table would help you see patterns emerge and enable you to hone in on a more systematic approach.

The table could also be used in combination with counters, as you could record your successful and unsuccessful solutions as you work with the counters.


Question: Reflect on the approach you used to solve the problem. Was it effective? Did you need to change your approach at any point in the problem-solving process?

Show Answer
Our Answer:
Answers will vary.

One point to remember is that, for teacher or student, Problem Solving is one of five Process Standards. It provides a context in which mathematical content, as defined by the Content Standards, can be taught. By improving your ability to approach problems using a variety of strategies and reflecting on not only the solution, but also the process you used to reach the solution, you will become a better problem solver. This, in turn, will increase your ability to model good problem solving and to pose effective questions that will help your students become better problem solvers.

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