Think about how you solved the previous problems, finding all 12 pentominos and determining which made an open box. Then answer two of the following questions:
- Reflect on the approach you used to solve each problem. Was it effective? Did you change your approach at any point in the problem-solving process?
- What mathematical concepts arose in each problem? Please list them.
- What did you learn from the pentominos that did not form cubes without tops?
- What makes these problems worthwhile mathematical tasks?
One point to remember is that, for teacher or student, problem solving is one of five Process Standards. It provides a context in which the content 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. In turn, this will increase your ability to model good problem solving and to form effective questions to help your students become better problem solvers.
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