Think about how you solved the previous problems, and answer one or two of the following questions:

• Why are these problems worthwhile mathematical tasks?
• What mathematical concepts are developed in each problem?
• How did the different representations (cube cake, table, formula) help you reason through each problem?

Using reasoning and proof as a process for teaching and learning mathematics is especially important in the middle grades. As students begin to move from concrete experiences with specific numerical notation to developing abstract ideas using symbolic notation, they will become more confident in their understanding if they can reason through a mathematical process and support their reasoning with informal, and eventually formal, proof. The role of the teacher is to give students regular opportunities to use mathematical reasoning by providing tasks that allow students to investigate mathematical relationships.

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