## Lesson abstract

The lesson consists of a single investigation: which is the better fit - a round peg in a square hole or a square peg in a round hole? The investigation here is somewhat structured to support students, but could be presented in a more open way if desired. Students work together on understanding the problem and formulating the problem mathematically and then solving it. The task may be used for assessment.

## Mathematical purpose (for students)

An opportunity to improve problem solving skills and use circle formulas to answer an intriguing question.

## Mathematical purpose (for teachers)

This lesson poses a problem. The processes involved in its solution include: drawing 2-D diagrams of a 3-D situation; deciding how to model (and hence compare) ‘fit’ mathematically; devising a strategy to solve the problem; and either generalising from numerical cases or using algebra. Solutions use area formulas and also revisit the geometric arguments of earlier lessons. Problem solving involves uncertainty, which can generate stress for students. This lesson offers support to help students to work through this.

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