## Lesson abstract

This lesson begins by approximating the area of a circle, between the area of an inscribed square and circumscribed square. Students next work in groups to understand one of four proofs of the exact formula *A* = π*r*^{2} and explain their proof to others. In the process they refine both their own understanding and their explanations.

## Mathematical purpose (for students)

The area of a circle can be proved to be exactly equal to π*r*^{2}.

## Mathematical purpose (for teachers)

Students will first see a demonstration that the area of a circle is between 2*r*^{2} and 4*r*^{2}. They will be given the opportunity to understand a student-accessible proof of the formula that *A* = π*r*^{2}. The range of proofs used gives teachers the opportunity to allocate students to a proof that is likely to be accessible to them.

Students explain their proofs to others because understanding is frequently deepened in this way. Students learn that mathematical results can be proved in ways which they can understand and that there can be multiple proofs. They engage with mathematical reasoning and develop skills in communicating it clearly.

## At the end of this lesson, students will be able to:

Understand the circle area formula.

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