Students use their knowledge of the relationship between the circumference and diameter of a circle to see why the area of a circle is π*r*^{2}. Guiding questions encourage students to think about issues of accuracy and informally introduce the idea of the circle as a limiting shape. The lesson involves visualisation and explanation.

This sequence is for students who:

- know basic properties of circles.
- know the formulas for the circumference of a circle and the area of a triangle.
- are familiar with π as the ratio of circumference to diameter of a circle.

### Lesson 1: Four Demonstrations

Students work in groups to understand one of four demonstrations of the formula *A = *π*r*^{2} and explain to others why the formula works. In the process, they refine both their own understanding and their explanations.

Last updated June 21 2020.