From Area Into Integration

Area is an exciting topic to teach! We start by introducing young children to area and perimeter of simple shapes, move through to curved shapes and volume, meet $\pi$, and eventually move on to using calculus to solve real world problems involving areas and volumes.

Some Thoughts on Teaching about Area

Stage: 3, 4 and 5

This article explores some ideas that are important to bear in mind when teaching about area, and suggests some resources that may be useful.

Perimeter Possibilities

Stage: 3 Challenge Level:

This problem combines both area and perimeter by inviting students to consider the different possibilities for the perimeter when the area of a rectangle is fixed.

Fence It

Stage: 3 Challenge Level:

This problem challenges students to work systematically while applying their knowledge of areas of rectangles.

Curvy Areas

Stage: 4 Challenge Level:

This problem offers students the opportunity to calculate areas of parts of circles and use $\pi$ in calculations.

Integration Matcher

Stage: 5 Challenge Level:

This problem offers students insights into differentiation, integration and the relationships between the two without needing to get involved with technical manipulations.

Curved Square

Stage: 5 Challenge Level:

This problem draws together coordinate geometry, equations of circles, and surds, and can also be approached using integration.