Students develop a strong intuitive sense that the ratio of circumference to diameter is the same for all circles and use a variety of approaches to find a more accurate value for the ratio. They then apply their knowledge by making a diameter measuring tape, from which they can read off the diameter of a cylindrical object.

These lessons assume only elementary knowledge of circles—that all the points on the circumference are the same distance from the centre—and an intuitive understanding of ratio.

### Lesson 1: Spheres in a Cylinder

Students compare the height of a cylinder containing three tennis balls to its circumference. They ask what would happen if the balls were smaller or larger and conclude that it is always the case that the circumference is a little more than three times the diameter. They apply this to estimations relating to real world circular objects.

### Lesson 2: A Better Value for *π*

Students are reminded of the conclusion from the previous lesson that the ratio of circumference to diameter is ‘3 and a bit’. Students use a variety of contexts to find the ratio of circumference to diameter and hence find a better value for *π*. They discuss how the accuracy of the value they find could be increased.

### Lesson 3: Measuring Trees

Students apply their knowledge of the ratio of circumference to diameter to make a d-tape, which can be wrapped around a cylindrical object such as a tree to instantly measure its diameter.

Last updated January 22 2019.