Sorting equations of circles 1

This lesson develops the concept of using Pythagoras’ theorem to derive the equation of a circle and translating between the geometric features of circles and their equations.

The initial activity involves looking at a circle with end points of the diameter at (6, 0) and (–6, 0). Questions relate to information it is possible to derive about the circle, for example, a point on the circle has coordinates (2, m) and students must write possible values for m.

The next activity links the equation of a circle with Pythagoras’ theorem, looking at circles with the same radius but different centres. Students then sort 16 cards with equations of circles according to the radius of the circle and its centre.

There are pre-lesson and post-lesson formative assessment tasks. Detailed teacher notes give suggestions on questioning and how to use the resources. Full solutions are given for each of the sections.

This is a concept development lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.