Sorting equations of circles 2

This lesson develops the concept of using the equation of a circle. In particular students develop their knowledge of how to:

• Translate between the equations of circles and their geometric features
• Sketch a circle from its equation

In the introductory activity a circle has been drawn on a grid and students are presented with the equation of the circle. The task is to draw the x-axis and y-axis on the grid and to label the divisions. The next activity is to write the equation of a circle that has two x-intercepts but just one y-intercept and a radius of 6.

The next task considers three circles, each of which might be considered to be the odd one out. Students must choose a circle and write what properties the other two circles have got in common that the third does not have. Work in this section draws in work on Pythagoras’ theorem.

A collaborative task presents a set of equations of circles together with some axes for sketching the circles. Students must determine how many x-axis and y-axis intercepts each circle has. They place their cards on a grid and look to see if there is a general pattern that they can find that avoids the need to sketch.

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.