These notes are intended to be read in conjunction with the resource files for the main task, Teddy bear, including the teacher notes and solution.
This is a low-threshold, high-ceiling activity where learners are “simply” invited to match some circles on a graph with their equations. The circles are drawn to scale, but the axes are not labelled. The resource can be used to consolidate learning shortly after the Cartesian equations of circles are introduced, or as a revision task.
Introducing the task and suggested ways of working
Students could work in pairs or small groups to encourage sharing ideas and justifying statements. Throughout the task encourage students to record their reasoning so that they can present or adapt their argument.
The circles diagram can be printed on A3. Students could be given 2 minutes to look at the diagram before they are given the problem sheet with the equations. Students should note what they see in the diagram (common centres, variation of radius or variation of the position of the centre) and share these ideas in pairs.
Part way through the task, invite all groups to share ideas. Students could suggest a circle that they have matched, make an observation, describe their strategy or ask a question.
Cartesian equations of circles, completing the square
Skills involved in this task
Relating equations of a circle to the position of its centre, completing the square, sketching curves, estimation, reasoning and deduction