Shapes in Circles
This is an ‘always, sometimes, never true’ activity using dynamic geometry software to explore the properties of shapes. The activity will help pupils to focus on strengthening geometrical reasoning, leading towards a deeper understanding of proof.

Year 9 Objectives covered:
• Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons, justifying inferences and explaining reasoning with diagrams and text
• Pose questions and make convincing arguments to justify generalisations or solutions
• Recognise the impact of constraints or assumptions
Year 10 Objectives:
• Distinguish between practical demonstration and proof in a geometrical context
• Examine and refine arguments, conclusions and generalisations
• Produce simple proofs
Year 11 Objectives:
• Prove and use facts about angles in a circle
• Show step-by-step deduction in solving more complex geometrical problems
• Make progress by exploring mathematical tasks, developing and following alternative approaches
• Examine and extend generalisations
• Support assumptions by clear argument and follow through a sustained chain of reasoning, including proof

The activity has opportunities for:
• Pupils to focus on strengthening their geometrical reasoning
• Pupils to produce simple proofs
• Whole class teaching
• Paired work
• Independent use of ICT
• Discussion and reflection