If you ask a mathematics teacher about their favourite GCSE topics, Circle Theorems almost always makes the top 5. Why is this? Their proofs can be derived from basic angle facts, and for some students it will be the first time they have succeeded in deriving their very own mathematical proof. Then that joyful ‘detective feeling’ when they spot the theorems hiding in each problem. Finally when they manage to apply the ideas and solve some impressively complex, multistep problems. Prerequisites Students won’t get very far without basic circle vocabulary and fluent knowledge of basic angles facts. Also, it’s a great chance to have a go at geometric proof so some idea of how proofs work will also help. Labelling activity Mixed angles worksheets from Maths4everyone Scaffolded proofs of basic angle ideas are a nice way to build confidence with proof (Opposite angles in a triangle sum to exterior angle and Sum of interior angles in a quadrilateral (from 2 triangles)). Investigate/Discover Circular geoboards are slightly less daunting than using blank circles. You may find it’s more accessible for students to use the dots to draw and investigate the theorems. Geogebra have interactive versions so you can explore with the whole class. https://www.geogebra.org/m/PKd72hpZ NRICH have some great starting points for investigating the Theorems for the first time. We have also created some resources based on these. www.tes.com/teaching-resource/-12596281 After the students have explored using the geoboards, you might want to show them how the rules will work for any configuration within the theorem. These Interactive circle theorems are great to project (or for exploration on individual student devices should you have this resource!): students can watch the changes in the angles, and make predictions and conjectures https://www.geogebra.org/m/EzaeAWNH Good practice sets
Challenging problems https://donsteward.blogspot.com/2010/12/cyclic-quadrilateral-angles.html https://donsteward.blogspot.com/search/label/circle%20theorems Circle theorem stacks - @keyboardmonkey www.tes.com/teaching-resource/circle-theorems-revision-exercise-2-11657482 Enjoy the resources and teaching this fantastic topic. Please share any Circle Theorem teaching ideas that you love in the comments!
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