Young geometers flex their transformation muscles in this brief but powerful exercise using dilations and translations to develop the similarity of circles. The plan provides guidelines to help learners navigate a pair of deceptively simple questions, leading to the conclusion that all circles are similar. Suggestions for the teacher help with teaching methods, possible introduction techniques, and provide a thoroughly fleshed out answer key.

Concepts

similarities, dilation, translations, transformations

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Additional Tags

math

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Instructional Ideas

• Could be used as part of a development of the equation of the general circle from the unit circle

Classroom Considerations

• No student worksheet is provided—student questions are under the heading Task at the start of the lesson plan
• Questions and answers are at a high language level and might require adapting for ESL considerations

Pros

• Clearly aligned to a single standard, with specific directions
• Learners are expected to explain and extend their thought process, not just give a calculated answer

Cons

• A referenced "experimental GeoGebra worksheet" is not linked or provided, but is not essential to the activity

Common Core

HSG-C.A.1 MP1 MP8