Squares, and circles ... and squares, and more circles. In this high school assessment task, pupils investigate the ratio of areas of two squares that are circumscribed and inscribed in a circle. They then determine the ratio of the area of two circles circumscribed and inscribed in a square.

Concepts

circles, squares, inscribed

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Additional Tags

math

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Instructional Ideas

• Consider having learners construct the diagram with a compass and straightedge

Classroom Considerations

• While the task is aligned to eighth-grade geometry standards, the task is intended for high school classes
• Learners must have knowledge of the Pythagorean Theorem, of inscribed and circumscribed circles, and of ratios

Pros

• Rubric allows for multiple approaches
• Simple mathematical context makes this a great, universal resource for all learners

Cons

• The diagram is not exact

Common Core

8.G.B.7 MP2 MP3 MP6 MP7