Circles and Squares

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.

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CCSS: Designed
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