As a more open inquiry, this prompt could lead in different directions. Students' initial questions or observations usually focus on the meaning of 'fits better' and how a 'fit' can be measured. Students have suggested using percentages or fractions to find the proportion of the shape 'covered' by the inscribed shape or the region of the shape left 'uncovered'. Through considering the regulatory cards, the class might decide to construct the inscribed shape accurately with a ruler and a pair of compasses. For others, the inquiry has continued with an inductive phase based on sketches of one or more diagrams. The inquiry has moved quickly to a deductive proof when students understand the mathematical similarity of the diagrams, especially if they are accustomed to expressing areas in general terms.

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