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Dissecting squares

Dissecting squares

Barrie Galpin

Område:

Labels Fractions, Scattergraphs, Algebra, Geometry

A square is dissected to form three triangles and a quadrilateral. What fraction of the square is each part?

A square is divided into three triangles and a quadrilateral by drawing a diagonal and a line joining one of the other vertices to the midpoint of a side. TI-Nspire calculates the area of each part of the square and poses a question: what fraction of the area of the square is the area of each part?

Varying the size of the square allows students to collect data that can be plotted as a scattergraph. This leads to a derivation of the fractions for each part. 

A separate problem allows the result to be checked using coordinate geometry and algebra. 

Finally there is an extension problem that allows students to work towards a generalisation of what happens when, rather than the midpoint, the side of the square is divided in the ratio r:1.