Pick's theorem

Investigating perimeter and area using geoboards

Key stage: 3
Subjects: mathematics, shapes


Fashion design and garment construction provide an ideal context to explore intriguing mathematical concepts via hands-on tasks, strengthening the pupils' visualisation skills and deepening their understanding of geometry and its place in mathematics as well as in the world around us.

This resource pack was developed specially for Y7 pupils with prior knowledge about the area of simple shapes. See also the Y8 counterpart under 'Queen Dido'. Both can be adapted for use with other year groups.

The sequence of lessons starts with an investigation of shapes on a geoboard (inspired by Pick's Theorem), moves into studying shapes with the same area or same perimeter, leading to practical activity designed to consolidate the meaning of perimeter and address misconceptions common at this age.

This activity is part of a series of fashion design themed resources, resulting from a project developed by the Royal Institution, inspired by the work of the fashion designer Julian Roberts. In his Subtraction Cutting Masterclass, Julian uses straightforward ideas of perimeter, area and volume. His innovative approach to garment construction is intriguing and puts to the test anyone's visualisation skills. Understanding the approach and outcomes requires abstract concepts such as the topology of surfaces, curvature and space-filling curves. Julian uses his own body to take measurements and has developed his own 'tricks' to estimate the perimeter and area of shapes.

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