## Lesson abstract

Students are presented with the challenge of finding the number of faces, edges or vertices of a pyramid or prism given the number of sides of the base shape. They explain the relationships between these numbers and describe them with algebraic expressions. Students then use the expressions to find prisms and pyramids with specified numbers of faces (etc.) and also use the expressions to verify Euler’s Formula for these 3D shapes. They test whether Euler’s Formula holds for regular and irregular polyhedra of students’ own construction.

## Mathematical purpose (for students)

Algebra can be used to describe relationships, to make predictions and to show that relationships are always true.

## Mathematical purpose (for teachers)

The main purpose is for students to use simple algebra in a meaningful context. Algebra is used in three modes. First, students find patterns in the numbers of faces, vertices and edges and express them algebraically. Then they can use these algebraic expressions in an equation solving mode to identify mystery shapes. In the additional task, students use algebra in a generalisation mode to prove that Euler’s formula is true for all prisms and pyramids. Students will incidentally build their spatial skills through construction of pyramids and prisms.

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