Algebra: Prisms and Pyramids

Australian curriculum number (ACMNA175)

Students build their skills in algebra by developing algebraic rules for the numbers of faces, edges and vertices in prisms and pyramids. They make deductions about unknown prisms and pyramids from these rules (links to equation solving) and then use their algebraic expressions to show that Euler’s Formula works for all prisms and pyramids. Students also build their spatial skills through construction of pyramids and prisms and learn about a new class of polyhedra, antiprisms.

This sequence provides an accessible context for students to use simple algebra. The emphasis is on developing algebraic relationships through visualisation, rather than through looking at patterns in tables. The sequence is for students who:

  • understand that pronumerals stand for numbers and know the most basic conventions of algebra.
  • can collect like terms, e.g. they will need to be confident that 2b ≠ b+2 and be able to simplify expressions such as (b+2) – 2b.
  • can solve very simple equations.

 

Lesson 1: Faces, Edges and Vertices

Students determine the number of faces, edges and vertices of prisms and pyramids in terms of the number of sides of the ‘base shape’. They use these results to show that Euler’s Formula holds for all prisms and pyramids.

Lesson 2: Antiprisms

Students learn about a new class of polyhedra called antiprisms. They build on Lesson 1 to determine the number of faces, edges and vertices of an antiprism given the number of sides in the ‘base shape’.

 

Last updated December 19 2018.