## Classroom topics in focus: Prisms and Pyramids

Written by Kristen Tripet

A phrase that we often use in our resources as a prompt for inquiry is ‘What do you notice?’. This question asks students to focus on what they see as the salient features of the information they are given.

There are varied teaching techniques asking students to focus on particular aspects of a task. Many of these techniques, such as using a table to look for patterns, are important mathematical tools that we encourage students to use. However, using them at the start of a lesson may lessen the inquiry by expecting students to notice only what we want them to notice. It may also take away the power of students visually recognising these regularities for themselves. Asking students to notice more generally affords them the opportunity to ‘own’ the patterns and regularities that they see and to form their own mathematical generalisations.

Below is one of our Year 7 resources, Prisms and Pyramids, that asks students to ‘notice’. Take some time to notice for yourself and then check out the task on the website. Also, think about how you could use the question ‘What do you notice?’ in your own classroom.

## Prisms and Pyramids (Year 7)

This is a pentagonal prism.

Imagine a hexagonal prism. What can you say about its faces, edges and vertices? Why?

Imagine a prism whose base has lots of sides. What can you say about its faces, edges and vertices? Why?

This is a pentagonal pyramid.

Imagine a hexagonal pyramid. What can you say about its faces, edges and vertices? Why?

Imagine a pyramid whose base has lots of sides. What can you say about its faces, edges and vertices? Why?

The activity is deliberately structured to draw students’ attention to the numbers of faces, edges and vertices. But rather than making a table and looking for numeric patterns, imagining a base with “lots of sides” focuses attention on the geometric structure. Students quickly make the conclusion that for a prism the number of faces is always two more than the number of sides on the base because there is a top and bottom and a rectangle for each side. Similarly, the number of vertices is twice the number of sides on the base, and the number of edges is three times the number of sides on the base. These observations can then be expressed algebraically.

The resource then presents some problems to solve, giving students certain information and asking them to decide whether the shape could be a prism or pyramid and to complete the remaining information. It also asks students to use their results to verify Euler’s Rule for prisms and pyramids. Lesson 2 introduces a new shape—the antiprism.