Planes of Symmetry in 3D Shapes

March 12, 2023

Differentiated Learning Objectives

• All students to identify the planes of symmetry in a cube.
• Most students to identify the planes of symmetry in 3D shapes using isometric paper.
• Some students should be able to identify and sketch the planes of symmetry for any solid.

Links to Lesson Resources (Members Only)

Starter/Introduction

 Prompts / Questions to consider

• Do vertices or edges connect faces?
• Do edges or faces join at a vertex?
• What is another word for vertex/vertices?
• How can we count the hidden faces, edges and vertices?

Planes of Symmetry in 3D Shapes

Discuss with the class a plane of symmetry bisects a shape into two halves that are mirror images of each other. Therefore, it is essential to show the plane of symmetry as a face rather than a line. Students often forget that planes of symmetry can run diagonally as well as horizontally and vertically. Watch the video above for further examples.

Students could attempt to sketch all the planes of symmetry for the hexagonal prism on the handout provided. Encourage students to work in pairs for peer support. Students should hold up their work to the teacher for feedback.

 Prompts / Questions to consider

• How is a plane of symmetry different to a line of symmetry?
• Does the plane of symmetry split the shape in half?
• Can planes of symmetry be diagonal as well as vertical and horizontal?
• Do all shapes have planes of symmetry?

Plenary

 Prompts / Questions to consider

• Where are the planes of symmetry for each solid?
• What is the same/different about each solid?
• Could any more solids with the same property be included?

Differentiation

More able students could attempt to sketch the planes of symmetry for non-regular solids such as tetrahedrons. Less able students could have templates of the solids already printed for them.

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