Pythagoras 3D problems

A complete lesson on using Pythagoras’ theorem for 3-dimensional scenarios.

Activities included:

Starter:
Two questions involving a spider walking along the faces of a cuboid. For the first question, pupils draw or use a pre-drawn net and measure to estimate the distance travelled by the spider. This leads into a discussion about finding exact distances using Pythagoras’ theorem, followed by a second question for pupils to apply this method to.

Main:

• Highly visual example and quick questions for pupils to try on finding the space diagonal of a cuboid.
• A set of questions with a progression in difficulty, starting with finding space diagonals of cuboids, then looking at problems involving midpoints and different 3D solids.
• An extension where pupils try to find integer dimensions for a cuboid with a given space diagonal length.

Plenary:
Final question to discuss and check for understanding.

Printable worksheets and answers included.

Please review if you buy as any feedback is appreciated!