Geometry (2D & 3D shapes): Bee Hotel

The Problem

Whilst on his holiday, a school teacher called Mr M discovered an impressive bee hotel in a park (see opposite). You’ll notice that on the photographed face of the hotel, there are lots of interesting geometric shapes next to each other. Mr M thought that it would be a great idea to design something similar for his school, so he challenged his class to create a bee hotel design on square, dotty paper that included the following number of shapes:

• 3 triangles
• 4 rectangles
• 2 pentagons

If you were asked to design a bee hotel that had a face with exactly this number of shapes, and no spaces between them, what would it look like?

Did you know?

The osmia bicolor bee is a fascinating solitary bee species that makes its nest inside empty snail shells!

Visualising the Problem and Getting Started

Before tackling the main problem, you might want to have some experience of moving tangram shapes around and seeing how they fit together. This can be done by visiting the tangram builder page on the Mathigon website.

Look closely at the bee hotel below.

What do you see?

Can you see a shape with 4 right-angles?

Can you see a pentagon? Is it regular or irregular?

How many hexagons can you see?