What it shows
Some shapes, like squares, triangles and hexagons, can cover a floor without gaps. Others, like circles, leave gaps. This is why floors are tiled with certain shapes.
The science
When tiles meet at a point, the angles around that point must add up to a full turn, with no gap and no overlap. Squares, equilateral triangles and regular hexagons have angles that fit this way. Circles and regular pentagons do not, so they leave gaps. This covering of a surface is called tessellation.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- Coloured paper or old greeting cards (free)
- A ruler and pencil
- Scissors
- Glue
- A big sheet of paper
- A paper cup to trace circles
Safety
For this project: An adult must help children with scissors.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
8 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Cut ten squares of the same size from coloured paper.
Place them edge to edge on the big paper and check for gaps.
Cut ten equal triangles and try to fit them side by side without gaps.
Cut ten circles using the cup as a guide and try to fit them together.
Write the answer for each shape: gaps or no gaps.
Cut ten hexagons if you can with help, and try them too.
Glue the best fitting shape on your paper to make a floor design.
Look at a real tiled floor or a honeycomb picture and tell which shape it uses.
What you should see
Squares, triangles and hexagons fit with no gaps while circles always leave gaps, and you glue a tile pattern.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1What is tessellation?
Covering a surface with shapes with no gaps or overlaps.
2Which shape left gaps?
The circle.
3Why do bees use hexagons?
Hexagons fit with no gaps and use less wax.
4Name a floor pattern you have seen.
Square tiles are common at home.
Take it further
Try mixing two shapes, like squares and triangles, to make a new pattern.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
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