Tessellations

Quick answer

A tessellation is a pattern made from shapes that fit together perfectly, without any gaps or overlaps. You can make tessellations with regular shapes like squares, triangles, or hexagons, or even with more interesting shapes like animals or flowers.

Learning outcome

By the end of this page, you will be able to make your own tessellation pattern using shapes that fit together perfectly, and you will understand how tessellations appear in the world around you.

• You can identify shapes that can tessellate (fit together without gaps)
• You can create a simple tessellation pattern using repeated shapes
• You can find real-world examples of tessellations in your home, school, or outside
• You can explain how tessellations are used in art, design, and nature

Why this matters

Tessellations are not just fun patterns – they are important in many real-life situations. Architects use tessellations to design floor tiles and building facades. Artists and designers use tessellations to create beautiful and repeating patterns in fabrics, wallpapers, and posters. Nature also uses tessellations, like the hexagonal pattern of a honeycomb or the scales on a snake’s skin. Understanding tessellations helps you see the maths in the world around you and gives you ideas for creative projects.

How it works

Tessellations are made by repeating a shape over and over again to cover a surface completely. The shapes must fit together perfectly, with no gaps or overlaps. Here’s how to make a tessellation:

1. Choose a shape that can tessellate (like a square, triangle, or hexagon)
2. Draw or cut out the shape
3. Place the shape next to another shape, making sure they fit perfectly
4. Repeat the process, keeping the shapes aligned
5. Continue the pattern across a surface

Examples you can see

Let’s look at some shapes that tessellate and some that do not.

Try drawing a square on a piece of paper. Now, place another square next to it, touching its sides. If you continue this pattern, you will see how the squares fit together perfectly to make a tessellation.

Try it as a mini adventure

Adventure: Build a Pattern Kingdom

You are the designer of a magical kingdom made of shapes! Your job is to create a tessellation pattern for the kingdom’s floor tiles. You have a set of shapes: squares, triangles, and hexagons. Your mission is to make a path using one of these shapes that tessellates perfectly.

1. Choose one shape to use for your path
2. Draw or cut out at least 6 copies of the shape
3. Arrange them on a piece of paper to make a pattern
4. Make sure there are no gaps or overlaps
5. Trace your pattern and colour it in!

After you finish, look around your house for other tessellations. Are there any tiles on the floor? Are there any patterns on wallpaper or fabric?

Common mistakes

• Mistake: Thinking that any shape can tessellate.
• Why it happens: Children may not understand that shapes must fit together perfectly without gaps or overlaps.
• Fix: Try placing shapes next to each other and see if they fit. If there are gaps or overlaps, the shape does not tessellate.
• Mistake: Thinking that a tessellation must be made of the same shape only.
• Why it happens: Some children believe that all tessellations are simple and repetitive.
• Fix: A tessellation can be made with two or more shapes that fit together.
• Mistake: Forgetting to check if the pattern repeats correctly.
• Why it happens: Children may focus on one part of the pattern and not notice if it continues correctly.
• Fix: After placing a few shapes, check if the pattern can continue the same way.

Parent and carer guide

Helping your child with tessellations is a fun way to explore geometry and creativity together. Here are some ways you can support them:

• Ask your child to show you tessellations they see in the house or outside (like floor tiles or brick walls).
• Encourage them to draw or cut out shapes and try to make a pattern.
• Use pattern blocks or shape cutouts to help them experiment with tessellations.
• Try the "Build a Pattern Kingdom" adventure together to make it more engaging.
• Don’t worry if the pattern isn’t perfect at first – it’s all part of the learning process.

Remember, tessellations are not just about maths – they are also a way to be creative and see the beauty in repeating patterns. Let your child explore and enjoy the process!

Practice questions

1. Which of these shapes can be used to make a tessellation? Circle your answer.
   • A. Circle
   • B. Square
   • C. Pentagon
   • D. Triangle
   Answer: B and D
2. True or false: A tessellation must always be made with the same shape.
3. Answer: False – tessellations can use different shapes that fit together.
4. How many triangles can meet at a point to make a tessellation?
5. Answer: Six triangles
6. Can a hexagon be used to make a tessellation? Why or why not?
7. Answer: Yes, because hexagons fit together perfectly with no gaps.
8. Draw a simple tessellation pattern using squares.
9. Answer: (No visual, but the pattern should show squares placed side by side with no gaps or overlaps)

FAQ

What is a tessellation?

A tessellation is a pattern made from shapes that fit together perfectly without any gaps or overlaps.

Can any shape be used to make a tessellation?

No, only certain shapes can tessellate. Shapes like squares, triangles, and hexagons can fit together perfectly, but circles and pentagons cannot.

Where can I find tessellations in everyday life?

You can find tessellations in floor tiles, wallpaper, brick walls, honeycombs, and even in art and fabric designs.

Are tessellations only in maths?

No, tessellations are also used in art, design, architecture, and nature. They are a beautiful way to combine maths and creativity.

How can I make my own tessellation?

You can use shapes like squares, triangles, or hexagons. Place them next to each other, making sure they fit perfectly with no gaps or overlaps. Then, repeat the pattern!