Wallpaper Patterns
Years 4 - 8


  • Print this Board.
    You will make patterns on it.
  • Print these Tiles and cut them out.
  • Find a camera.
    It will be great for recording the patterns you make.
  • Write the title of this challenge and today's date on a fresh page in your maths journal.
In this activity most of your recording will be done with the camera.
But keep notes in your journal about your thinking and actions.

Investigating Wallpaper Patterns

A piece of wallpaper like this is made from just one small square that is repeated all over the paper by following a rule.

We will call that small square a tile.

Before the wallpaper is printed the edge lines of the tiles are removed.

Then you can see the pattern more clearly.

This might look good as the wallpaper in a gymnasium office.
Can you think of a different place it could be used?

If we put back the edges of the design tiles the wallpaper would look like this one below.

It doesn't look quite so good now does it.
Perhaps it looks a bit more like a tiled floor than a piece of wallpaper.

In this activity:

  • Sometimes you will be a designer working with tiles to create a new wallpaper design.
  • Sometimes you will be a thief trying to figure out how someone else's design works so you can copy it.

The mathematics of movement geometry will help you.
Movement geometry is usually called transformation geometry.
Transformation geometry includes movements such as reflection, rotation and translation.
Translation is sliding an object in a straight line.
It starts here X----- and ends here ----->X.
The line can be in any direction.
This activity only uses horizontal and vertical.

Getting Started

  • Take a good look at your cut out tiles. They are not all the same. Sort them into piles of the same tile.
  • When you have the piles correct each pile will have the same number of tiles.
In your journal, sketch one from each pile. Which transformation will turn one into the other?

  • Open this Wallpaper Patterns Starter.
    You can read it on screen or print it.
    You will also need the board you already printed.
  • Follow the Starter through to begin creating wallpaper designs.
  • When you get to the Challenge, it only asks you to make up one of your own.
    But go crazy if you want to and make up more.
    Just remember to photograph what you make and record the rules for making it.
Have fun exploring Wallpaper Patterns.

How Were They Designed?

  • Print this collection of designs which have all been made from your tiles. (6 pages)
    If printing 6 pages is too much then look at the challenges on screen and just print the design rules.
  • Print this list of design rules. (1 page)
Your challenge is to match the design with the rules that made it.
We have made it a bit easier by leaving in the tile edges.
You don't have to do them all. Some are a bit tricky.
The answers are below.

Your Turn

Now you know how to design this type of wallpaper:
  • Start with a square.
  • Draw something interesting in it. The best results happen if the inside drawing is not symmetric.
  • Use a transformation rule to move the tile into the next section across and down.
  • Remove the edges of the design tiles.
When you are ready, have a go at designing your own wallpaper. If you have a computer with drawing software you can do it on screen. If not, do it with a pencil and ruler and careful drawing like they did in the old days. If you measure the Start square first you will know what size to make your tiles so you can move them around on the board.

We would love to see anything you create.

Just Before You Finish

A mathematician has much more in the skill toolbox than just numbers and tools to combine them.
In this activity you have learned about some geometry tools.
  • In your journal explain all you know about transformations.
  • Can you also describe how to move a tile from the start to the next space in two different ways and still get the same result?


Answers & Discussion

Answers to How Were They Designed?.

These notes were originally written for teachers. We have included them to support parents to help their child learn from Wallpaper Patterns.

Send any comments or photos about this activity and we can start a gallery here.


Maths At Home is a division of Mathematics Centre