Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Reflecting Squarely

Click here for a poster of this problem.
## You may also like

### Frieze Patterns in Cast Iron

### The Frieze Tree

### Friezes

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

Age 11 to 14

Challenge Level

*Reflecting Squarely printable sheet
Reflecting Squarely printable grids*

The three pieces below can be fitted together to make shapes with at least one line of symmetry.

The vertices of each piece must lie on grid points, and you must not overlap two pieces.

The pieces must be placed edge to edge, so this is not allowed.

This arrangement does not satisfy the criteria because the shape does not have a line of symmetry.

Can you find all the possible solutions? (There are more than six.)

**How can you be sure you've found them all?**

Here are some further questions to explore:

Design your own set of three shapes, with a total area of 10 square units, as above.

How many ways can they be arranged to make symmetrical shapes?

Can you find a set of three such shapes which can be arranged into more symmetrical shapes than those in the original problem?

Can you find three such shapes which can **never** be arranged to make a symmetrical shape?

*You may wish to print copies of the shapes.*

Here is an interactive you might like to use to try out your ideas. The red dot can be used to rotate the pieces and the blue dot can be used to move the pieces. To flip the pink piece, click on it.

*This problem is based on one found in the Dime "Line Symmetry A" pack, produced by Tarquin Publications*

Click here for a poster of this problem.

A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.

Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?

Some local pupils lost a geometric opportunity recently as they surveyed the cars in the car park. Did you know that car tyres, and the wheels that they on, are a rich source of geometry?