Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Domino Square

## Domino Square

**Why do this problem?**

### Possible approach

### Key questions

### Possible extension

### Possible support

## You may also like

### Consecutive Numbers

### Roll These Dice

Or search by topic

Age 7 to 11

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

These are the 'double-3 down' dominoes.

Use these dominoes to make this square so that each side has eight dots.

This task is designed to test your thinking! Do you have the resilience and the strategies to solve it?

Dominoes are a great resource and this problem uses them in an intriguing and curious way. Not only does this activity require logical thinking but it is also an interesting way of practising addition and subtraction, and it provides an opportunity to talk about different ways of recording.

If you have an interactive whiteboard, you may find our Dominoes Environment useful for this problem.

You could introduce the challenge by laying out ten large dominoes in a square on the floor (it does not matter which dominoes go where). Ask the class to gather round and ask a few questions about the sum of dots on each side so that learners understand how the corner spots are counted in both the horizontal side and the vertical side.

Introduce the problem itself and ask pairs of children to talk for a minute or two about how they might tackle the problem. Share some of their suggestions among the whole group before giving them time to work in their pairs with dominoes. Using real dominoes whenever possible would be advantageous, but if that isn't possible then you could cut out some dominoes from our printable resources page. Squared paper would also be useful for jottings and recording.

As well as talking about the solutions in the plenary, you could focus on how children recorded their solutions. Some may well have just used the dominoes and moved them around as they went but how did they keep track of what they had tried? Some may have jotted down pictures of different arrangements. It would be useful to have a conversation about what ways of recording are most useful in this context.

Tell me what you have done so far.

What do the numbers on this side add to?

What do you need to make eight?

What could you try instead?

Use the 'double 4 down' dominoes to make a rectangle with equal numbers of dots on each side. Repeat with 'double 5 down' etc.

What numbers of dominoes can be made into a true square? Explore the numbers that emerge and explain why certain numbers of dominoes cannot be made into a square.

Use real dominoes and sort out the '3 spot down' ones and use them to make a square. Then count the dots on the sides and work on the problem on a 'trial and improvement' basis.

You could start with the 'double 2 down' dominoes making each side add to 16 and using a square like this:

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?