Why do this problem?

When we use structured apparatus such as Cuisenaire rods, dominoes, Numicom etc. we often assume that children understand more about the structure than perhaps they do. This activity encourages children to explore the structure in their own way - and you may be surprised at how many different ways there are. You could use this activity in one of two ways, depending on your children. The most obvious way is to focus on the different patterns that can be built up, but you could also use the activity to focus on the explanation or justification of the children's description or argument. You might like to have a go yourself before offering this activity to the children...

The task, along with Amy's Dominoes as a follow-up, also offers the chance to focus on any of the five key ingredients that characterise successful mathematicians.

Possible approach

You will need several sets of dominoes (you could make laminated card sets from this print out), one set between three or four children. If the dominoes are usually stored in a box, transfer them to a bag so that the children don't have a sense of a box being full.

Ask the children to tip the dominoes out onto the table and have a look at them, perhaps having an opportunity to play with them and arrange them into different patterns if this is the first time they have seen them.

Suggest that they may or may not be full sets and that before we can use them for a game we need to know if any are missing. Could they help you by finding out? Allow some time for this.

When a group gives you a definitive answer ask them how they know and challenge them to arrange the dominoes on the table in some way to show you that they have/have not got a full set. Again allow some time for this.

When, and if, appropriate you could suggest that the children move around the classroom to have a look at what other groups have done. You may then want to offer a little more time for those groups who haven't made much progress to have another go, having seen others' responses.

Groups will respond in different ways. In increasing order of sophistication, groups may:

- play a domino game where they match dominoes into a long train or loop, for example:

- make piles or groups of dominoes with numbers in common, for example:

- arrange the dominoes into a pattern or array, for example:

In each case, ask how the pattern/structure they have chosen helps. The most sophisticated explanations will use the idea of all possible pairings of the numbers 0-6.

The interactivity here may be helpful for whole class discussions of this activity and/or for learners to use as they work on the task, if real dominoes are not available.

Key questions

How many are there with blanks?

Are there the same number of dominoes with ones?

Tell me how you're arranging them. Why did you choose that way?

Could you organise them in a different way?

How does this show you that you have/haven't got them all?

Possible extension

What if you had a set of 0-9 dominoes (download a set here). How many do you think you would have? Do you need to make a set? How else could you record your ideas?

The task Amy's Dominoes is a natural extension to this activity and can be solved using the dominoes as a resource, or without them by more confident children.

Possible support

Reducing the number of dominoes can make a pattern easier to spot. Offer a subset, say 0-4, and allow time to play and look for patterns before asking if they have a full set.