## Missing Middles

Here are eight sets of dominoes. Each set should have three dominoes that make a sequence.

Which domino would go in the middle of each set to complete the sequence?

How do you know?

Printable NRICH Roadshow resource.

**Why do this problem?**

This problem uses the idea of number sequences in a very tangible form. Children will be challenged to recognise odd and even numbers, as well as to count fluently both backwards and forwards. They will also have opportunities to justify their answers.

Possible approach

Ideally, children should be familiar with dominoes through free-play and domino games before attempting more formal tasks such as pattern building as in this problem.

You could start by using a very simple sequence of dominoes such as ones that are blank at one end and 1, 2, 3 etc at the other. This could be done with either floor dominoes, drawn on the board (or an interactive whiteboard - try our

Dominoes Environment) or made out of card.

You could then progress to an example in which there is a sequence on both the top and bottom of the dominoes, so that the children have some experience of looking at both. Ask them to justify their choices and listen out for reasons such as "It's the next number counting in twos" or "The tops are all the same".

After this introduction children could work in pairs on the problem. If possible each pair should have a set of dominoes to use.

This sheet might be useful for both rough working and recording. At the end children could give their answers, which might not be all the same, always giving reasons for their choices.

### Key questions

What numbers are at the top/bottom?

What number might come between these two? How do you know?

Possible support

The activities Next Domino and Domino Sequences would be good precursors to this task as they invite learners to extend sequences as opposed to completing the middle of a sequence. Having a set of real dominoes that can be manipulated makes the problem less abstract. You could encourage learners to start with just the 'tops' of the dominoes, then look
at the 'bottoms'. Children will benefit from saying the numbers in the sequence out loud to reinforce the familiar counting patterns.

### Possible extension

Children could work in pairs inventing domino sequences of their own. A set of 9-spot dominoes would be very useful so that longer and more complicated sequences can be made. Always expect the children to be able to justify the dominoes they have chosen. A set of 9-spot dominoes can be made from these
sheets.