## Amy's Dominoes

Amy has a box containing ordinary domino pieces but she does not think it is a complete set.

She has $24$ dominoes in her box and there are $125$ spots on them altogether.

Which of her domino pieces are missing?

### Why do this problem?

This problem requires learners to understand the numbering system on dominoes and use this to solve a problem. Learners will need to use addition, subtraction and multiplication as well as logical reasoning.

### Possible approach

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

You could start by giving the whole group sets of dominoes to sort out in pairs or alternatively, if the children are already familiar with dominoes ask questions such as "How many domino pieces have four spots on them altogether?" and "How many domino pieces have five spots on them?"

Children could then work in pairs on the actual problem with a real set of dominoes or use the dominoes on this sheet which will need to be cut up.

In a plenary, children could discuss not only the solution, but what information they needed to have to work it out and what calculations they had to do along the way. There will be several different approaches which will not only help other children but also inform you about their thinking.

### Key questions

How many dominoes are there in a complete set? So how many are missing in Amy's set?
How many lots of six spots are there in a set of dominoes? How many is that altogether?
How many spots are there altogether in a complete set of dominoes?

### Possible extension

You could ask some follow-up questions, such as: If Amy had not $104$, but $140$ spots could you have found a solution? Is there just one possible answer or more? What was the fewest number of spots that could have been on the dominoes if four of them were missing? What could have been the greatest number of spots on a set that was missing four pieces?
Some learners may also like to explore a "double nine" set of dominoes which can be found on this sheet.

### Possible support

Children could sort a real set of dominoes by first taking all the blanks and arranging those systematically, and then all the 'ones' (except the blank/one which will be in use) and then all the 'twos' (except those already in use), and so on.

Some children might find it easier to attempt Domino Sets first.