If you put three beads onto a tens/units abacus you could make the numbers $3$, $30$, $12$ or $21$.

Explore the numbers you can make using six beads.

### Why do this problem?

This problem is a good, yet simple, activity that can get pupils thinking hard about numerals, numbers and place value.  It also provides a context for discussing different ways of recording.

### Possible approach

You could start the children off by showing them one of the examples for three beads and then asking for other ways the beads could be arranged, reading the numbers together. You may want to use a basic drawing of the abacus on an interactive whiteboard and have 'beads' to drag into place. At this stage, you could encourage learners to try and explain how we know we have all the different ways.

After this the children could work in pairs on the six beads problem so that they are able to talk through their ideas with a partner. Have available a range of equipment which they could use, but allow them to make their own choice.  You may have, for example, a real abacus, counters, paper, beads, coloured pencils/pens etc. They could use digit cards to make the number which is represented on the abacus.

In the plenary, children could compare the ways in which they have recorded their findings and you could discuss the advantages of each. You could then talk about which recording methods would be best if we wanted to be sure that we had all the ways of using six beads. At this point, you could share any that have used such a system, or you could demonstrate your own way.

### Key questions

What can you tell me about the numbers you've found?
Are there any other ways you can arrange those beads?
How can you tell if you have them all?

### Possible extension

Learners could increase the number of beads or they could be asked to investigate what would happen if there were three columns: units, tens and hundreds.

### Possible support

Some children may find it easier to use four beads, rather than going straight on to six. Using practical apparatus, such as counters, is essential for those having difficulties in understanding the problem.