### I'm Eight

Find a great variety of ways of asking questions which make 8.

### More Mods

What is the units digit for the number 123^(456) ?

### Repeaters

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

# What Is the Question?

### Why do this problem

This problem is based on one of many ways of supporting multiplication. The examples consider numbers from 6 to 9 but does the method work, or can it be modified to work for other numbers? The focus is on the why, rather than any sense that this is a preferable way of calculation. But this is an interesting representation nevertheless and leads to the question, "What sort of person could have thought of this for the first time?".

### Possible approach

Rather than show the images on the site it might be good to take a small number of learners in the group into your confidence and ask them to show examples and give the answers without explanation, asking the rest of the group to make sense of the code.

Once the code has been cracked the question has to be asked why it works. This may be something you wish to leave learners to think about over time, returning to the problem if and when any light is shed.

### Key questions

Can you find a way of defining the number of fingers you multiply and the numbers you add?

### Possible support

Discussion of complements of 10 first might support learners in making the necessary connections.

### Possible extension

Could you start at 16 on each hand? What adjustments would you need to make?