Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

I'm Eight

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

Dice and Spinner Numbers

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

1, 2, 3, 4, 5

1, 2, 3, 4, 5

Using the numbers $1, 2, 3, 4$ and $5$ once and only once, and the operations $\times$ and $\div$ once and only once, what is the smallest whole number you can make?

Why do this problem?

This short problem could be used to start a lesson or fill a gap made by those who finish early. It will promote thinking about numbers and offers opportunities to practise multiplication and division.

Key questions

What results can you find obeying these rules?
Why don't you put all your answers in order?
What things do you notice about your different results?
Why do you not get any divisions by $5$?
Does it help to multiply by $1$? If not, why not?

Possible extension

Learners could make the largest number that they can using the same rules, and then as many results in between as possible.

Possible support

Using a calculator will help some children.