### Magazines

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

### Stairs

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

### Month Mania

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

# The Numbers Give the Design

##### Stage: 2 Challenge Level:

How about making designs like the ones above?

It's just a matter of getting a group of numbers together that repeat and then using a simple drawing rule, then colouring the pattern in.

A good way to start is to take a number sequence that you like, for example square numbers or the $3$ times table.
Just keep the ones (units) of those numbers, for example $1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4$ etc. or $3, 6, 9, 2, 5, 8, 1, 4, 7, 0, 3, 6$ etc.
You may notice that with these, and perhaps your own sequences, they go to a $0$ and then repeat.

For this challenge, you just need the numbers that go as far as just before the zero, for example $1, 4, 9, 6, 5, 6, 4, 1$ or $3, 6, 9, 2, 5, 8, 1, 4, 7$.

Now to draw ...

Using squared paper and starting somewhere in the middle, take each of the numbers in turn to tell you how long to draw the line and turn a right angle to the left after you've drawn each line.

This may help you to see what to do, using the example of square numbers and starting with the red $1$. I've coloured each new line with a different colour:

After the final $1$ you start again as shown below:

and so on until you get back to the beginning.
Some squences that you choose may not come back to the start but just keep stepping away!

So now it's your turn ...
You may like to change a rule or two after a while. (For example, you could change the turn to $60^\circ$ instead of $90^\circ$.)