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## 'Lawn Border' printed from http://nrich.maths.org/

I was trying to imagine what my lawn would look like with a nice
paved border around it. So I used some tiles that were all the same
size but different colours, to build a little model. This is how it
looked:

Make some kind of model or picture of
your own that shows the same sizes.

Look at the number of tiles for
different parts.

I wondered what my border would be like if I changed some of the
tiles. I made it like this:

What do you notice has changed?

I decided I'd make some more changes to my model garden. I did
this.

How does this compare with the last
one?

I made one last model with some different tiles. Here it is. I
liked this one.

Have a good look now at the numbers of
the different tiles in different places for each of my models.

If I use $12$ tiles to make a lawn, how many tiles would I need
to make a border?

How many differently shaped lawns can you make with $12$
tiles?

Do you need a different number of border tiles to go around each
lawn shape?

Can you make models to show what the different gardens would
look like?