### Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

### Fencing Lambs

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

### Numerically Equal

Can you draw a square in which the perimeter is numerically equal to the area?

# Lawn Border

##### Age 5 to 11Challenge Level

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?