### Geoboards

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

### Tiles on a Patio

How many ways can you find of tiling the square patio, using square tiles of different sizes?

### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

# The Big Cheese

##### Stage: 2 Challenge Level:

Chloe, Emily, Rebecca, Scarlett, Chloe, Alana, Isobel, Shauna and Joel from Griffithstown Primary School sent in various solutions that were all very interesting and showed hard work. Here is a summary taken from their suggestions.

I found out that we can share the $13$ slices of the big cheese between $5$ people. This is how we did it:
The first person had a slice of cheese that was $25$cm$^2$.
The second person had $3$ slices of cheese that was $20$cm$^2$ + $4$cm$^2$ + $1$cm$^2$ = $25$cm$^2$.
The third person had $5$ slices of cheese that was $12$cm$^2$ + $6$cm$^2$ + $4$cm$^2$ + $2$cm$^2$ + $1$cm$^2$= $25$cm$^2$.
The fourth person had $2$ slices of cheese that was $16$cm$^2$ + $9$cm$^2$ = $25$cm$^2$.
The fifth person had $2$ slices of cheese that was $16$cm$^2$ + $9$cm$^2$ = $25$cm$^2$.
So everybody had an equal share of cheese but in different sizes.

Cherian from Quarry Bay School sent in the following;

Solution for the third investigation for The Big Cheese. My solution:
First you imagine the two $1$ by $1$ by $1$ cubes put on top of each other.
Then you put the $1$ by $1$ by $2$ layer beside the other one.
After that, put another $1$ by $1$ by $2$ layer in front of it, so that you will have a $2$ by $2$ by $2$ cube.
Now you have to put $2$ by $2$ by $1$ layer on top of it.
Then you put $2$ by $3$ by $1$ layer on the left side.
After that you put a $3$ by $3$ by $1$ layer behind it.
Then you put another one on your cube.
Now you put a $3$ by $4$ by $1$ layer beside it.
Then put a $4$ by $4$ by $1$ layer behind it.
Now you have a $4$ by $4$ by $4$ cube.
After that you put a $4$ by $4$ by $4$ layer on top of it.
Then put a $4$ by $5$ by $1$ layer beside it.
Now put a $5$ by $5$ by $5$ layer behind it, so now you have a $5$ by $5$ by $5$ cube!!