### Cubes

How many faces can you see when you arrange these three cubes in different ways?

### 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?

### Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

# Forgot the Numbers

##### Age 7 to 11 Challenge Level:

If you are a teacher click here for a version of the problem suitable for classroom use, together with supporting materials. Otherwise, read on ...

On my calculator I divided one whole number by another whole number and got the answer $3.125$.

I know that both numbers were less than $50$, but can't remember what they were.

Can you work out what they were?

Once you've had a chance to think about it, click below to see how four different pupils began working on the task.

Here is Gemma and Flo's work:

Richard wrote the following:

He explained:

"I multiplied $3.125$ by $1$, then I tried multiplying $3.125$ by $2$, then I multiplied $3.125$ by $3$ ..."

Here is the start of Thomas' work:

I first looked at the number $0.125$ and worked out what fraction of $1$ it is. It turned out that it was an eighth.

Can you take each of these starting ideas and develop it into a solution?