Boyang from Mountfields Lodge and Caroline from St Jude's C of E School looked at this problem very logically. To balance 7 on the left using two "half" weights on the right, Boyang told us:

The two numbers on the right hand side could be:

$\frac{1}{2}$ + $6\frac{1}{2}$

$1\frac{1}{2}$ + $5\frac{1}{2}$

$2\frac{1}{2}$ + $4\frac{1}{2}$

$3\frac{1}{2}$ + $3\frac{1}{2}$

$4\frac{1}{2}$ + $2\frac{1}{2}$

$5\frac{1}{2}$ + $1\frac{1}{2}$

and finally, $6\frac{1}{2}$ + $\frac{1}{2}$.

I wonder whether the first solution is different from the last one? What do you think?

Caroline wasn't sure whether you are allowed two weights on the same hook, but I think that's fine.

Nobody has looked at hanging three weights on the right-hand side, or having quarter divisions on the balance. If you do investigate these situations, let us know! Please don't worry that your solution is not "complete" - we'd like to hear about anything you have tried.Teachers - you might like to send a summary of your children's work.