If you had 36 cubes, what different cuboids could you make?
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
What size square should you cut out of each corner of a 10 x 10 grid to make the box that would hold the greatest number of cubes?
There are lots of answers to this problem, depending on what questions you choose to ask.
Have a go yourself, and if you discover anything interesting, email us to tell us what you've done! 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 in a summary of your children's work.