We have some square sheets of paper measuring 15 cm by 15 cm and we are going to use them to make little boxes without lids.

We will do this by cutting out squares at the corners and then folding up the sides.

We want to find what sized corners must be cut out so that the box holds as much as it can, that is, have the maximum volume.

What size corners would should we cut out?

Cut out, or work it out for, different sized square corners and see.

Make a table of your results and draw a graph.

When you are happy that you know the answer for a 15 cm square, try different sized squares, both smaller and larger, and see if what patterns emerge.

(Adapted by Jenny Murray from the ATM publication, Primary Points of Departure, Sept 1997. ISNB 1898611 017.)