More Christmas Boxes

This well known challenge is one which gives pupils opportunities to further their understanding of volume and the factors which affect size. It covers that part of understanding where common sense may not be sufficient.

It would be good, after introducing the challenge, to allow those who wanted to cut out squared paper to help with the exploration.

How did you find the number of cubes?

Is there any way in which you could change this challenge?

When exploring the volume - as distinct from the number of cubes - what about cutting a square $1.5$ by $1.5$ from each corner?

Suppose the $10$ by $10$ sheet had two smaller sheets cut from it? What would the total volume of the two boxes be?

Some pupils will need assistance to cut off the squares accurately.