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More Christmas Boxes
Age 7 to 11
Challenge Level 
Why do this problem?
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.
Possible approach
It would be good, after introducing the challenge, to allow
those who wanted to cut out squared paper to help with the
exploration.
Key questions
How did you find the number of cubes?
Is there any way in which you could change this
challenge?
Possible extension
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?
Possible support
Some pupils will need assistance to cut off the squares
accurately.
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