Why do this problem?
This problem gives pupils the opportunity to use knowledge and skills associated with spatial awareness, addition and multiplication, and to explain their thinking. It also involves keeping to rules that must be followed. The further they progress through the activity, the greater the opportunities for learners to use a whole variety of
problem-solving skills. The activity also opens out the possibility of pupils asking “I wonder what would happen if . . .?”
Pupils' curiosity may be easily aroused while trying to find solutions to the challenges.
It would be good to demonstrate the kind of arrangements that are allowed as well as making those that break the rules for the pupils to decide on what is ok.
You may decide that you want the pupils to work in groups of three or four. One set of numbered cubes will be needed for each group. Having set them the first challenge, it may be sufficient to stop there. Challenges 2, 3 and 4 can be introduced straightaway or left to another occasion.
It is worthwhile noting that in the "steps" arrangement as shown on the problem page, the 5 and 6 both have four faces showing; the 1 and 4 both have three faces showing. So, the cubes that have the same number of faces showing can be swapped allowing for more arrangements to be possible.
You may find this copy of the task useful to print off and give to learners: SixNumberedCubes.pdf
How are you working out the totals?
How have you got to this arrangement?
Tell me about your shape.
How sure are you that ...?
Some pupils may require help with getting the cubes to stack. Those who are unable to record their arrangements could have them photographed.