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'Picture a Pyramid ...' printed from http://nrich.maths.org/
Why do this problem?
This problem requires pupils to visualise the described pyramid in order to answer the questions. Your class will also be using knowledge of square numbers to solve the problem.
It might be best to introduce this activity orally so that children do not have to read lots of text. You could jot down a few reminders on the board for them to refer to as they try each part of the problem. Before asking them to picture the cubes vertically above and below each other, you might like to ask pupils to tell you where particular numbered cubes are in the pyramid so that you can
check everyone is imagining the same thing. You might suggest that at first they try to answer your questions without writing anything down, and talk about any difficulties this poses, but soon give them the opportunity to record the pyramid in whatever way they find most helpful. Share some of these representations with the whole group before going on to try the problem itself.
This sharing is a very valuable part of the visualisation process as it is a skill in itself not only to describe your own visualisation, but also to understand someone else's and compare it with you own.