Why do this problem?
is a challenging one. It uses the learner's knowledge of square numbers and gives the opportunity of practising addition in an unusual context. It is a useful problem through which to discuss different methods of approach.
You could start by reminding the group about square numbers, perhaps by playing a game of 'I like ...' where you write up numbers you 'like' (i.e. are part of a set) to one side of the board and numbers you 'don't like' (i.e. are not in your set) to the other, as children suggest numbers. The idea is for children to determine the name of your set.
You could then use the small cycle given at the beginning of the problem to introduce the idea of a cycle of squares, encouraging learners to check that each pair of numbers does indeed add to a square number.
(The cycle goes like this: 14 - 2 - 7 - 9 - 16 - 20 - 29 - 35 -.)
Then you could go on to introducing the actual problem. Learners could work on this in pairs, using numbered counters that can be moved round experimentally or number cards printed from this sheet
At the end of the lesson, all learners could be involved in a discussion of how they tackled the problem, building up the cycle on the board, number by number. You could invite them to comment about the advantages/disadvantages of the different methods used and they may decide that one method is particularly efficient.
Can you think of a good way to start?
Have you made a list of square numbers up to 100?
Which of the numbers given can be added to that one to make a square number?
If you cannot go on from there, what could you try instead?
Learners could make their own cycle of squares using different numbers, or invent cycles using a different number property.
Making a list of the square numbers up to 100 will help some children get started on this problem. Encourage the learner to choose one number and see which of the numbers given can be added to it to make a square number. Numbered counters to work with could be very helpful and a calculator might free-up some children who find calculation difficult.