In Hamilton's 'Dotty Triangles' investigation, children use trial and improvement to find different ways of making a given total by adding three small numbers.
Children apply prior learning to recognise pairs of numbers that make 3, 4 and 5, before the investigation is extended to totals of 6 and 7. They are directed to look for patterns in the numbers of possibilities. One of the aims of the investigation is that children will begin to make predictions about the next number in a sequence.
As well as successfully finding a range of ways to arrange 5 counters, this learner shows good evidence that he understands how to record an addition calculation.
He has not found all possibilities, yet, for the arrangement of 5 counters. The teacher might help him see how to work through the possibilities systematically, perhaps by simplifying the task and focussing on the possible arrangements for 3 counters, starting with the largest number first, i.e., 3+0+0, 2+1+0, 1+1+1.
Try the Dotty Triangles Investigation with your class.