This practical investigation will increase children's confidence with manipulating and rotating shapes, and they may even be able to visualise how the pieces fit together before checking.
It would be good to get quite young children having a go at this investigation by providing them with a square piece of card. A pre-drawn line could be useful for some pupils, to help them on their way. The line goes from half way along one edge to half way along an adjacent edge. The triangle can then be cut off and the shape covering explored. Here
is a sheet of pre-drawn squares which you may find useful.
Ideally, pupils could work in twos or threes and take turns, having a chat together so that when one solution is suggested it has to be justified to the other(s).