This activity invites discussion amongst pupils which will encourage them to use vocabulary associated with position and transformations.
The problem could be introduced using the interactivity so that it is easy for everyone to see clearly. However, it is also important for children to have paper or card copies of the shapes to work on the activity. This sheet contains four copies of the square or you could make your own on squared paper (the line dividing the square in two is drawn from one corner to the midpoint of the opposite side). It may be a good idea to use paper which is coloured on one side only and talk about whether the new shape should be the same colour all over.
Encouraging learners to be systematic in their discovery of 'new shapes' is important if they are going to be asked how they "know" they have found every solution. Look out for those children who have developed a system and ask them to share their method with the whole group. For example, they might keep one shape fixed and find all the ways of placing the second shape.
How will you record your findings?
How do you know you have found all the shapes?
Invite children to make another cut so that they have three pieces. How many new shapes can they make now? What cuts make the 'best' new set of shapes?
Having several copies of the square will mean that children can stick down each arrangement.