The Folding Sheet

About this tool

The Folding Sheet is a square of squared paper on the class screen. Children colour squares — anywhere, on both halves. Then somebody says where they think the mirror is, and puts the crease there. Then you fold, and the paper answers. It takes a minute to learn and a term to exhaust.

When the sheet folds, the far half lands on the near half like a transparency. Where colour meets colour you see two layers. Where colour meets bare paper you see one layer, because one thickness of paint is thinner than two. Where two different colours meet you get a third thing. Nothing is marked and nobody is told they are wrong — single thickness is a property of paper, not a verdict.

The crease is the interesting part, and it is why this is a tool rather than a worksheet. "Is it symmetric?" has no answer at all until you say along which crease. A shape can fold beautifully down the middle and not at all across. So two children put the crease in two different places, and both of them fold, and the argument is settled by the paper rather than by the grown-up. Then you move it again.

It refuses a lot on purpose. Nothing is timed, nothing is scored, there is no right answer and no counter anywhere. It never counts how many ways a shape folds, because that is a much later idea and counting it here would turn a conversation into a test. Nothing is saved: close the page and the sheet is gone.

How to use it in class

• Open it on the class screen so everyone is looking at the same sheet.
• Let children come up and colour squares — on both halves, not just one.
• Before folding, ask where the mirror is. Put the crease exactly there.
• Ask what they think will happen, then fold it in front of them.
• Look together: which squares came out with two layers, and which with one.
• Open it out, move the crease somewhere else, and fold it again.

Classroom ideas

• Colour a lopsided blob on purpose and ask the class to find a crease that makes any of it match. The failures are as useful as the successes.
• Colour only one half, then tap Show me the mirror and let a child commit the partners one at a time before you fold.
• Press and hold a square so its partner lights up. Ask a child to predict the partner before you press it.
• Use the corner-to-corner crease on a figure the class already folded down the middle, and ask why it stops working.
• Data and shape work like this sits in the early primary curriculum; finish by copying the folded sheet onto squared paper, one square per square.