Nets and folding

Hello, and welcome to Myriora Maths! Here are six squares, joined edge to edge. If you cut them out and fold them, will they make a cube? Some shapes do, and some don't. In the 11 plus, you have to tell which, without any scissors!

Let's fold this cross. The middle square is the bottom of the cube. The four squares around it fold up, to make the sides. And the last square folds over the top, like a lid. Six squares, six faces: a cube!

Here's the most useful trick. In a straight line of three squares, the two end squares are opposite faces of the cube. Here's one pair. Here's another. And the two arms are a pair too. Every face has exactly one opposite.

How many different nets make a cube? Exactly eleven. Turning or flipping a net doesn't make a new one. Of all thirty-five ways to join six squares, only these eleven fold into a cube.

Now, two warning signs. First: a two by two block. Only three faces of a cube meet at a corner, so four squares round one corner can never fold up. Any shape with a two by two block fails.

Second: five squares in a row. Four squares wrap all the way round the cube. The fifth lands right on top of the first! So never more than four in a row.

So how do you check a net? First, look for the warning signs: a two by two block, or five in a row. Then pick one square as the bottom, and fold the rest up in your head, one at a time. If two squares land on the same face, it doesn't fold.

A common mistake is thinking any six squares will do. Six squares, six faces, so it must be a cube? Look at this U shape. Both ends fold up onto the same face, and one face is left open! Only eleven shapes work, so always check.

Your turn! Which of these four nets folds into a cube: A, B, C, or D? You've got twenty seconds, or pause the video. Go!

Time's up! In A, the two flaps on the same side land on the same face. B has a two by two block. D has five squares in a row. Only C, the staircase, folds into a cube!

Quick review. A cube has exactly eleven nets. A two by two block, or five in a row, means it won't fold. In a line of three, the end squares are opposite faces. And when in doubt, fold it in your head, one square at a time. See you next time!