Nets of a Cube
Shape & Space · Year 5–Year 6
Build six squares and see whether they fold. Eleven nets to find.
About the cube nets
Tap squares on the grid to build an arrangement of six, and the board says whether it folds into a cube. There are exactly eleven that do, and the ones a class finds are collected in the eleven slots beside the grid, so the lesson has an end to it: find the lot.
The board works the fold out rather than looking it up. It rolls a cube over the squares one at a time and notes which face lands where, so an arrangement fails because two faces of the cube would end up in the same place, and that is what the board says. It is the reason a shape with four squares in a block never works, whatever else is round it.
This is the thing that cannot be done with paper in a lesson. Cutting out an arrangement, folding it, finding it does not work and starting again takes ten minutes per attempt, so a class gets through two. Here they get through twenty, and the ones that fail are as useful as the ones that work.
Squares that will not fold are shown in a different colour from the ones that will, so a class sees the answer before they read it, and the line underneath says which of the two things went wrong: not joined up, or two faces in the same place.
Finding all eleven unaided is harder than it sounds, so the board helps twice. When six squares are on the grid and moving one of them would make a net, it says so, which is the difference between guessing and getting somewhere. And Hint puts one you have not found into the collection, drawn pale rather than gold: copy it onto the grid and it turns gold, so the collection always says which ones the class worked out.
The eleven sort into four families by the longest line of squares in them, which is the way to hunt them down rather than guess. Six of them have four squares in a line, four have three, and one is the staircase with no more than two in a line anywhere. A class that has found the six with a row of four has found more than half of them.
How to use it on your whiteboard
- 1Tap squares on the grid to build a net. Tap again to take one off.
- 2Watch the count: a net needs six squares, because a cube has six faces.
- 3When six squares fold, the net is added to the collection on the right.
- 4Press Again to clear the grid and go looking for another one.
- 5Press Hint if you are stuck: one you have not found goes into the collection to copy.
- 6Keep going until all eleven are in the collection. Tap Fullscreen to fill the board.
Questions
- How many nets does a cube have?
- Eleven. The board does not have that list in it: it works out whether each arrangement folds by rolling a cube over the squares, and the eleven are what that comes to. A test in the code checks it by trying every arrangement of six squares on the grid.
- Why will my arrangement not fold?
- Either the squares are not all joined edge to edge, or two faces of the cube would land in the same place when it folded up. The board says which. Anything with four squares in a block falls into the second case.
- We are stuck. Is there any help?
- Two kinds. With six squares on the grid, the board says when moving one of them would make a net you have not got, which turns guessing into hunting. And Hint puts one you have not found into the collection to copy: it goes in pale rather than gold, so the collection still says which ones the class worked out.
- Is there a way to hunt them down rather than guess?
- Yes: sort them by the longest line of squares. Six of the eleven have four squares in a line, four of them have three, and one is the staircase with no more than two. Working through one family at a time finds them all far faster than trying arrangements at random.
- Is a net turned round a different net?
- No, and the collection treats it as the same one. A net rotated or flipped is the same net, which is why there are eleven rather than fifty-four.
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