Determine whether a 2D arrangement can fold into a cube.
Free to use and free to share. There is no sign-up, no score, and nothing a child does here is recorded or sent anywhere.
Practise it now
Only one of these layouts folds up into a cube. Fold them and watch what happens, then pick the one that closes.
This exercise practises validate a cube net alongside its own main skill, Recognising a Cube Net.
It covers most of this skill rather than all of it.
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A worked example
One question of the kind this skill is tested with, worked all the way through: the reasoning, and what the wrong answers are there to catch.
The arrangement that will not close up
Which one of these four arrangements does NOT fold up into a cube?
Four arrangements of six squares, each one drawn edge to edge on squared paper.
Three of these are real cube nets and one is not.
No square may be moved, and no square may be folded onto another one.
A row of four squares, with one square above the first square and one square above the last square
A row of four squares, with one square above the first square and one square below the last square
A row of four squares, with one square above the second square and one square below the second square
Two rows of three squares, joined so that the right-hand square of the lower row sits directly beneath the left-hand square of the upper row
Answer: A row of four squares, with one square above the first square and one square above the last square
How you get there
Every one of these has six squares, so counting will not separate them. Bend the row of four into a band and it makes the four sides of the cube, leaving the top and the bottom open. In the first arrangement both spare squares hang off the TOP edge of that row, so both of them fold down onto the top face and land on top of each other. The bottom is left open and one square has nowhere to go. The other three all close both ends exactly once, so those three are nets and the first one is not.
Why the other answers tempt
The first two arrangements look almost identical: a row of four with two squares hanging off it. Which SIDE of the row each spare square sits on is the entire answer, and it is the easiest detail in the question to stop noticing.
If they are stuck, say this
Hold the band of four in your head, then take the leftover squares one at a time and ask which open end each one closes. Two squares closing the same end means it is not a net.
Only one of these layouts folds up into a cube. Fold them and watch what happens, then pick the one that closes.
This engine’s own main skill is Recognising a Cube Net. It practises validate a cube net alongside it, and covers most of it rather than all.
Layout A is the only one whose six squares close onto six different sides of the cube, which is what makes it a net. Fold layout B instead and the square in the top row, far left lands on the same side as the square in the bottom row, third from the left, so one of them would have to cover the other. Every wrong layout here is a single square away from being a real net, so a layout that looks almost right usually is only almost right.
Step 1. Fold them. Tap two of the layouts to watch them try to fold. Only a real net closes into a cube - any other layout lands two squares on the same side.
Step 2. Which one is a net?. Now pick the layout that folds into a cube with nothing covered up.
What to say if they get stuck
Fold a layout one flap at a time and keep a finger on the square you started from. Watch where each flap ends up.
Every layout here fills the grid and every one of them is a square away from folding, so nothing on the surface separates them. Fold each one up, keeping a finger on the square you started from.
A layout is a cube net only when its six squares land on six different sides. Two squares on the same side means one would have to cover the other, and that layout is out.
The 11+ does not test these skills in isolation, and practising one in the wrong order wastes the practice. These are the skills the curriculum map connects this one to.
Both require folding representation, but generic paper folds and cube topology differ.
How validate a cube net differs from the skills beside it
The same exercise practises one other skill, and telling them apart is often the difficulty rather than the exercise itself. On this page the skill is: determine whether a 2d arrangement can fold into a cube, and it stops where excludes marked-face tracking.
Answered from what the skill map records about this skill, not from a template. Every answer here is on the page, and the same questions are the page's FAQ structured data.
Determine whether a 2D arrangement can fold into a cube. It is one of 22 named non-verbal reasoning skills in the 11+, in the spatial strand, and this page carries 1 interactive exercise that practises it.
The first two arrangements look almost identical: a row of four with two squares hanging off it. Which SIDE of the row each spare square sits on is the entire answer, and it is the easiest detail in the question to stop noticing. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.
Point at the next move rather than explaining the whole rule. Hold the band of four in your head, then take the leftover squares one at a time and ask which open end each one closes. Two squares closing the same end means it is not a net.
Once it is secure, the skill map opens track opposite cube faces. Opposite-face reasoning presumes a foldable cube net.
The skill map draws the line here: Excludes marked-face tracking. A question past that line is testing a different named non-verbal reasoning skill, which is worth knowing before you spend a week practising the wrong one.
The skill map connects it to track a paper fold. Both require folding representation, but generic paper folds and cube topology differ. That skill has its own page here.
Use The Net Checker, embedded on this page. It is the exercise the skill map attaches to validate a cube net, it runs in the browser with no account to make, nothing is scored, and nothing a child does here is recorded or sent anywhere. It also has its own link, so you can send it to a child without sending them anywhere else first.
Validate a cube net is the step before track opposite cube faces
A free diagnostic maps the whole run of skills either side of this one, so practice follows the order the paper actually needs.
