Unusual shapes: 11 Plus non-verbal reasoning practice
Letters, cogs, pinwheels, clouds and more: turning, mirroring and symmetry with shapes you have not met before.
OftenIn many papers, especially GL AssessmentAbout 45 seconds a question in the test
The big idea
Most non-verbal questions use squares, triangles and arrows. Real papers sometimes use shapes you have never seen, and the same thinking still works: is it turned, is it flipped, and what stays the same?
Some shapes, such as an F, a boot or a lightning bolt, look different at every angle. Others, such as an S, a pinwheel or a cog, look the same after part of a turn, but their mirror image is a different shape.
Symmetry questions ask how many ways a shape folds onto itself (lines of symmetry) and how many times it fits on itself in one full turn (the order of rotational symmetry).
Tips that save marks
Pick one feature, such as the foot of the F or the toe of the boot, and follow it from figure to figure.
A turned shape can always be turned back to match; a flipped one never can.
To count lines of symmetry, fold the shape in your head through every corner and through the middle of every side.
A worked example
An S shape is turned half a turn. Does it look the same?
Picture the top curl moving to the bottom and the bottom curl to the top.
The top curl opens to the left and the bottom curl to the right, so after half a turn they swap places exactly.
Yes: an S has rotational symmetry of order 2, but no line of symmetry.
Now try five
Try each one before you look at the answer: answering from memory is what makes it stick. Tap an option to check it. Most children get three or four right at first; five out of five means move on to the next topic.
Question 1Aim for about 45 seconds
Which option is the same figure, only turned (rotated)?
Show the worked answer
Answer: C
How to work it out
The right figure is the tick turned half a turn (180°).
The others are its mirror image, and no turn ever undoes a flip.
Why the other options are wrong
A: This is the tick flipped, not turned. Turning never swaps left and right, so it can never match.
B: This is the flipped tick turned 90° anticlockwise. It looks turned, but it is still a mirror image.
D: This is the mirror image of the right answer: it is flipped, and turning cannot undo a flip.
E: This is the flipped tick turned 90° clockwise. It looks turned, but it is still a mirror image.
Question 2Aim for about 45 seconds
Which shape looks the same after half a turn but has no line of symmetry?
Show the worked answer
Answer: E
How to work it out
The pinwheel fits on itself after half a turn, yet no fold makes its halves match.
Check both parts for every shape.
Why the other options are wrong
A: This E shape looks different after half a turn, and it has a line of symmetry too.
B: This U shape looks different after half a turn, and it has a line of symmetry too.
C: This leaf looks different after half a turn, and it has a line of symmetry too.
D: This regular heptagon looks different after half a turn, and it has a line of symmetry too.
Question 3Aim for about 45 seconds
Which figure comes next in the series?
?
Show the worked answer
Answer: D
How to work it out
The boot turns 45° anticlockwise each step and its shading alternates black and striped.
One more turn from the last figure gives the answer.
Why the other options are wrong
A: This turns one step too far: it is two turns of 45° anticlockwise on from the last figure, not one.
B: This is half a turn away from the right angle: count the turn from the last figure again, step by step.
C: This is the mirror image of the right figure. The series only turns the boot; it never flips it, and no turn makes a flipped one match.
E: This keeps the last figure’s angle. The shape turns again on every step, so the next one must be turned further.
Question 4Aim for about 45 seconds
Which figure comes next in the series?
?
Show the worked answer
Answer: C
How to work it out
The boot turns 45° anticlockwise each step and its shading alternates black and striped.
One more turn from the last figure gives the answer.
Why the other options are wrong
A: This keeps the last figure’s angle. The shape turns again on every step, so the next one must be turned further.
B: This is half a turn away from the right angle: count the turn from the last figure again, step by step.
D: This turns one step too far: it is two turns of 45° anticlockwise on from the last figure, not one.
E: This is the mirror image of the right figure. The series only turns the boot; it never flips it, and no turn makes a flipped one match.
Question 5Aim for about 45 seconds
How many lines of symmetry does this shape have?
Show the worked answer
Answer: E, 1
How to work it out
The T shape has 1 line of symmetry: along each, one half folds exactly onto the other.
Why the other options are wrong
A (0): This misses a line. Try a fold through every corner and through the middle of every side.
B (4): This is too many: only 1 fold makes the halves match; fold along the others in your head and the halves do not line up.
C (2): This is too many: only 1 fold makes the halves match; fold along the others in your head and the halves do not line up.
D (3): This is too many: only 1 fold makes the halves match; fold along the others in your head and the halves do not line up.
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