Non Verbal Reasoning: Shape Transformations

Eleven-Plus Preparation Specialists

This question type is common in the GL papers, and involves a shape being transformed into another. You’ll have to follow that sequence, then use it to perform another transformation.

What does this question type involve?

You are provided with one shape that has been transformed into another shape. You must assess the transformation, then decide how another shape will be transformed. In other words, you are being presented with two short shape sequences.

Let’s look at an official past paper question:

In this question, a shield with solid lines becomes a square with solid lines. It doesn’t change shape or otherwise alter. Therefore, it is logical to assume that a shield with dashed edges would transform to become a square with dashed edges – i.e. the opposite.

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Example question

Here’s another example question taken from an official past paper.

Here, the shape inside has been replicated on the outside, and rotated 90 degrees anticlockwise. Meanwhile, the original shape on the inside has been shaded. Therefore, the correct answer is A, which features the shape on the outside correctly rotated, and the correct shading inside as well.

4 Steps: Shape, Rotations, Shading, Size

Your approach here should involve looking at four core factors. These are shape, rotation, shading, and size. It’s likely that the answer will be found in some combination of these.

You should begin by looking at the shapes themselves. In the first example above, we can see that the shape changes, and that is the main transformation taking place. In the second example, we see that a shape clones itself, so again the shape does change.

Next, look at the rotations. In the second example above, we see that the shape inside rotates when it moves to the outside. Note the amount of rotation and the direction of rotation.

After you’ve done that, consider the shading. This should involve both the shapes – which might be shaded, unshaded, or have a particular pattern of shading (which can rotate, for example) and the lines on the outside, which might be dashed, dotted or solid.

Lastly, you should consider size. Have some parts of the shape changed in size? This change can sometimes be frustratingly subtle, so make sure to look out for minor changes here. In particular, elements of shapes that move into or out of another shape can change in size – a typical transformation involves one shape moving into another, and the sizes swapping.

Worked Implementation

We’ll look at another official past paper question. This is again taken from a GL assessments paper.

Let’s begin by looking at the shapes themselves. We note that the main shape does not change. It remains the exact same, a five sided shape. However, within it the shapes change – there is one fewer triangle. On the outside the shapes change too, with an additional triangle.

Rotations are next. Whilst not exactly a rotation, we should notice that the new shape on the outside is actually a mirror of the shape next to it. There are no other rotations to pay particular attention to.

Now, let’s consider shading. The key here, which should be fairly obvious, is that the outer shapes are shaded and the inner shapes are not. Whilst the two shapes are similar (both triangles) they are not the same.

Last is size. There is no change in size here – the main shape remains the same, the triangles remain the same, and the black triangles on the outside are the same size throughout.

That means that the correct order must follow all the above rules. Therefore B is correct. It has one fewer chevron, and the top chevron is removed as it is in the example. The chevron has been added to the other corner at the top, and it is mirrored compared to the one on the other corner.

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Top Tricks

Focus on each part of the process. Don’t become confused by shapes that involve various different elements, and instead work through piece by piece. Most puzzles will be more simple than you’d think at first if you stick to the process.

Common Pitfalls

Make sure to look at different types of shading, and the rotation of all shapes. In particular, the shading of lines (e.g. dotted, dashed) can catch students out.


To summarise, your approach should be focused on shape, rotations, shading and size, and should allow for more complexity as needed as you work through the order.
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