Non Verbal Reasoning: Missing Shape Sequences

Eleven-Plus Preparation Specialists

This question type relies on your ability to spot a pattern through a series of figures.

What does this question type involve?

You will be given a set of five squares, each of which has a shape in it, bar one. That one has been purposefully left empty. You need to understand the pattern, or sequence, and thus figure out what is missing.

Here’s an official past paper question:

In this sequence it should be immediately clear that the number of arrows increases each time. However, there’s a second rule – the arrows flip from pointing down to up alternately. Therefore the fifth square must have five arrows pointing down – meaning that C is correct.

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Example question

Let’s take a look at a second example question.

In this question the shape alternates between a hexagon and a pentagon. Equally, the shading alternates – even within the hexagon. Note that it is shaded from bottom left to top right in frame 1, then from top left to bottom right in frame 3. Therefore the correct option must be A must be correct, with the hexagon correctly aligned and the shading also angled the same as in frame 1.

6 Steps: Number, Shape, Rotations, Shading, Size, Position

As with all NVR questions, you’ll be considering shape, rotations, shading and size. However, here we begin with number.

Look at the number first. How many shapes are in each square? Does the number increase or decrease?

Next, you can move onto shape. Does the shape alternate from square to square, like it does in the example above? Whilst there will be few questions this obvious, there will be plenty with more complex iterations on this.

The third consideration is rotation. Perhaps the shape rotates 90 degrees in each square, for example. In the first example above, the arrows are rotating 180 degrees each time.

Next you need to consider shading. Is a different shape shaded in each square? Is the same shape shaded in a different way from square to square? Check the angle of the shading as well – as in the example above.

Do the shapes change size? Is there one shape that grows bigger from square to square? Do shapes change size in inverse ways, with one growing larger while the other gets smaller?

Last is position. This can be vital for these types of questions. Where do the shapes sit? Do they move around in a logical way? This should be differentiated from rotation.

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Worked Implementation

This question is taken from an official sample paper. It’s relatively simple but shows a clear pattern, which is useful for learning.

Let’s begin by considering number. Is the number of shapes the same in each frame? It should be quickly obvious that each frame has two shapes only – a small circle and a larger rectangle.

Now, let’s look at shape. Does this change from frame to frame? You should see that the shapes remain unchanged.

Does rotation change? No, the rotation is the same.

Does the shading change? We note that the circle alternates between unshaded and shaded.

Does anything change size? No, neither shape changes size.

Lastly, what about position? We should note that the circle follows a logical sequence of top, bottom, middle, on repeat, and the rectangle follows bottom, top, middle, etc. They move in different directions.

Therefore, we put this information together to see that the circle should end up at the bottom in frame 5. It should be unshaded. The rectangle should be at the top. That means that D must be correct.

Top Tricks

Number and position can be key to these questions, and are the two factors that you might not consider, as they feature less in other question types. Therefore make sure to remember them as you work through the process. If you quickly spot a pattern, don’t be afraid to work with what you’ve noticed and give a quick answer – in the question we just did, you might very quickly note the pattern. However, you should always double check – otherwise you might miss that the rectangle moves as well as the circle, for example.

Common Pitfalls

Always double check your answer, especially when there are two options to choose from that are very similar.  


To summarise, follow the same cour four factors of shape, rotation, shading and size, but make sure to also focus on number and position.
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