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Non Verbal Reasoning: Nets & Folding Shapes

Eleven-Plus Preparation Specialists

This question type relies on a simple concept that you will have encountered in your maths lessons, but can be difficult – especially as more complex patterns are placed on the nets to make the process more difficult.

What does this question type involve?

You will be given one net on the left. Then, you will be provided with five cubes that either can or can’t be made from that net. You have to look at the different parts of the net and use them to decide which cubes are suitable. This is best illustrated through an example. Here’s one taken from an official past paper.

Here, we’ve been asked to find the cube that cannot be made from the net – in other words, four of them can be made. We could therefore work through in order, and see if each can be made. Looking at a, Z it features an arrow pointing away from an X, and an X next to that arrow. Looking at B, we find that this cannot be made. That’s because the arrow points at the black dot – yet this is impossible looking at the net. The arrow would be on the side next to it, pointing up alongside it.

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Example question

Let’s look at another example question, again taken from an official past paper.

Again, we’ve been asked to find the cube that cannot be made. This time the answer is E. Whilst the dots are correctly positioned next to the smiley face, the smiley face has changed rotation – it should be rotated 90 degrees right.

Two step approach: Opposites, Rotations

Your approach to this type of question can actually be very simple. It should come down to opposites, and rotations.

Remember that you might be asked to find either the shape that can be made, or the shape that cannot be made. It’s also possible that you’ll be asked to identify the net of a particular cube.

Let’s think about opposite shapes first. In the example above, for example, the square must be opposite the circle, and the dots must be opposite the triangle. Every option follows this rule, i.e. none have any of these shapes next to each other or out of place. In essence, if you can see one of these shapes, you shouldn’t be able to see the other.

Your next step is to look at rotations. This can be more tricky, and the papers will often put subtle rotations in. In fact, the question above is a brilliant example. In general, you should look for arrows that have the potential to rotate, or a shape like the triangle above which could easily be rotated 90 or 180 degrees so that it is ‘pointing’ the wrong way. Above, the smiley face has been rotated so that it is facing the wrong direction, meaning that the cube produced is in fact impossible from that net.

After this, you’ll need to check the position of each shape in more detail.

Worked Implementation

Let’s look at an official past paper example. Here, we’ve been asked to find the cube that can be made from the net – in other words, four can’t be made and one can.

So, we begin by looking at opposites. The arrows are opposite one another, and the square is opposite the diagonal shading. That means we shouldn’t see both arrows, or both the square and the diagonal shading, if it’s possible to make the cube. However, this rule is followed throughout, so we need to move on to rotations.

Here, we find that a is incorrectly rotated, the diagonal shading is incorrect with the arrow pointing towards it. B is impossible because of the rotation of the arrow compared to the circle. C features the arrow incorrectly rotated again, as it should be 90 degrees clockwise from where it is shown. However, D is correct – the arrow is rotated correctly and the circle is in the right place.

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Top Tricks

The opposite rule can be used to quickly eliminate incorrect options without unnecessary complexity.

Common Pitfalls

Many students find it difficult to visualise the shape in 3D. Practising is one way round this, and the other is following the simple rules outlined here. The use of shapes means that often this question is as much about spotting irregularities in the shapes as it is about visualising nets.

Summary

In summary, focus on opposites first, then rotations, then check the position of the sides relative to one another.
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