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11 plus challenging topics: non-verbal reasoning

By Atom | Nov 21, 2023, 2:43 PM

Child playing with a Rubiks Cube

Non-verbal reasoning is a type of visual problem-solving using shapes, diagrams and pictures. Your child will be tested on their ability to use logic to solve problems and identify patterns, and their spatial awareness.

There is some overlap with Key Stage 2 maths, such as geometry, position and direction, but non-verbal reasoning is not taught as part of the national curriculum.

11+ non-verbal reasoning topics

Non-verbal reasoning tests cover two main topics: interpreting shapes and manipulating shapes. Your child will likely see a combination of questions for each topic:

Interpreting shapes

  • Recognise and associate: find the odd one out, match to a group, and match to a pair

  • Extending a pattern: pairing shapes, sequences, matrices, and odd-shaped matrices

  • Finding a code

Manipulating shapes

  • 2D shapes: parts within a shape, shape logic, rotations and reflections, and following folds

  • 3D shapes: nets and cubes, rotating 3D shapes, nets from 3D shapes, combining 3D shapes, and shapes from above

Take a look at examples of non-verbal reasoning questions in 11 plus exams.

The most challenging non-verbal reasoning topics

We've found that children using Atom to prepare for 11+ exams find these non-verbal reasoning topics the most challenging:

  • Shape logic

  • Nets from 3D shapes

  • Combining 3D shapes

Shape logic

There are three different types of 'shape logic' questions. Children may need to combine shapes, form silhouettes, or form shapes:

  • Combining shapes: your child must choose the option that correctly combines two shapes into one new image

  • Forming silhouettes: children will see a silhouette and need to choose the answer options which, when combined, make up the silhouette

  • Forming shapes: this is similar to forming silhouettes. However, children will see a complex shape (there may be lines within the shape, rather than just seeing an outer border). Children will need to figure out which shapes piece together to form the original.

To answer shape logic questions, look closely at each shape. Identify key features of each shape that need to be present in the answer.

Here's an example shape logic question on Atom. To answer this question, children need to select the image from 5 answer options which contains the main shapes within it.

An example shape logic question on Atom

The correct answer must contain both of the shapes in the question. We have to watch out for shapes that have been rotated – they can be tricky to spot!

  • First shape: present in A, C and D

  • Second shape: present in D and E

We can rule out B and C because the second shape is clearly incorrect. We can also rule out A, because the second shape has the wrong proportions.

D is the only option that contains both of the shapes. The first shape has rotated 180 degrees, and the second shape has rotated 90 degrees clockwise. This means that D is the correct answer!

Note that it would have been easy to mistake E for the correct answer, but this is a *red herring. At first glance it looks like the first shape has rotated 90 degrees clockwise, and the second shape has rotated 180 degrees. But look closely at the stripes – they have not rotated in the same way as the rest of the first shape.

Nets from 3D shapes

Your child might be shown a net and asked to identify which 3D shape can – or cannot – be made from the net. Take a look at the example from Atom below.

A nets from 3D shapes question on Atom

There are three different rules to bear in mind when answering these types of questions:

  1. Look for a dud: a dud shows shapes or colours that are not present on the net or cube it needs to be associated with.

  2. Breaking the opposites rule: some 3D shapes can’t be made from a net, and vice versa, because their faces are shown next to each other on the net when they should be opposite on the 3D shape.

  3. Breaking the orientation rule: some 3D shapes can’t be made from a net, and some nets can’t make 3D shapes, because they show shapes in the wrong orientation. For example, an arrow pointing in the wrong direction.

To answer this question correctly, we need to look for the one net that cannot make this cube.

C could not make this cube because it breaks the opposites rule. It shows faces opposite each other on the net that are next to each other on the cube.

We can see on the cube that all the picture faces are on adjacent faces. If we folded up C, the circle and the triangle would be opposite each other. This means that C is the only net that cannot make this cube.

Combining 3D shapes

To understand complex 3D shapes, we need to picture them as smaller 3D blocks. Some blocks will be completely visible, while others will be partially hidden or obscured.

In 'combining 3D shapes' questions, your child will need to think about the dimensions of the blocks – e.g. how many unit cubes they are made up of. They then need to work out whether the blocks have been rotated in the answer options.

Take a look at an example from Atom below.

A question on combining 3D shapes on Atom

Let's start by counting the visible cubes in the top layer of the shape. There are 6.

We know that these 6 cubes must be sitting on 6 cubes in the middle layer, and 6 cubes in the bottom layer. This means there are 12 cubes hidden underneath them.

Next, we can count the visible cubes in the middle layer of the shape. There are 3.

We know that these 3 cubes must be sitting on 3 cubes in the bottom layer, so there are 3 cubes hidden underneath them.

Finally, we can count the visible cubes in the bottom layer of the shape. There are 2.

When we add these values together (6 + 3 + 2 visible cubes, plus 6 + 6 + 3 hidden cubes), there are 26 cubes. This means that the correct answer is E.

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Verbal reasoning paper

Top tips for solving tricky non-verbal reasoning questions

Seeing lots of shapes on the page at once can be overwhelming. Encourage your child to read the question carefully and work through it methodically, looking at just one shape at a time.

When looking at shapes, try to spot identifying features. Consider features such as movement, orientation, placement, and symmetry.

Lastly, don’t get caught out by red herrings. These are answer options that look very similar to the shape in the question, but might have a very subtle difference.

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