Understanding spatial reasoning - part two
By Natalie at Galore Park
22 Nov

In the second of a two part blog, we’ll be covering other types of questions which test children's understanding of spatial reasoning, and showing you how to practise reasoning skills utilising Galore Park non-verbal reasoning resources.

What do 2D spatial reasoning questions look like in non-verbal reasoning tests?

The questions below specifically target skills in spatial reasoning (through reflection, rotation or translation/change of position) AND standard non-verbal reasoning questions that include spatial reasoning as one or more of its element. A number of variations on these questions can appear in 11+ tests from year to year. 


Finding reflections

These following questions are all variations on reflections (being able to work out what a picture will look like if it is reflected in a mirror) with additional tasks introduced to increase complexity.  

Question 1) Identify a simple reflection of the picture on the left.


Question 2) Reverse the colours of all the flags in the left-hand picture and reflect them in the vertical line. 


Question 3) The arrows show how the shape is folded before holes are punched in the final diagram. Identify the unfolded square on the right that represents the unfolded shape.


Spotting rotations and translations
The first of these questions tests rotation skills, the second translation (where an image is placed in another position, but not rotated) and the third combines the two skills together. 

Question 4) Choose the picture on the right that shows the picture on the left after it has been rotated 180°.


Question 5) Choose the picture on the right that contains the shape on the far left. 

Question 6) Choose the three shapes on the right that combine to make the picture on the far left. 

All of the question types above are introduced and explained in Chapter 3 (Links of position and direction) of the Non-Verbal Reasoning Study and Revision Guide.



2D questions that include spatial reasoning elements

Complex question types specifically involving skills in reflection, rotation and translation are explained in Chapters 4, 5 and 6 of the Galore Park Non-Verbal Reasoning Study and Revision Guide.
Almost all non-verbal reasoning questions can include an element of spatial reasoning even though this is not immediately obvious. However, because Galore Park specifies the skills needed to solve each question in the answers it is easy to find out, after answering, whether there is a spatial element included. This knowledge can help your child target areas of weakness. 
The following questions are examples of standard questions that include an element of spatial reasoning. The answer explanations are provided to show where these elements are.

Question 1) Work out the feature represented by each letter then apply the code to the final picture to find the correct answer code.

Answer) b
Vertical reflection – the letters A and B stand for whether the Z-shape is reflected in a vertical line so A is reflected and B is not; direction – the letters N, O and P represent the direction of the missing quadrant in the circle so with N the gap points top right, O the gap points downwards and P the gap points top left.

Question 2) Work out the option on the right that completes the sequence on the left. 


Answer) e
Position – the shading on the triangle swaps position in alternate boxes; rotation – (a) the gap in the outer circle rotates clockwise 45°, (b) the gap in the middle circle rotates anticlockwise 45°,  (c) the gap in the inner circle rotates clockwise 45°.

Question 3) Work out which option on the right completes the grid on the left. 


Answer) a
Translation – the shapes assemble along the diagonal, top left to bottom right with the complete shape in the central column; position – the orientation of the shape changes between the diagonals.


Practising spatial reasoning skills

Galore Park's brand-new non-verbal reasoning range has been written specifically for independent school entrance exams, including CEM, GL and ISEB. Galore Park has worked with 11+ tutors, independent school teachers, test writers and specialist authors to create this series. The range has been constructed to help children follow three steps to examination success...

1) Non-Verbal Reasoning Study and Revision Guide
Learn the skills and understand the question types for all pre-tests and 11+ independent school entrance exams.

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2) Non-Verbal Reasoning Workbooks
Increase exam confidence with over 160 questions in each of the books, with even more question variations and application of knowledge learned in the Study and Revision Guide.
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3) Non-Verbal Reasoning Practice Papers
Perfect exam technique by practising with a variety of exam-paper styles under time pressure. Books 1 and 2 contain four training tests, nine model exam papers and fully explained answers for final test preparation. 
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