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11+ Non-Verbal Reasoning Matrices | 4-square grid
These questions contain 4 squares which form a pattern.

NVR Progression - Fill in the Blank in a 2 x 2 Grid

Welcome to the second section of our 11+ Non-Verbal Reasoning exam illustrations. In it we shall be looking at 4-square and 9-square matrices. What are these exactly? Well, basically they are just small grids which have all but one of their squares filled in with patterns.

They are a variant of the Progression style questions we looked at in the previous section on Complete the Series. It’s just that the style in which they are put to children is different.

How Are These Kinds of Question Posed in The Exam?

In this first article, we shall look at 4-square matrices, as these are the ones most commonly found in exam papers.

Candidates are shown a grid made up of four squares. Three of the squares have shapes in them, but one is blank. They are also given a choice of shapes (usually four or five), one of which will fit in the blank square to logically complete the grid.

The best way to show you is with an example:


The large square on the left of the page contains smaller squares that form a pattern. Choose one of the shapes on the right to fill the blank square and complete the pattern.


This is a great example to help children understand the way articulating the symbols can help.

Firstly, ensure that you know which way the progression works – you are going to work in columns rather than rows this time, so let’s talk the change through from top-left to bottom-left.

  1. The circle stays where it was, but becomes horizontally shaded.
  2. The crescent stays where it is but reflects in the vertical axis. (Imagine a straight-line top-bottom acting as a mirror – the crescent in the top left box is a mirror image of the one in the bottom left).
  3. The triangle stays in position, but flips over in the horizontal axis.
  4. The two lines stay as they were.

Now you simply read through the corresponding shapes for the second column and cross off the irrelevant answers:

  1. As the circle became shaded, so the diamond should become shaded. Cross off ‘a’ and ‘e’.
  2. The pentagon, like the crescent, should be flipped in the vertical axis – this, of course, gives something that looks identical! Now we can cross off ‘d’.
  3. The step lines should be flipped over as the triangles were, but both our remaining symbols have this.
  4. Finally, the long line should stay the same, whereas in ‘b’ there is an extra line. The answer, of course, is ‘c’.

Once children are used to this technique they can rush it through mentally along the lines of – ‘circle, shaded; diamond, shaded... crescent flips, pentagon flips... triangle turns upside-down, steps turn upside-down.’ They can then be crossing off the letters of the answers which are irrelevant.

Technique Tip

This is cheeky but it works. I always encourage a child to look ahead at what is coming up, but of course you cannot write anything outside of the given time or even turn any pages. However, many non-verbal reasoning tests are written in separate sections, each with practice questions.

When I invigilate testing I am given a set list of things that I must do; this includes waiting for children to complete the practice questions as long as they are not being unreasonable. There is a chance to exploit this time by not whizzing through the questions, which are almost always identical, and looking ahead to the other questions on the page instead. If you make a big deal of doing this or start crossing things out then you will obviously get into trouble, but it’s easy to answer a couple of questions mentally while bluffing your way through the practice questions.

Ethical? Just about. It’s all about playing the system, I suppose. That’s the sort of technique that could allow a child to get two more correct answers in time per section, and that may make ten points improvement in the standardised figure. The difference between a pass and fail, perhaps? It’s worth knowing all the little tricks.

Sample Tests

So, now you have been introduced to Matrices questions and how they look in the exam. 4-square matrices really are very simple, and you know all you need to tackle them now. We have 8 quizzes on Matrices in the 11+ Non-Verbal Reasoning section of the Education Quizzes site. You can try them out right now if you want to.

Here are links to each individual quiz:

Matrices 1

Matrices 2

Matrices 3

Matrices 4

Matrices 5

Matrices 6

Matrices 7

Matrices 8

The first 7 of these quizzes are in the form of 4-square matrices. However, there is one more type of matrix used in the exam – the 9-square matrix. This is the last quiz in our Matrices section, and you may want to read through the next two lessons before you try to tackle it. See you there!

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