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11+ Non-Verbal Reasoning Matrices | 3 x 3 grid pattern
These questions are all about forming patterns.

NVR Progression - Fill in the Blank in a 3 x 3 Grid (1)

In the last article we looked at how Matrices questions are posed in the 11+ Non-Verbal Reasoning exam. The majority take the form of 2 x 2 grids. But there is another kind, which we will focus on n the next two articles – 3 x 3 grids.

These are a variation on the examples we showed you in the first section, all about Filling in the Blank. They are almost identical, in the sense that you’re following a progression. You just have to help your child get used to the progression working along the horizontal, vertical or even the diagonal rather than just in a straight line.

One way to think of them is as sudoku puzzles with a little bit more. Often, one of the main ways they are worked out is that each column and row has the same amount of each symbol in it. Of course, there is more to it than that, like rotation for example, but that is a good place to start.

How Are These Kinds of Question Posed in The Exam?

These are very similar indeed to 2 x 2 matrices. It’s just that there are more squares in the grid. This time, candidates are shown a grid made up of nine squares. Eight of the squares have shapes in them, but one remains empty.

They are also shown four or five other shapes. It’s up to them to find which one of these belongs in the blank space.

Let’s show you exactly what I mean with an example question:


Pick one of the five boxes on the right to fit in the blank box in the diagram on the left.


Let’s look at the possible things we could be looking for – don’t forget to refer back to the list of nine possibilities if you aren’t sure.

We could look at the number of items, but there seems little to be gained by this as there are four boxes with two in and two with each of one and three items.

Let’s look at the shapes and movements instead. Treat each type of shape, regardless of size, as something similar. There are circles in each box – in each row and column there is a small, medium and large one. The one that is missing in the bottom row is a small circle so we can discount ‘e’.

The large circles are always central, but the medium and small ones seem to be in the top, middle or bottom of the box.

There is a little one in the top of the middle top box, while there is one in the middle of the central right box. Therefore, it makes sense to have one in the bottom of the blank box so we can discount ‘d’.

Now we can look at the other shapes. The dot-shaded triangles are a red herring, as they only run on the diagonal.

There appears to be one square in each row or column and there’s no need to put an extra one in. Note that there is one behind the circle in the bottom centre box. That means discounting ‘b’ as neither the row nor column needs an extra square.

At this stage your child should either be working out what’s needed or looking at the remaining options and deciding what makes them different. The position of the diamond is the only thing different between choices ‘a’ and ‘c’ so we must look at where it should be.

The top row has a diamond on the bottom while the middle row has a diamond in the middle. Therefore, we should complete the series by having a diamond at the top. Answer ‘a’.

Sample Tests

3 x 3 matrices are not commonly found in the 11+ Non-Verbal Reasoning exam, but we have included them in these illustrations for the sake of comprehensiveness. For that same reason, we have only one quiz in this format on the Education Quizzes site, but that should be enough for your child to practise with. Here’s a link to it:

Matrices 8

If you’d like more practise, then we do have 7 quizzes on 2 x 2 grids, which are similar and will help your child with 3 x 3 grids too. You’ll find them in the 11+ Non-Verbal Reasoning section of the Education Quizzes site, or you can follow these links:

Matrices 1

Matrices 2

Matrices 3

Matrices 4

Matrices 5

Matrices 6

Matrices 7

So, now that you’ve been introduced to 3 x 3 Matrices style questions, you know the gist of how they work. There are a couple more things I’d like to show you though, and we’ll look at those in the next article. You might want to read through that first, before you go to the quiz. See you there!

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