NVR Progression - Fill in the Blank in a 3 x 3 Grid (2)

This is the third and final article in this section all about Matrices questions. In the previous one we introduced you to 3 x 3 grids and how they can be solved. As I said before, these do not appear often in the 11+ Non-Verbal Reasoning exam. Nevertheless, they do sometimes show their face, so I thought it best to show you one more example of them.

As you’ll remember, they are usually worked out by looking at the contents of each row and column, in much the same way that sudoku puzzles are done – only, this time with shapes rather than numbers.

How Are These Kinds of Question Posed in The Exam?

As you’ll remember, these questions take the form of grids made up of nine squares. All but one of the squares has one or more shapes or symbols in it. Candidates must choose from a list of options which one belongs in the blank square.

Let’s take a look at another example:

Example

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

The first thing to do in this type of question is to work out which of the column / row / diagonal combinations we can use.

Here it is clearly rows that give us the answer, as the middle and bottom rows are each composed of similar types of shapes but different to the top row. Therefore, we are looking for a shape similar to the top left and top right objects – not a lot of help, all of the options are!

So how are the answers different? Firstly, the direction of the arrow is important, secondly the position of the line and finally the direction of the shading. Make sure your child follows the same sort of path if they are not able to see the answer.

Let’s look at the way that the symbols change as you move along the row. The same thing will happen in each row, so we need to examine our two sample rows.

The shading in the second row is angled top-left to bottom-right for the first symbol but then the opposite way for the other two.

The bottom row has identical ‘shading’ in the first and third and opposite for the middle one. This suggests a dead-end for our basic logic, so we need to look at something else.

The lines move from the left or right to the opposite side, but only in the third box, while in the first row that doesn’t happen.

If you (or your child) have not sussed it out yet, it’s time to head back to the original list and look for something else.

Imagine that you are using a mirror and reflecting the symbols in a horizontal or vertical axis; this is something which all children should have experience of by year 5 if not earlier. The first image can be treated as the basic shape. If you reflect that image in a horizontal axis (in other words flip it over, top to bottom) then the second image is created. The third image is the first image reflected in the vertical axis (in other words flip it across, from left to right).

So, the answer to this puzzle is ‘a’. The arrow flips to pointing upwards, the line flips to the bottom of the box and, importantly, the shading is flipped to face the opposite way. There are several tricky elements thrown into this question but it’s basically simple – reflect the objects.

Sample Tests

So, that completes this section of our exam illustrations all about Matrices. We’ve seen that they usually take the form of 2 x 2 grids, but occasionally come in the guise of 3 x 3 grids. Now that you’ve seen how to deal with both types, it’s time to get in some practise.

There are 8 Matrices quizzes on the Education Quizzes site. The first 7 are devoted to 2 x 2 grids (as these are more common) and the last to 3 x 3 grids. Go through each one with your child. You may find that, like some children, they have an innate talent for these. If not, don’t worry. Just show them the techniques you’ve learned in these lessons and they’ll soon be solving them like a natural.

Here are links to each individual quiz:

Now you’ve completed this section, it’s time to move on to the next. That’s all about relationships between symbols. See you there!