In the last two articles you were introduced to progression style questions, and how they look in the 11+ Non-Verbal Reasoning exam. So far, we’ve looked at series created by rotation, and at alternate progression of patterns. In this third lesson, we shall focus on how numbers can be used to form series made with shapes.

You should be familiar by now with how Complete the Series questions look. Nevertheless, here’s a quick recap.

Candidates are shown an incomplete series of shapes. They are also given several other shapes, one of which will complete the series in the most logical way. It’s up to them to find it.

Okay, let’s have an example question:

**Example **

*Pick one of the five boxes on the right to fit in the blank box and complete the series on the left.*

Now, I told you previously that this lesson looks at how numbers are used, but there are no numbers in the question, are there? Well, the quick amongst you may immediately see what the progression is here but, for the majority of people, it will not be obvious. It’s time to take a look at the list of what to look for.

The fourth box seems to be an end to a sequence which then restarts with box five. Whatever fits in the empty box does not necessarily have to relate to the octagon in the final box; it might just be that the octagon is the start of the sequence all over again.

Now, what did you pick from the list of possible ideas to explore? There seems to be no connection between the first and second shape of the progression as one is regular and the next is irregular. However, count the number of sides. You will find that the first shape has eight sides, the next has seven, the next has six and that suggests that the empty one should have a five-sided shape in it. The only five-sided shape available as an answer is (d). This must be our answer.

The really tricky variant of this problem...

Imagine the five-sided shape was not an available answer and was replaced by a heptagon (a seven-sided figure). Now what would the answer be?

You are looking for patterns and series, so let’s write the numbers of sides of the shapes in the progression in a row:

8 |
7 |
6 |
? |
8 |

Can you see that, although we wanted to put a ‘5’ into the blank space when we had that as an option, the series could be completed with a ‘7’ instead?

Think about the symmetry that would create – start at 8 and count down, only to count back up to the starting point again. Tricky, but the sort of thing that they could put in to pick out the real brainboxes!

Hopefully, you’ll have noticed the way that numbers and symbols can be interchanged in these questions. Abstract shapes are awkward, but numbers are easier to deal with.

Numbers and shapes is possibly the most difficult form of Complete the Series question. Now you know (and can share with your child) some of the devious ways examiners can use to fool you!

Feel ready for some practise yet? If so, here are some links to the 7 Complete the Series quizzes we have in the 11+ Non-verbal reasoning section of the Education Quizzes site:

But there are still a couple more ways in which these kinds of question can be made. The next two articles might be very useful to you before you try the quizzes. I’ll see you there!