Can being vague lead to clear responses?

Consider the following diagram:

3ishAsk yourself the following:

– What’s “3-ish” about the diagram?

Quite a vague question i’m sure you would agree. Once you’ve thought of something consider the next question.

– If this is the 3rd pattern in a sequence, what would the rest of the sequence look like?

The beauty of this exercise is not that it requires little to no work to set up (lazy teaching FTW!) but rather that it allows each pupil to attack it from their own viewpoint. There is no right or wrong answer to the question as you’re asking for the pupils opinion.


Yet despite the ambiguity of the task, I rarely have to prompt a class into giving me what I want. Not because the class are experts at ‘guess what Mr Lyons is thinking’, but rather, patterns in shape often make more sense than number strings. (Not found any real theory to back that up but search your feelings, you know it to be true 😉 )

This is the pattern I was working towards.


Hopefully you may have considered this as an option.

So now we have a completed pattern, I ask you to consider two more questions:

– What changes?

– What stays the same?

Again, Vague questions; but also powerful ones. Being able to spot changes is an important skill and one that we have being doing for a long time (re: this) but rarely do we consider what has stayed the same. In this instance the blue square has remained the same and will continue to remain the same no matter how long we make the sequence.

I’m not going to give you an nth term solution for the diagram above as you may already know it/ have learnt an algorithm to solve them without thinking or have enough clues already but I will say that sometimes, asking direct questions is not the best way to get a pupil to think. Sometimes it’s better to be a little bit vague.


Andy x

All credit for this approach must go to the truly excellent Debbie Barker from the MEI. What a superstar!