The detail is as important as the essential is. When it is inadequate, it destroys the whole outfit.

Christian Dior

In my previous post, I talked about how Craig Jeavons‘ idea of “*if I only had five questions to get students to the objective I want them to achieve, what would they be?*” looked to be thought process through which I can get students to explore conceptually challenging questions quickly in a lesson.

I was conscious, however, that I didn’t really go into detail regards what this actually looks like. So inspired by William Emeny’s follow up of Naveen Rivzi’s exploration of multiple-choice questioning, I offer up some examples.

Remember the idea is conceptual and procedural variation from question to question…

**One step at a time**

So, let’s a have a look at, say, expanding pairs of brackets. What do we actually want them to consider? Well, here’s a ‘minimally different examples’ style set of questions:

- (x + 1)(x + 2)
- (x + 1)(x – 2)
- (x – 1)(x – 2)
- (x + 1)
^{2} - (x – 1)(x + 1)

Probably a little simplistic and obvious, but it’s pretty clear what’s happening each time. It has to be said in this case the numbers are irrelevant – it’s the procedures that are important.

Let’s take it up a notch. I set my Y8 students these five questions as part of an introduction to multiplying fractions recently:

In this example, not only am I varying the concept – moving from unit to vulgar to algebraic fractions – I’m also varying the procedure, setting questions that might throw up a few misconceptions or ‘open goals’ – e.g. realising that the bottom right fraction will simplify to 2, or that some students might correctly multiply the numerators to get a^{2}, but then incorrectly may think that they need to cancel both numerator and denominator by 2 to get a/9.

What was nice about this was that they were dealing with concepts in terms of the algebraic fractions that we would classically leave until much later in their secondary school Mathematics studies.

I replicated this methodology with dividing fractions, and it’s worked quite well – there’s still a little bit of tweaking to do around knowing when and how to simplify properly, but their conceptual understanding of multiplying fractions is pretty sound.

There’s some way to go with this. I am by no means perfect, and here’s some things I’ve learned so far:

- The time you allow the students is crucial. For the multiplying fractions exercise I gave just 5 minutes maximum. My Y10 groups have been looking at area and volume scale factor problems – I’m not so harsh not to allow them at least 10-15 minutes on tackling 5 of those kinds of questions.
- Don’t make the steps too big. There has to be some kind of connect from one question to another, and whilst it doesn’t have to be immediately obvious it shouldn’t require too much brain power. The goal is to make big conceptual and procedural leaps via all 5 questions, not between one question and the next.
- Keep the entry point simple. Give students chance to get something right quickly, and you’ll hold their attention a little bit longer. If you are allowing enough lesson time to cover a single concept, you’ll be able to do this much easier than if you’re trying to cram too much into a lesson – but then you knew that anyway, didn’t you?

**Conclusion**

Writing 5 questions on a topic is easy to do. Writing 5 questions that build on a fundamental process and vary the parameters to make connections and develop problem solving skills is not so straightforward. Like any pedagogy it’s easy to understand but difficult to truly master. But it’s certainly something I’m going to pursue.