Blog: Ian Davies, Director of Secondary

# No better way to start the year: let’s talk mathematics

Posted: 5/09/16

Here at Mathematics Mastery we LOVE talking about mathematics and ‘number talks’ are an integral part of our approach. Number talks are a great way of engaging students with mathematical thinking, as well as developing mathematical language.

**It’s not just about number**

Here’s a great example of an activity for a maths talk – the classic ‘odd one out’. Which of these is the odd one out, and why?

After a little thought, it’s clear any of the shapes could be chosen and there are a wide variety of reasons. Some simple, some more complex.

You can challenge the answer to develop the language: *“Shape B has more sides than the other two” *can become* “Shape B is a pentagon whilst shapes A and C are both quadrilaterals”.* You could push for, or suggest yourself, *“Shape C is the only one that isn’t regular”*, asking what assumptions have been made to conclude this.

You can ask for answers determined by certain properties that you want to revise/assess – *“Give me an answer based on symmetries”* or *“How can you classify the shapes by considering the types of angles they have?”* You can extend, if you wish to, by suggesting choose their own three shapes.

**If you know…then you know…**

Mathematics is all about making connections – connections between numbers, connections between topics etc. If you are given one fact, it’s often easy to deduce other facts from this. So try giving students a starting fact and ask them to explain how they know another. For example:

42 × 16 = 672

**What else do you know?**

After re-ordering the calculation and listing the corresponding division facts it’s usual to go down the ‘powers of 10’ route – 42 x 160 or 67.2 ÷ 16. Other facts are also (fairly) obvious e.g. 84 x 16, but what about 43 x 16? What do you need to add on, and why? How many steps to get to 840 x 17? You could model a few and then open it up.

Again, it doesn’t have to be number: If you know a shape is regular, what else do you know? (Sides, angles, symmetries?) If you know the probability of an event, what else do you know? If you know the mean of a set of (say) five numbers, what else to you know? If you know then mean of 8, 11 and 80, do you know the mean of 80, 110 and 800? What else can you deduce?

**What’s the same, what’s different?**

You can do this variation of “odd one out” with almost anything – shapes, numbers, equations, graphs, solutions etc. Let’s consider these two expressions:

9*a ^{2}* and 6

*ab*

For integer *a*, the first must be square – why? Can the second ever be a square? When would it be a square? They are both multiples of 3, anything else?

These are just a few ideas to get mathematical talk going, offering great insight into what students have remembered from last year, or may need to be reminded of in the near future.

Have any other great ideas for getting learners talking about maths? Please share any other ideas you may have!