Presenter Ben (video by Rob Langman) introduces classroom activities to develop generalisation and early algebraic thinking. He demonstrates three tasks — 'odd one out', POG (peculiar, obvious, general), and 'sometimes/always/never' — and shows sample prompts and responses to encourage speaking, listening, justification, and deeper reasoning in children.
Chapters
Hi, my name's Ben. In this video we're going to be looking at making generalizations which help us to begin to think algebraically. Now a lot of these activities, which I'm going to show you three, really focus on the speaking and listening element of maths, which is massive. Children have really got to be confident and articulate in what they're speaking about. And this will help them with algebra and general problem solving too. So this is a great question to kick start off. And it doesn't have to be shapes, you can do it with numbers. And the question is quite simple, which is the odd one out? And let the children then have a go at trying to explore and explain. They could say the square because it's the only shape with right angles. They could say the circle because it's got no straight sides. Or they could say the triangle because it's red. Or each of those on their own are fine. You could then push that a bit further and say, how could we make the triangle fit with the others? And they would have to again articulate their answer. And another one here is called pog, which stands for peculiar, obvious and general. And if you give them a key element to look at, they then got to try and fit something into each section. So if they're peculiar, they might look at drawing a scalene triangle where all the sides are different lengths. They may look at an equilateral triangle where each length is the same. Or they may look at general, and this is a general statement here. So all triangles have three sides and their internal angles total 180 degrees. And it's really good. And you can, you can do that with numbers, you can do it with shapes, which is fab. This one I think is really good. And you can really push on the children here, including your more able learners. And that's the sometimes, always, never. So here we have four statements. A number with three ones is bigger than a number with no ones. Now at first glance you would say, oh yeah, always. Unless of course, the number with three ones might be three and the number with no ones might be 10 or 20. It all depends on the context. And that's where the children have got to speak and listen. An odd number added to an odd number will always make an even number. That's a brilliant one for them to go and explore. Go and try it out. That one is an always. We then have, there are three numbers between 7 and 11. Well, that's 8, 9, 10, unless of course you're dealing with decimals, which then it could be sometimes. And again, that talking around the problem is where the children really begin to understand maths. And finally, a triangle has nine lines of symmetry. Well, an equilateral triangle, which is the regular shape, only has three, so that will be a never. These are really, really good ideas to get your class talking, and they're really useful to help understand and articulate their generalization.
