Teaching with Concrete Resources: What, how and when to use them

We actually started using concrete materials before we started using the Maths — No Problem! textbooks, because I think we started before the textbooks were available.

Just experimenting, we got together as a staff and we looked at the curriculum and talked about: if you’re teaching ratio, what would you use to help you? We looked at the strands and figured out what could be used when and where, and what was going to be most useful.

You can’t expect people to use the textbooks and not have number disks. And that’s the responsibility of the leadership at the school, to make sure that the equipment is there.

What should you consider when using concrete resources?

If we look, I’ve got my trains here. Now I wouldn’t do this in class because I’ve got blue trains on a blue table. So I would either pick a different coloured train, or by putting them on a piece of different coloured card — for some children, that makes them more visible.

We always give our numbers or our problems in a story. It’s always a practical problem. And we try as much as possible in the early years to have materials that actually match the story. So I’m not going to write a question about penguins and then give them some trains — if the question is about trains, we’ll give them trains.

How can you scaffold learning with concrete resources?

As time goes on, we could maybe replace those trains. Maybe we’re still talking about trains, but I haven’t got any trains — I’ve got bricks. So that could be a train and that could be a train [shows two linking cubes]. And what I’ve done is try to keep some kind of continuity, so we’ve still got the same colour.

If I’ve got counters, I might choose to do a question about cake because they’ve got the same shape. I try as much as possible to make a connection between things where we can. So they might move from the actual physical ‘next best thing’ from an actual train, to representations that are a little more abstract.

And then again, as time goes on, they might move to smaller counters because I might be using bigger numbers. Once you go past 20, these [shows linking cubes] get a little bit cumbersome. So we might then move to the smaller counters.

When can organising concrete resources support part–whole strategy?

When you buy the smaller counters, they arrive like this [shows a container of multi-coloured cubes]. And there are many, many classes and many teachers who will see this and know that, as soon as they give these counters to children, they’re going to start sorting them, and put the pink ones over there and the red ones over there. So we tried to get that out of the way straight away, and we sort them by colour. And we only give them one or two colours, depending on what the problem might be.

So if we’re adding, we would often give them two colours so they can show the two groups within one, and the ‘part–part–whole’ is there. And again, by having them in different colours, we can make sure that the colour contrasts with the tables.

Can concrete resources help develop mental maths strategies?

At the moment in Year 4, for addition and subtraction, they’re using Dienes. So the ones, the tens, the hundreds and then the thousands that are over there because they’re huge [gestures across the classroom]. These are really good for showing regrouping and renaming. Even in mental strategies yesterday, there was a girl, she was struggling to see why when you’re adding 97, you would just take it up to 100.

But then, when I showed her 97…

Well, I say I showed her — when she showed me 97, and we had a 100 nearby, it suddenly became very obvious to her that adding 97 was quite a big job, but adding 100 was really simple. And she could just take 3 from the other number and add them on.

She needed the concrete materials to get to that mental strategy. And obviously it is a mental strategy and you want her to be able to do it in her head, but without these, she wasn’t going to get there. So it gives her that way in, that eventually, she learns those patterns and soon she’s going to see the number 97, she’ll remember this and she’ll know.

At the moment when she sees it, she still questioned it. And I said, “remember when we did this?”

And she said, “oh!” and she went and grabbed the handle, and she brought them over to her table. And she knew that she could do it when she had them. So it gave her some independence, rather than relying on a grown-up, she was able to use these.

We use them through everything. They’re not just part of the anchor task, they’re available all the way through the lessons, all the time.

Where should you store concrete resources in the classroom?

I don’t have them living in one place in the classroom. There are some over there for the children who sit here, there’s some over there for the children who sit there, and some over there for the children who sit there [gestures around the classroom].

So nobody has to go too far, that’s just my personal choice. Some people store them all in one area, but I want them to be able to go very quickly, grab their nearest tub and bring them back again.