This short instructional video (presented by Ben) shows how to teach early algebra by moving from concrete manipulatives (counters, dominoes) and pictorial diagrams to tabular representations and finally symbolic notation. Using a tables-and-seats example, Ben distinguishes constant parts (a fixed 4 seats) from the variable part (2 seats per table), constructs input–output tables for specific inputs (1,2,3,4,5,10), and generalises to the algebraic rule 2n + 4. The video emphasises hands-on exploration, colour-coded visuals to show invariant vs changing parts, and the pedagogical sequence concrete → pictorial → symbolic.
Chapters
Hi, I'm Ben and in this video we're going to be looking at how to represent algebra in a pictorial form. It's worth noting, actually, when I've taught this personally, I've also used concrete apparatus, which is really helpful, so the children can see how to build it up in stages. So I've used counters and dominoes rather than just drawing it, but it is helpful to draw it too, so the children can see how it builds up. So here's our question. What will happen to the number of seats as we add more tables? In a previous video, we've talked about making generalizations and statements, so to try and build up children's confidence with algebra. And a really good statement would be here. Do the children recognise that when more tables are added, more seats are added? That's a really, really simple statement. They can see that something is increasing. So my question for the children would be, how many seats would there be if there were four tables or five or ten or any amount? And then we're starting to get into the language of algebra and making those generalizations and the children can play with the dominoes and counters or they can draw it out. When we've had a play around and when the children have experimented with all the tools, it's then good to try and represent it in a table form. So you can see here, we've got the number of tables and the number of seats. We call this here the input and this is the output. Because if we have one table, we have six seats. And then getting them to explore and see what is the difference, how do we get from 1 to 6? An obvious answer will be that we add 5, which is great, that's good to talk about. But then does that rule, that generalization, does that carry through? So then two add five, does that equal eight? Oh, and then it's really useful if children are starting out in algebra that you maybe introduce them to the fact that the function from the input to the output maybe has two steps. And then we get onto the pictorial again. So looking at the counters or looking at the pictures to have them in different colours is really, really helpful. So we can see here, on our first table, we have our six seats and you can see that the constant, the red seats, they never change, it's only the green seats that increase every time. And then we can start to try and apply some numbers and sometimes tables in here. So with one table we have two seats, with two tables we have four, with three we have six. So one table equals two. So we're looking at the two times table, one times two plus the four which are always there, then two times two, which is four, plus the four which are always there,. There's your eight. And then they can see that it builds up. And that's why it's really useful to have it as dominoes, as counters, as a picture, and then to represent that in that table. If you've got that table going down to 4, 5, 10, that will really, really make it clear for the children. And then they can see. And you could really summarise all this with, how do we write that down? What if I said, what if there were 10 tables? Or what if there were N tables, which could be any number you choose, and then it doesn't matter as long as they can follow that rule, for example, they'll soon realize that n times 2 add 4. So number 1 times 2 is 2, add 4 is 6. Or again, if you want to push that a little bit further, you can say that the rule is 2, n add 4, and there's your algebraic statement. And if you've used all those concrete and pictorial representations first, it will really, really help the children.
