Hello there little mathematicians welcome back. Today we thought we'd spend some time exploring this little structure here, which we call a ten-frame. We use these a lot. They're really helpful in helping us understand and investigate and explore quantities and numbers. And so we thought it would be a really good time to really get in and analyse what exactly is this ten-frame all about. And so we thought that we might start off by actually trying to draw one. And that's a really important idea, because mathematicians like writers know that when they really come to understand words or mathematical representations like a ten-frame, that they can also draw them too. So before I can draw it, I need to notice things about my ten-frame.

So what are some things that you can tell me about what you see here? Ah, ok, it has ten boxes. Let's check that. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Ok, so something we notice. There are ten boxes. Something else that you notice? Oh, yeah, around the outside, there's a big box isn't there? In fact, it's a big rectangle and there's one of them. So there's one big rectangle. Yeah, you're right, and the ten boxes sit inside the one big rectangle. Don't they 'cause there's the big rectangle and there's one box and another box and a third box and the fourth box and a fifth box. The sixth box and a seventh box and an eighth box and a ninth box and the tenth box. And they all sit inside. Oh yeah, so there's this big rectangle and then there's other lines inside it that help partition it, don't they?

How many other lines are there? Yeah, there's one big line down the middle. One line down the the middle. You're right, it's one long line. Nice revising there mathematicians. One long line down the middle and then there's these shorter lines aren't there? And how many of those are there? Yeah, you could say there's eight 'cause you go 1, 2, 3, 4, 5, 6, 7, 8. You're right, or if you drew the whole line, that would be one wouldn't it? 1, 2, 3, 4 shorter lines.

So actually, let's use our fingers and trace around. So let's check we have ten boxes. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. One big rectangle. One long line down the middle. And four shorter lines.

Ok little mathematicians over to you, I'm going to put this representation of our ten-frame up here and now that we've thought about all the things that we can see over to you to draw one. So pick up your pencil and get your paper. And get ready now to draw a ten-frame. And while you do that, I'm going to do the same thing. How did you go? Does yours look a little bit like mine too? Ah.

Should we try to draw a ten-frame that has some things in it 'cause this one at the moment is representing zero. Because there's nothing inside the boxes. Let's have a look at one that has some things inside it. What about this one? How many can you see here? Four that's right, it's representing four.

So little mathematicians I wonder now if you could, first of all, take a picture in your mind of what that looks like. And then think about tracing around, so the one big rectangle with your finger. The one line down the middle. And four shorter lines. And then we also need to represent four. So then I would colour in one dot. Colour in a second dot. Colour in a third dot. And color in a fourth dot.

Now that you've got that picture in your mind. Pick up your pencil or your marker and draw your representation of four on a ten-frame. Over to you, and I'm going to have a go at the same time, but this time I'm going to draw it myself underneath here so that you get a chance to think in your brain as well, ok? You get started and I'll join you.

That's right, I'm thinking about the rectangle too. Like that. Then I'm thinking about the line down the middle. Then I'm thinking about four shorter lines that go inside my rectangle. 1, 2, 3, 4. Then I was thinking about four. And I think it had four dots at the top because I remember the bottom row was empty and so was this space here. So then I have to colour in my four dots. OK, can you show me your drawing? Do ours look the same or similar? And let's see if it looks like our representation of four. Yeah, I can see four here and I can see four here. I can still see the ten boxes look, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. I can see the big rectangle. I can see the line down the middle and I can see the four shorter lines, 1, 2, 3, 4. And look at this mathematicians, even if I turn it around, I can still see this. Look, ten boxes. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. One big rectangle, one big rectangle with four sides. One long line down the middle like that. And four shorter lines, 1, 2, 3, 4.

And I still have four dots for this one too. 1, 2, 3, 4. Ok, I'm going to show you another representation. And this time I'd like you to take a picture in your mind's eye. Here it comes.

Ok, and over to you to draw. So, pick up your pencil's now. And draw the representation that you just saw. Would you like to see it again to check? Here we go. Take a picture in your brain. And look at the details. How many dots are there? Where are they? Ok, have a go at drawing that from your mathematical imaginations. I'm gonna draw it too over here. Ok. How did you go? Does your drawing look like this? This is what mine looks like. There's my six. Yeah, so I can see I have four shorter lines, 1, 2, 3, 4. One line in the middle, one big rectangle and ten boxes, 2, 4, 6, 8, 10. I know I went backwards that time didn't I? And even if I turn it like this where it's really wonky. I can still see it. You're right, one big rectangle. One line down the middle and four smaller lines. That's right.

Ok, I'm leaving you with one left to challenge you little mathematicians. Here it comes. Notice the features of the ten-frame and notice how many dots there are. Uh-hm. Ok. You might like to draw it in the air and show what you saw in your brain. And then draw it on your piece of paper. I'm gonna draw one too.

Ok, are you ready to have a look together? Ok, here was our ten-frame that we had. And how many dots is it showing us Six, Yeah, 'cause it's four empty spaces and six is four less than ten. And I also know it's six, you're right, 'cause there's five on the top and one down the bottom. Here's my drawing of six. How did yours go? Very nice and you know mathematicians. I noticed something, look. This one I did was six. Where's my marker? Look, 2, 4, 6. This one was six. Five, six. And they are two different ways of representing six on the ten-frame. This one has one, three and a second three or two, two and two. And this one shows me six with one row of five and one more. I wonder how many other ways that I could represent six dots on a ten-frame?

That sounds like an investigation to me mathematicians. Over to you. Ok, press pause here little mathematicians, go investigate and come back and we'll show you what some other mathematicians came up with.

So firstly, what was some of the maths? One is, we realise that when you use a ten-frame for example, you can represent the same quantity, the same amount like six in different ways. That's important cause it helps us see different things about those numbers. That mathematicians can record their ideas in different ways. Ten-frames is one of these. The ten-frames can be described as a mathematical pattern because they always have the same structure and they always show us ten boxes. We also realise that when we draw representations, it helps us to make meaning from them, as we notice features.

So, let's look at what some other mathematicians discovered today. Riley saw six as four and one and one. And Sicsa, three and three. Erica saw six as five and one more. And she saw it as four and one and one. And Louise saw six as two and two and two.