Dot card talk 1

Okay mathematicians, welcome back. I am about to show you a collection of dots and I'd like you to think about, you know, how many dots are there? But I'm really interested in is, how do you see them? Okay ready, it's subitising, so you don't get to look at it for too long.

Here we go. How many dots? And how do you see them? You're right, it was fast 'cause we're getting in on your capabilities to subitise and instantly recognize quantities. So there are a lot of dots there. So what I'd like you to think about, I'll show you again, but I'd like you to really think about looking for chunks. So looking for things that you can see inside all of those dots. Some things that are familiar to you that you could use. Okay, and then see if you can see a few of those chunks.

Alright, ready to have a look again. Okay, how many dots and how do you see them? Ah, yes, so you've thought about some chunks now. Good. You're right, it is a little bit like if you've done number talks in your classroom, isn't it? Using a dot card this time? So you might be sitting there and thinking, going oh my fist means, I'm just thinking.

This means, I've got one way of thinking about the chunks and how I see that collection of dots. Yeah, and then if you got one way of thinking about it, is there another way you could have seen them or imagined them? Okay, should we have a look together? Okay, so here is the collection and the first thing we need to work out is, how many dots are there altogether?

Yes, there's 8. Okay, so I have 8 in my collection here. Now what I'm most interested in is, how do you see this collection of eight? What's one way that you could think of? Ah, okay, some of you are saying you saw a chunk of five here, like on a dice pattern. And then three more like an arrow or a triangle? Okay, let's record that way, as one way of thinking. So I'm drawing the 4 squares, the 4 dots like a 4 and then one more makes a 5 dice pattern. And then 3 like a triangle. 1, 2, 3 like that. And that's 5 and 3. Better write 'and' in there.

Okay, what's another way of thinking about it? Ahhhh, some of you were saying you saw this triangle in this end, but also at this end and then 2 more dots. Okay, so a chunk of 3, a chunk of 2, and another chunk of 3. So here's one chunk of 3. Here's the chunk of 2. I better write that 3. 2, and the other chunk of 3. Like that. And I need, an and, and an and. So we see 3, 2 and 3.

Ah, you like my use of color to correspond. Thank you, I do too. Sometimes I don't worry about color, but sometimes it really helps get inside people's brains and understand their thinking and also convey ideas. And you're right, I could improve this too actually, 'cause if I drew a line underneath there, mmmm, it makes it easier to see one way of thinking compared to another way of thinking.

Okay, I think we have another way of thinking, actually, where someone was saying they read it like a book. You know across each row. Yeah, and they saw 3 and 2 and 3. Okay, so I'm going to do 3 across the top. Oh, I know some of you are going, "That's not my way yet." It's okay, we're coming. 'Cause there's, I know it's amazing, isn't it that you can look at something and go "Well, we know it's 8 dots but there's all these different ways of thinking about it. Yeah, that's why we, well part of the reason why we love mathematics. It's 8 dots but look at how many different ways we can imagine those eight dots. Here we have 3 and 2 and 3 more.

Ah yes, I saw this too, and this way, it's going to be tricky for me to draw it, but I'll try. I saw a chunk of 5 and a chunk of 5, and these 2 dots overlap. So I actually saw 5 and 5 - wheew and then minus 2. Yes, I know. I'll, I'll draw it and then I will explain it. So drawing 5 on my dice. So in this case, look, I do 5 like 4 and one more. And then in this case I could draw 5 like 3 on a dice. And 2 more. I know that's a fun strategy. And then what happened? I need my scissors actually, is, is, this 5 slides across, whoosh, and covers that 5.

Um, so it's 5 and 5 minus, yeah, the 2 that I covered, so I might write this as 5 and 5, but then minus, and if I'm going to be careful using color, I might,I might use the 2 to get rid of the 2 here, 'cause they're the ones, yeah, that I sort of see sliding over. So I think that represents my thinking. A 5 and a 5, minus 2 which is also 8. And now what I'm thinking about actually, is there's lots of different ways to represent 8 and I'm wondering what's another way that we could prove that these are all in fact 8? Even though there's different chunks of meaning inside of them.

Okay, let's have a look. Okay mathematicians, let's use this balance scale to check out some of this thinking. So on this side, I'm going to put a peg on 8 because I knew my representation was 8. That's how many dots we worked out that we had. And now what we want to do is the first thing we said was eight was 5 and 3 more. So let's put a peg on 5. Oh and nothing's happened, and let's try with 3 and see. Yeah, and there I can see that 8 is equivalent to 5 and 3. So the other one we looked at was it it was 3 and 2 and 3. So if I take this off. That's right, it goes all the way down, doesn't it? To say to me it is not balanced and if I put the 2 on, it didn't even move it, did it? Okay, and then I guess for the 3, I put that on the other 3 peg. And I just have to balance the white bit so they're the same too.

Look at that! 8 is 2 and 3 and 3 or 8 is 2 and 2 threes. Ha!

Nice work mathematicians. Okay mathematicians. What was the maths? Hmm, that's right, we notice that mathematicians can see the same representation and think about it quite differently. That numbers, but bigger numbers like 8 are made up of smaller numbers like 5 and 3. So we saw 8 is 5 and 3. That 8 is also 3 and 2 and 3. That 8 is 2 and 2 threes. Remember how we balance that on the balance scale? Yeah, and that actually 10 is 2 more than 8. Yeah, and we also really saw today how how a careful or intentional use of color can help us make and convey meaning as mathematicians.

Now what I wonder for you is.. Did you see that representation in a different way? What about people in your family? How do they see the dots? Off you go to go and investigate. See you next time.