Dot card talk 4

Okay welcome back mathematicians.

It's time to get your eyeballs ready. It's time for some visual recognition and subitizing. Ready? How many dots are there and how do you see them? Mmm, and how many dots are there in total? What are you thinking? Okay, and how did you work it out?

I'd like to show you one possible strategy that you could use and that involves our mathematical imaginations. So you can imagine one dot moving from the bottom ten frame, mm-hmm, up to the top one, so then we would have instead of nine and three, we would have 10 and 2 and we can rename that as 12.

Look.

Aha, see that? Yeah, that happened in my imagination and I know it happened in some of yours. Okay, let's see if we can use the imagining strategy with the next dots we look at. Are you ready? Okay. Ohhh. Yes, so see if you can imagine the dots moving to help you work out how many there are in total. Ahah! Because we're using our knowledge of things, like what we know when we see a full ten frame, and also maybe ideas about place value like renaming.

Okay, so here's what I imagined. I imagined two of the red dots, so down the bottom there's five, and I imagined two of those dots moving up to me, join the blue ones, so that would give me 10 at the top and three at the bottom. And I could rename that as 13. Here, I'll show you what that looks like. There we go.

Ahh yeah, you might have imagined moving two different dots, like this, for example. But it still leaves one ten and three, so it's still 13. Ahh and you could have moved it like this as well. Yeah, so that's really interesting, because that showed us it doesn't matter which two dots we moved, it still kept it as 13 in total. That's a really important idea.

Okay, ready? Let's think about how we could use our mathematical imaginations to work out how many dots there are in our next collection. Here we go! Mmm, you're right that was faster. So maybe this time think about what was missing at the top and what was missing at the bottom and what you might do. Okay.

Yes, like some of you I had two strategies this time too. Firstly, I knew the top was eight and I knew the bottom was eight, that is represented in different ways. Yeah, because there were two missing on each of them so I know when there's two missing it on a ten frame, it has to be 8, because 8 and 2 makes 10, or 8 is 2 less than 10. And so one of the doubles facts I know is that when 8 of something is combined with 8 of something it always makes 16 of something. It's a mathematical regularity, it's a pattern. Ahh hah, so that's one thing. The other thing is, I could have reimagined so for me I moved in my mind two of the dots from the bottom collection up to the top collection and that changed 8 and 8 into 10 and 6, and we just renamed that as 16. Here's what it looked like for me. Yeah, was yours similar? Mm-hmm.

You might have also thought about it the other way, yes, where you move the two dots down and then we'd have 6 and 10, which we also know is called 16. Yes, and it didn't matter where you move them from again, yes, because now we see our six as five and one more. Uh-huh. Okay, ready? Let's see if we can use our imaginations now to work out how many dots there are in the next collection in total? Here we go.

Oh, so imagine in your mind, what did you see? Okay and are you ready? All right, let's have a look. So I imagined the dots moving again, and I joined two dots to join the eight, so that would make a 10 and then I joined one dot at the top. Would you like to see it? Mm-hmm, here's what it looked like. There's the two dots moving, and there's the one, and I could rename that as 18.

Yes, and I can hear some of you thinking, I could have done it another way. You're right, I could have, and that's one of the beautiful things about mathematics, there's always, or almost always, lots of different ways that we can think about things.

Okay mathematicians, so what's the mathematics here? So some of the important ideas is that quantities can look different but have the same value. So in both of these there's a total of 16, yeah, but in one collection, I have eight at the top and eight at the bottom, that's 16 in total. And in the other collection I have 10 at the top and 6 at the bottom, still 16 in total. Yes, so this is really important for me to know about numbers, I can be really flexible with them and also that we can use our imaginations to imagine parts of one collection moving across to join another collection, and we don't always have to do it in the same way as everyone else. Yeah, and then we can use what we know to work out how many there are in total.

All right mathematicians, until we meet again may your mathematical imaginations blossom! Okay, over to you.