# Dot card talk 4 – number talk (9 and 3)

A thinking mathematically targeted teaching resource focussed on combining and separating quantities to develop additive strategies

## Syllabus

Syllabus outcomes and content descriptors from Mathematics K–10 Syllabus © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2023

• MAO-WM-01
• MAE-RWN-01
• MAE-RWN-02
• MAE-CSQ-01
• MAE-CSQ-02

• MAO-WM-01
• MA1-RWN-02
• MA1-CSQ-01

## Watch

Watch Dot card talk 4 video (6:32).

Number talk investigating ways to visualise a collection.

### Speaker

Okay welcome back mathematicians.

It's time to get your eyeballs ready. It's time for some visual recognition and subitising.

Ready? How many dots are there and how do you see them?

[Screen briefly shows a rectangle with vertical lines and a horizontal line in the middle creating 10 boxes, a ten frame. In the 10 boxes there are 9 blue dots, 5 in the top row and 4 in the bottom row towards the left. Underneath is another rectangle with vertical lines and a horizontal line in the middle creating 10 boxes, a ten frame. There are 3 red dots in the boxes, 2 in the top row on the far left and one in the bottom row on the far left.

Screen reads – How do you see the dots? And how many are there in total?]

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.

[Screen shows 2 ten frames as before and leaves them on the screen. In the first ten frame there are 9 blue dots, 5 in the top row and 4 in the bottom row towards the left. Underneath, in the bottom ten frame, there are 3 red dots, 2 in the top row on the far left and one in the bottom row towards the left.]

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.

[Screen shows one red dot move from the bottom ten frame to the top ten frame to join the 9 blue dots and make 10. This leaves 2 remaining red dots in the bottom ten frame.]

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.

[Screen briefly shows 2 ten frames again. In the first ten frame there are 8 blue dots, 4 in the top row and 4 in the bottom row towards the left. Underneath, in the bottom ten frame, there are 5 red dots, one in the top row on the far left and 4 underneath towards the left.]

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 10 frame, and also maybe ideas about place value like renaming.

[Screen shows 2 ten frames as before and leaves them on the screen. In the first ten frame there are 8 blue dots, 4 in the top row and 4 in the bottom row towards the left. Underneath, in the bottom ten frame, there are 5 red dots, one in the top row on the far left and 4 underneath towards the left.]

Okay, so here's what I imagined. I imagined 2 of the red dots, so down the bottom there's 5, 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.

[Screen shows 2 red dots move from the bottom row of the ten frame to join the 8 blue dots in the top ten frame and make 10. This leaves 3 remaining red dots in the bottom ten frame.]

Ahh yeah, you might have imagined moving two different dots, like this, for example. But it still leaves one 10 and 3, so it's still 13.

[Screen shows presenter move a different 2 red dots to the top ten frame, this time selecting one from each row of the bottom ten frame. This still leaves 3 remaining red dots in the bottom ten frame.]

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.

[Screen shows presenter move a different 2 red dots to the top ten frame, this time selecting 2 from the middle of the row in the bottom ten frame. This still leaves 3 remaining red dots in the bottom ten frame, but the 3 dots are separated into 2 dots and one dot.]

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.

[Screen briefly shows 2 ten frames again. In the first ten frame there are 8 blue dots, 5 in the top row and 3 in the bottom row towards the left. Underneath, in the bottom ten frame, there are 8 reds dots, 4 in each row towards the left.]

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.

[Screen shows 2 ten frames as before and leaves them on the screen. In the first ten frame there are 8 blue dots, 5 in the top row and 3 in the bottom row towards the left. Underneath, in the bottom ten frame, there are 8 reds dots, 4 in each row towards the left.]

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.

[Screen shows presenter move 2 red dots up to join the 8 blue dots in the top ten frame and make 10. This leaves 6 remaining red dots in the bottom ten frame, 3 in the top row and 3 underneath in the bottom row.]

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.

[Screen shows presenter move 2 blue dots down to join the 8 red dots in the bottom ten frame and make 10. This leaves 6 remaining blue dots in the top ten frame, 3 in the top row and 3 underneath in the bottom row.]

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.

[Screen shows presenter move a different 2 blue dots down to join the 8 red dots in the bottom ten frame and make 10. This leaves 6 remaining blue dots in the top ten frame, 5 in the top row and one underneath in the bottom row.]

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.

[Screen briefly shows 2 ten frames again. In the first ten frame there are 7 blue dots, 5 in the top row and 2 in the bottom row towards the left. Underneath, in the bottom ten frame, there are 8 reds dots, 5 in the top row and 3 in the bottom row. There are 3 more red dots sitting outside the ten frame to the right.]

Oh, so imagine in your mind, what did you see? Okay and are you ready? All right, let's have a look.

[Screen shows 2 ten frames as before and leaves them on the screen. In the first ten frame there are 7 blue dots, 5 in the top row and 2 in the bottom row towards the left. Underneath, in the bottom ten frame, there are 8 reds dots, 5 in the top row and 3 in the bottom row. There are 3 more red dots sitting outside the ten frame to the right.]

So, I imagined the dots moving again, and I joined 2 dots to join the 8, 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 2 dots moving, and there's the one, and I could rename that as 18.

[Screen shows presenter move 3 red dots sitting outside the ten frame. They move 2 red dots into the bottom ten frame to join the 8 red dots and make 10. They then move the remaining one red dot into the top ten frame to join the 7 blue dots and make 8.]

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 8 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.

[Screen shows 4 ten frames, 2 on the top and 2 on the bottom. The top left ten frame has 8 blue dots and the top right ten frame has 10 dots, 8 blue and 2 red. The bottom left ten frame has 8 red dots and the bottom right ten frame has 6 red dots.]

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.

[End of transcript]

## Instructions

• Watch and follow along with the video, listening carefully and using your imagination skills.

• Pause throughout the video when asked to imagine the collection shown.

• How many dots are there?

• How did you see them?

• What were you thinking?

• How did you work it out?