# Subitising (match my collection)

A thinking mathematically targeted teaching opportunity focussed on recreating a hidden quantity by looking and thinking

## 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

## Collect resources

You will need a collection of 10 things, like dried pasta or blocks .

## Watch

Watch Subitising (match my collection) video (9:54).

Recreate collections by looking and thinking.

### Transcript for Subitising match my collection video

[A title over a navy-blue background: Subitising - match my collection. Small font text in the upper left-hand corner reads: NSW Department of Education. In the lower left-hand corner is the white waratah of the NSW Government logo.

A title on a white background reads: You will need…

• Some dried pasta or blocks or counters
• A table or an area that you can work on

### Speaker

Before we get started, make sure you've got some dried pasta or blocks or counters, a table or an area that you can work on, and your speedy eyeballs at the ready. If you don't have those things just yet, just click pause, go find them and then come back and play the video again. See you soon.

[On the floor is a pink sheet of paper and a pink bowl of pasta.]

### Speaker

Hello there, little mathematicians. I hope you're having a really lovely day today. Today we're gonna practice around with our skills in subitising and that means that when we can look at something and see how many there are without having to count.

[The speaker takes a couple of pasta pieces and places them on the paper.]

### Speaker

So, for example, if I put this many pieces of pasta out, how many can you see? Two. Yeah, I can see two…

[She points to the pieces.]

### Speaker

…as well and I didn't have to count them. And so when this happens to me, it's called subitising.

[She places the pieces back to the bowl.]

### Speaker

And so what we're going to do today is I've got some plates over here…

[She holds up a couple of paper plates.]

### Speaker

…that have things like counters and dice patterns on them…

[She holds up a paper plate with pompoms on it.]

### Speaker

... and I'm gonna show them to you really quickly and turn it over.

[She flips the plate onto the floor.]

### Speaker

And then we're both gonna have a turn of trying to imagine what it was that we saw on the plate and recreate it here.

You can use counters or blocks or pieces of even toys that you like. I'm gonna use pasta today to help me make these representations and then we're gonna turn our plate over again…

[She flips the plate right side up.]

### Speaker

…and check to see what happened.

[She takes the plate away.]

### Speaker

So, if your little eyeballs are ready, we can get started. Are you ready? Excellent. So, here comes the first one…

[She holds up a paper plate.]

### Speaker

…and I think you've already seen it but have a look.

[She flips the plate to reveal 3 green pompoms.]

### Speaker

OK…

[She flips the plate onto the floor.]

### Speaker

… and now think about how many did you see and how did you see it and let's try to recreate it. So, I'm gonna cover this up…

[She holds up a pink sheet of paper over the one on the floor. She takes some pasta pieces.]

### Speaker

…so that I don't disturb your thinking. And I think I saw that many. And I think it looked a bit like that. Let me think. Yeah, OK. Can you show me your representation? Let's see if we were thinking the same.

[She takes the overlayed paper away. There are 3 pieces on the paper.]

### Speaker

This is what I was thinking about. I think I saw three because in my mind I could imagine seeing two and one more and I know two and one more is three.

[She flips the plate right side up.]

### Speaker

But let's check and see exactly what I saw. Let's check, is it three? Yeah, because here's two…

[She points to the 2 pompoms at the top.]

### Speaker

…or two and one more. We could count them all to check.

[She points to each of the 2 pompoms.]

### Speaker

One, two, three.

[She points to each of the pasta.]

### Speaker

So, I have one, two, three counters, the pasta, and you had that too. And I did see two together…

[She points to the 2 pastas at the top.]

### Speaker

…and one more…

[She points to the pasta at the bottom. She points to the 2 pompoms at the left.]

### Speaker

…but actually these ones are a bit closer.

[She moves the top pasta on the left closer to the bottom pasta.]

### Speaker

So, if I was really being really precise, my representation would have looked a little bit more like this where these ones…

[She points to the left pompoms and pastas.]

### Speaker

…were closer together and this one…

[She points to the top pasta on the right.]

### Speaker

…was further away but I was still able to see three. Should we have another go together? Excellent.

[She takes the plate away.]

### Speaker

Put this one away.

[She takes the pastas away.]

### Speaker

I'll take my pasta away. Here we go, fast eyeballs ready.

[She holds up a paper plate with a square with 1 black dot. She flips the plate onto the floor.]

### Speaker

What are you thinking? How many did you see and how did you see it?

[She holds up a pink sheet of paper over the one on the floor.]

### Speaker

OK, I've got a picture in my brain and now I'm gonna recreate it as well and let's see if we were thinking the same or seeing the same.

[She takes the overlayed paper away. There 1 piece on the paper.]

### Speaker

One, is that what you saw too? Let's check.

[She flips the plate right side up.]

### Speaker

Ah, it is one. And this one looks like one on a dice doesn't it? Because of the square outline. OK, let's see. Here comes another one. Eyeballs really, good job.

[She holds up a paper plate with 3 green pompoms. She flips the plate onto the floor.]

### Speaker

Oh OK, how many did you see this time?

[She holds up a pink sheet of paper over the one on the floor. She takes some pasta pieces.]

### Speaker

I'm going to make my representation while you make yours.

OK, are you ready? I imagined it in my brain and what I thought I saw was a…

[She traces a triangle shape on the overlayed paper.]

### Speaker

…triangle and one dot in each of the corners of the triangle. And I know a triangle has three corners and so…

[She takes the overlayed paper away. There are 3 pieces on the paper set up like a triangle.]

### Speaker

…I made my representation look like this. Yours was similar? Shall we check?

[She flips the plate right side up.]

### Speaker

OK, let's see. Huh, there we go.

[She points to the pompoms.]

### Speaker

Three, one, two, three, in a triangle shape.

[She points to the pasta.]

### Speaker

One, two, three, like a triangle. OK, let's try another one.

[She takes the plate and pasta away.]

### Speaker

Eyeballs ready. OK, here we go.

[She holds up a paper plate with 4 pompoms set like a square.]

### Speaker

Oh…

[She flips the plate onto the floor.]

### Speaker

…over to you now, take a picture in your brain, think about what you saw, and then try to recreate it. I'm going to do the same. [DESCRIPTION: She holds up a pink sheet of paper over the one on the floor.]

### Speaker

Let's see... OK. What did you think you saw? Ah, so, some of us are thinking about similar things. I also thought I saw a square…

[She traces a square shape on its side on the overlayed paper.]

### Speaker

…but I thought it was twisted on its side a little bit.

### Speaker

And I saw a square but actually some of the counters were one colour and there was one down the bottom, I think, that was a different colour.

[She takes the overlayed paper away. There are 4 pieces on the paper set like a square on its side.]

### Speaker

And so when I used my pasta shells, I made it like this so that I could see that it's a square…

[She traces over the pieces.]

### Speaker

…just twisted slightly.

[She turns the paper to the right.]

### Speaker

See if I turn it this way, it looks like a square…

[She turns the paper back to the left.]

### Speaker

…and this way it's still a square because there were four corners.

[She points to the piece on the bottom of the set.]

### Speaker

And this one I did upside down to try to show that I think there were three green ones…

[She points to the pieces on the top of the set.]

### Speaker

…I think, and one…

[She points to the piece on the bottom of the set.]

### Speaker

…that was maybe pink or purple. Did you see that too? Let's have a look. Ready?

[She flips the plate right side up.]

### Speaker

Ah, did you have that also? Yeah. And, you know, pasta is really tricky in this case because it usually only comes in one colour and if I had different coloured pasta…

[She flips the bottom piece right side up.]

### Speaker

…I would sometimes like to be able to show that in a different colour. But you might have had it like this as well because you saw four…

[She points to the pasta.]

### Speaker

…and this is also a really good way of thinking because what this…

[She circles the pompoms.]

### Speaker

…shows us in this representation is four is made up of…

[She points to the pompoms.]

### Speaker

…three and one more and we see that really obviously. And this one just shows us four as one clump of four and if I spin it this way…

[She turns the paper to the right.]

### Speaker

…it just looks like four in a dice pattern that's just gone…

[She turns the paper back to the left.]

### Speaker

…a little bit wonky. So, I can still trust that it's four. Alright. Shall we try one more together?

OK, let's do it.

[She takes the plate and pasta away.]

### Speaker

Clear away these things and let's... oh, yeah. Are you ready? OK.

[She put down a paper plate with 4 pink pompoms arranged in a square and 1 pink pompom above the top right corner pompom. She flips the plate onto the floor.]

### Speaker

OK, I hope you took a picture in your brain and you're imagining now how many you saw. And then on with your equipment, now try to recreate it. OK, I'm gonna do the same.

[She holds up a pink sheet of paper over the one on the floor with her right hand. Her left hand is under the paper.]

### Speaker

Let's see. I think I saw it like that.

[She swaps hands.]

### Speaker

I don't need that. OK, what were you thinking when you saw that representation? I can hear different ideas.

[She traces a square shape on the overlayed paper.]

### Speaker

Some of you were thinking that you saw four on a dice pattern and…

[She points to the paper.]

### Speaker

…one more and that's what you imagined. Someone else was saying that they think they saw three…

[She points to the paper three times, going down each time.]

### Speaker

…one, two, three, and…

[She points to the left of where she pointed, and points down twice.]

### Speaker

…another two. Yeah, and that's how I saw it. I sort of thought I saw it like six…

[She points to the same spots.]

### Speaker

…one, two, three, four, five, six, but one was missing.

[She takes the overlayed paper away. There are 4 pieces arranged in a square and 1 piece above the top right corner.]

### Speaker

And so what I was thinking of doing was to show…

[She places an upside down piece in the top left corner of the set.]

…a piece of pasta there that then went away.

[She takes the piece away. She flips the plate right side up.]

### Speaker

So, let's have a look. Yeah, so, we could see…

[She points to the 4 pompoms arranged in a square.]

…one, two, three, four like a dice. If I cover this up…

[She places a red square over the lone pasta piece.]

### Speaker

…that looks like four on dice…

[She places the red square over the lone pompom.]

### Speaker

…and then the one more or you might have seen the three first…

[She places the red square over the first column of pasta pieces.]

### Speaker

…see the three…

[She places the red square over the first column of pompoms.]

### Speaker

…and then the other two.

[She places the red square over the second column of pompoms and pasta. She takes it away.]

### Speaker

Yeah or this idea of one more being…

[She places a pasta in the first row and column of the pompoms.]

### Speaker

…here which would have been six and if I get rid of it…

[She takes it away.]

### Speaker

…the number before six is five. That's a really good way of thinking it. That idea that actually you could have moved this dot…

[She moves the lone pasta into the centre of the other pasta.]

### Speaker

…down here to have made five like a dice pattern. Really nice thinking mathematicians and really nice subitising.

[Text over a blue background: What's (some of) the mathematics?]

### Speaker

So, what was the mathematics today?

[A title on a white background reads: What's (some of) the mathematics?
Text below reads: When we subitise, we can work out how many there are without having to count everything we see.

Below the text is an image of the pasta pieces arranged in a square with a centre piece.

On the right of the image is text: We can see there are 5 things here. We worked it out by looking and thinking.]

### Speaker

So, what we realise is that when we subitise that means we can work out how many there are without having to count everything we see.

[A title on a white background reads: What was the mathematics?
Text below reads: Visualising helps us build our mathematical imaginations.]

### Speaker

We also know that visualising helps us build our mathematical imaginations…

[A title on a white background reads: What was the mathematics?
Text on the left side below reads: Exploring how different people use subitising and other knowledge they have to work out how many there are in a collection help us learn different things about numbers.]

### Speaker

… and that exploring how different people use subitising and other knowledge they have to work out how many there are in a collection helps us learn different things about number numbers.

[On the right side, a blue textbox appears. The title in the textbox reads: Here was one collection we wanted to subitise. Under the title is an image of 5 pompoms. Below the image is text on the left and images on the right. The first text reads: Cate knew it was 5 because she saw 2 and 3. The image is of the pompoms with a red sheet of paper covering the 2 pompoms on the left; two white dots are on the paper where the pompoms were. The second text reads: James knew it was 5 because he saw 4 and 1. The image is of the pompoms with a red sheet of paper covering the 1 pompom on the top; a white dots is on the paper where the pompoms was. The last text reads: Michelle knew it was 5 because she saw 1 less than 6. The image is of the pompoms with a pasta in the top left corner.

### Speaker

So, just by looking at that collection of five today, Kate helped us see that five is made up of three and two. James helped us see that five is made up of four and one, and Michelle helped us see that five is one less than six. This is really important as we get older as mathematicians so that we can learn to use numbers flexibly.

Nice work today, guys.

[Over a grey background, the red waratah of the NSW Government logo appears amongst red, white and blue circles. Text: Copyright State of New South Wales (Department of Education), 2021.]

[End of transcript]

## Reflection

• How did you go determining the total without having to count everything?
• Were you able to use your mathematical imagination?
• Did you find that you saw things in a different way to other people in your house?