Splat! (conceptual subitising to 10)

This is a thinking mathematically context for practise resource focussed on using conceptual subitising to visualise hidden quantities.

Adapted from Steve Wyborney – Splat

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-CSQ-01

Collect resources

You will need:

• coloured pencils or markers

• paper or your workbook.

Watch

Make sure you have your subitising eyes ready to look for meaningful chunks. Watch Splat! (conceptual subitising to 10) video (7:32).

Investigate subitising visible and partially visible collections.

Transcript of Splat! (conceptual subitising to 10) video

[Text over a navy-blue background: Splat! Smaller text beneath reads: Adopted from Steve Wybborney. Small font text in the top right-hand corner reads: NSW Department of Education. In the lower right-hand corner is the red waratah of the NSW Government logo. ]

Speaker

Hello there, mathematicians. We are gonna play a game called Splat by Steve Wyborney. You might need a pencil and some paper so you can draw down your ideas. And you will need your subitising eyes, which means that you're looking for chunks that you recognise instantly without having to count.

[Text in a rectangular, pink speech bubble in the top right-hand corner of a white background reads: How many dots are there in total? How do you see them?]

Are you ready? Here we go. How many dots are there and how do you see them?

[5 blue dots form a square-like pattern, 4 dots surround one in the centre. The pattern disappears.]

Oh, what are you thinking, mathematicians? Can you draw down how many dots you think you saw? OK. Shall we have a look together? Great.

[Text in a rectangular, yellow speech bubble in the top right-hand corner of a white background reads: I see a 5 like a dice pattern…a bit on it’s side. Beneath the speech bubble are 5 light green dots in the same pattern as the previous blue dots.]

Speaker

Here's one way of thinking. This person said, I see five like a dice pattern, it's a bit on its side. Oh, and that's how some of you saw the dots. OK. Did you see it like this person?

[Beneath the light blue dots, text in a rectangular blue speech bubble reads: I see 3 in a triangle and 2 more.]

They said, I see three in a triangle and two more.

[5 dots, appear in the same pattern beneath the blue speech bubble. The lower three dots forming a triangle are blue, the two dots to either side of the top of the triangle are pink.]

Look, see the three in the blue triangle and two more, the pink dots? Uh-huh. And they said, you know, that we think it's five, five dots all together, and it is five, look.

[The number five appears in a black box to the top right-hand side of the page. It disappears and the original 5 blue dots appear in its place.]

Aha, and you can see it as three and two, or five like a dice.

[The number 5 in a black box in the top right-hand corner of a white background. The pattern of five blue dots appears on the right-hand side of slide.]

Speaker

OK. Now that you've thought about how many dots there are and how you see them, get ready for the challenge. Ready?

[A black image in the shape of a star covers the 3 dots in a triangle formation at the bottom of the pattern. Text in a rectangular, pink speech bubble appears to the left of the slide: What do you already know? How can you use that to help you work out how many dots are covered?]

Splat. Aha. So, now what we wanna know is, how many dots are being covered up? And because we're working like mathematicians, we're gonna think about what do we already know, and how can we use that to help us? So, remember what you drew, yeah, and we're trying to use what we saw, not counting everything by ones.

[Beneath the pink speech bubble, text in a rectangular, blue triangle reads: I saw 3 in a triangle and 2 more. I can still see the 2 more but the triangle is covered. I think 3 dots are covered.

And remember, this person said that they saw three in a triangle and two more. So, they can see the two more, but the triangle is covered and they said, I think that means three dots are covered. Ah, can you see how they're using reasoning, and they are not having to count them? Let's see.

[The black shape covering part of the pattern becomes translucent, revealing the 3 dots beneath.]

Oh, yeah, there you go, three dots being covered. OK, let's play again, ready? Here's our next collection.

[Text in a rectangular pink speech bubble on the left-hand side of a white background reads: How many dots are there in total? How do you see them?]

Speaker

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

[2 extra dots appear on the right-hand side of the original pattern. The pattern disappears.]

Oh, what are you thinking now? You could draw it down, mathematicians. How many dots are there, and how do you see them? Oh, I like that you're thinking about, some of you are thinking about that you might have seen a five in there before, like the one before, that's a good idea.

Oh, and some of you are thinking about different dice patterns. OK. Is it like this?

[Text in a rectangular, yellow speech bubble on the left-hand side of a white background reads: I see a 5 like a dice pattern and 2 more. Beneath the speech bubble, 5 blue dots form the original pattern with 2 green dots establishing the new pattern.]

Here's one way, one suggestion. This person said, I see five in a dice pattern and two more. Uh-huh.

[Text in a rectangular, blue speech bubble reads: I see 6 from a dice and 1 more. Beneath the speech bubble the same pattern of dots appears with two rows of 3 blue dots and a yellow dot in-between and to the left.]

And this person said, I see six from a dice pattern and one more, look. Isn't that amazing how the same collection of dots, we can see them quite differently?

[The number 7 in a black box appears in the top right-hand corner of the slide.]

And they both have seven, yes, look.

[7 blue dots appear forming the pattern.]

Speaker

Alright. Are you ready for the splat? Think about holding in your head what you know and how you saw the dots, it's really important, ready? Here it comes.

[A black image in the shape of a star covers one dot on the top right and two on the lower right of the pattern.]

Splat. Oh, and how many dots are being covered?

[Text in a rectangular, pink speech bubble to the left of the pattern reads: What do you already know? How can you use that to help you work out how many dots are covered?]

And we wanna use what we already know. So, imagine in your mind's eye how many dots you saw. We know there were seven, and think about how you saw them. And then imagine which of those dots is now covered.

[Beneath the pink speech bubble, text in a rectangular, yellow speech bubble reads: I Saw a 5 like a dice pattern and 2 more. 1 of my dots from the 5 is missing and so are the other 2 dots. I think 3 dots are missing.]

Oh, so you might be thinking like this. I saw five like a dice pattern and two more. One of my dots from the five is missing, and so are the other two dots. I think there's three dots missing. Do you agree? Nice reasoning, mathematicians.

[The black shape covering part of the pattern becomes translucent, revealing the 3 dots.]

Let's have a look. Yeah, there's the one dot from the five that's missing and two more. OK, let's do one more.

[Text in a rectangular, pink speech bubble on the left-hand side of a white background reads: How many dots are there in total? How do you see them?]

This one has got quite a few dots. Are you ready?

[A new pattern of 8 blue dots appears. The pattern disappears.]

OK. How many dots are there, and how do you see them? Oh, I know, that was super tricky. Would you like one more look? Here we go.

[The pattern of 8 blue dots re-appears. The pattern disappears.]

So, what are the chunks that you saw there? You definitely have to use a chunking strategy. Oh, yeah. You could draw it down if you like. OK. Shall we share some other people's thinking?

[Text in a rectangular, yellow speech bubble on the left-hand side of a white background reads: I see a 4 like a dice pattern…a bit on it’s side. 2 and then 3 like an arrow.]

Speaker

OK. So, this person said that they see four like a dice pattern, but it's a bit on its side. Can you imagine that in your mind's eye? Imagine four on a dice pattern and a bit on its side. Can you draw that in the air for me? Oh, yeah. And then they said, and then there's two more, and then three like an arrow, like the top of an arrow, like a triangle. Let's see.

[The pattern re-appears with 3 orange dots forming an arrow, which points toward 2 pink dots, one on top of the other, with four blue dots in a dice pattern on the left.

Oh, yeah. And look at that, how we can use the colour to help us see the chunks that they saw. See the four there in the blue? Aha. And the two more in the pink?

Yeah. And the three more in the orange. Aha. And we know four and two is six 'cause if we move those dots around that would be like six on a dice pattern. And six and three more. Yeah, we could count on, six, seven, eight, nine.

[The number 9 in a black box appears in the top right-hand corner of the slide.]

It's nine, or it might be something that you know. Alright. Eye balls ready, mathematicians, because here comes the splat. So, think about the chunks that you can see there, the four, the two and the three, and splat.

[A black image in the shape of a star covers the central three dots of the pattern. Text in a rectangular, pink speech bubble to the left of the pattern reads: What do you already know? How can you use that to help you work out how many dots are covered?]

Uh-oh. Now, let's try to imagine what we already knew in our brains. We knew there was a four. And we knew, yes, there was a three. And we knew there was a two. So, what part of the four is missing? Oh. One part from the four, you think? And is there a part from the three missing? The orange triangle. Ah. So, you think there's one missing from the orange arrow or triangle? And is there any of the pink ones missing, the two? One missing from there too.

[Beneath the pink speech bubble, text in a rectangular, yellow speech bubble reads: I saw 4 like a dice pattern and one is missing. There is also 1 missing from the 2 I saw and 1 missing from the arrow. I think there are 3 dots covered by the SPLAT.]

So, we think that there might be three dots being covered by the splat. Let's check to see.

[The black shape covering part of the pattern becomes translucent, revealing 3 dots, one of each colour.]

Oh, that's great.

Nice reasoning today, mathematicians. Until the next time we splat, have a lovely day.

[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]

Instructions

• Follow along with the video, using your subitising eyes to look for meaningful chunks.

• When working out how many dots in the collection, think about:

• How many dots are there in total?

• How do you see them?

• When part of a collection has been covered with a 'splat', think about:

• What do you already know?

• How can you use that to work out how many dots are covered?