# Sorting dominoes

A thinking mathematically targeted teaching opportunity focused on investigating doubles and near doubles using dominoes

## 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
• MA1-RWN-01
• MA1-RWN-02
• MA1-CSQ-01

## Collect resources

You will need:

• pencils or markers
• paper
• dominoes (if you have them).

## Sorting dominoes

Watch Sorting dominoes video (13:27).

Investigate strategies to sort and categorise sets of dominoes.

### Transcript of Sorting dominoes

[Text over a blue background: Sorting dominoes. In the lower right-hand corner of the screen is the waratah of the NSW Government logo. Small font text in the lower left-hand corner of the screen reads: NSW Mathematics Strategy Professional Learning team (NSWMS PL team).]

### Speaker

Today, we're going to do some sorting with dominoes.

[Black title on a white background: You will need…

· something to write with

· something to write on

· dominoes.

Beside the bullet points is an image of two Sharpie markers sitting on top of a blue piece of paper.]

For this activity, you'll need something to write with, something to write on, and some dominoes, if you have them.

[White text over a blue background: Let’s talk!]

So, let's talk.

[A blue sheet of paper sits on a table. The paper is divided into four equal sections. Each section contains two dominoes.]

Hey, mathematicians, we've been playing with some dominoes today, and my friend has sorted her dominoes, and she's asked me if I can try and figure out how she's sorted them. But I think I need some help. What do you notice about the dominoes?

[White title over a blue background: What do you notice?

Below the text is an image of the dominoes on the blue paper.]

Pause the video here and record some of the things that you notice.

[The screen returns to the view of the domino layout. The speaker points out the four groups.]

Yeah. She sorted them into four groups. I wonder what each of these dominoes have in common.

[The speaker points at the dominoes in the top right section of the paper. The first domino shows two patterns of 8 dots on its face. The second domino shows two patterns of 9 dots.]

When I looked at the dominoes, I started to notice that the ones up here have the same amount on each side. Can you see the same domino pattern on either side of the domino?

[The speaker places a yellow sticky note under the right-hand side domino. They point out the dot patterns on either side of the domino.]

### Speaker

Yeah, I can see on this domino nine on this side and nine on this side. And I know it's nine because I can see three threes.

[The speaker writes “9 on both sides” in blue Sharpie on the sticky note. Underneath, they also write “3 threes”. They point out the rows of three on the domino.]

So, this domino has nine on both sides. Oh, wow. Oh, that's right. We knew it was nine because it was three threes. Can you see? One three, two threes, three threes.

[The speaker places a sticky note under the left-hand side domino. They point out the rows of dots on the domino, and a blank space in the middle of the pattern.]

And when I look at this domino, I noticed the dot pattern almost looks similar. I can see the three at the top and the three down the bottom. Yeah, that's right. There's one missing from the three in the middle. So, I know that this side of the domino, and this side because it's the same, must have one less than these dominoes.

[The speaker writes “8 on both sides” on the sticky note.]

So, this domino has eight on both sides. Wow. Can you notice anything else?

[The speaker points to the left-hand side domino in the top left section. The domino shows a pattern of nine dots on one side, and two dots on the other side.]

I'm looking over here. This domino, I know that's nine. It's got nine on this side and two more on this side. Let's write that down.

[The speaker places a sticky note under the left-hand side domino. They write “9 and 2 more”.]

This domino has nine and two more. So, it's not the same as this one that has nine on both sides or eight on both sides.

[The speaker places a sticky note under the right-hand side domino. The domino shows a pattern of eight dots on one side, and one dot on the other side. They point to the left-hand side domino in the top right section, and indicate the two patterns of eight dots. On the sticky note, they write “8 and 1 more”.]

And this domino here, well, it's got a dot pattern the same as that one, so I know it's eight, but this one's got eight on one side and then one more on the other side. Hmm, that's interesting.

[The speaker points to the dominoes in the top right section, and the patterns of dots on both sides of each tile.]

So, these ones have the same pattern on each side of the domino.

[The speaker points to the dominoes in the top left section, and the patterns of dots on each tile.]

These ones are different.

[The speaker points to the two dominoes in the bottom left section of the paper. They place a sticky note underneath the left-hand side tile, which shows a pattern of four dots on one side and five dots on the other side.]

What about these ones down here? You know, if I use my mathematical imagination, I feel like I can see my four here and I feel like I can see it hidden over here. Let me show you what I mean.

[The speaker draws the four-dot pattern from the domino on the sticky note. They draw the same four-dot pattern beside it.

I've got my four over here just like this, but when I look at this domino over here, I can see the four on the outside dots. And I just imagine that one dot in the middle disappear. And then if I did that, then I would see that this domino has four on both sides, and then my one more dot that disappeared.

[In brown Sharpie, the speaker draws a dot in the centre of the four-dot pattern on the right side. Underneath in blue, they write “4 on both sides 1 more”.]

So, I am going to draw him in here in another colour because he just disappeared. So, that would mean that I have four on both sides and one more. Oh.

[The speaker points out the patterns on the dominoes in the top right section.]

You know, mathematicians, I think there's a special word to describe when we see two of something, do you know what it is? Yeah, that's right. It's doubles.

[The speaker places a pink sticky note in the top right section. They write the word ‘doubles’.]

These two dominoes over here are showing me doubles.

[The speaker points to the top left section. They place a pink sticky note in the section and write “not doubles”.]

These ones over here though, they're definitely not doubles, and I think I can add that in. I think I'm starting to see now how my friend has sorted the dominoes here today. Not doubles. So, now that I know that we're looking for doubles, I wonder if we can see any more hiding in these dominoes down here.

[The speaker places a yellow sticky note in the bottom left section of the paper. They draw the five-dot pattern on the left side of the domino onto the sticky note.

Let's take another look at this domino. But let's look at this side first. We've got our five dots that we see all the time when we roll the dice. I wonder if you can see our five dots within this pattern over here.

[The speaker draws the four-dot pattern from the domino on the sticky note. On the sticky note above, they cross out the brown dot in the centre of the five-dot pattern. On the bottom sticky note, they draw a brown dot in the centre of the four-dot pattern.]

So, I'm gonna draw... Now, just like we imagined this dot in here disappearing, I wonder if we can imagine a dot here appearing. Look at that.

[On the bottom sticky note, the speaker writes “5 on both sides” and “double 5 and 1 less.”]

Let's imagine that there's a dot here because now we can see that there are now five on both sides. We know that's called double five, don't we? So, double five. But we have to remember to take that one off, don't we? Because we're only pretending it's there. So, double five and one less.

[The speaker points to the two patterns containing brown dots.]

Oh, look at that, mathematicians. We saw the double here when we imagined one disappearing and we imagined a double here when we imagined one dot appearing on this side of the domino. So, we can think about doubles as near doubles. Doubles and one more and doubles and one less.

[The speaker points to the domino on the left-hand side in the bottom left section. They place a yellow sticky note under the domino.]

[The speaker points to the pattern on the domino. It shows nine dots on the left side, and eight dots on the right. They point out similar patterns on the dominoes in the top right and top left sections.]

Now, I remember both of these domino patterns from our dominoes up here. So, I already know there's eight on this side and nine on that side.

[The speaker draws the nine-dot pattern from the domino onto the sticky note, then the eight-dot pattern beside it. They use a brown Sharpie to place a dot in the blank space in the centre of the pattern.]

Oh, I wonder if we can use our mathematical imagination again to find the hidden double. So, let's have a look over here. You got three, two, and then another three. And look at that. Can you see the hidden double? Yeah, look at that.

[The speaker writes “double 9 and 1 less” on the sticky note.]

We can add one more in and now it's double nine, which we knew is 18 from up here, and we imagined that one in, so we have to remember to take him out. So, it's double nine and one less.

[The speaker adds another sticky note in the bottom right section. They draw the eight-dot pattern from the domino on the right side, then the same pattern on the left side.]

But you know, mathematicians, we like to see things different ways. So, let's have a look at the other way we could think about this domino. We could start with our eight dots over this side. And we could imagine our eight dots over this side by pretending or imagining that this dot here has disappeared, we've made it the same.

[The speaker points to the nine-dot pattern on the left side of the domino. They write “double 8 & 1 more” on the sticky note.]

So, now we can imagine this dot in the domino in the middle here missing. We can now see where the double is. So, now it's double eight. So, we have to remember to put that one more back on, and one more.

[The speaker points to the top right section, then to the top left section. They place a pink sticky note in the bottom left section. They write “near doubles” on the sticky note.]

So, we've got our doubles here. And these ones are definitely not doubles. What do you think this one might be? I think that these ones over here are near doubles. Because they're so close.

[The speaker writes “1 less or 1 more” on the pink sticky note.]

We could even think about them as double and one more or double and one less. Oh, wow. Look at that.

[The speaker points to the dominoes in the bottom right section.]

What about these ones over here? Are there doubles hidden inside here, too? Let's see if we can find them.

[The speaker places a yellow sticky note under the left-hand side domino in the bottom right section. The domino shows a pattern of three dots on the left of the tile, and five dots on the right. The speaker draws the three-dot pattern on the sticky note.]

Let's start with this one over here. I can see my three dots going down here. Can you see three dots on the other side hidden inside this five?

[The speaker draws the same three-dot pattern on the sticky note beside the first. Below the patterns they write “double 3 and 2 more”.]

Yeah, I can see it, too. Look, there it is, three dots. Hidden on this side of the domino. So, this domino has double three, but what else has it got? It's got double three, and this time it's got two more. Oh, my goodness, great noticing, mathematicians. Look at all these hidden doubles that we found.

[The speaker places another yellow sticky note in the section, under the right-hand side domino. The domino shows a pattern of nine dots on the left and seven dots on the right.]

[The speaker draws the seven-dot pattern onto the sticky note. They draw the same pattern beside it.]

I think I'm going to start with my seven, and I know that it's seven, because look at this. I can see my six that I see on lots of dice and my one more in the middle. Wonder if I can see my seven hidden in this nine. I can see the three there. And I can see my other three over here, just like in the six. But this one. Yeah, imagine these two dots over here disappear.

[The speaker uses a brown Sharpie to draw two additional dots into the pattern. Below, they write “double 7 and 2 more”.]

I'm going to draw them a little bit differently this time. Look, let's just see them here. There they are. So, now on this one, I've got double seven and two more. Oh, look at that.

[A blank yellow sticky note appears in the bottom right section. The speaker indicates the right-hand side domino in the section.]

Now, when I look at this domino again, we thought about double seven and two more. But I think I can imagine this side of my domino. I think I can see it as nine dots too.

[The speaker points to the blank spaces in the seven-dot pattern on the domino.]

And if I imagine a dot appearing here and a dot appearing here, then I have my three threes again.

[The speaker draws the nine-dot pattern from the domino on the blank sticky note, then beside it draws the seven-dot pattern.]

So, let's have a look. Got our nine on this side. And we know that there's seven on this side.

[The speaker uses a brown Sharpie to draw two additional dots in the pattern. In blue, they write “double 9 and 2 less”.]

But let's see if I can find my imaginary double. Look, there it is. I've now got double nine and two less. Now, I knew that double nine was 18, and two less than 18 is 16, and I knew that double seven was 14 and two more than that is 16. And look at that. We can think of these doubles in different ways using what we know about more or less.

[The speaker places a pink sticky note in the bottom right section. They point to each of the other pink sticky notes. On the blank sticky note, they write “near doubles 2 less or 2 more”.]

So, we've got our labels for doubles, not doubles, near doubles with one less and one more. I was wondering, what do you think my friend thought these dominoes have in common? They are near doubles too, aren't they? But this time they weren't one less and one more, they were two less or two more.

[White text on a blue background: What’s (some of) the mathematics?]

So, what's some of the mathematics that we explored today?

[Black title on a white background: What’s (some of) the mathematics?

Text: When we are combining two groups that are the same size (they are equal), we can call them a double.

Below the text is an image of one section of the domino layout, with two tiles showing identical patterns. Under the tiles are two yellow sticky notes. One note reads: 8 on both sides. The other note reads: 9 on both sides 3 threes. A pink sticky note below reads: doubles.]

When we are combining two groups that are the same size, they are equal. We can call them a double.

[Text: When we are combining two groups that are NOT the same size (they are not equal), they are NOT doubles.

Below the text is an image of another section of the domino layout. Two domino tiles show unidentical patterns. Two yellow sticky notes below read: “9 and 2 more” and “8 and 1 more”. A pink sticky note below reads: not doubles.]

When we're combining two groups that are not the same size, they are not equal, so they are not doubles.

[Text: When we know doubles we can use them to find near doubles.

Below the text, an image shows the two bottom sections of the domino layout. The pink sticky notes at the bottom read: “near doubles 1 less or 1 more” and “near doubles 2 less or 2 more”.]

When we know doubles, we can use them to find near doubles. Today, we used our mathematical imagination to imagine the dots appearing and disappearing and this helped us to find the doubles.

[White text on a blue background: Over to you mathematicians, can you find some dominoes, dice or other resources that show doubles, not doubles and near doubles.]

So, over to you, mathematicians. Can you find some dominoes, dice or other resources that show doubles, not doubles and near doubles?

[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

• Record what you notice about the way these dominoes are sorted.

• As you watch the video draw some pictures to show where you saw the hidden doubles in the dominoes.

### Discuss

• Can you find some dominoes, dice or other resources that show doubles, not doubles and near doubles?

Category:

• Combining and separating quantities
• Mathematics (2022)
• Representing whole numbers
• Stage 1
• Thinking mathematically