# Dice patterns

A thinking mathematically targeted teaching opportunity, focussed on recognising and representing numbers on a six-sided dice

## 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

You will need:

## Watch

Watch Dice pattern investigation 1–4 video (15:00).

Investigate the numbers 1 to 4 using dice patterns.

### Transcript of Dice pattern investigation 1-4

#### Speaker

Hello there mathematicians! Let's investigate dice patterns.

So today you need a pencil and some paper, or a book and we'll need those straight away to get started and later we'll need this sheet of paper and some scissors so you can cut them up to make some cards. It's OK if you don't have a printer at home, you can copy them like I did it onto a piece of paper; you'll need to do that really carefully.

[Screen reads, you will need … a pencil, some paper, a pair of scissors and this sheet of paper and there is a picture of a pencil, clip board and scissors.

#### Speaker

The screen shows 2 sheets of paper with 3 vertical lines and 5 horizontal lines, creating 24 boxes. On both pages in the far-left column, the numerals, 1, 2, 3, 4, 5, 6 are written and in the second column the words one, two, three, four, five and six are written. In the third column of the first page, a dice is displayed in each box. The first dice has a black square outline with a black dot. The second dice has a black square outline with a red and black dot. The third dice has been rotated and has a black square outline with diagonal black dots. The fourth has a black square outline with 4 black dots in a standard dice pattern. The fifth has a black square outline with 3 blue dots in diagonal line and 2 red dots on either side. Lastly, the sixth dice shows 6 black dots as 2 rows of 3 with no outline.

In the third column of the second page, a dice is displayed in each box. The first dice shows a black square outline with 1 black dot. The second dice is blue with a white and yellow dot. The third dice is black with 3 white dots. The fourth dice is white with 4 black dots. The fifth dice is white with 3 blue dots in diagonal line and 2 red dots. Lastly, the sixth dice shows 6 black dots as 2 rows of 3 with no outline. The fourth column on both pages is the same and shows different representations of the numbers using dot patterns.]

OK, let's start investigating dice patterns. You may already know some dice patterns and you might already know a lot of things about them. They are really important patterns that we see a lot as we work and learn like mathematicians. So, it's really important to us that we can recognise them, trust them, draw them, but also make meaning from them and use them to help us solve problems.

OK, let's get started. So how many dots can you see here?

[Screen shows white dice with a black dot.]

#### Speaker

One, that's right, say it with me. One. I can see one dot.

We might see one of something when we look up into the sky. For example, I can see one warm yellow sun.

[Screen shows a white sun with yellow rays emanating from it.]

#### Speaker

When we see this dice pattern, we know it represents one. We can record how many dots we see using symbols. And using words.

[Screen shows a white dice with a black dot, one written as a word and as a symbol or numeral, 1.]

#### Speaker

OK, so this is the dice pattern for one and it's still one, even if it's really small or orientated a little bit differently and in a different colour.

[Screen shows white dice with a black dot in the middle sitting flat and then a pink dice with black dot the middle titled on an angle.]

#### Speaker

It's still one if it's big, it's actually still one, even if I replace the one dot with a unicorn and it's still one, even if that one thing is slightly off center.

[Screen shows a small dice and then a big dice and one written as a word and a symbol or numeral, 1. The dot in the middle is then replaced with a unicorn picture, showing it is still one. The unicorn is replaced by a green dice with one black dot slightly off center showing it is still one.]

#### Speaker

So, this is something now that I can trust. So, what we know as a mathematician, is that drawing representations helps our brain to remember them, so watch the screen.

[Screen shows white dice with one black dot.]

#### Speaker

OK, now let's use your mathematical imaginations, and draw the dice pattern for one in the air. Use your pointy finger.

Great, how many dots did you draw? That's right one. Now let's draw the dice pattern for one on a piece of paper with your pencil ready, draw one.

Oh yes, I can see. So have a look at it and describe how many dots you have.

Does it look a little bit like this from Willow and Meila?

[Screen shows 2 hand drawn dice with black outlines and one black dot in the middle. Under the first one, ‘from Willow’ is written and underneath the second one ‘from Meila’ is written.]

#### Speaker

Does your picture look similar? Great! Now, as mathematicians, we know that we can represent ideas in different ways, so we can use drawings. But we can also use symbols, so watch the screen to look at how to draw the symbol for one.

[Screen shows a dice with black outline and one black dot in the middle and the numeral for one with a red dot on the top and then the red dot slides to the bottom of the number one.]

#### Speaker

OK, now using our imaginations, put your pointy finger up into the air and write the number one.

Great, now write it on your piece of paper next to the dice pattern for one that you drew.

Have a look at what you wrote and read it to me. Does your picture look similar to these?

[Screen shows 2 hand drawn dice with black outline and one black dot in the middle, and one written as a numeral and in word form to the side. Under the first drawing, ‘from Willow’ is written, and underneath the second drawing, ‘from Meila’ is written.]

#### Speaker

Yes, that's the symbol for one next to your drawing for one. And here is what the word one looks like.

OK, should we have a look at the next dice pattern? Yes, let's do it.

[Screen shows a dice with black outline and 2 black dots.]

#### Speaker

How many dots can you say here? 2, I can see 2 dots. We might see 2 of something when we look up into the sky to discover why has it grown so dark. And then we see 2 dark clouds are blocking the sun.

[Screen shows 2 clouds.]

#### Speaker

So here is the dice pattern for 2, we can represent 2 also using symbols, and using words.

And the dice pattern for 2 can look like this one we see on the screen, but this also represents 2, and even if it's a little bit turned around, it still represents 2. Even when it's a different colour, I can see 2, and even when it's big and the dot's a, a different colour, it's still 2. It's 2 when the dots are close together, or when one dot is bigger than the other, and in fact it's still 2 even if I don't have dots at all, but I have snowmen, that's right.

[Screen shows a dice with black outline and 2 black dots and number 2 and 2 in word form written to the right side. The dice is then made smaller, it is then turned around to sit in a corner, it is then changed to the colour green. Then the dice is made larger with dots changing colour to make one white and one yellow. The dice is then changed to be orange and the dots move close together, then one dot is made larger. The dots are finally replaced with 2 snowmen figures on a purple background.]

#### Speaker

So, this pattern of 2 doesn't always have to look exactly the same, but it does always have to represent 2 of something.

[Screen show 7 dice, all with varying sizes and colours 6 of the dice have 2 dots and one has 2 snowmen.]

#### Speaker

That's why it's a pattern, look, I still have 2 things: one, 2 or one, and 2.

[Screen shows dice with 2 snowmen. One shakes then the other, then screen shows a dice with 2 dots one flashes then the other.]

#### Speaker

This is something that we can trust.

So, as we know, drawing mathematical representations helps our brain to remember them. So, watch the screen.

[Screen shows a dice with black outline and 2 black dots.]

#### Speaker

OK, take a picture and put it in your mind. Great, now let's use our mathematical imaginations using your pointy finger. Draw a dice pattern for 2 in the air for me. Off you go.

Great, how many dots did you do? 2.

OK, let's draw the dice pattern for 2 on a piece of paper with your pencil. OK, draw 2.

Oh, I can see some of you are being very careful in colouring in the 2 things. And that's right, some of you don't have dots and you're drawing.

Oh, I see, 2 love hearts! Or 2 squares. That's right because it just has to be 2 things.

OK. Does your picture look like these ones from Willow and Meila?

[Screen shows 2 hand drawn dice with a black outline and 2 black dots in the middle. Under the first one, ‘from Willow’ is written, and underneath the second one, ‘from Meila’ is written.]

#### Speaker

Great, now let's write the number 2.

[Screen shows a dice with a black outline and 2 black dots. The numeral 2 is written on the right-hand side and a red dot is at the start of the number.]

#### Speaker

We know that mathematicians represent ideas in lots of different ways. So, watch the screen.

[Screen shows a dice with a black outline and 2 black dots, with 2 written to the right-hand side and a red dot at the start of 2. The red dot slides down and traces to the end of the number 2.]

#### Speaker

OK, now let's imagine. Pick up your pointy finger and draw the number 2 in the air. Great, now let's write 2 next to the dice pattern you drew. Off you go.

OK, have a look and read to me what you wrote.

Yes, that's a symbol for 2. And here's what the word '2' looks like.

[Screen shows 2 hand drawn dice with black outlines and 2 black dots in the middle and 2 written next to the dice. Under the first drawing, ‘from Willow’ is written, and underneath the second one, ‘from Meila’ is written. The numeral and word for 2 is written to the right of the drawings.]

#### Speaker

OK, should we have a look at another dice pattern? Yes, let's do it. 3. How many dots can you see here?

[Screen shows a white dice with black outline and 3 diagonal dots.].

#### Speaker

That's right, this is 3. We might see 3 of something when we notice some of the houses around us. Some of them have strong, sturdy roofs that look like triangles.

[Screen shows picture of a house.]

#### Speaker

I can see a triangle in the roof of this house. The triangle has 3 corners, 1, 2, 3 and 3 sides. 1, 2, 3.

[Screen shows picture of a house, and an orange circle is drawn around each of the 3 corners of the roof, and a line is drawn joining the 3 corners to make a triangle and show there are 3 sides.]

#### Speaker

When we see this dice pattern, it represents 3.

[Screen shows dice with black outline and 3 black dots in a diagonal line.]

#### Speaker

We can record how many dots we see using symbols. This is the symbol for 3 and using words, here's the word 'three'.

[Screen shows dice with black outline and 3 black dots in a diagonal line and to the right 3 is written as a numeral, or symbol and written in word form.]

#### Speaker

So, the dice pattern doesn't always have to look exactly like this, look, here's 3 with the middle dot a little bit wonky. Here's 3, even though it's now on its corner, it's orientated differently.

[Screen shows dice with black outline and 3 black dots in a diagonal line with one dot off to the right slightly and to the right 3 is written as a numeral, or symbol and written in word form. The dice is then moved to display on its corner.]

#### Speaker

Yes, and I see that too. It looks a little bit like a traffic light now.

[Screen shows dice with black outline and 3 dots, one red, one amber and one green, and is displayed on its corner.]

#### Speaker

And I can still see 3 here even when it's really small or here when it's really big and the dots are pointing in a different direction, and in fact some of the dots are different colours and look, I can still see 3, even though there's no outline of my dice and I can see 3, even though there's no dots at all and I have dinosaurs, right?

[Screen shows small dice with black outline yellow background and 3 small black dots and then it is enlarged with no outline a pink background and 3 diagonal dots, black, white, and black. The dice changes again, removing the background to show 3 red dots in a diagonal line. Finally, it changes to a dice with blue background and 3 white dinosaurs.]

#### Speaker

So, the pattern of 3 doesn't always have to look exactly the same, but it does always represent a collection of 3.

[Screen shows the 6 different dice representations of 3. Firstly, 3 red dots in a diagonal line, a dice with black outline and 3 blacks dots with one slightly off center, a larger pink dice with 3 dots in different colours, a smaller dice on its corner with black outline and 3 vertical dots, a dice with blue background and 3 dinosaurs and a much smaller dice with black outline, yellow background and 3 diagonal dots.]

#### Speaker

Look, we still have 3 things - 1, 2, 3 or 2, 3. Yes, I just realised that too. Look, inside of 3, we can see 2 and one more.

[Screen shows 3 red diagonal dots, with 3 written as a numeral or symbol, and in word form to the right. The dots shake individually as the presenter counts. Then the dice changes to a black outline with 3 diagonal dots one black, one green and then one black sitting on its corner with 3 written as a numeral or symbol, and in word form to the right. Then it changes again to a larger dice with 3 diagonal black dots with 3 written as a numeral or symbol, and in word form to the right. The middle dot on the dice disappears and 2 is written as a numeral or symbol and in word form to the right, then a red dot is added back into the middle and 3 is written again to the side. Showing that 3 is made up of 2 and one more.]

#### Speaker

That's 3, so this dice pattern represents 3 and it's something that we can trust. So, let's have a look at how we might draw 3.

[Screen shows a dice with black outline and 2 black diagonal dots drawn first, then the third added in the middle.]

#### Speaker

Watch carefully now. OK, take a picture in your brains. And now let's imagine the dice pattern for 3. Use a pointy finger and draw the 3 patterns in the air, off you go.

Great, now let's draw the dice pattern for 3 on a piece of paper with your pencil, off you go.

Oh! I can see! Yes, some of you have drawn 2 on a dice pattern first and are putting the one in the middle for 3.

OK, let's have a look at your pictures. Can you describe it to me?

Let's have a look at these ones from Willow and Meila.

[Screen shows 2 hand drawn dice with black outlines and 3 black dots in the middle. Under the first drawing, ‘from Willow’ is written, and underneath the second one, ‘from Meila’ is written.]

#### Speaker

Does your picture look similar? Great.

OK, let's write the number 3. Ready, watch the screen.

[Screen shows a dice with a black outline and 3 diagonal black dots with the numeral or symbol 3 written on the side and a red dot at the beginning of the 3. The red dot then traces the outline of the 3 to the bottom of the 3.]

#### Speaker

Good job! Now, let's imagine drawing the number 3 in the air with our pointy finger. Off you go.

Great! Now let's write the number 3 next to the dice pattern that you drew. OK, write 3.

OK, have a look at what you wrote.

Can you read it to me? Great.

Does your symbol for 3 look like Willow and Meila's?

Yeah, that's what 3 looks like and here's what the word 'three' looks like.

[Screen shows 2 hand drawn dice with black outlines and 3 black dots in the middle and the numeral or symbol 3 written next to the dice. Under the first drawing, ‘from Willow’ is written, and underneath the second one, ‘from Meila’ is written. The numeral or symbol for 3 and the word form is written to the right of the drawings.]

#### Speaker

What do you think we might look at next? 4?

Yes! Yes, I know we're using a pattern as we investigate patterns. Each time we look at the next dice pattern it increases by one.

OK, let's explore 4.

[Screen shows a dice with a black outline and 4 black dots.]

#### Speaker

OK, how many dots can we see here? 4, I can see 4 dots.

We might see 4 of something when we're looking at the television, we can see a rectangle on the surface of our TV screen, and the rectangle has 4 corners.

[Screen reads I can see a rectangle in the screen of this television. The rectangle has 4 corners and 4 sides.]

#### Speaker

And 4 sides, look, 1, 2, 3, 4.

[Screen shows a tv screen with orange circles on each corner and an orange line is drawn around the outline of the tv showing four sides as the presenter counts to 4. An orange building appears in the middle of the tv with ‘Construction Masters’ written underneath the building.]

#### Speaker

And this is the dice pattern for 4, represents 4, and we can record it using symbols, and using words.

[Screen shows a dice with a black outline and 4 dots and 4 is written as a numeral or symbol and in word form to the right.]

#### Speaker

But 4 doesn't always have to look exactly like this.

Let's have a look.

This is still 4 even if it's twisted on its side.

[Screen shows a dice tilted on one corner with a black outline and 4 dots and 4 is written as a numeral or symbol and in word form to the right.]

#### Speaker

And even if it's 4 and, it's really teeny tiny.

[Screen shows a smaller dice with black outline, yellow background and 4 dots off center and 4 is written as a numeral or symbol and in word form to the right.]

If it has 4 squares instead of 4 dots, it's still representing 4 even if the 4 are different colours, it still shows us 4.

[Screen shows a dice with a blue background and 4 yellow tilted squares and 4 is written as a numeral or symbol and in word form to the right. The dice then changes to have a light blue background with 2 darker blue dots and 2 white dots.]

#### Speaker

The 4 could be different sizes and 3 could be one colour and one could be another, and in fact I can still see it's 4 even when there's no outline of my dice, it's still a mathematical pattern that represents the quantity 4.

[Screen shows a dice with red background and 4 dots, one larger black dot and 3 white dots. This dice is then replaced with 4 green dots with no outline or background.]

#### Speaker

I still have 4 things.

[Screen shows dice with no outline around dice with 4 blue dots which flash individually as the presenter counts.]

#### Speaker

Look 1, 2, 3, 4 or 2, 4.

[Screen shows a dice with 4 blue dots. The 2 dots on the left flash and then the 2 dots on the right flash as the presenter counts.]

#### Speaker

And yes, little mathematicians, I can see that too. Look, inside of 4, we can see 2, that I imagined turning around like this and then, 2 more and that is... 4.

[Screen shows dice with black outline and 2 red dots diagonally, with 2 written as a numeral or symbol and in word form to the right. The dice is then turned around and 2 purple dots are added diagonally in the other direction, making a total of 4 dots, with 4 written as a numeral or symbol and in word form to the right.]

#### Speaker

So, this dice pattern represents 4 and it's something that we can always trust.

Let's have a look at how we might draw it. Watch carefully now.

[Screen shows a black square line of a dice being drawn in firstly with 2 black dots added one way diagonally, then another 2 black dots added diagonally.]

#### Speaker

OK, take a picture in your mind's eye and let's imagine.

Use your pointy finger and draw the dice pattern for 4 in the air. How many dots did you draw?

Great! Now let's draw the dice pattern 4 on a piece of paper with your pencil ready, draw 4.

That's OK, keep going. I can wait for you.

OK, let's have a look.

Did your picture looks similar to these ones?

[Screen shows 2 hand drawn dice with black outlines and 4 black dots in the middle. Underneath the first drawing, ‘from Willow’ is written and underneath the second drawing, ‘from Meila’ is written.]

#### Speaker

Great. Alright mathematicians, now we know it's really important to be able to represent 4 using, using its symbol as well, the number 4.

[Screen shows a dice with a black outline and 4 dots with 4 with a red dot at the beginning of the 4.]

#### Speaker

So, let's have a look at how we would draw that.

[Screen shows a dice with a black outline and 4 dots with 4 written as a numeral or symbol on the right side and the red dot at the beginning of the 4 traces the outline of 4.]

#### Speaker

OK, using your imagination, pick up your pointy finger and draw 4 in the air.

Great, now write the number 4 next to the dice pattern you drew. Have a look at what you wrote and read it to me.

[Screen shows 2 hand drawn dice with black outlines and 4 black dots in the middle. Underneath the first drawing, ‘from Willow’ is written and underneath the second drawing, ‘from Meila’ is written. The numeral or symbol and word form for 4 is written to the right of the drawings.]

#### Speaker

Yes, that's the symbol for 4.

This is what Willow thought about and Meila's. Let's look at what the word 'four' looks like.

[Screen shows 4 in word form written under the symbol for 4.]

#### Speaker

There it is.

[Screen reads, to be continued…]

[End of transcript]

## Watch

Watch Dice pattern investigation 5–6 (12:54).

Investigate the numbers 5 and 6 using dice patterns.

### Transcript of Dice pattern investigation 5-6

#### Speaker

[Screen reads – In part 1, we just finished exploring 4 – get ready for part 2!]

[Screen shows 2 hand drawn dice with black outlines and 4 black dots in the middle. Underneath the first drawing, ‘from Willow’ is written, and underneath the second drawing, ‘from Meila’ is written. The numeral or symbol and word form for 4 is written to the right of the drawings.]

And what do you think we might look at next? 5? Yes, you're right. We are using a growing pattern, so each dice pattern that we look at increases by one each time. That means we're adding one each time.

OK, let's explore 5. How many dots can you see here? 5.

[Screen shows a dice with a black outline and 5 dots.]

So, we can see 5 of something when we see one hand or one glove, I can see 5 fingers on the gloves look - 1, 2, 3, 4, 5, fingers in total.

[Screen shows open hand with 5 fingers. As the presenter counts, each finger is circled, until a total of 5 fingers are circled.]

And this is the dice pattern for 5. It represents 5, and this is how we can represent 5 using symbols and using words so the dice pattern for 5 doesn't always have to look exactly like this look.

[Screen shows a dice with black outline and 5 dots. The numeral, or symbol for 5, and word for 5, is written to the right of the dice.]

I still have 5, even when there's no outline of my dice or when it's orientated differently or even if some of the dots are a bit wonky, it doesn't matter either if the dots are different colours or even if I made the dice pattern for 5 out of apples.

[Screen shows a dice with 5 blue dots and no outline, and then a dice with 5 red dots and no outline orientated differently. They then show a dice with a red background and white dots which are wonky and off center. Then they show a dice with different coloured dots and then 5 green apples in a dice formation. The numeral, or symbol for 5, and word for 5, is written to the right.]

Every time I see things arranged like this; I know it's a collection of 5 things.

It's a mathematical pattern that represents 5. I have 5 things look - 1, 2, 3, 4, 5 or 1, 2, 3, 4, 5 or you might have also spotted this...

[Screen shows a dice with 5 blue dots and no outline. The numeral, or symbol for 5, and word for 5, is written to the right of the dice. As the presenter counts, each blue dot flashes. The first time they count, the dot in the top left hand corner flashes , then the bottom left, then the top right, then the bottom right and lastly the middle. The second time they count, the dot in the top left hand corner flashes, then the top right, then the bottom left, then the bottom right and lastly the middle dot flashes.]

Smaller dice inside bigger numbers of dice.

Look here is 4 and one more makes... 5.

[Screen shows a dice with black outline and 4 dots in each corner. The numeral, or symbol for 4, and word for 4, is written to the right of the dice. The 4 dots flash at once, then a pink dot is added into the middle to make 5. The numeral, or symbol for 5, and word for 5, then appears to the right of the dice.]

You might have seen it like this too, look, if we look really carefully, here's 2 that I can imagine turning around, and 3 more, it’s 5! It still represents 5.

[Screen shows a dice with black outline and 2 red dots one in the top right corner and one in the bottom left corner. The numeral, or symbol for 2, and word for 2, is written to the right of the dice. The dice then rotates to the left so the red dots are in the top left corner and the bottom right corner, and 3 blue dots are added diagonally. The numeral, or symbol for 5, and word for 5, is written to the right of the dice.]

Now, as mathematicians, it's really important that we can draw mathematical ideas. So, watch the screen. Watch carefully now. Yes, it's 5.

[Screen shows a dice with black outline and 4 black dots appear in each of the corners. Then one more dot is added into the centre to make 5.]

Take a picture in your brain. Now let's visualise. So, can you draw the dice pattern for 5 in the air for me please? Off you go.

[Screen reads – Now, let’s imagine…]

Excellent! How many dots did you draw? 5! OK, now let's draw the dice pattern for 5 on a piece of paper with your pencil, off you go.

I can see some of you are starting to think about the little dice or the little quantities, the little numbers inside the bigger numbers, so as you're drawing 5, you started with 4 and then you're adding one more and some of you started with 2 and now you're doing the dice pattern for 3 because you know inside of 5 there's 2 and 3.

And some of you, yes, are not drawing dots, you're drawing squares or triangles, I see. And rainbows! They're nice things to include.

OK, have a look at your picture and describe it to me. Does it look similar to these ones from Willow and Meila? Excellent.

[Screen shows 2 hand drawn dice with a black outline and 5 black dots. Underneath the first drawing, ‘from Willow’ is written, and underneath the second one, ‘from Melia’ is written.]

OK, now mathematicians, let's look at how we write the number 5. Remember that as a mathematician you can represent ideas in lots of different ways, so we need to be able to know about all of them. Watch the screen.

[Screen shows a dice with black outlines and 5 dots in the dice pattern. The numeral or symbol for 5 is written to the side with a red dot in the top left corner of the 5. The red dot traces the line vertically then goes around the round part of the 5. When it gets to the bottom of the 5, it moves back to the top left corner and traces across the top of the 5 horizontally.]

OK, now use your imagination and your pointy finger and draw the number for 5 in the air. Great, write it next to the dice pattern you just drew.

[Screen reads – Now, let’s imagine…]

Write the number 5. Have a look at it and read it to me. Does it look like the symbol for 5? Yes, and here's what the word looks like, 5.

[Screen shows 2 hand drawn dice with black outlines and 5 black dots. Underneath the first drawing, ‘from Willow’ is written, and underneath the second one, ‘from Melia’ is written. The numeral, or symbol for 5, is written in children’s handwriting next to each drawing. The numeral, or symbol for 5, and word for 5 appears on the right side of the screen next to the drawings.]

OK. Should we have a look at another dice pattern? What do you think it might be that we look at next? Yes, 6, because one more than 5 is 6.

That's the same as saying the number after 5 is 6, 'cause we're using this pattern where we add one each time.

OK, let's explore 6. Here it is. How many dots can you see here? 6.

[Screen shows a dice with a black outline and 6 dots – 3 on the left and 3 on the right.]

So, we might see 6 of something when we're out investigating nature, we might be in our gardens, at a park or even at school.

Here I saw a beautiful butterfly with 6 white spots for each wing there were 3 white spots. Look 1, 2, 3 on the left and 1, 2, 3 on the right, that's 6 spots in total. And this is what the dice pattern for 6 looks like.

[Screen shows a purple butterfly with 3 white spots on each wing. The screen then shows a dice with a black outline and 6 dots – 3 on the left and 3 on the right. The numeral, or symbol for 6, and word for 6 appears on the right side of the screen next to the dice.]

Here's how we can represent that in symbols. And here's how we can represent it in words.

And you might have noticed that too, little mathematicians, that inside of 6 you can see the dice pattern for 4 in the 4 corners and the dark blue dots, see that? And then 2 more.

[Screen shows a dice with a black outline and 6 dots – 3 on the left and 3 on the right. The 2 middle dots on either side are light blue and the other 4 in each corner are dark blue. The numeral, or symbol for 6, and word for 6 appears on the right side of the screen next to the dice.]

That still shows us... 6! There it is.

So, the dice pattern doesn't always have to look exactly like this, so look, even when their collection of dots are a bit wonky, or they're small, and they don't need the boundary outside the die, or even when they're turned sideways, the dots can be different coloured.

[Screen shows a dice with a red background and 6 white dots which are a wonky and off centre. Then it shows 6 small blue dots in a dice pattern with no outline followed by another 6 red dots horizontally with no outline. Then the slide shows a dice with black background and 6 dots – the top 2 are red the middle 2 are orange and the bottom 2 are green. The numeral, or symbol for 6, and word for 6 appears on the right side of the screen next to the dice.]

Yes! Like we saw in the traffic lights with 3 and this time we see 2 3s which is 6, and you don't actually need dots at all, you could get out some sport equipment and make the dice pattern for 6 using things like soccer balls and basketballs.

[Screen shows a square with 3 soccer balls lined up horizontally in the top row and 3 basket balls lined up underneath inside the square. The numeral, or symbol for 6, and word for 6 appears on the right side of the screen next to the dice.]

Because every time I see things arranged like this, I know it's a collection of 6 things. It's a mathematical pattern that represents 6. Look! 3 and 3 more, is still 6, or 4 and 2, I have 6 things.

[Screen shows a dice with 6 dots with no outline. There are 3 dots on the left and 3 dots on the right. The left 3 dots flash, then the right 3 flash showing that 3 and 3 more makes 6. Then the screen shows 6 red dice in the same dice pattern. The bottom 4 dots flash, then the top 2 dots flash showing that 4 and 2 more also makes 6.]

OK, as we know drawing mathematical ideas and representations helps our brain to remember them.

So, watch the screen. OK, watch carefully now. And. Ah ha. OK, take a picture of that in your mind.

[Screen shows a dice with a black outline and 4 dots in each of the corners showing the dice pattern for 4. Then 2 more dots are added in middle on each side to make the dice pattern for 6.]

And now let's imagine.

Use your pointy finger and draw a dice pattern for 6 in the air for me, off you go.

How many things did you draw? 6, great! Now let's draw the dice pattern for 6 on a piece of paper with your pencil, off you go.

Yes, this one might take a while 'cause there's so many things in our collection.

I can wait for you though, it's OK.

Oh, I can see some of you are starting to think about using different colours too. Yes.

That's right, because it's not about what it looks like so much as what it represents, the quantity that it represents.

And so, there's some things that we can play around with. But you still have to be able to see the structure of the 6.

That's right. OK, let's have a look at your drawing. Can you describe it to me?

OK. Did your picture looks similar to these ones? Great. Let's look at the symbol for 6. Ready?

[Screen shows 2 hand drawn dice with black outlines and 6 black dots. Underneath the first one, ‘from Willow’ is written, and underneath the second one, ‘from Melia’ is written.]

OK, now imagine the symbol for 6 and using your pointy finger, draw the number 6 in the air, off you go.

[Screen reads – Now, let’s imagine...]

Great, now let's write the number 6 next to the dice pattern you drew.

[Screen shows a dice with a black outline and 6 dots. The numeral, or symbol for 6, appears on the right with a red dot at the top. The red dot traces down and around the 6, finishing in the middle.]

OK, have a look at what you wrote and read it to me please. Let's see, yes, that's the symbol for 6, and here is what the word '6' looks like.

[Screen shows 2 hand drawn dice with a black outline and 6 black dots. Underneath the first one, ‘from Willow’ is written, and underneath the second one, ‘from Melia’ is written. The numeral, or symbol for 6, is written in children’s handwriting next to each drawing. The numeral, or symbol for 6, and word for 6 appears on the right side of the screen next to the drawings.]

OK, it's almost time to play a game, but before we do, let's talk really clearly about some of the important mathematics that we just discovered.

[Screen reads – What was the mathematics?

So, we realised when we look at all of those collections of 2, that it doesn't matter what colour, orientation, or even what shape or size the dots are, the most important information was how many things there are, the quantity.

And so, for example, we can look at all the different ways we can still see 2.

[Screen shows 7 dice in a group, all showing the number ‘2’ in varying ways. The first has an orange background with 2 black dots the same size close together. The second is larger with a dark background and a white and yellow dot. The third has a green background and 2 black dots. The fourth has a black outline with 2 black dots but is rotated to change the orientation. The fifth has a purple background and 2 white snowmen. The sixth has an orange background with 2 back dots, one bigger than the other. The last dice has a black outline with two dots and is slightly tilted.]

We also realise that inside some of the bigger dice numbers, the bigger dice patterns, we can see some of the smaller dice patterns.

So, look, we noticed that 3 is 2 ... and one more.

[Screen reads ‘3 is 2 and 1’ and shows a dice with black outline and 3 diagonal dots. There is a black dot in the bottom left and top right, and a red dot in the centre. The numeral, or symbol for 3, and word for 3 appears to the right of the dice.]

And that 4 is 2 and 2.

[Screen reads ‘4 is 2 and 2’ and shows a dice with black outline and 4 dots in each corner. There are 2 red dots and 2 purple dots in each of the diagonal corners. The numeral, or symbol for 4, and word for 4 appears to the right of the dice.]

We also saw that with 5, we can imagine 3 on the dice and 2 on the dice, and that would show us 5 …

[Screen reads ‘5 is 3 and 2’ and shows a dice with black outline and 5 dots in a dice pattern. There are 2 red dots in the top left corner and the bottom right corner, and 3 blue dots diagonally from bottom left to top right. The numeral, or symbol for 5, and word for 5 appears to the right of the dice.]

And that with 5, we could also imagine 4 on the dice and one more in the middle...

[Screen reads ‘5 is 4 and 1’ and shows a dice with black outline and 5 dots in a dice pattern. There are 4 teal dots in each corner of the dice with one pink dot in the middle. The numeral, or symbol for 5, and word for 5 appears to the right of the dice.]

And we can also see 4 inside of 6...

[Screen reads ‘6 is 4 and 2’ and shows a dice with black outline and 6 dots in a dice pattern. There are 4 black dots in each corner of the dice and 2 blue dots in middle on either side. The numeral, or symbol for 6, and word for 6 appears to the right of the dice.]

They're some really important mathematical discoveries.

And now, let's play.

[The screen shows a sheet of cardboard with 3 vertical lines and 5 horizontal lines, creating 24 boxes. On the page in the far-left column, the numerals, 1, 2, 3, 4, 5, 6 are written and in the second column the words one, two, three, four, five and six are written. In the third column of the page, a dice is displayed in each box. The first dice has a black square outline with a black dot. The second dice has a black square outline with a red and black dot. The third dice has been rotated and has a black square outline with squares for dots. The fourth dice has a black square outline with 4 black dots in a standard dice pattern. The fifth dice has a black square outline with 3 blue dots in a diagonal line and 2 red dots on either side. Lastly, the sixth dice shows 6 black dots as 2 rows of 3 with no outline.

In the fourth column of the page, a dice is displayed in each box. The first dice shows a blue background with 1 black dot. The second dice has a black outline and 2 black dots in a standard dice pattern. The third dice has a black outline and 3 diagonal dots – the first one is black, then red, then black. The fourth dice has no outline and 3 black dots and a smiley face slightly off centre. The fifth dice has been rotated and has 5 black dots and no outline. Lastly, the sixth dice shows 6 as 2 columns of 3, with 2 dots on the top and bottom and 2 squares in the middle.]

OK, it's time to get ready to play, so the first we need to do is cut up our cards.

[Speaker gets a pair of scissors and starts cutting up the cardboard along the lines creating 24 cards. The video then speeds up to show them cutting the final cards.]

And when we've done that, we shuffle them around. And turn them over. And set up an array. So, we're going to have 4 rows.

[Speaker shuffles the card and places face down.]

With 6 cards in each row. So, 1, 2, 3, 4, rows. That's right, now I have 4 rows, one row, the second row, third row, and a fourth row, and there's 6 in each row. Look 2, 4, 6. OK.

[Speaker then moves the cards into 4 vertical rows with 6 cards in each row. The video then speeds up while they finish putting all cards in place. The presenter then uses their finger to trace each row, moving their finger from left to right as they count each row. They then use two fingers to point to 2 cards at a time as they count the cards in the first row by 2s to check there are 6.]

So, then you just take turns. If you're playing with someone else, or you can play by yourself to look for a pair that represent the same quantity, so I might turn over this one and that says, 'one' and this one, said.... that’s not a pair. They don't match. That 6, and that's one.

[Speaker turns 2 cards over – the fourth card in the second row which displays the word ‘one’ and the second card in the third row which displays 6 dots. They point to the cards indicating they do not match.]

OK, your turn. Did you get one? Not yet, I'm going to try again.

I'm gonna try 4 and... that was one again, wasn't it?

[Speaker turns 2 cards over – the fourth card in the second row again which displays the word ‘one’ and the second card in the second row which displays the word ‘four’.]

So, I need to make sure I remember which cards I've turned over. Your turn.

OK, my go. That's the number one, and I think one was here, yes, and now I have a pair, so I can take those 2 and put them here.

[Speaker turns another 2 cards over – the fourth card in the fourth row displaying the numeral 1 and then they remember to turn over the fourth card in the second row from earlier which displayed the word ‘one’. They point to them indicating they are a pair and then remove the 2 cards and move to the side.]

And then we keep playing until we've found as many pairs as possible. Over to you mathematicians! Have fun!

[End of transcript.]