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(Duration: 8 minutes and 59 seconds)

[Text over a navy-blue background: 6 is…. Small font text in the lower left-hand corner reads: NSW Mathematics Strategy Professional Learning Team (NSWMS PL team). In the lower right-hand corner is the white waratah of the NSW Government logo.]

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

Bullet points below read:

· some coloured pencils

· paper

· you might also like to use some blocks or paperclips to help you come up with ideas.

On a large white sheet, there are 2 paper places around the top middle section. On each paper plates are 6 little coloured balls. On the left paper plate, there are 4 yellow balls, 1 green and 1 red. On the right paper plate, there are 3 red and yellow balls.]

Speaker

Hello, little mathematicians, welcome back. You know, I was thinking a little bit more about these two representations of six...

[She points to each plate. She waves her hands around.]

Speaker

...remember we were trying to work out which one if they had more, the same or if one had less, and what we realised was that even though they look quite different, they actually both show six things.

[On the plate on the right, she points to the balls.]

Speaker

Because here I can see three things, and three things, more when I combine that together...

[With her finger, she circles the entire set of balls.]

Speaker

...it's equivalent in value to six. And if I'm not sure about three and three combining to make six yet, I might see this as three...

[She points to the red balls.]

Speaker

...and then I could count on, so three, four, five, six...

[She points to the yellow balls.]

Speaker

...in total, or I might count them all...

[She points to each of the red balls, then the yellow ones.]

Speaker

...one, two, three, four, five, six.

[She points to the left plate.]

Speaker

And over here as well, we also worked out this as six, and I can see a chunk because of the use of colour, I can see this section over here...

[She points to the yellow balls.]

Speaker

...looks like, yeah, it looks like four on a dice pattern.

[She points to each of the yellow balls.]

Speaker

One, two, three, four, and then there's two more, so four, five, six.

[She points to the yellow balls, then the green ball, then the red.]

Speaker

And it started to get me wondering now, what are some other ways that we could make six? So, to start with, to prove that I have six...

[On the right plate, she places yellow blocks over the yellow balls.]

Speaker

I'm gonna use my blocks, which is another way that I can prove that these have the same value, the same quantity.

[On the left plate, she places yellow blocks over the yellow balls.]

Speaker

And 'cause you know sometimes as a mathematician, I like to have the same colours, sometimes I don't worry so much...

[She places a green block over the green ball.]

Speaker

...but today I'd like to have the same.

[On the right plate, she places red blocks over the red balls.]

Speaker

And I'm gonna put one block for each of my counters...

[On the left plate, she places a red blocks over the red ball.]

Speaker

...and then I can restack them together now into a tower.

[Over the right plate, she picks up the red blocks and snaps them together. Then she picks up the yellow blocks and assembles them to the stacked red blocks.]

Speaker

And actually, what I can see here, can you see this too?

[She splits the stacked blocks into red and yellow halves.]

Speaker

If I break this apart, I can see that there's one three, and another three, and so even though these three...

[On the right plate, she points to the red balls, and then the yellow balls.]

Speaker

...look different 'cause it's in a line, and these three is in a triangle, I can still see that they have the same value, the same quantity of three, and when I join them together...

[She joins the 2 halves of the block together.]

Speaker

...I know that that's six.

[She places the stacked block vertically on the sheet.]

Speaker

And if I join these ones together...

[On the left plate, she points to the yellow blocks, and starts stacking them.]

Speaker

...I said I saw the four like a square, or four like on a dice, two to four, and one more is five...

[From the left plate, she picks up the red block ands stacks it on the assembled yellow blocks. She picks up the green block and stacks it over the red.]

Speaker

...and another one is six, and if I lay them together like this, and line them up...

[She places the 2 stacked blocks against each other.]

Speaker

...I can see that they still have the same number, they are the same height.

[She takes the plates away.]

Speaker

And so that's one way that I can say that this...

[She brings the plates back. Over the left plate, she circles the balls.]

Speaker

...collection of six, is equivalent in value to this collection of six, they're the same.

[Over the right plate, she circles the balls. She takes the plates away.]

Speaker

And so even though they look different, things can be the same...

[She moves the stacked blocks up the sheet.]

Speaker

...it's a really interesting mathematical finding. And so what I was wondering is, if I have some blocks over here, which I do have...

[She places some blocks in the space on the right side of the stacked blocks.]

Speaker

...and I put these three colours, I wonder if there's another way that I could make six using one, or two, or three, of these different colours that's different to these two ways of making six, can you have a think, what would you like to make? Well, I guess there are more blocks. Oh, I think that's a nice idea, someone was thinking about we could have two green blocks...

[She picks up 2 green blocks and starts joining them.]

Speaker

...two orange blocks...

[She picks up 2 orange blocks and starts joining them to the greens.]

Speaker

...and two red blocks...

[She picks up 2 red blocks and starts joining them.]

Speaker

...like that...

[She joins the red blocks to the rest.]

Speaker

...and that would make six. Well, look we can check...

[She aligns the block with the other blocks on the sheet.]

Speaker

...yeah, they're the same height, so that also must be six.

[She separates them slightly.

On the left block, she points to each of the colours.]

Speaker

So, here we have one, and one, and four...

[On the middle block, she points to the red and yellow sections.]

Speaker

...and here we have three, and three, six...

[On the last block, she points to the red, yellow and green sections.]

Speaker

...and here we have six as two, and two, and two, and probably what I should do now as a mathematician, is start to record down some of my ideas.

[She gets a marker.]

Speaker

And I know that I'm working with six...

[She writes 6 over the first block.]

Speaker

...so I can say 6 is...

[She writes ‘is’ next to 6.]

Speaker

...oops, and I better move that down a bit so that you can see it...

[She pulls the sheet down.]

Speaker

...there you go I think that's better, yeah. 6 is...

[On the left block, she points to the green, red, and yellow sections.]

Speaker

...one and one and four

[Under the left block, she writes: 1 and 1 and 4.]

Speaker

...so 1 and 1 and 4, and here...

[She points to the middle block.]

Speaker

...we said 6 is three and three...

[Under the left block, she writes: 3 and 3.]

Speaker

...3 and 3, and here...

[She points to the last block.]

Speaker

...we saw six...

[She points to the red, yellow and green sections.]

Speaker

...yeah, 2 and 2 and 2.

[Under the last block, she writes: 2 and 2 and 2.]

Speaker

Yeah, and some of you I like what you're thinking, that there's...

[She points to the red, yellow and green sections.]

Speaker

...1 two, a second two, and three twos, so I could also record that in a different way and say...

[Under the text of the last block, she writes: 3 twos.]

Speaker

...I saw 3 twos. Oh, and can you see another tower that I could record in a similar way to this? Can you point it out for me? Yeah, this one...

[She points to the middle block. Then to the yellow and red sections.]

Speaker

...'cause I have one group of three, and another group of three, so I could also say I have one three, and two threes...

[Under the text of middle block, she writes: 2 threes.]

Speaker

...2 threes like this. Do you think there's another way that we could make six? What are you thinking now? Oh, OK, I like this idea too, someone was suggesting we could make five of one, the green one.

[She picks up green blocks and starts joining them.]

Speaker

OK. So, that's two, three, four, five, and a red one...

[She picks up a red block and joins it to the green block.]

Speaker

...it's a bit like Christmas, or traffic light, actually they all look a bit like traffic lights, especially that one.

[She puts the new block down to the right of the others. She points to the 3 2s block.]

Speaker

And how could we describe this one?

[She points to the new block.]

Speaker

6 is...

[On the new block, she points to the red and green sections.]

Speaker

...one and five, OK...

[Under the text of new block, she writes: 1 and 5.]

Speaker

...1 and 5, ah, yeah, I can see that too, that in some of our towers of six, we just used two colours, look, this one...

[She points to the new block.]

Speaker

...has two colours, red and green, and this one...

[She points to the second block from the left.]

Speaker

...has two colours where we just used orange, and red, and sometimes we used three colours, look

[She points to the first block.]

Speaker

...a red, a green, and orange, and here...

[She points to the third block from the left.]

Speaker

...we used red, orange, and green. Do you think we could make a tower of six with just one colour?

Yeah, use the red ones, OK...

[She picks up some red blocks and starts joining them.]

Speaker

...so I put these together, remove this one on the way, and how could I check that that's six without having to count them all?

[She holds up the stack of 6 red blocks.]

Speaker

Oh, yeah. I could use that strategy...

[She places the red block in between the third and last blocks.]

Speaker

...where I know this is six, we checked, and if I line it up...

[She places the blocks together.]

Speaker

...it's the same height, and I can check all of them, they're still the same height, my tower, so I know they're all six.

[She moves the blocks back above their text descriptions.]

And that's right, I wanna jump up my representations and say, how could I name this tower over here?

[She points to the red block.]

Speaker

Oh six, 6 is 6...

[Under the text of last block, she writes: 6]

Speaker

...I see 'cause in this case, we're using colour intentionally to see parts, aren't we? Oh, this is making me think about one thing about how mathematicians sometimes use colour so that they can see bits of information about numbers, and also I'm really wondering is, are there other ways that we could make six using one, two or three different colours? Now, you might not have these blocks at home...

[She moves the spare blocks under the text.]

Speaker

...but you could use coloured pencils, and draw some pictures, or some bricks like these that you could use...

[A title on a navy-blue background reads: Your challence. A text below the title reads: What are all the different ways we can make 6?

Bullet points below read:

· with just 1 colour pencil?

· with 2 different colours?

· with 3 different colours?

Record your ideas]

Speaker

...and I wonder if you could go and find, are there some other ways that we could represent 6 using three different colours, either just one colour, two different colours, or all three of them in the same tower? Over to you, little mathematicians, what else can you find out about the number six?

[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]