6 is...

Hello little mathematicians, welcome back.

You know I was thinking a little bit more about these two representations of 6. Remember we were trying to workout which 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 6 things, because here I can see 3 things and 3 things more when I combine that together, it's equivalent in value to 6.

And if I'm not sure about 3 and 3 combining to make 6 yet, I might see this is 3 and then I could count on so 3, 4, 5, 6 in total. Or I might count them all 1, 2, 3, 4, 5, 6 and over here as well. We also worked out this was 6 and I can see it chunk because of the use of color. I can see this section over here looks like...

Yeah, it looks like 4 on a dice pattern 1, 2, 3, 4, and then there's 2 more so 4, 5, 6.

And it started to get me wondering about what are some other ways that we could make six so to start with to prove that they have six, I'm going to use my blocks, which is another way that I can prove that these

have the same value, the same quantity. And because, you know, sometimes as a mathematician, I like to have the same colour, sometimes I don't worry so much, but today I'd like to have the same and I'm going to put one block for each of my counters.

And then I can re-stack them together now into a tower.

And actually what I can see here? Can you see this too? If I break this apart, I can see that there's one 3 and another 3, and so even though this 3 looks different because it's in a line and this 3 in a triangle, I can still see that they have the same value, the same quantity of 3, and when I join them together, I know that that's 6. And if I join these ones together, I said, I saw the 4 like a square or a 4 like on a dice at 2, 2, 4 and one more is 5 and another one is 6 and if I lay them together, like this in line them up.

I can see that they still have the same number, they are the same height and so that's one way that I can say that this collection of 6 is equivalent in value to this collection of 6, they are the same. So even though they look different, things can be the same.

It's a really interesting mathematical finding and so what I was wondering is if I have some more blocks over here which I do have, and I use these three colours, I wonder if there's another way that I could make 6 using one or two or all three of these different colours that's different to these two ways of making 6.

Can you have a think what would you like to make? While I get some more blocks.

Oh, I think that's a nice idea. Someone was thinking about we could have 2 green blocks, 2 orange blocks and 2 red blocks like that and that would make 6. But look we can check. Yeah, the same height so that also must be six. So here we have 1 and 1 and 4 and here we have 3 and 3, 6.

And here we have 6 as 2 and 2 and 2 and probably what I should do now as a mathematician is start to record down some of my ideas and I know that I'm working with six so I can say 6 is... Oops I better move that down a bit so that you can see it.

There we go, I think that is better. So 6 is 1 and 1 and 4, so 1 and 1 and 4. And here we said 6 is 3 and 3, 3 and 3. And here we saw 6 yeah, 2 and 2 and 2.

Yeah, and some of you I like what you're thinking that there's one 2, a second 2 and three 2's, so I could also record that in a different way and say I saw 3 twos Oh, and can you see another tower that I could record in a similar way to this?

Can you point to it for me? Yeah, this one 'cause I have one group of 3 and another group of 3 so I could also say I have 1 three and 2 threes, 2 threes.

Do you think there's another way that we could make six?

What are you thinking now? Ah ok, I like this idea too. Someone was suggesting we could make five of one the green one, ok so that's 2, 3, 4, 5 and a red one, it's a bit like Christmas or a traffic light. Actually they all look a bit like traffic lights, especially that one.

And how could we describe this one 6 is? 1 and 5 ok, 1 and 5. Ha. Yeah I, I can see I can see that too that in some of our towers of six we just used two colours look, this one has two colours, red and green and this one has two colours where we just used orange and red.

And sometimes we used three colours look, a red a green and orange, and here 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 so. I'll put these together. Move this one out of the way. And how could I check that that's 6 without having to count them all?

Oh yeah, I could use that strategy where I know this is 6, we checked and if I line it up 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. That's right, I want to jumble up my representations and so how could I name this tower over here? Ah 6. 6 is 6. I see 'cause in this case we're using colour intentionally to see the parts aren't we?

So 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 about I'm really wondering is, are there other ways that we could make 6 using one, two or three different colours?

Now you might not have these blocks at home, but you could use coloured pencils and draw some pictures or some bricks like these that you could use. And I wonder if you could go and find are there some other ways that we could represent six using our 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 6?