Dot card talk 2

Ok mathematicians, get your eyeballs ready.

We are about to do some subitising or technically subitising and visual recognition.

So I am about to show you a collection of dots and I'd like you to see if you can see how you see the dots. Think about how you see the dots and how many there are in total.

Okay, let's see what you notice. Here we go. Oh, I know I could hear you groaning.

It's meant to be fast mmm because in this case we are really trying to get inside of how your brain sees collections. Uh-huh, so we're using our subitising and visual recognition skills. So try to recreate what you think you saw at least in your mind.

So for me I saw a lot some large blue circles and inside those circles were some smaller pink dots. So I'm trying to workout how many large blue circles I saw and how many small pink ones were inside.

Okay, would you like to have another look to check? Here we go.

Okay, so what I'm really trying to get you to think about is how do you see the dots, because that will help you answer this question of 'And how many are there in total?' Okay, ready? Here's what it looks like. Yeah, and now let's have a think about how different people saw these dots.

So this, this is what Michael was thinking. So when he saw this collection of dots he could see the five groups um because he saw the two and the three more and he knew that was five, and then he knows 5 sevens is 35, so he could actually see that quantity as a whole.

But Sharon, when she saw it, she was looking she actually saw some chunks. So inside of the five groups where the seven dots are, she saw the seven as five and two more. So she said what she knew in her head was that 5 fives is 25 and then 5 twos is 10 and she was able to join 25 and 10 together to get 35.

But Lucy thought about it differently. She saw four groups like on a dice pattern and one more group of seven. So she said she worked out 4 sevens, which is 28, and then added another seven dots to get to 35.

Yeah, and Millsy thought about it like this. She saw the five big groups altogether and inside of them she saw six like on a dice pattern. Yeah, and the one more dots. So she worked out 5 sixes and then 5 ones.

Yes, and so what's really amazing about doing dot card talks like this is that we can see that lots of different people can think about quantities differently, and so this got me thinking about I wonder how we could rearrange these dots into different structures so that we can see different ways of thinking.

And here I'll show you what happened in my imagination.

When Millsy said this, that she saw 5 sixes and 5 ones, this made me think about what happens if I take out those boundaries of the group like this and rearrange them so I can still see the 5 sixes and the 5 ones, but now it looks like an array. Yes, so if I come back to all of these different ways of thinking, here is Millsey's original way of thinking. And here it is just rearranged in an array structure.

So your job mathematicians is, 'Can you imagine the other collections reforming into arrays and draw what they would look like? Okay, I'll put them back up on the screen for you. It would be a good idea to pause the video here.

Okay, shall we have a look together after you've had a chance to draw? Okay, so here's what I left you to think about. Let's have a look at what Sharon did in her thinking, so here was how she chunked the seven together into fives and twos and here's what that would look like as an array. Is that similar to yours? Yeah, 5 fives and 5 twos and yes, I can see that too.

What I can see now that inside of 5 sevens where there's 5 fives is a square number. Yeah, I've never thought about that before that inside of 5 sevens is 5 fives, so inside of 5 sevens is a square number, and now I wonder actually how many other square numbers are in there. Oh, okay, you can go and investigate that if you're curious also.

Let's have a look at what Lucy's might look like. Yes, so you can see that too. So the 4 sevens are in one colour and the 1 seven more is in the other. And so where Lucy partitioned her array in this way where she partitioned the 5 into four and one, the five groups into four and one, Sharon partitioned it in different way where she kept the five groups, but she partitioned the part inside the group, the seven into five and two more.

Alright, and Mark's was. Yes, would look like this.

Alright mathematicians, so let's talk about what the maths was in there that we saw. Or some of it anyway, 'cause it's quite a lot.

One thing is that it helped us see that quantities can quite different but have the same value and that we can represent quantities in different ways and that also we can think about multiplicative situations with the same flexibility we use for whole numbers, and this is really helpful for us as we come to start using really efficient strategies in multiplication and division.

Alright mathematicians, until next time. See you then.