Counting with understanding

Welcome back mathematicians. Over here with my one of my most favorite little mathematicians today, Holly. Hi Holly.

Hi!

Are you ready to do some maths with me?

Yeah.

Excellent, so we have got some pegs here and some cards and can you turn this card over for me?

What number is that?

6

And then can you use these pegs to attach six pegs onto the cards? Yeah, I'll let you start.

I am going to do it in a pattern.

Ok

[Silence while Holly adds pegs to card]

It got so heavy.

It is heavy. Can you prove to me or how do you know that is six?

Because, I lost track and I thought is that 6? So I counted in my head, I was like 1,2,3.... and you can even do it in twos like 2, 4, 6.

Cool. You also said Holly, that you wanted to do it in a pattern, so can you show me where the pattern is that you made?

Well I did blue, red, white, blue, red, white. And I did it in threes. See 3 plus 3 equals 6.

OK, let's try the next number. What about this one?

2.

[Silence while Holly adds peg to card]

OK, and what about the next one?

0 so that means any.

No pegs?

What about this number?

It's one.

[Silence while Holly adds a peg to card]

And what about this number here, Holly?

Three. 1, 2, 3.

[Holly mumbles to herself as she adds peg to card]

What about this number?

5. 1, 2...

[Silence while Holly adds pegs to card]

OK, and this is the last one about this number Holly? What's that number.

4.

OK, can you put that many pegs on there?

[Silence while Holly adds pegs to card]

And we don't need these pegs so I'm going to move them out of the way and then Holly I was wondering if you could. Now we've got all these numbers here, with the pegs on there. Could you order them for me from the smallest number over here to the biggest number over here?

That's the biggest number.

Which is that one?

6. This one goes here.

[Silence while Holly moves the cards into order from left to right]

Screen which reads: You might also like to ask some other questions.

[Adult takes away card 3]

What number is missing?

3.

How do you know?

Because, 1, 2. It goes 0, 1, 2 but it wouldn't go 4, 5, 6. So it has to go 3, but theres no 3.

So if I put the 3 back. Close your eyes again now for me, Holly.

[Adult takes away 2 and 4]

What about now? What's missing?

4 and 2.

How do you know?

1, look. 0, 1, look 3 and 5, 6. it has to be 0, 1 and then 2 but there's no 2 and then it has to go, 3, 4 but there's no 4.

[Adult removes 2 and 4]

What about now? What's missing?

4 and 2.

How do you know?

one...

1, look. 0, 1, look 3 and 5, 6. it has to be 0, 1 and it has to go 2 but there's no 2 and then it has to go, 3, 4 but there's no 4.

So the numbers have to go in order. Is that right? OK and maybe,

[Adult replaces 4 and 2 in the wrong order]

Is that right now?

No it doesn't go 0, 1, 4, 3, 2, 5, 6.

How does it go?

[Child puts 2 and 4 into the correct order]

Every time.

Yes. So for example, if this was me,

[Child moves cards around while she is talking, first out of order and then back to order]

I'd go like, so this goes here and that goes here. I'm done. And that goes 0, 1, 6, 4, 3, 5, 2. Not how it goes. They need to go in their exact same spot.

And that's the right order? We always count in the same way that, is that right?

Uhuh

I have one other question for you Holly. Let's look at #5. So let's choose the number 5 'cause are you still 5?

Yes

So let's choose the number 5 because it's the same age as you. So how many pegs are on that card Holly?

5.

And what happens now, may I have the card, is it OK? What happens if I like spread them out like this? Do you need to count them again?

No.

How many are there?

There's still 5.

What if I move this on this side? How many pegs are on the card?

There's still 5.

What if I go like this?

Still 5

What if I change this white peg for this clip? How many things are still attached to the card?

5

So are you saying to me Holly that it doesn't matter if they are really close together, or really spread out, or even on one side and the other side, it's still 5?

Yeah.

Even if I swapped one peg for a clip, I still have five things attached.

Yeah look. I'll show you.

Show me.

When they're all spread out, see 1, 2, 3, 4, 5. And when they're on the other side... 1, 2, 3, 4, 5.

And so 5 doesn't, say, you know you counted 1,2,3,4,5. Five doesn't tell me that this peg's name is 5 like your name is Holly or my name is Michelle. The five says this is how many things are here.

Yeah.

Oh, so it doesn't matter if I go 1, 2, 3, 4, 5, 1, 2, 3, 4, 5 or change these, it's just about how many things are attached. Is that right?

Yes!

Thanks, Holly.

Bye bye.

See you.