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

It got so heavy.

It is heavy. Can you prove to me or how do you know that is six? OK so I lost track and I thought is that 6? so I counted in my head like 1,2,3.... and you can even do it in twos like 2, 4

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.

OK, and what about the next one? 0 so that means any. No pegs?

What about this number?

Right?

It's one. And what about this number here, Holly?

Three. 1, 2, 3 what about this number?

5. 1, 2...

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?

And we don't need these pegs so I'm going to move them out of the way and then Holly 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 Which number is missing? 3.

How do you know?

because, 1, 2. It goes 0, 1, 2 but window 4, 5, 6. So 3. So if I put the 3 back, close your eyes again now for me, Holly

What about now? What's missing? 4 and 2, how do you know?

0, 1 look. 0, 1, be 2 but there's no 2, 3, 4 but there's no 4.

What about now? What's missing? 4 and 2. How do you know?

one...

0,1 and it has to be 2 but there's no 2. 3, 4 but there's no 4.

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

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

Every time. Yes.

So for example, if this was me

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? aha

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

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 pig for this clip? How many things are still attached to the card? 5

So are you saying to make 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, see12345. And when they're on the other side...

12345. And so 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 12345, 12345 or change these, it's just about how manythings are attached. Is that right? Thanks, Holly.

Bye bye. See you.