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[Bold, white text on a dark blue background: Quantifying collection – paddle pop sticks 1. In the bottom left corner is the white waratah logo of the NSW Government. In the top left corner in small font is the text: NSW Department of Education.

On an area of carpet are two rectangles of paper. On the left is orange paper and on the right is white paper. On each rectangle of paper are 10 paper cups arranged in 2 rows of 5. Below the paper is a pile of loose paddle pop sticks.]

Speaker

Hi there, mathematicians. I hope you're having a really lovely day today. I was wondering if you could help me quantify or determine how many paddle pop sticks I have. OK. That sounds really nice. Thank you for your help. And when I look at this quantity when I estimate, I think there's definitely more than ten. What do you think? I agree with you, too. It looks like too big a pile. So, what I thought we could do today is use some ten frames I've made to help me quantify the collection. So, I know, they look unusual for ten frames, don't they? We usually have ones with grids on them. But if you look carefully, you'll see the grid is still there.

[The speaker indicates the white paper and uses her finger to draw a circle around the first 2 cups in the top row and the then other 3 cups. She then indicates to the row underneath, showing that it is the same as the top row. She also indicates to the cups on the orange sheet, showing that the arrangement of cups is the same.]

Look, on this one over here, I've got my outside boundary, which I'm using as the paper, and in the top row, yeah, there's five. Look, because I can see two here and three here because I can subitize that. Yeah, and two and three combines to be five, and then there has to be five down the bottom because for each cup there's another cup. Yeah. So, that's ten. And over here I can see there's another ten.

[The speaker places one paddle pop stick into each cup.]

Alright, so let's count together. One, two, three, four, five, six, seven, eight, nine, ten. Ten ones. So, now if I keep going, you're right. I have to regroup them and rename them. And so, when we get ten of something, we collect them all together.

[The speaker re-collects all the sticks and ties them together with an elastic band. She places the group of 10 sticks in to the top right cup on the orange sheet.]

And we regroup them, the ten ones, and we make them, yeah, one ten.

[The speaker places a handwritten label above the white sheet of cups which says: ones. She places a similar label above the orange sheet stating: tens.]

So, I probably need to label my ten frames and say these ones are in the ones place and this one is representing the tens place. OK, so, let's keep going because I have more counters here.

[The speaker places a loose stick into a cup on the white sheet. She has a card with the number 11 on it which she places beneath the cups.]

So, I have one ten and one, which we call 11. And what I might do is actually put out some cards now too as I'm counting. So, we've counted one ten and one more, which we name 11.

[She adds a stick to a second cup on the white sheet. She places a card with the number 12 on top of the 11 card.]

And now I have one ten and two, which we call 12.

[She adds a stick to a third cup and places a card with the number 13 down on top of the existing numbers.]

And now we have one ten and three, which we call 13.

[She adds a stick to a fourth cup and adds the number 14 to the pile.]

One ten and four ones, which we call, yes, 14.

[Another stick is added to a fifth cup and the number 15 is placed on the pile.]

One ten and five ones, which we call 15.

[On the second row of cups on the white sheet, another stick is added. The number 16 is placed on top of the pile.]

One ten and six ones, which we call 16.

[A stick is added to a seventh cup. The number 17 is placed on the pile.]

One ten seven ones, and we call that, yes, 17.

[The speaker adds a stick to an eighth cup. The number 18 is placed on the pile.]

One ten and eight ones. What do we call that? Yes, 18.

[She adds a stick to the ninth cup and places the number 19 on the pile.]

One ten and nine ones. What do we call that? Yes, 19.

[She adds a stick to the final cup on the white piece of paper.]

And one ten and ten ones. One ten and ten ones, what do we call that? You're right.

[The speaker collects all 10 paddle pop from the white-paper cups and ties them with an elastic band. She adds that group of ten sticks to a second cup on the orange paper. She places a card with the number 20 on it on top of the existing pile of numbers.]

OK, so what I have to do is I have to regroup them because my ten frame is full. That's right. Once I've got a collection of ten, I need to regroup and rename.

[With two groups of 10 sticks in cups on the orange, the speaker adds a loose stick to a cup on the white paper. She places a card with the number 21 on top of the pile of cards.]

So, now it goes over here, and I have two tens and no ones, and we call that 20. Nice work. So, two tens and one. What do we call that number? Yes, 21.

[She adds a stick to a second cup and places the number 22 on the pile.]

Two tens and three ones... Oh, two tens and two ones. What do we call that? 22

[She adds another loose stick to a third cup on the white sheet and places the number 23 on top of the pile.]

And now, two tens and three ones. What do we call that? Yes, 23.

[She adds the last loose stick to a fourth cup and places the number 24 on the pile.]

And there's one more paddle pop stick, two tens and four ones, which we call 24. Let's count them backwards. Yeah, I think that's a really good idea, too. So, two tens and four ones, which we call 24.

[She removes one stick from the white-paper cups and the 24 card.]

And now I have two tens and three ones, 23.

[She removes one stick from the white-paper cups and the 23 card.]

And now I have two tens and two ones.

[She removes one stick from the white-paper cups and the 22 card.]

And if I take one away... 21.

[She removes one stick from the white-paper cups and the 21 card.]

And if I take another one away... 20 And now what do I do, because if I want to take one more away, yes, I have to ungroup. That's right.

[She picks up one of the groups of 10 sticks and unties them. She places each stick into a cup on the white paper.]

So, I'll use this one. So, before I can take one away, I have to ungroup them.

[She removes one stick from the white-paper cups and the 20 card.]

And now I can take one away, which is counting backwards.

[She removes one stick from the white-paper cups and the 19 card.]

And I have one ten and nine ones, which is 19.

[She removes one stick from the white-paper cups and the 18 card.]

And if I take one away to keep counting back, 18.

[She removes one stick from the white-paper cups and the 17 card.]

And then I'll have 17. Yep, one ten and seven.

[She removes one stick from the white-paper cups and the 16 card.]

And then I have 16.

[She removes one stick from the white-paper cups and the entire pile of cards.]

And then 15. OK, now without the cards.

[She removes a stick from the white-paper cups one at a time until there are no sticks left on the white paper and one group of 10 on the orange paper.]

One ten and four, which is 14. OK. 13. 12, one ten and two is 12. Yes, one ten and one is 11. Now I have one ten, which is the same as ten. And what do I need to do? Yeah, ungroup and rename.

[She unties the second group of 10 sticks and places them in to the white-paper cups.]

So, into here.

[She removes a stick from the white-paper cups one at a time until there are no sticks left.]

So, now we have ten, nine, eight, seven, six, five, four, three, two, one, zero. Nice work, mathematicians.

[White text on blue background: What’s (some of) the mathematics?]

Alright, mathematicians, what was the mathematics?

[New slide text:

• We noticed that there’s a pattern – every time to get to 10 of something, you re-group and re-name it.
• We explored out number system:
• We reground and renamed quantities every time we got to a collection of 10 ones (and we called this 1 ten)
• We ungrouped and renamed to help us count backwards.
• Today we also practised some important aspects of counting with understanding. Today we:
• Connected the counting words as say to the items as we counted them
• Counted forward and backwards.

Below the text is an image of the maximum number of paddle pops, 2 groups of 10 and 4 ones with the number 24 on a card underneath.]

So, we did notice something today that is a pattern. Every time we get to ten and something, we regroup it and we rename it. And that helped us explore our number system. So, we regrouped and we renamed collections every time we got to ten of something. We also ungrouped and renamed to help us count backwards. And today we also practiced some really important skills that are involved in counting with understanding. So, we made sure that we were matching the number words that we say to the items as we counted them. And we also made sure that when we can count forwards, we can also count backwards. Until next time.

[The NSW Government logo flashes on screen. Text below reads: Copyright, State of New South Wales (Department of Education), 2021.]

[End of transcript]