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# Maths Years 3–4 with Ms Kirszman: Our place value system

**Subjects: Maths **

**Years: 3–4**

### Learn how to measure using 10 as a unit to iterate.

In this lesson, Ms Kirszman demonstrates how to measure using 10 as a unit to iterate – rather than using a smaller unit.

You will also explore how renaming, using place value parts, can help you when working with numbers. The place value number system will be looked at in some depth, as well as the importance of the periods in the number system.

You'll be a detective looking for patterns in how we say and write numbers.

**Acknowledgements**

Special thanks to Ms Kirszman, Ms Tregoning and NSW Dept of Education.

**Production Date: **2020

**Copyright**

^{Metadata © Australian Broadcasting Corporation 2020 (except where otherwise indicated). }^{Digital content © Australian Broadcasting Corporation (except where otherwise indicated). }^{Video © Australian Broadcasting Corporation and NSW Department of Education. All images copyright their respective owners. }^{Text © Australian Broadcasting Corporation and NSW Department of Education.}

## Transcript

Hello Brainiacs. It's Ms Kirszman. Time to get mathematical.

Okay, let's warm up our brains. I've got a piece of string and I'd like to know how long it is. I could measure it, but that's not really fun. I want to see how many of these it would take to measure my whole line. So I'm looking at my line and it's quite long. These are quite small. My first estimate is probably around a hundred but I've learned this really great strategy from Doug Clements about getting your eye in. So I'm going to see what five looks like. Okay, so I've got five. So let's see, two, three, four, five, six, seven. So maybe around 35 blocks. So I could keep making them, but I'm thinking that I've been working a lot with tens and ones and I think that that structure of 10 can be really helpful here. So what I might do is I might actually create a unit of 10 so there's six, eight, and ten.

So that's my one unit of ten and I'm going to create another one here. And this time I don't actually have to count because I can use direct comparison. So I know that the that the green one is definitely ten. This one's a little bit longer, so I'm going to chop that bit off and now I know that they're both ten so I'll start measuring. Okay, I'm going to make another one. Actually, if I keep making them, I'm still counting by ones. So I think I'm going to use that structure of ten but then I'm going to iterate that unit. So let's see how that can work. Okay. So I've got one ten here and I'm going to use this orange one, the orange colour, just to keep the place. So there's one ten another ten and another ten.

Okay. Another one here. It looks like I might get another two in. Let's see though.

All right. And oh yes I can. And I've got a few extra here. So I might choose these red ones for my extras. And it looks like I've got one, two, three, four, five tens, which we call 50 because the T in the word 50 means groups of ten, so five tens and three more, which we would call 53. So my brain is nice and warmed up after that, which is just as well because I've got a challenge here. My friend Michelle sent me this because she knows I love a challenge that gets my brain nice and sweaty. And her challenge to me is to create the biggest number possible using just these number cards and only these number cards. So this is what she sent me. Seven, forty, thousand, five, two and hundred

Mathematicians use concrete materials and what I'm going to use for this task is my place value chart. And it's really good that the warm-up really got me thinking about place value. So this is my place value chart. You can see these sections here, this is called a period. This is the ones period, the thousands period and the millions period. And within those periods you've got ones, tens, and hundreds and that's referring to the ones. Ones, tens, and hundreds, referring to the thousands. And one, tens, and hundreds, and that's referring to the millions. So what I might do is I might organise my cards, so I'll put my five, my seven and my two here, my forties here, my hundreds there, my thousands there and the word and. Now the 40 is actually really interesting because it's referring to four tens and zero ones here.

So I could put it here and its value would be 40. I could put it here and its value would be 40,000 or I could put it here and its value would be 40 million. But I can see that here I don't actually have a millions card. So unless I do some really clever renaming, which I don't think is part of this challenge, but very fun normally, um, I'll have to settle for a six digit number. So I'm talking about hundreds of thousands, so hundred thousands which is this part here. So let's have a look. Ooh, 700 and 745,002 but I don't have another and card so that doesn't actually work. So because I don't have another and card, I might have to settle for a five digit number. So let's see what I can do. Okay, let's see. 7,542 now that works, but it's not a five digit number, but I can still put this on my place value chart. So I'll do that now. So I've got 7,000 and its value here is one in the thousands period. So 7,542. Now I can definitely go bigger I think. But here I'm talking about tens of thousands. So I think I'll need my 40 so let's try 42,705.

Okay, Let's see. So I've got 42,705. Okay. Can I go a little bit bigger here? I think I can, if I do, if I swap these around now I have 47,000 and I swapped this here, 502. So 47,502. Okay so I guess now my question to you is, have I made the largest possible number? And how, how do you know? Also if I could do some fancy renaming, how big could my number get? And if I had another and card, what could I do with that? And I know that if Michelle was here she would be asking me, okay, you've made the biggest number, now create the smallest number using all the cards. I wonder how you can go with that. So one thing that I've been looking at with some students is how mathematicians work and how they don't work. And one thing that we noticed about mathematicians is that mathematicians look for patterns. So as mathematicians, we've been looking for patterns, um, and I think that some patterns are actually starting to emerge here. Okay, so let's see what we've noticed.

So I think that this could be a pattern that's emerging here that we seem to be saying the word 'and' after we say the number of hundreds in any of the periods. So 112. 112 million, 112,000 so that seems to be a pattern, but I think I need to explore that a little bit more and maybe you'd like to explore that a little bit more with the numbers that you know. There also seems to be a pattern in place here with, in each period, with ones, tens, and hundreds. Ones, tens, and hundreds. So it's a repeating pattern with a core of ones, tens and hundreds is repeated. And I think this will continue to be repeated as numbers get bigger, but I'd need to investigate that. And I wonder if it actually continues into the decimals. Another thing that I've noticed is that we seem to be saying that the word thousand after we read four, five or six digit numbers. So let's think about that a little bit more. So how would you read that number? So I'll just rub my board out while you think about that.

So that number there is 1010 but if you didn't get that, if you didn't answer 1010 that's actually very common. As we become mathematicians and as we get more confident with larger numbers, there's some numbers that are a little bit trickier. And these numbers here with zero within, within the number inside the number are actually quite tricky. And a lot of people when they're still learning will read that number as 101 or something else. That's something, you know, that way they make a mistake. So let's look at how we can use the place value chart to help us read these numbers. So I've got, it's a four digit number, so I'm going to use these four. So let's have a look at how we would read that 1010 okay, so I said the word thousand. Let's look at the smallest number I can create. That's a four digit number.

Actually that's not right. I could go smaller than that. So I would read this number as 1,111. So I said the word thousand, I would read this number as 1000 so I still said the word thousand. Let's look at the largest number that I can make. 9,999 so I still said the word thousand in there. And let's have a look at other numbers that are somewhere in between. So something like this.

So 2036. It seems that when you see a four digit number, you need to be saying the word thousand. So when you see a number like this, if you're not sure how to say it, think about the need to say the word thousand. So it seems that we're onto something here. We do seem to be saying the word thousand when we read four, five, and six digit numbers. But before we can confirm that, I think we need to explore more. So can you find a case where you might say a four, five or six digit number without saying the word thousand. There's your challenge, over to you.