Lesson video

Hi, my name's Ms. Lambell.

I'm really pleased that you decided to pop by and do some maths with me today.

Welcome to today's lesson from the Place Value Unit.

The title of the lesson is deepening understanding of place value in integers.

By the end of this lesson, you will be able to state the value of any digit in any given integer in any given form.

Okay, so some key words it would be worth reminding ourselves of that we will be using throughout today's lesson, you've seen these before, a digit, an integer.

So, today's lesson, we're gonna split into two learning cycles.

First of which is going to be reading integers aloud and considering the context of those integers.

Okay, what I'd like you to do is to just say this integer aloud.

So, Lucas, Aisha and Laura read this integer aloud.

I'd like you to have a think about who says it correctly.

So, Lucas says, "It's 1 million." Aisha says, "I think it's 1,000 thousands." And Laura says, "It's 10 hundred thousands." So, just have a think a moment, who says it correctly? Okay, so let's take a look at these numbers.

Let's start with Lucas.

Lucas said 1 million.

So, we've got our place value chart here, and we can see that if we were going to put this into the place value chart, then we've got to identify the millions column.

We have 1 million, and don't forget those placeholders.

We need those placeholders to go in all of the other columns.

Okay, then we had Aisha.

Now, Aisha said thousand thousands.

So, this time we need to identify the thousands column and we're putting in a thousand.

And then, again, don't forget those place value holders to make sure that we maintain the value of the one in the correct column.

And then we have Laura.

Laura said 10 hundred thousands.

So, 10 hundred thousands.

Let's identify that hundreds thousands column.

And then we're putting in 10 hundred thousands.

So, let's put in the 10, and again, those placeholders.

What do we notice about all of those numbers? Actually, they have all created exactly the same number.

So, they were said in different ways, but actually they are different ways of saying exactly the same number.

Okay, so now let's just do a quick check for understanding.

So, I'd like you to pause the video and answer this question.

Okay, let's take a look.

So, select the correct ways of saying 1,250,000.

Okay, so we can now see as I've read the number out that actually A is definitely a correct way of saying that number.

Okay, and let's see which others.

So, 12,500 hundred hundreds is another way of saying that correctly.

And also D, 1,250 thousands.

Here's Sam.

They're really lucky.

They've just had their birthday and been given some money.

They've decided that they'd quite like to save for something special, so decide to open a bank account.

The person who is opening the account for them asks for their mobile phone number.

Sam thinks, right, I'm gonna be really clever here.

I'm going to save my mobile phone number is an integer.

So, he says it's 7,300,000.

Wait, no, that's not right, hmm.

Do you think that even if Sam was able to say his mobile phone number as an integer, the person recording it would've written it down correctly? I'm not sure they would.

Would you be able to say your mobile number as an integer? Maybe pause the video and have a go.

So, sometimes we adapt the way we say numbers based on the situation, based on the context.

So, in this situation, we wouldn't say our mobile phone number as a integer 'cause actually it's not an integer.

It's just a combination of numbers that allows people to contact you.

Okay, so here we've got Jun and Alex.

And Jun has asked Alex to measure their height.

Okay, so Alex measures Jun's height and he says, "You're one five seven centimetres tall." And Jun says, "You mean I'm 157 centimetres tall?" So, in this situation we are talking about an integer, okay? The height of Jun is 157 centimetres tall.

Here it would not be appropriate to say, just list the digits, one, five, seven.

Okay, so here we've got a slide, okay? And there are four statements.

Izzy, Jacob, Sophia, and Andeep have all made a statement.

I'd like to pause the video and to think about what integers are being referred to in each of these statements, and then when you're ready, just come back and unpause the video.

Okay, so Izzy says, "I ran 5k at the weekend." You may run 5k, some part runs of 5k.

Often when we talk about distance, people use the letter k to represent a thousand.

So, this means that Izzy ran 5,000 metres.

She ran 5,000 metres at the weekend.

I say, well done, Izzy.

Okay, so Jacob says, "My mum's new car costs 10 grand," and sometimes when we talk about money, people use the word grand to represent 1,000.

Okay, so let's have a think about that then.

So, that means Jacob's mum's car costs 10,000 pounds.

Then, we've got Sophia.

Now, she's just moved into a new house and says that her new house cost a quarter of a million pounds.

So, when talking about bigger integers, sometimes we compare them to a million.

All right, let's have a think then.

Ah, so Sophia's house cost one quarter of a million, which is 250,000 pounds.

And then, we've got Andeep, "I'm running the 15 hundred metres on sports day." You too may have run the 15 hundred metres on sports day.

How far will Andeep run? Andeep will run 1,500 metres.

So, depending on the context that we are using, we sometimes change the way we say integers.

Okay, what I'd like you to do now is to pause the video and to match the pairs.

So, something on the left hand side to the correct integer on the right hand side.

When you're done, come back.

Okay, brilliant, well done.

So, let's have a look.

Let's just check those, so 50k.

So, remember we said that k often means a thousand, so 50k would be 50,000.

So, hopefully, I'm sure you did, you matched that first top one to the bottom one.

All right, then we've got half a million, so half of a million, a million and half of that would be 500,000.

So, well done if you managed to pair those two up, and then pretty obvious the last two are going to pair up, but let's just check that, five grand.

So, remember I said that grand is another way of saying thousand.

So, that would match to 5,000.

Brilliant, well done.

Okay, so what I'd like you to do now is to pause the video and to have a go at filling in either the missing integers or words in each of these four statements.

When you're done, come back and we'll have a check and see how you got on.

Super, well done, good.

So, let's just check through these answers then.

So, we've got 300,000, so the missing word there was thousands in the first case, and then 3,000 hundreds, so we were missing the 3,000, then 30,000 tens.

So, there we were missing the tens.

Okay, B, 45,000.

So, we started off, we were missing the 45.

The next one we had 450.

And to make that correct, we would need hundreds.

And then 4,500 tens.

C is 5,600,000.

Okay, if we were to read that number out, which is the same as 56 hundred thousand, which is the same as 560 10 thousands, and that's the same as 56,000 hundreds.

Okay, so onto the last one, getting a little bit more tricky.

So, this one is 84,500,000, and that's the same as 8,450 10 thousands, eight million 450,000 10s, or well done if you've got this one right, 84.

5 millions.

Okay, great, let's move on then to the second learning cycle.

In this learning cycle, we're going to be looking at the fact that there are actually different ways of saying the same integer.

So, the same integer, but we can say it in multiple different ways.

So, let's get started.

When Americans say some numbers, they say it in a way that we might not necessarily say.

So, this example here will illustrate that.

So, in America they often use the term hundreds.

So, here we've got 19 hundreds.

We are gonna write that as an integer.

So, just as we did in the previous learning cycle, we're going to identify the hundreds column.

Here's our hundreds column and we've got 19 hundreds.

So, there's our two boxes for the 19.

So, we've got our 19 in there, and just as we did previously, we are going to put the two placeholders in the tens and the ones column.

Okay, so 19 hundreds as an integer is actually 1,900.

So, in this country we would be more likely to say 1,900 rather than 19 hundreds.

The two things mean exactly the same thing.

They're just read in different ways.

Let's take a look at another example.

So, let's look at this one, a 145 tens.

We want to write that as an integer.

So, we are going to write it using digits only, and we are not going to use the word tens.

So, we're gonna identify firstly, the tens column.

So, tens column, and we've got 145 tens.

So, we're gonna put 145, and then remember that placeholder.

So, actually another way of saying 145 tens is 1,450.

Exactly the same integer, it's just written in two different ways.

Okay, let's look at the next example.

So, this is 54 10 thousands.

So, again, using our place value chart, we are going to identify the 10 thousands column.

We are going to put 54, making sure that that four goes in the 10 thousands column, and then our placeholders.

So, that means that 54 10 thousands as an integer is 540,000.

And right guys, I'm sure we are ready now to have a go at this check for understanding.

Okay, so this is a true or false check for understanding.

What I'd like you to do is decide whether you think the statement is true or false.

So, 25 10 thousands is equal to 2,500 tens.

I've included the place value chart in the top corner, so that you can use that should you need a little bit of help.

Remember, you could write this down.

I'd like you to decide is it true or false, but not only that, can you give the correct justification? So, is it A, or is it B? Brilliant, superb, well done for coming back.

Let's take a look and see if you've got that right.

I'm sure you have.

So, the question we were answering was, is this true or false? 25 10 thousands is equal to 2,500 tens.

So, you may have used the place value chart, or you may have come across another method, another technique for working out the answer to this question, it's actually false.

So, well done if you said false, and the justification is A, the twos do not have the same place value.

In 25 10 thousands the two would be in the a hundred thousands column and in 2,500 tens, the two would be in the 10 thousands column.

Therefore, they are not equal.

Okay, so now I'm gonna get you having a go at a task.

So, in this task, what I'd like you to do is when I've finished describing what you're gonna do is pause the video.

So, the idea of this is you are going to test your skills that we've just checked with our check for understanding, and you are going to identify the odd one out in each set.

So, in each row, three of them will be equal and one of them won't.

What I'd like you to do is to identify which is the odd one out.

Which one is not equal to the other three? So, pause the video now, and then as soon as you're done, come back and have a look and see how you've got on.

Okay, now there's a question two to this task as well.

So, what we're going to do in this task is I'd like you to use all of the digit cards, so the nine, the seven, the zero, the six, and the eight to create a number that satisfies each of the things you've been asked to do.

So, for example, the first one, an integer with 76 hundreds.

I'm just gonna tell you here, there is more than one possible answer, okay? So, if you get one answer and you think, oh, actually I'd like a challenge, you could have a go and see if you could find other ways of writing that particular answer.

Okay, or answering that question I should say.

So, what you're gonna do again now is pause the video and then you're gonna come back when you've had a go and we'll see again how you've got on.

Absolutely superb.

Right, okay, let's take a look and see how we've got on those then with those two tasks.

Right, so in the first one then, the odd one out was 40 10 thousands.

That was not equal to the other three integers represented by those words.

In B, it was the third one, 60,000 thousands.

That was the odd one out.

In C, it was the first one, 1,200 tens.

And then, in D, we were getting a bit tricky here, now going into the much, much bigger numbers, we've got 578 million was the odd one out.

So, that was in the final column and then E.

So, again, a little bit more challenging with that decimal there.

The odd one out was the 8,400 hundreds.

Okay, moving on to C, an integer was 76 tens.

Again, more than one answer.

Well done if you've got more than one.

So, as long as the seven is in the hundreds column and the six is in the tens column, well done.

You've got that right, and then D, an integer.

So, this one's a little bit trickier maybe because we've got that zero there.

So, an integer with 90 hundreds.

So, the example here is 79,068.

So, here, as long as the nine is in the thousands column and the zero is in the hundreds column, well done.

You've got those right.

Now, let's just summarise what we've been doing this lesson, and I'm sure you've done really well at this.

So, we started off and we were looking at different ways that we could read integers aloud.

So, actually we can say things in different ways.

They still would give us the same integer.

We then looked at the context.

So, the situation that you might be in.

So, remember, think back, we looked at Sam and his mobile phone number and we talked about the fact that actually a mobile phone number is really just a list of digits, whereas when we were looking at Jun and his height, we wouldn't want to say that as a list of digits.

And I think if I remember rightly, it was 157 centimetres tall.

And then, finally, in that last part of the lesson, we were looking at the fact that you can write or read integers in different ways.

So, if you remember, we started off with 19 hundred and we used our place value chart, and we were able to work out that that was actually the same as 1,900.

We had a go at that odd one out task, which I'm sure you did really well on, and a super well done if you managed to get more than one example for those last questions.

Thank you so much for joining me today.

It's been fantastic.

Bye.