Lesson video

Hello, my name's Mrs. Hopper and I'm really looking forward to working with you in this lesson.

The lesson comes from our unit on "Multiples of 1,000." So we're going to be looking at those bigger numbers.

How are they put together? How are they composed? Where do we find them in real life? And how can we learn about them so that we can work with them when we're solving problems? So if you're ready to make a start, let's get going.

So in this lesson, we're going to be looking at the composition of 100,000 and looking to see how it is composed of 50,000s, 25,000s and 20,000s.

We've got two keywords in our lesson today, multiple and gridlines.

So I'll take my turn and then it'll be your turn.

My turn, multiple.

Your turn.

My turn, gridlines.

Your turn.

You may well be familiar with those words, but let's just check their meaning.

We're going to be using them in our lesson today.

So a multiple is the result of multiplying a number by an integer, not a fraction.

So multiplying by a whole number.

And a gridline is a horizontal or vertical line that helps organise data on a graph or chart.

There are two parts to our lesson today.

In the first part, we're going to be looking at common partitions of 100,000s.

Ways that it's often broken up when we see it used in real life.

And then in the second part, we're going to look at those common partitions in context.

So let's make a start on part one.

And we've got Aisha and Alex in our lesson with us today.

So what is the size of each missing part in these models? You might want to have a think about this before we talk it through together.

Aisha says, "The first whole is divided into two equal parts and the second whole is divided into four equal parts." So a hundred divided by two is equal to 50.

And a hundred divided by four is equal to 25.

And we're thinking of those divisions as divided into two equal parts and divided into four equal parts.

And Alex says, "The last whole is divided into five equal parts." The whole is still a hundred.

So a hundred divided into five equal parts is equal to 20.

So our first bar model has two equal parts of 50.

When a hundred is divided into two equal parts, each part has a value of 50.

When a hundred is divided into four equal parts, each part has a value of 25.

And Alex says, "When a hundred is divided into five equal parts, each part has a value of 20." What do you notice this time? How can you find the size of each part now? We were looking at divisions of a hundred.

Now we're looking at a hundred thousand.

"Each whole has been divided into the same number of parts as before." Two, four, and five equal parts.

"However, each whole is now 100,000 instead." It was 100 before.

But we can still think in the same way.

100,000 divided by two will be equal to 50,000.

100 divided by two is equal to 50.

If we know that 100 divided by four is equal to 25, then 100,000 divided by four will be equal to 25,000.

And 100,000 divided by five will be equal to 20,000 because 100 divided by five is equal to 20.

So when 100,000 is divided into two equal parts, each part has a value of 50,000.

When 100,000 is divided into four equal parts, each part has a value of 25,000.

And when 100,000 is divided into five equal parts, each part has a value of 20,000.

So what's the same and what's different? Aisha says, "The structure of the bar models below are the same as the bar model above." So if the top bar model has been divided into two equal parts, the bottom one has as well.

And then in the middle, we've got four equal parts in the top and the bottom and five equal parts on the right.

Alex says, "However, the whole is 1,000 times larger, in the bottom bar models, so each part is also 1,000 times larger." When 100 was divided into two equal parts, each part was equal to 50.

100,000 is a thousand times bigger than a hundred.

So our parts are a thousand times bigger.

50 becomes 50,000.

And you can count beyond a hundred thousand in each of these common partitions.

So our first bar model takes us to 100,000, then another to 20,000, then another to 30,000.

Aisha says, "Let's count up in multiples of 50,000." So we'll count from zero.

Aisha will start with this and then we'll carry on.

Are you ready? Zero.

50,000.

100,000.

150,000.

200,000.

250,000.

300,000.

What common partition do you think we're using now? Ah, well, there's our bar model with four equal parts.

100,000 divided by four was equal to 25,000.

And again, we can mark those on the number line, but we can continue with another 100,000 and another 100,000 all the way up to 300,000.

Okay, Aisha, let's count up in multiples of 25,000 this time.

We'll start from zero, Aisha will count with us for a bit, and then we'll carry on on our own.

Zero.

25,000.

50,000.

75,000.

100,000.

125,000.

150,000.

175,000.

200,000.

225,000.

250,000.

275,000.

300,000.

What do you think we're going to be counting in this time? Right, so we've divided 100,000 into five equal parts worth 20,000 each.

And again, we can mark those divisions on our number line and we can add another 100,000 and keep counting and another 100,000 and keep counting.

And obviously, that line would just keep on going.

We could keep adding a hundred thousands.

Oh, I knew this was coming! Okay, Aisha, let's count up in multiples of 20,000 this time.

We'll start from zero.

Aisha will count with us for a bit and then we'll carry on.

So zero.

20,000.

40,000.

60,000.

80,000.

100,000.

120,000.

140,000.

160,000.

180,000.

200,000.

220,000.

240,000.

260,000.

280,000.

300,000.

You could see that pattern of counting in twos there.

But the way we read our numbers, we read all the thousands.

So we read 120,000 rather than 12 lots of 10,000.

Have a look at the bar model and give the value of each part.

The parts are equal.

Pause the video, have a go, and we'll come back for some feedback.

What did you work it out as? 100,000 divided by four is equal to 25,000.

So each of our four equal parts is worth 25,000.

Can you draw a bar model now to represent this equation? 100,000 divided by five is equal to? So pause the video, draw your bar model, and then we'll have a look at the answer together.

What did your bar model look like? This is what mine looks like.

100,000 divided by five, divided into five equal parts.

And Sofia says, "The value of each part is 20,000." Time for you to do some practise.

For question one, can you write a multiplication equation and a division equation to represent each of these bar models? Question two, can you fill in the missing numbers in the sequences? And we're counting in equal-size steps each time.

And then for question three, starting at 300,000, can you write the next five multiples of, 20,000 for the top row, 25,000 for the middle, and 50,000 for the bottom row? So pause the video, have a go at your tasks, and we'll come back for some feedback.

How did you get on? So for our first bar, we can say that 50,000 multiplied by two is equal to 100,000.

Or 100,000 divided by two is equal to 50,000.

For the second bar, we've got those four equal parts.

So we're multiplying and dividing by four.

25,000 multiplied by four is equal to 100,000.

100,000 divided by four is equal to 25,000.

And for our final bar model, we were thinking about that relationship of five times or dividing by five.

20,000 multiplied by five is equal to a hundred thousand.

100,000 divided by five is equal to 20,000.

In question two, you were filling in the missing numbers in the sequences.

So could you use the information there to work out what the jumps were each time? Well, we've got 50,000, 100,000, so that's a gap of 50,000.

So we're counting in 50,000s here.

So our missing numbers are 150,000, 200,000.

We've got 250,000.

And the final one, 300,000.

What about B? We haven't got two together, but we can see that we've gone from 25,000 to 75,000, which is a jump of 50,000.

So our gap must be half of that.

So we must be counting in 25,000s.

So 25,000.

50,000.

75,000.

100,000.

125,000.

150,000.

And for C, I can see 40,000, 60,000.

So I've got a gap of 20,000 there.

So 20,000 less than 40,000 is 20,000.

And then counting on from the 60,000, we've got 80,000, we know the 100,000, and we've got 120,000.

And in question three, starting with 300,000, you were going to write in the next five multiples of those numbers.

So for the first one, we're sort of counting in steps of 20,000.

So 300,000.

320,000.

340,000.

360,000.

380,000.

400,000.

For the next one, we were counting in multiples of 25,000.

So starting with 300,000, 325,000.

350,000.

375,000.

400,000.

425,000.

And for the bottom row, we're counting in multiples of 50,000.

So starting again at 300,000, we'll have 350,000.

400,000.

450,000.

500,000.

550,000.

And did you notice that because our steps are bigger each time, we end on a higher number in each of those counts? So let's move on to the second part of our lesson where we're going to look at common partitions of a hundred thousand in context.

And we're going to look at a graph.

So this graph shows the number of ice creams sold this year by the local dairy farm.

How many of each ice cream did they sell, do you think? Lucas says, "It looks like Salted Caramel is the most popular." It has got the tallest of the bars, hasn't it? "But it's hard to say exactly how many of each ice cream sold with so few gridlines." We've only got one gridline between our zero and our 100,000 on the scale.

So we've got a lot of estimating to do.

It will be difficult to do with just that one gridline.

Lucas says, "The scale on the y-axis," that's the vertical axis of our graph, "is divided into two equal parts, so the midpoint is 50,000.

It's still tricky to identify the value of each bar though." But he's made some estimates.

So these are his estimates.

He thinks for Mint Choc Chip, it's 25,000, because he's reckoning it's roughly halfway between zero and 50,000.

Raspberry Ripple.

Well, it's between 25,000 and 50,000.

It's quite close to 50,000 so Lucas reckons about 45,000.

Would you agree? Lemon Meringue.

It's the least popular.

Which is a shame.

I like lemon meringue.

Well, it's well below 25,000, isn't it? Maybe around 10,000, Lucas thinks.

And what about Salted Caramel? Well, it's over 50,000 but not by much.

So Lucas says 55,000.

And if you notice, his estimates are all sort of to the nearest 5,000, aren't they? He's not bothered to think about hundreds in this because we just can't be that accurate given how few gridlines there are on the graph.

What do you notice this time? Ah, well, Lucas says, "This time the scale on the y-axis is divided into four parts, so each interval is a multiple of 25,000." So we can put those onto our gridlines.

Oh, so now, we've got a bit more information.

Lucas says, "I think this helps me see some of the values more easily as there are more gridlines." "In fact," he says, "my mint choc chip estimate was pretty good!" He said 25,000, didn't he? And it is pretty much bang on the line, maybe a tiny bit over.

He says, "Here are my new estimates." Now he's got these extra gridlines.

Yes, he's gone just above 25,000.

So he's gone for 26,000 for Mint Choc Chip.

40,000 for Raspberry Ripple.

It's still over halfway, but it's not at the 50,000.

Lemon Meringue.

He's gone for 11,000.

12,500 would be halfway, wouldn't it? But he's gone for just below that, so 11,000.

And for Salted Caramel, still that 52,000.

It's just over 50,000, isn't it? What do you notice this time? Well, as Lucas says, "This time, the scale on the y-axis is divided into five parts, so each interval is a multiple of 20,000." We know that 100,000 divided by five is equal to 20,000.

We might have thought 100 divided by five is equal to 20, but we're thinking in thousands this time.

So we can put on those multiples of 20,000 on our scale to mark our gridlines.

"This may also help me to see some of the values more easily," says Lucas.

"In fact," he says, "I'm not sure I'd change any of my estimates, maybe except for Raspberry Ripple." Hmm.

So 26,000 still for Mint Choc Chip.

But he's taken his estimate for Raspberry Ripple down to 41,000.

Lemon Meringue, still 11,000, just over halfway.

And Salted Caramel, still 52,000.

50,000 would be halfway, and we're just over that halfway point.

He says, "So having more gridlines can often provide us with better information to read the data more accurately." Time for you to do some approximating.

Have a look at the bar chart and estimate how many Rocky Road ice creams were sold approximately in the year.

Pause the video, have a think, and we'll come back and discuss our answers.

So what did you reckon? Well, if we put the line across to that y-axis, we can see that it's above the 30,000 but it's not that close to the 40,000 yet.

So yeah, I agree with Lucas.

"I think they sold about 35,000 Rocky Road ice creams." Time to check your understanding again.

We don't always see these common partitions on a line scale, like a number line on a graph.

Sometimes we see them in a circular scale on a measuring device, such as a scale for weighing the massive things.

So have a look at this scale on this circular scale and decide what value the arrow is pointing to.

Pause the video and we'll discuss your answer.

What did you reckon? What did you see? Well, Lucas says, "There are four intervals, so the scale is going up in lots of 25,000.

So the arrow is pointing to 50,000." It's halfway between zero and 100,000.

Time for you to do some practise.

We've got some more of these scales for you to look at.

Can you write down the value that the arrow is pointing to in each one? And again for these ones.

And then for question two, the bar chart shows the yearly wage of members in a family.

So we'd like you to look at the bar chart and do three things.

One, estimate how much each family member earns in the year.

B, estimate the difference in earning between the highest-paid person and the least-paid person in the family.

And C, estimate how much they earn altogether as a family.

So pause the video, have a go at your tasks, and we'll come back for some feedback.

How did you get on? So for question one, you had to write down the value that the arrow is pointing to.

So did you spot that, again, we had four equal divisions on our scale? So we were thinking about 25,000s.

So our first arrow was pointing to 25,000, then 50,000 and then 75,000.

What about this scale? How many equal parts had our 100,000 been divided into? It was five this time.

And we know that 100,000 divided by five is equal to 20,000.

So our arrows were pointing to 20,000, 40,000, 60,000 and 80,000.

And question two, we were looking at this bar chart about a family's wages over a year.

So we asked you to estimate how much each family member earns.

You might have spotted that the scale on our bar chart was going up in steps of 20,000.

And that will help us to make our estimates.

You may have got slightly different values from this, but these were our estimates.

So we thought Tim earned about 35,000, Corrine earned about 41,000, Zander earned about 12,000, and Toni earned about 26,000 pounds.

So B asked to estimate the difference in earning between the highest-paid person and the least-paid person.

So with our estimates, that was 41,000 subtract 12,000, which is equal to 29,000.

So that was the difference in earning.

And for C, we had to estimate how much they earned as a family altogether.

So we had to total up our estimates.

And using our estimates, their total earnings were 114,000 pounds.

As I say, your answers may have differed slightly, but hopefully they were roughly the same as ours.

And we've come to the end of our lesson.

We've been explaining that 100,000 is composed of 50,000s, 25,000s and 20,000s.

And you quite often see them on scales.

So they're useful ones to practise.

They're not the only ways that we can compose 100,000 though.

So what have we learned? We've learned that when 100,000 is divided into two equal parts, each part has a value of 50,000.

When 100,000 is divided into four equal parts, each part has a value of 25,000.

And when 100,000 is divided into five equal parts, each part has a value of 20,000.

And multiples of these amounts are commonly used in graphs and represented on gridlines.

Thank you for all your hard work and your mathematical thinking today.

I hope you've enjoyed the lesson as much as I have.

And I hope I'll see you again soon.

Bye-bye!.