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 a thousand, so we're gonna 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 exploring the composition of 10,000.

We're going to look at how it can be composed from 5,000s, 2,500s and 2,000s.

So let's make a start.

There are two key words in our lesson today, we've got multiple and grid lines.

I'll take my turn, then it'll be your turn to say them.

My turn, multiple, your turn.

My turn, grid lines, your turn.

Let's just check we're sure what they both mean, they're words we're gonna be using a lot in our lesson.

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

And a grid line is a horizontal or vertical line that helps organise data on a graph or a chart, and we're gonna be looking at some graphs and charts as we go through this lesson.

There are two parts to our lesson today.

In the first part, we're going to be looking at common partitions of 10,000.

And in the second part, we're going to be looking at those partitions in context.

So let's start with part one.

And we've got Sofia and Lucas helping us in our lesson today.

So what is the size of each missing part in these bar models? Do you want to have a little look first? And then we'll look at them together.

Okay, let's have a look.

Sofia says, "The first whole is divided into two equal parts, and the second whole is divided into four equal parts." So let's look at the first one.

10 divided by 2 is equal to 5, and the second one, 10 divided by 4 is equal to 2.

5.

10 divided by 4 is the same as half of 10, and then half that again.

So half of 10 is 5 and half of 5 is 2.

5, two and a half.

And Lucas says, "The last whole is divided into five equal parts." 10 divided by 5 is equal to 2.

So, "When 10 is divided into 2 equal parts, each part has a value of 5.

When 10 is divided into 4 equal parts, each part has a value of 2.

5," or two and a half.

And, "When 10 is divided into five equal parts, each part has a value of 2." So we've completed our bar models.

What do you notice? How can you find the size of each part now? Look at what's happened to the whole in each of our bar models.

Well, Sofia's noticed, "Each whole has been divided into the same number of parts as before." So our 10 was divided into two equal parts.

Our 10 was divided into four equal parts and then into five equal parts, so we've got the same number of equal parts.

"However," says Lucas, "each whole is now 10,000 instead." So we've gone from 10 to 10,000.

So can we just think about applying what we knew about 10 to 10,000, a thousand times bigger? 10,000 divided by 2 is equal to 5,000.

10,000 divided by 4 is equal to 2,500.

And 10,000 divided by 5 is equal to 2,000.

And we're thinking about dividing into equal parts, two equal parts, four equal parts, and five equal parts.

So, "When 10,000 is divided into 2 equal parts, each part has a value of 5,000.

When 10,000 is divided into 4 equal parts, each part has a value of 2.

5 thousand," or 2,500.

And, "When 10,000 is divided into 5 equal parts, each part has a value of 2,000." So let's look at all the bar models we've created.

What's the same and what's different? You might want to have a think about that before we share our ideas together.

Sofia says, "The structure of the bar models below are the same as the bar model above it." So we can see that 10,000 has been divided into two equal parts and 10 was divided into two equal parts, and the same for the four and the five equal parts.

Lucas says, "However, the whole is 1,000 times larger, so each part is also 1,000 times larger." We've got 10 divided into two equal parts of 5, and 10,000, a thousand times bigger, divided into two equal parts of 5,000.

5,000 is a thousand times bigger than 5.

So you can count beyond 10,000 in each common partition.

So the common partition here is that 10,000 can be broken into two parts of 5,000.

So we've got 5,000, 10,000, another set and another set along our number line, all the way up to 30,000.

Sofia says, "Let's count in multiples of 5,000." So she's gonna start us off and we'll continue.

Let's start from zero.

Are you ready? Zero, 5,000, 10,000, 15,000, 20,000, 25,000, 30,000.

So what's our common partition going to be this time, do you think? We're going to look at the common partition into four equal parts.

So 10 divided into four equal parts was two and a half, 2.

5, 10,000 divided into four equal parts gives us four parts of 2,500, a thousand times bigger.

And we again, we can build up our number line using those common partitions and add in another 10,000 and another 10,000.

Lucas says, "Let's count in multiples of 2.

5 thousand," 2,500 or 2,500.

Are you ready? Zero.

2,500, 5,000, 7,500, 10,000, 12,500, 15,000, 17,500, 20,000, 22,500, 25,000, 27,500 and 30,000.

We could have counted zero, 2,500, 5,000, 7,500 to 10,000.

But each time we've got that 500, we've got another half of a thousand.

So 12,500 is the same as 12.

5 thousands, 12 and a half thousands.

And let's look at the final one.

This common partition into five equal parts.

10 divided into five equal parts, each part was worth two.

So 10,000 divided into five equal parts, each part is worth 2,000, a thousand times bigger.

So we can build up our number line and then we can add in another 10,000 and another 10,000, all the way up to 30,000.

Okay, Sofia, "Let's count up in multiples of 2,000," from zero.

Zero, 2,000, 4,000, 6,000, 8,000, 10,000, 12,000, 14,000, 16,000, 18,000, 20,000, 22,000, 24,000, 26,000, 28,000, 30,000.

We're counting in two thousands, aren't we? And I'm sure you're very familiar with counting in twos, but this time we're counting up in groups of 2,000.

Time to check your understanding.

Have a look at this bar model.

There are equal parts of our whole, so what's the value of each equal part? Pause the video, have a go and we'll look at the answer together.

So 10,000 divided by 4 or divided into four equal parts, gives equal parts of 2,500.

And we can use our knowledge of 10 divided into four equal parts of 2.

5.

So 10,000 divided into four equal parts will be 2.

5 thousands or 2,500 or 2,500.

And another check.

Can you draw a bar model to represent this equation? 10,000 divided by 5 is equal to something, so draw the bar model to represent the equation.

Pause the video and we'll look at it together.

What did your bar model look like? This is what ours looked like.

So we had our whole of 10,000 and our five equal parts to show 10,000 divided by 5.

So each equal part is worth 2,000.

As Sofia says, "The value of each part is 2,000." Time for you to do some practise.

For part one, you're going to write a multiplication equation and a division equation to represent each bar model.

In part two, you're going to fill in the missing numbers in these sequences, counting in steps of an even size each time.

And for part three, starting with 30,000, you're going to write in the next five multiples of, and for each list you're given what multiple you're counting in.

So multiples of 2,000, multiples of 2,500 and multiples of 5,000.

So can you continue those counts? Pause the video, have a go at your tasks and we'll get together for some feedback.

How did you get on? So in question one, you were asked to write a multiplication equation and a division equation for each bar model.

So we had a bar model at the top there of 10,000 as our whole and two equal parts of 5,000.

So we could have said 5,000 multiplied by 2 is equal to 10,000 or 10,000 divided by 2 is equal to 5,000.

So the second one still had a whole of 10,000, but this time divided into four equal parts.

2,500 multiplied by 4 is equal to 10,000.

10,000 divided by 4 is equal to 2,500.

And for the final one, again, a whole of 10,000, but five equal parts of 2,000 this time.

2,000 multiplied by 5 is equal to 10,000.

10,000 divided by 5 is equal to 2,000.

And in question two, you're filling in the missing numbers in the sequences, counting in steps of equal size each time.

So we started with 5,000, 10,000, 15,000, 20,000.

We were given 25,000, 30,000.

So we were counting in steps of 5,000.

What were we counting in in B? Well, I can see lots of 500s there, and so I think we might be counting in steps of 2,500.

So 2,500, 5,000, 7,500, 10,000, 12,500, 15,000.

Well, you might have said 2,500, 5,000, 7,500 as we did earlier in the lesson.

And what about C? I can see lots of even numbers of thousands there.

4,000, 6,000, I think we might be counting in 2,000's here, but we've got to fill in the number before 4,000.

Well, that will be 2,000.

So we've got 2,000, 4,000, 6,000, 8,000, 10,000, 12,000.

That nice pattern of counting in twos, but in our units of thousands this time, so counting in 2,000s.

And for part three, starting at 30,000, you were going to write the next five multiples of 2,000.

So 30,000, 32,000, 34,000, 36,000, 38,000, 40,000.

And then counting in multiples of 2,500.

So 30,000, 32,500, 35,000, 37,500, 40,000, 42,500.

And finally, counting in multiples of 5,000.

So a bit like counting in fives from 30, but counting in 5,000s from 30.

So 30,000, 35,000, 40,000, 45,000, 50,000, 55,000.

I hope you could see some common patterns of counting that you're very familiar with, but used with a unit of thousands rather than a unit of ones.

And on into the second part of our lesson, where we're going to look at those common partitions of 10,000 in context.

So the amount of money made after expenses, so the profit, of a small, local business is shown on this bar graph.

So a company will make lots of money, but then it will have to pay out for things, like the materials it's used to make its product or the building it operates out of.

The money that's left after they've paid all of that is its profit.

So this is the profit made by a small, local business shown in a bar graph.

So how much profit did they make each year? Well, let's have a look.

We need to think about the y-axis.

The y-axis is the vertical axis for our graph.

So what is the scale on this axis? So Lucas says, "The y-axis has been divided into four equal parts.

The whole of the axis is 10,000, so each interval has a value of 2,500." Remember the bar models from part one of the lesson? And there is the bar model from part one of the lesson.

10,000 divided by 4 is equal to 2,500.

"That means," Lucas says, "we can count in multiples of 2,500," from zero to 10,000.

2,500, 5,000, 7,500, 10,000.

So we've got our intervals marked on now.

How much profit do you think they made each year though? Well Lucas says, "I think Year One is about 7,000." So we've got 5,000 up to 7,500 there.

So we've got 2,500 in there.

So yeah, I think 7,000's about right.

It's well over halfway and close to 7,500.

Lucas says he reckons Year Two is about 4,000.

Closer to 5,000 than 2,500.

Sofia says, "Year 3 is about 8,000." It's only just over the 7,500, isn't it? Quite a long way to go before it gets to 10,000.

And what about Year Four? Well, Year Four's only just over 7,500.

So what do you notice this time? Well, Lucas says, "The y-axis has been divided into two equal parts," this time.

"The whole of the axis is still 10,000, so each interval has a value of 5,000." Do you remember the bar model from the first part of the lesson? There it is again to help us think about 10,000 divided into two equal parts.

"That means we can count up in multiples of 5,000." So zero, 5,000, 10,000.

Lucas says, "I much preferred making estimates on the graph with more grid lines." Sofia says, "I agree." It's really quite difficult now to think about what those bars are close to.

None of them are very close to the grid line of 10,000 or 5,000 or even zero, so I'm not sure how good our estimates would be.

What do you notice this time? Lucas says, "The y-axis has been divided into five equal parts.

The whole of the axis is still 10,000, so each interval has a value of 2,000." And there's our bar model from the first part of the lesson to show 10,000 divided into five equal parts, each part having a value of 2,000.

So Lucas says, "That means we can count up in multiples of 2,000." So zero, 2,000, 4,000, 6,000, 8,000, 10,000.

He says, "These grid lines make it even easier to estimate more accurately." So going back and looking at his estimates again, he says, "I think Year One is nearer to 6,500." I think he might be right.

"Year Two is about 3,900." It's just under 4,000, isn't it? "Year Three is exactly 8,000," says Sofia.

It sits right on that 8,000 grid line.

And, "Year Four is just over 7,750," she reckons.

It's just below 8,000, isn't it? How much profit do you think they made in Year Five? Use the grid lines to help you.

Pause the video and we'll come back for some feedback.

So what did you reckon to the profit in Year Five? It sits about halfway, doesn't it? Between 8,000 and 10,000.

If we look at the bottom of the black line, that's pretty much halfway, isn't it? So Lucas says, "I think they made about 9,000 pounds in Year Five." That would make sense, wouldn't it? Time to check your understanding again.

We don't always see these divisions on the axis to a graph, we sometimes see them in scales used for measurement.

So can you give the value that the arrow is pointing to on this circular scale? Pause the video, have a go and we'll look at the answer together.

So Lucas says, "There are four intervals, so the scale is going up in lots of 2,500." So you can see we've got zero going all the way 'round the circular scale to 10,000.

And we've got 1, 2, 3, 4 equal parts.

So we've gone three of those jumps along.

"So the arrow must be pointing at 7,500." Time for you to do some practise.

Can you write down the value that the arrow is pointing to on each of these scales? And again, for this set of scales.

And then in question two, the bar chart shows the number of runners attending at an event each year.

Can you explain how the bar chart could be improved? Pause the video, have a go at your tasks and we'll get together for some feedback.

How did you get on? What did you spot about this scale? Well, it was very similar to the scale in our check for understanding, wasn't it? So the scale was divided into four equal parts from zero to 10,000, so each division was worth 2,500.

So the first arrow was pointing out to 2,500, then 5,000, then 7,500.

What about these ones? Well again, we're going from zero to 10,000, but this time our scale is divided into five equal parts.

And we know that 10,000 divided by 5 is equal to 2,000.

So 2,000, 4,000, 6,000 and 8,000 were the values that the arrow was pointing to on this scale.

And then for question two, we asked you to explain how the bar chart could be improved.

What did you think? Well, Lucas says, "The bar chart could be improved if there were more grid lines placed onto it to help read the number of runners who attended each year." I agree, it's quite difficult to make an estimate when you've only got zero, 5,000 and 10,000.

Perhaps if they counted up in one thousands, we'd be able to make a better estimate.

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

We've been explaining that 10,000 is composed in different ways and it can be composed of 5,000s, of 2,500s and of 2,000s.

Those are some common divisions that we see used quite often.

There are other ways, of course, that you can compose 10,000.

So what have we learned? We've learned that when 10,000 is divided into two equal parts, each part has a value of 5,000.

When it's divided into four equal parts, each part has a value of 2,500.

And when it's divided into five equal parts, each part has a value of 2,000.

And we can relate that to those divisions of 10 and think of them as being a thousand times bigger.

And we've also learned that multiples of these amounts are commonly used in graphs and represented on grid lines.

Thank you for all your good thinking and your hard work today, and I hope I get to work with you again soon.

Bye-bye.