Lesson video

Hi, my name is Mrs. Harris, and I'll be with you for your maths lessons day, as we have a look at powers of 10, up to 10 million! Here's our lesson agenda: there's just four parts to this lesson, and we'll get through them in no time.

Let's find out what we need.

Okay, I would like you to have a pencil, maybe a rubber, a ruler, and some paper or a book to write in.

If you haven't got any of them right now, pause the video, go and find them, and then come back to me.

Okay.

Get everything we need? Let's get started then.

We're going to begin with place value up to 10 million! I've got an empty number line here.

And I think this might work better than my counting stick, because you can see it all at once.

And we're going to use it to count, not in a hundred thousands like we did at the beginning of the lesson, but in millions.

So let's start with zero.

0, 1 million, 2 million, 3 million, 4 million, 5 million, 6 million, 7 million, 8 million, 9 million, 10 million.

Hmm, bit of a pattern there.

We could also, instead of writing the word "million," use the zeros.

So, we'll count again.

0, 1,000,000, 2,000,000, 3,000,000, 4,000,000.

There's so many zeroes on these numbers, aren't there? 6,000,000, 7,000,000, 8,000,000, 9,000,000, 10,000,000.

Wonder which was the easier way to see what the number was.

Here's both number lines.

Do you prefer a number line A, where we have the word "million?" Or would you prefer a number line B, where we have all the zero showing the place value? I prefer number line A.

It's easier when I have to say, say the numbers, but if we didn't have all the zeroes, we wouldn't be able to write it "8,000,000" or "9,000,000." So, both have a place.

But for the purpose of today, number line A was more useful.

Let's just have a look at how 1 million is made up, and what all them zeros represent.

So, here is 1,000,000 written.

Look how many digits it has: it has seven digits.

Look, how many zeros it has: six zeros.

Now there could be other digits, if our number was above 1,000,000.

And they represent millions, 100 thousands, 10 thousands, 1 thousands, hundreds, tens, and ones.

We have no ones.

We have no tens.

We have no hundreds.

We have no thousands.

We have no tens of thousands.

We have no hundred thousands, but we have 1 million.

So now we know that, we can look up, we can do, sorry, our powers of 10, up to 10 million.

This place value chart shows us the pattern.

Shows us how the 10s are all in each number, and how many zeroes each of them has.

Look at in the 1 column: the 1s.

Now we're doing integers today, so we're not going to look at the decimals.

We're going to go straight down to where it says "one." And if I wrote that number, you'd just be able to tell me, "one." If I wrote the number 10, you'd be able to tell me, "ten." But if I write this number.

you may need to use this chart, so that you can tell me what the number is.

Look at how many zeros it has, and then find the "1" on the column.

So this number is 10 thousand.

Let me add another zero on.

What is it now? That's right.

It's 100 thousand.

Okay.

What number is it, now? Just 100.

But if I wanted to make it 1 million, it would look like that.

Can you find that on the place value chart? That's how we would write 1 million.

Look at the relationship between all the numbers on the charts.

Great.

I hope you've noticed how many more zeroes each of them have, and how they've got greater in size.

So, your job now is to find what these numbers are called.

You've got some words.

You've got some numbers.

And I need you to fill in all the blanks.

Welcome back.

How did you get on? Did you use the chart to help you? I hope you did, because it's okay to use things to help us, especially when we're learning about these really large numbers.

I started with the "10,000,000." You might've started somewhere else, and that's fine.

And then started on the words.

So I went "ten million," "one million," and then I saw it was "one hundred thousand," "ten thousand." And I noticed that the numbers were getting smaller by the power of 10 each time.

That meant that I could lose a zero each time, to help me write the numbers.

I had "one thousand" in there.

I then went on just to do the "1," and the "ten," "one tenth," and "one thousand." And that just left me with one word to fill in, which was the word "one." The number line helped me count to 1 million, or even to 10 million.

And the numbers and the words help me start to understand the relationship of the powers of 10.

But it's the Gattegno charts, this that you can see now, that really helps me understand.

Let's have a look at the "2" column.

So, if we started with number 2, 20 is 10 times greater than it.

200 is 10 times greater than 20.

2,000 is 10 times greater than 200, and 20,000 is 10 times greater than 2,000.

And it just keeps going on like that.

The relationship is so clear on this chart, it's a really useful tool for you to have to refer back to as we're doing our lesson.

Hey, keep the Gattegno chart in mind, because it's really going to help us here.

Understanding that relationship on how numbers have got 10 times greater as they go up a column or row, sorry, is really going to help.

Let me show you what I mean.

Let's take the number, 1,000 and let's split it into two equal parts.

So we have 500 and 500.

That's not unlike splitting 100 into two equal parts, where we would have 50 and 50.

And it's not unlike splitting 10 into two equal parts, where we would have 5 and 5.

Let's look at splitting 1,000 into four equal parts.

We would have 250, 250, 250, and 250.

If we had the number "100," we would have 10 times less.

Our number would be 10 times less.

And so, the parts, the part part of our bar model, would be 10 times less as well.

So if the total was 100, we would have 25, 25, 25, 25.

Use that information to work out what we would use, if we were to split 1,000 into five equal parts.

Okay.

So it's not unlike splitting 10 into five equal parts.

We'd have 2, 2, 2, 2.

And if we split 100 into five equal parts, we'd have 20, 20, 20, 20, 20.

So here, because it's 10 times greater, we have 200, 200, 200, 200.

Now let's think about 1,000 into 10 equal parts.

Ooh, would it be a 10? I'm not sure it would be.

I think, it would be a 10 if our 1,000 was not a 1,000, but a 100.

Good spot.

Here we have the bar models for 1,000,000.

Think back to the last bar models we did, and the ones before them.

Can you see the relationship? 1,000,000 split into two equal parts, is 500,000 and 500,000.

It's not unlike 10 being split into two equal parts, is it? We just need to remember how many zeros, how many digits, we need.

Spend a second just looking at this and understanding the relationship between the powers of 10.

Hey, now it's time for your independent learning, so that you can show me everything that you've learned so far, and bring it all together.

I've got three word problems for you.

I'll read them to you quickly, but you have them.

So question one: "It is about 10,000 kilometres from Manchester to Cape town.

A plane is a quarter of the way through the journey.

How many kilometres of the journey does it have left?" Question two: "About 1 million people live in Birmingham.

About one fifth of them are over 60 years old.

Approximately how many of- how many over 60-year olds live in Birmingham?" "A builder orders 1,000 kilogrammes of sand.

She has 100 kilogrammes left.

What fraction of the total amount does she have left?" So you're going to need to think about the number, the starting number.

You're going to need to think about what's actually being asked of you.

And I would do a few bar models, if I had to answer these questions.

So, pause the video now, and have a go at your task.

Welcome back.

Let's have a look at the answers together.

So, it is about 10,000 kilometres from Manchester to Cape Town.

So I started with that, and that became the top of my bar model.

And I know I need to split that into four equal parts because we have the information that the plane is one quarter of its way through its journey.

Now, I know that one quarter of 100 is 25.

I know that one quarter of 1,000 is 250.

And so I know that one quarter of 10,000 kilometres is 2,500.

So I can fill all them in.

But that's not the end of our solving of this question.

We know it's already travelled one quarter.

So all that remains now, that I've crossed one quarter off, is to add these up.

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

The plane has 7,500 kilometres left to travel.

Let's see the next problem.

Okay.

This one's about Birmingham, isn't it? And we know that approximately 1,000,000 people live in Birmingham.

Your first challenge was to write 1,000,000, wasn't it? 'cause I did it in words, for you.

And that becomes the top of our bar model.

And we're working in fifths this time, there's about one fifth of them are over 60.

So I need to do my bar into five equal parts, one, two, three, four, five.

Now I can think back to my Gattegno chart.

And I can think back to my other powers of 10.

My 1,000, my 100, even my 10.

If I split my number 10 into five equal parts, each of them would be worth 2.

Here, as I split my 1,000,000 into five equal parts, The answer is 200,000.

That is one fifth of 1,000,000.

It's hard to fit in one box.

I don't need to fill the rest in because the question asked, "Approximately how many over 60-year olds live in Birmingham?" And this is the answer: 200,000.

And that just leaves us with one problem to look at.

So, this one was a little bit different.

A builder orders 1,000 kilos of sand.

There is it.

And she has 1 kilo left.

No, she doesn't.

She has 100 kilos left.

Need to read the questions carefully, don't you? We need to know how many, 100 kilos are in 1,000 kilos.

We can do that one on our fingers: 100, 200, 300 400, 500, 600, 700, 800, 900, 1,000 kilos.

She has 1 kilo left.

Ahhh, she has 1 10th left.

And that was your answer to the final problem of your independent learning.

Great work on the powers of 10, up to 10 million in this lesson.

If you'd like to share any of your work with me, or everyone at Oak National, you could ask your parent or carer to share your work on Twitter, or other social media, tagging @OakNational.

I've just got one more thing for you to do, though.

Now, you need to go and complete the quiz.