Lesson video

Hi, welcome to your maths lesson.

My name is Mrs Harris.

We're going to be looking at the digits in large numbers, making sure we really understand what they represent.

Here is what we're going to do.

We're going to start with partitioning, move on to missing number problems, and then go to go to an independent task.

You're going to need a pencil, ruler, paper and a book, or a book sorry.

Something to write on anyway.

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

Okay, that's everything we need.

Let's get on with our learning then.

We're going to start with partitioning.

I've got a number here, a seven digit number.

I can read it as five million, three hundred and eighty one thousand, four hundred and ninety two.

By using the place value chart that you can see on the screen, we can quite easily see, what each of them digits represents.

We can see that the five represents millions.

We have five of them.

We can see that the eight represents the ten thousands.

We have eight ten thousand.

Eighty thousand.

And we can see that the two represents the one's.

So we finish our number with a two.

We can also use this chart.

It may be one you've seen before.

It's a gattegno chart.

And it's really helpful for working out all the ways that our number is composed.

So, I'd like you to pause the video, and circle all the digits you can find in our number.

Don't worry, I'll show you what I mean in a little minute if you're a little confused.

Okay, did you have a go? Let me show you.

I started with the five million.

Can you see where I've put the star around it? And can you see it in my number? I then went to the three hundred thousand, the eighty thousand, the one thousand, the four hundred, the ninety, and the two.

This is how my number has been made up to make five million, three hundred and eighty one thousand, four hundred and ninety two.

If you didn't quite get it right, pause the video and have a look at what I've done a little more closely and where you got in a bit of a muddle.

So, here is this number again.

Here are all the things I took from the gattegno chart.

The five million, the three hundred thousand, the eighty thousand, the one thousand, the four hundred, the ninety and the two.

And together, these make up our number.

I've done an expression.

And my expression is representing millions, add hundred thousands, add ten thousands, add thousands, add hundreds, add tens and add ones.

I've had enough of working with five million, three hundred and eighty one thousand, four hundred and ninety two.

I'm going to try a new number.

But, I would like you to break it down into an expression like I have.

Remember you can look at your gattegno chart and then, I'd like you to come back.

Hey, did you have a go? Did you get, this.

Three million, plus seven hundred thousand, plus, fifty thousand, plus five thousand, plus one hundred, plus ninety, plus six.

Well done if you did.

Now, I'd like you to have a go at this one.

Looks a bit different.

Haven't got the numbers, but got place value counters.

So pause the video, and work out what this number is and how you could write it as an expression.

That's where I had every bit broken down with the pluses in between.

Okay, let's have a look.

I have one, one million, two, two hundred thousands, three, three ten thousands, six, one thousands, and one, ten.

That really doesn't look like a seven digit number does it? And that is definitely what I needed.

I think I've missed some spaces out or some numbers out because I needed to put a zero in where I didn't have any of a certain value.

I haven't got any, hundreds, and I haven't got any ones.

I needed to put plus zero where they were.

Write this.

And that, would have helped me get my final number of one million, two hundred and thirty six thousand, and ten.

So be careful that if you ever see place values counters like this, you look for the ones that are missing.

Have a go at this problem.

The numbers are to the line, they are not arranged.

Which ones have we got? Are we missing any? Pause the video, and have a look.

Okay.

I've got, two million, so I've got my two million, I haven't got, no I haven't got my two million.

I've got my two hundred thousand.

I've got my two hundred thousand this is not going to be a seven digit number.

I've got my ten thousand.

Hm, I haven't got any thousands.

Just going to put myself a zero there, so I remember.

Hm, I have got a hundred, I've got one hundred.

That doesn't go there Mrs Harris, it goes there.

And I've got, and I have got any ones.

So, my number becomes, two hundred, and ten thousand, one hundred and twenty.

So, well done if you worked out that number.

I'd like you to take the time to do a little talk task for me.

You'll have some face value counters in your download or on the worksheet, and I'd like you to do what it says on the screen.

Pick six counters.

What's the largest number you can make? What's the smallest number you can make? And if you want a challenge, can you make a number as near to five hundred thousand as possible? Or a number as near to nine hundred thousand as possible? Pause the video and have a go, now.

Okay, so the largest number you could make was six million.

If you only had six counters.

And the smallest number you could make with six counters, surely was six.

And did you do the challenge? Well done if you did.

How close did you get I wonder? We're going to work on some missing number problems now.

They won't really be problems for us we'll solve them easily together.

So here's the first one.

You see how the number has been broken down? That's how we broke down the numbers on the gattegno chart, or an a place value chart.

We've got, seven hundred and sixty one thousand, nine hundred and two.

Well, I got the seven hundred thousand, I've got the one thousand, I've got the nine hundred and the two, so what am I missing? Write it down.

Yeah, I'm missing the sixty thousand.

Okay, let's try another one.

Oh, a bit more missing this time.

My number, can you quickly say it? Two hundred, not two hundred, two million, one hundred and twenty four thousand and three.

Well, I got my equals and I got my gap, my missing number, then I got my plus three.

So I've got my ones digit.

What am I missing? Can you write it down for me? Okay, I've missing, two million, one hundred and twenty four thousand.

You must be the zeros in, otherwise it would've said two thousand one hundred and twenty four.

And the number above, the first one that was missing, the sixty thousand would've said six.

Although that is the digit, it's not what is represents, is it? Okay, next one.

What are we missing now? Write it down.

Okay.

And now, what are we missing in this one? There are two missing numbers.

Let's see how you got on.

On the first one, we was missing, nine hundred and twenty thousand.

We had the three thousand, the five hundred, the ten and the six.

So we had three thousand five hundred and sixteen.

But we were missing the first part of the number, the nine hundred and twenty thousand.

Your second problem, we had four million, eight hundred thousand, six hundred and seventy two.

Well, we had after the equals sign, four million, eight hundred thousand and seventy.

What were we missing? We were missing the six hundred, the six thousand.

Oh, it should have been six hundred.

Too many zeros there.

We were missing six hundred weren't we.

And, we were missing the two.

Now it's time for you to do your independent learning.

For your independent learning, I'd like you to return to your place value counters.

But this time, you can only choose three of them.

And actually, of them three, you can only have ones that show.

One million, one thousand, and ones.

Put all the others aside.

I'd like you to write all the possible combinations you can make using just them three values and just three counters.

So pause the video now, have a go at your independent learning and then, come back to me and we'll look at the answers together.

Welcome back from your independent learning.

I wonder how you got on with it.

And if you chose to work systematically.

That's how I tried this problem.

Remember, we can only have three counters.

So I started off with the three with the greatest value.

And I gave myself, three million.

Then, I decided I would change one of my millions.

So I had two million counters, and one thousand counters.

And that was my three counters.

After that, I chose to change the million again.

This time just had one counter in my million place.

And I had two in my thousands place, so I have one million, two thousand.

Hm, I thought of another way of using my two million.

So, I use my two million counter again and it had no thousands this time.

But, one in the ones column.

Then, I went with one in my millions, one in my thousands, and one in my ones.

But I still wasn't done.

I could have one million, one million, and two.

After that, my numbers got a little bit smaller.

I could have, three thousand, I could have, two thousand and one.

I could have one thousand and two.

And I could number three.

Every time I've used all my counters.

I wonder if you found any other combinations, or if you didn't find all of these? So we've reached the end of the lesson.

I think we really understand what all them digits mean, and numbers now, especially the big numbers like we've been working with.

Perhaps you would like to share some of your work with me or Oak National.

If you would like to, ask your parent or carer to share your work on twitter or other social media, tagging @oaknational.

But just before I say goodbye, I want you to remind you that it's time for you to do the quiz.

Bye.