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 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 counting forwards and backwards in powers of 10 to and from any multiple of 1,000.

I'm sure you've done lots of counting forwards and backwards in your time, but this time we're gonna be counting in those different powers of 10 and thinking about what changes and what stays the same in the numbers as we count.

So let's see what's in the lesson.

We've got one key word today, and that's "multiple".

So I'll say it then it'll be your turn.

My turn.

Multiple.

Your turn.

Well done.

I'm sure you know what multiple means.

Let's just double check so we're really clear.

So a multiple is the result of multiplying a number by an integer.

So by a whole number, not by a fraction.

And we're going to be thinking about multiples as we go through our lesson today.

There are two parts to our lesson.

In the first part, we're going to be counting in steps of 1,000 and 10,000.

And in the second part, we're going to be counting from any number.

So let's make a start.

And we've got Sophia and Lucas helping us with our lesson today.

We can use our knowledge of counting in ones to help us count in multiples of 1,000.

"Counting up in thousands is just as easy as counting in ones", said Sophia.

So let's start counting from 17.

Are you ready? 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27.

"And backwards", said Lucas.

He's gonna count the first couple and then we'll carry on.

27, 26, 25, 24, 23, 22, 21, 20.

19, 18, 17.

So to count in thousands, Sophia says, "All we have to do is make each number 1,000 times the size".

So we can start with 17,000.

So are you ready to count up? Again, Sophia will start us off and then we'll carry on.

17,000, 18,000, 19,000, 20,000, 21,000, 22,000, 23,000, 24,000, 25,000, 26,000, 27,000.

I think she was right.

It was just like counting up from 17, but adding thousand on the end.

'cause everything was 1,000 times bigger.

And Lucas says, "Can we do it backwards?" And again, Lucas will start us off and then we'll carry on on our own.

So 27,000, 26,000, 25,000, 24,000, 23,000, 22,000, 21,000, 20,000, 19,000, 18,000, 17,000.

Well done.

Good counting.

Sophia says, "We can now apply this to larger numbers".

Let's have a look at 794.

Let's count on in ones.

795, 796, 797, 798, 799, 800, 801, 802, 803, 804, "And backwards", says Lucas.

Again, he'll start with us and then we'll carry on.

804, 803, 802, 801, 800, 799, 798, 797, 796, 795, 794.

Sophia says, "Now we can make each number 1,000 times the size".

So instead of just counting 794, we'll have 794,000.

Let's count up again.

Sophia will start us off and then we'll carry on.

794,000, 795,000, 796,000, 797,000, 798,000, 799,000, 800,000, 801,000, 802,000, 803,000, 804,000.

"And backwards", says Lucas.

He'll start us off and we'll carry on.

804,000, 803,000, 802,000, 801,000, 800,000, 799,000, 798,000, 797,000, 796,000, 795,000, 794,000.

It really wasn't much harder.

It just took a bit longer 'cause we had to put the thousand on the end of each number.

Over to you to check your understanding.

Knowing what we know about counting and how we can use counting in hundreds to help us count in hundred thousands, can you fill in the missing numbers? Pause the video, have a go, and we'll look at the answers together.

Did you use your counting to help you? 396, 397, but we're counting thousands.

So 396,000, 397,000, 398,000, 399,000, 400,000.

After 399 we get to 400.

We just made it 1,000 times bigger.

Sophia says, "Counting in ten thousands is just as easy as counting in tens! So here's 70 or seven tens, 80 or eight tens".

She says, "Let's carry on".

90 or nine tens, 100 or 10 tens, 110 or 11 tens, 120 or 12 tens, 130, 13 tens, 140, 14 tens, 150, 15 tens, 160, 16 tens, 170, 17 tens.

"And backwards", says Lucas.

So we're starting with 170, or 17 tens, 160, or 16 tens, 150, or 15 tens, 140, 14 tens, 130, 13 tens, 120, 12 tens, 110, 11 tens, 100, 10 tens, 90 is nine tens, 80, eight tens and 70 is seven tens.

Whew.

That was a lot of counting! "Once again though", Sophia says, "We can make each number 1,000 times the size.

So we can think about counting in 70,000 or seven 10 thousands.

80,000 or eight 10 thousands.

Let's carry on again".

90,000 or nine 10 thousands.

100,000, ten 10,000s.

110,000, eleven 10,000s.

120,000, twelve 10,000s.

130,000, thirteen 10,000s.

140,000, fourteen, 10,000s.

150,000, fifteen 10,000s.

160,000, sixteen 10,000s.

170,000, seventeen 10,000s.

Oh, Lucas, "And backwards!" again.

Are you ready? (chuckles) Here we go.

170,000 or seventeen 10,000s.

160,000 or sixteen 10,000s.

150,000 or fifteen 10,000s.

140,000, fourteen 10,000s.

130,000, thirteen 10,000s.

120,000, twelve 10,000s.

110,000, eleven 10,000s.

100,000, ten 10,000s.

90,000, nine 10,000s 80,000 is eight 10,000s.

70,000, seven 10,000s.

Phew.

Wow.

I'm exhausted after all that counting.

Are you? Oh, time for a bit of a break.

Let's check your understanding.

Can you fill in the missing numbers in this counting sequence? Use the counting that we've just done to help you.

Pause the video and then we'll have a look at the answers.

How did you get on? What do you think the gaps are? So if we're counting up 540,000, 550,000, 560,000, 570,000, 580,000, 590,000, 600,000.

Well done.

Time for you to do some practise and maybe a break from all the counting, although you might use counting to help you here.

Fill in the missing numbers in these sequences of numbers.

And remember, the gaps are the same each time.

We're counting in equal steps.

And Sophia says, "What do you notice?" Have a look at the numbers.

What changes? What stays the same? And for question two, Lucas is counting forwards in steps of 10,000 from zero.

Tick all the numbers that he will say in his count.

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

How did you get on? You were asked to fill in the missing numbers here.

So 8,000, 9,000, 10,000, 11,000, 12,000, 13,000.

And then did you notice 80,000, 90,000.

Can you see something that's the same? So we were counting in steps of 1,000.

Now we're counting in steps of 10,000.

80,000, 90,000, 100,000.

110,000, 120,000, 130,000.

So let's look at B.

Again, we were counting in constant size steps each time for each sequence.

Can you see some numbers repeating? Hmm.

Let's have a look.

So in the first row, we were counting from 77,000 and we had a gap, and then 79,000, so our thousands number is changing.

So 77,000, 78,000, 79,000, 80,000, 81,000, 82,000.

In the second row, we still had lots of sevens there, but this time we had 707,000, 709,000.

So we're still counting in thousands, but this time, rather than it being 77, it's 707,000.

So let's fill in those gaps.

707,000, 708,000, 709,000, 710,000, and then 711,000, 712,000.

What about the bottom row? We've got our 700,000 again, but this time we've got seven 10,000s as well.

So this time, instead of counting in steps of 1,000, we're counting in steps of 10,000.

So 770,000, 780,000, 790,000, 800,000, 810,000, 820,000.

So what about C? We're starting with 940,000 and we end on 880,000.

So I think we must be counting down this time.

So 940,000, we've got 910,000.

Should we try counting in 10,000 backwards? 940,000, 930,000, 920,000, 910,000, 900,000, 890,000, 880,000.

And the second row, we've still got a nine and a four.

We've got 900,000, but this time we've got 904,000.

So we've got thousands and we're counting down through 901,000 to 898,000.

So this time we're counting in steps of 1,000.

Let's count together.

904,000, 903,000, 902,000, 901,000, 900,000, 899,000, 898,000.

And what about the last one? Well, this time we've got 94,000.

We've got nine 10,000s and four 1,000s, and we're counting down through 91,000 to 88,000.

So it looks like steps of 1,000 this time again.

Let's try.

94,000, 93,000, 92,000, 91,000, 90,000, 89,000, 88,000.

And Sophia asked us what we noticed as we were counting.

I wonder what she spotted? I wonder what you spotted? She spotted that, "When you don't cross a boundary, only one digit changes".

A boundary is when we cross a whole number of thousands or a whole number of 10,000s or a whole number of 100,000s.

When we don't cross the boundary, only one digit changes.

So if we look at A, 8,000, 9,000, then we cross the boundary from 1,000s into 10,000s.

So one digit changes from 8,000 to 9,000, but then two digits change from 9,000 to 10,000.

And then only one digit changes again.

She says, "However, if you do cross a boundary, at least two digits change".

So if you look at where we counted in C, from 900,000 down to 890,000, our 900,000 changed to 890,000.

So two of the digits changed at that point.

Those are the tricky points where we really have to think about what's happening with our numbers.

Thinking about how many digits changes is really useful.

And in part two, Lucas is counting forwards in steps of 10,000 from zero.

So tick all the numbers that he will say.

So the numbers will all be multiples of 10,000.

So 90,000, 140,000, which is 14 lots of 10,000.

100,000, 10 lots of 10,000.

120,000, which is 12 lots of 10,000.

And 110,000, which is 11 lots of 10,000.

All the other numbers have numbers of single thousands in there, which are not multiples of 10,000.

I hope you spotted those.

And into part two of our lesson where we're going to be counting from any number.

Sophia and Lucas are playing a game called The Thousand Pound Count.

This sounds exciting.

There's lots of information so we need to pay attention here I think.

Each player has to answer a question.

If they get the question wrong, their opponent has 10 seconds to count their money down.

Wow.

If they get their question right, they get 10 seconds to count their money up.

Wow, I like the sound of this game.

They roll a dice to decide which multiple they have to count in.

So if they roll a one, they count in multiples of one.

A two, they count in multiples of 10, a three, they count in multiples of 100, a four, they count in multiples of 1,000, a five, they count in multiples of 10,000, and a six, they count in multiples of 100,000.

Gosh, I'd like to get a question right and be able to count my money up in multiples of 100,000 pounds.

That would be exciting, wouldn't it? If there is an incorrect count, so if they get their counting wrong, then the players turn finishes and their score sticks at the last correct value they said.

The winner is the person with the most money after five turns each.

This sounds like a good game.

Sophia and Lucas start playing the game.

They each start with 1,000 pounds.

Sophia says, "Okay, first question, name the first five square numbers".

Lucas says, "Easy! 1, 4, 9, 16, and 25".

Is he right? She says "Yes, correct.

Okay, roll the dice".

Lucas has rolled and he's counting in multiples of 10,000.

'cause he rolled a five.

"Okay, 10 seconds starts now.

you are counting up from 1,000 in 10,000s".

Let's see Lucas's count.

So 1,000, count on 10, 11,000, 21,000, 31,000, 41,000, 51,000, 61,000, 71,000.

And that's as far as he got in 10 seconds.

"Time! Wow, 71,000! You've got loads of money now", says Sophia.

So yes, his totals shot up to 71,000 pounds.

Well done, Lucas.

"Okay", says Lucas, "your turn".

True or false? An odd number plus an even number gives you an even number? "Er, false," says Sophia, "it gives you an odd number".

An odd plus an even would always give you an odd number.

Well done, Sophia.

"Correct", he says, "okay, roll the dice".

She rolls a four.

So she's counting multiples of 1,000.

"Okay, your 10 seconds starts now.

You can count up from 1,000 in multiples of 1,000".

Let's see how quickly Sophia can count.

1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, 11,000, 12,000, 13,000.

"Time!" says Lucas.

I'm not sure I counted exactly for 10 seconds there.

I hope you weren't timing me.

Anyway, Lucas says time.

"You said more numbers in 10 seconds than I did, but still have less money".

Oh dear.

Well that was 'cause she was counting in 1,000s and not 10 thousands, wasn't she? But she still has increased her score to 13,000 pounds.

"Okay, back to you", she says.

True or false: 10 thousands are equivalent to 1,000 hundreds? Hmm.

Have a think about that.

10 thousands are equivalent to 1,000 hundreds.

"I think that's true." says Lucas.

"Incorrect!" says Sophia.

It's 100,000.

Yes, 1,000 hundreds is the same as 100,000.

Oh dear.

She says, "Roll the dice, I hope he's not too big!" because she's going to count his score down now because he was incorrect.

He's rolled a two.

Multiples of 10.

"Oh, lucky you", says Sophia, "I only get to count down in tens".

"Okay", says Lucas, "your 10 seconds starts now.

You are counting back from 71,000 in steps of 10".

I wonder how far you'd get in 10 seconds? Let's see how far Sophia gets.

71,000, 70,990, 70,980, 70,970, 70,960, 70,950, 70,940, 70,930, 70,920, 70,910, 70,900, 69,890.

"Stop! You counted down 1,010 in the last step", he says.

Can you see that? She was only counting in multiples of 10, wasn't she? So she only needed to count back to 70,890, but she took away another 1,000.

Lucas says, "So my last score is the correct last count you did".

So that was 70,900.

So his score has gone down, but not by that much.

"Okay, it's your turn again", said Sophia.

So Lucas is going to ask her a question.

Well, here's a true false question.

One kilogramme of feathers is lighter than one kilogramme of stones? Hmm.

"Nice try!" Said Sophia.

"That's false.

They have the same mass".

One kilogramme and 1,000 grammes, whatever it is, will have the same mass, won't they? There'll be a lot of feathers though to weigh a kilogramme.

"Ah, you got me!" says Lucas.

"Roll the dice then".

Oh, she's got a five.

Multiples of 10,000.

"Another chance to get back into this", says Sophia.

So she's going to be able to count her score up in multiples of 10,000.

"Okay, your ten seconds starts now.

Count on in multiples of 10,000 from 13,000.

No mistakes!" says Lucas.

Go on, Sophia.

"13,000, 23,000, 33,000, 43,000, 53,000, 63,000, 73,000, 83,000, 93,000, 100,000", says Sophia.

"Stop!" says Lucas.

"After 93,000, it's 103,000.

You forgot about the 3,000".

So she added on 7,000 of her 10,000, but forgot the other 3,000, didn't she? Good spot, but just into the lead now.

So she's got 93,000 pounds now in her score.

Time to check your understanding.

For Lucas' next turn he got his question right and he counted on in multiples of 100.

So tick the numbers he could have finished on.

Remember, his starting number was 70,900.

So what numbers could he have finished on counting on in multiples of 100? So pause the video, have a go, and we'll come back for some feedback.

What did you reckon? What numbers could he have finished on? Well, he could have finished on anything that is a multiple of 100.

B, has a 30 in it, he wasn't counting in multiples of 10, and C, has a three in it, he wasn't counting in multiples of one.

So 72,300 and 72,000 were the only two numbers in that list that he could have finished on.

Okay, time to check again.

For Sophia's next go, she finished on 793,000.

So what multiple did she count in? Pause the video, have a think, and we'll come back for some feedback.

Sophia says, "Technically, it could have been any multiple from 1 to 100,000, however in the ten second time limit, it would have to have been multiples of 100,000".

She wouldn't have had time to count up all that in anything other than multiples of 100,000.

I hope you worked that one out.

Perhaps you also spotted that it could have been any of them, but not in the 10 seconds.

Time for you to have some practise.

You are going to play the game yourself with a partner.

So you'll need a dice and you might want to spend a few minutes down some mathsey questions to ask each other before you start playing the game.

It's difficult to make them up on the spot, isn't it? So we suggest that you start with 1,000 pounds each.

But Sophia says, when you've had a go, have a think.

"How could you make the game even more challenging?" So have a go at the game and then think about how you could make it more challenging.

Pause the video, have a go, and we'll come back and discuss what you did.

Did you have fun playing the game? I hope you did.

Sophia says to make it more challenging, "You could have started on any number you like".

We gave you 1,000, which meant that you were counting up from quite a friendly starting number.

But you could have started with any number you like.

Lucas says, "You could have rolled the dice twice and had to count back in a combination of two multiples".

For example, you could have rolled a five and a one.

So you might have had to count backwards in steps of 10,001 or something like that.

So different ways you could have made the game more challenging.

But I hope you've enjoyed counting on and back from any number in the context of our game.

And we've come to the end of our lesson counting forwards and backwards in powers of 10 to and from any multiple of 1,000.

What have we learned today? You can use your understanding of counting in ones and tens to help you count in multiples of 1,000 or 10,000.

When you don't cross a boundary only one digit changes each time.

Remember those boundaries were where we went from one multiple of 1,000 or 10,000 or a 100,000 into the next one.

And when you do cross a boundary, two or more digits may change depending on what your starting number is.

Those are the bits to focus on.

They can take a little bit more thinking to work out what number we're jumping to.

Thank you for all your hard work in this lesson.

I hope you enjoyed playing the game, and I hope I get to see you in another lesson soon.

Bye-Bye.