Lesson video

Hello.

How are you today? My name is Dr.

Shorrock.

I am so happy to be learning maths with you today.

You have made a great choice to learn maths with me and I'm here to guide you through the learning.

Today's lesson is from the unit, "Understand Place Value within Numbers "with up to Eight Digits." This lesson is called "Powers of 10 and their Multiples." As we move through the learning today, we will deepen our understanding of what these powers of 10 are and the relationships between them.

Especially considering 1 million and 10 million.

New learning can sometimes be a little bit tricky, but I know if we work really hard together and I'm here to guide you, then we can be successful in our learning.

So let's get started then, shall we? How can we identify and explain patterns in powers of 10? These are the key words for our learning today.

We have power of 10 and we have million.

You may have heard those terms before, but let's practise them anyway, shall we? My turn.

Power of 10.

Your turn.

Nice.

My turn, million, your turn.

Fantastic.

Now a power of 10 is when 10 is multiplied by itself a certain number of times.

Some examples of some powers of 10 are 0.

1, 100 and 1 million.

And 1 million is composed of 1000 thousands.

And we can write that as an equation.

1000 multiplied by 1000 is equal to 1 million, and we write 1 million as a one followed by six zeros.

Let's start our learning today by considering these powers of 10.

And in this lesson we have Laura and Jacob to help us.

Did you know? Birmingham is the second largest city in the UK.

I wonder if that's where you live.

There are about 1,000,000 people living there.

Oh, thank you, Jacob.

1,000,000 is read as 1 million.

So we could say that there are about 1 million people living in Birmingham.

1 million is a large number, you're right, Laura.

Did you know that we can count up to 100 in about a minute? Maybe try that at some point, but if we wanted to try to count in ones to 1 million, it would take about one month.

Wow! I wonder what 1 million looks like.

What do you think? And Laura is doing a 1000 piece jigsaw puzzle at the moment.

I wonder if that is something that you like to do and she makes a connection between this 1000 piece jigsaw puzzle and 1 million.

She would need 1000, 1000 piece jigsaws to have 1 million pieces.

Wow, that is a lot of pieces.

We can use Base 10 blocks to help her see 1 million.

Did you know that the small ones block has a length of one centimetre? So if we put 100 of the ones blocks together, they would measure 100 centimetres in length or one metre.

We could then make a cube that had one metre dimensions to one metre length, one metre width, and one metre depth.

And if we did that 1 million Base 10 blocks to fit inside the cube.

Wow, we can represent 1 million on a place value chart.

Take a look.

What do you notice? Do you notice that 1 million is one more thousand than 999,000? We know that if we add one to 999 we get 1000.

So if we add 1000 to 999,000, we must get 1000 thousands.

And we know 1000 thousands is the same as 1 million.

1 million is 1000 thousands.

Let's look at a place value chart where we have got the decimal fractional part of a number.

And Laura is saying, "Did you know that the headings in a place value chart "are the powers of 10?" And if you can remember, that's what we're learning about in this part of the lesson.

The powers of 10.

So the headings are the powers of 10.

So you've got ones, tens, hundreds, one thousand, ten thousand, hundred thousand, 1 million, 10 million, 100 millions, and you've got one 10th and 100th.

They are the powers of 10.

Each column is 10 times the value of the column to its right.

And that means that each power of 10 is equal to one group of 10 of the previous smaller power of 10.

So for example, 1000 is equal to one group of 10 hundreds.

10 hundreds are equal to 1000.

And we can use this knowledge to make connections between numbers.

The digit one becomes 10 times the size as it moves one place to the left.

We can say that 1000 is 10 times the size of 100.

I wonder if you could notice any other connections between those numbers.

Let's now look at the connection between 100,000 and 1 million.

We can say that 1 million is 10 times the size of 100,000.

That digit one has moved one place, value place to the left, hasn't it? So it means that number 1 million is 10 times the size of 100,000.

And we can write that as an equation.

1 million is equal to 100,000 multiplied by 10.

But we could also look at it the other way round.

And we could say 100,000 is one-tenth times the size of 1 million 'cause to go from 1 million to 100,000, the digit one moves one place value place to the right.

So it's become 10 times smaller or one 10th times the size.

And we can write that as an equation and we can represent that with place value counters.

We would need 10 one hundred thousands place value counters to equal 1 million.

Let's look at the relationship between 1 million and 10 million now on a place value chart.

Did you notice that 10 million is 10 times the size of 1 million? That digit one has moved one place value place to the left? We can represent this as an equation.

10 million is equal to 1 million multiplied by 10.

And if we look at it the other way round, we can compare 1 million to 10 million and say that 1 million is one-tenth times the size of 10 million.

And we can write that as an equation.

1 million is equal to 10 million multiplied by one-tenth.

And we can represent that using place value counters and we would need 10 one million place value counters to equal 10 million.

Let's check your understanding with this.

Could you complete the sentences using the place value chart to help you? 1 million is 10 times the size of mm.

And 10 million is 10 times the size of mm.

Pause the video while you do that, maybe compare your thoughts with somebody else.

And when you're ready to go through the answers, press play.

How did you get on? Did you say that 1 million is 10 times the size of 100,000 and 10 million is 10 times the size of 1 million? Fantastic.

Well done.

Let's remove the place value chart.

Ooh, what do you notice? That's right, Jacob.

The numbers are harder to read without place value headings, aren't they? So what can we do? That's right.

We can use commas and the decimal point to help us read the numbers.

So let's pop those commas in and let's practise reading these powers of 10 from the top to the bottom.

Are you ready to read with me? One hundredth, one tenth, one, 10, 100, 1000, 10,000, 100,000, 1 million, 10 million.

Now let's read from bottom to top.

Are you ready to read with me? 10 million, 1 million, 100,000, 10,000, 1000, 100, 10, one, one tenth, one hundredth.

Have you noticed anything about those powers of 10? That's right.

Thank you, Jacob.

As we read from top to bottom, the powers of 10 get 10 times the size, and as we read from bottom to top, the powers of 10 get one-tenth times the size.

Well done, if you spotted that.

Let's check your understanding with this.

Could you match the numeral to its word? So we've got 1,000,000.

Then we've got 10,000.

And then we've got 0.

1, and then we've got 10,000,000.

And then the numbers, you have one tenth, ten million, one million and ten thousand.

So if you could match the neural to its number word.

Pause the video while you do that.

When you're ready to hear the answers, press play.

How did you get on? Did you say that one followed by six zeroes is equal to one million? One and four zeroes is ten thousand.

0.

1 is the same as one tenth and the 10 and six zeroes is ten million.

Well done.

Your turn to practise now for question one.

Could you write these powers of 10 that I've given you in words as numerals? And for question two, could you write these numerals as number words? For question three, could you make some cards that you could use to remind yourself of the patterns and relationships between the powers of 10? I'd like you to make your cards up and then put them back in order.

And then could you work in a pair? One of you could read half the sentence and the other complete the sentence.

And then could you put these cards into two piles? Facts you know and facts you do not know.

And then you could draw some tens frame to support you to learn the facts that you do not know.

Here is an example of some of the cards that I made.

Pause the video while you have a go at questions one, two, and three.

And when you are ready to go through the answers, press play.

How did you get on with those? Let's have a look.

For question one you were asked to write these powers of 10 that were given in number words as numerals.

One million, well that's one and six zeros.

10 million must then be 10 and six zeros.

Ten thousand is a 10, and then three zeros.

One hundred thousand, well you've got 100 and then three zeros.

For question two, you were asked to write these numerals as number words.

One thousand, one hundred thousand, ten million and one million.

For question three, you were asked to make some cards that you could use to remind yourself of the patterns and relationships between the powers of 10, and then to mix them up and put them back in order.

And then you might have worked in a pair where one of you read half the sentence like Laura is doing here, "10 ten thousands are equivalent to," and then the other completes the sentence.

So Jacob would say, "One hundred thousand." And then you might have put the cards into two piles.

Facts she knew and facts she did not know.

And then drawn some 10 frames to help you to learn the facts that you do not know.

How did you get on with those questions? Well done.

Fantastic learning so far.

You have really deepened your understanding of what these powers of 10 are.

We are going to move on now and look at multiples of powers of 10.

So let's count up in 100,000s.

Are you ready to count with me? Zero, 100,000, 200,000, 300,000, 400,000.

Wait for it.

500,000, 600,000, 700,000.

Oh, did you notice that? We're back counting back down, aren't we? 600,000, 500,000, 400,000.

Here we go.

Watch for the change.

500,000, 600,000, 700,000, 800,000, 900,000, 1,000,000.

And we know that 10 one hundred thousands are equal to 1 million.

So after 900,000, we could say 1,000,000 or we could say 1 million.

We know 1 million is 10 times the size of 100,000 because that digit one has moved one place value place to the left.

100,000 we can also say is one-tenth times the size of 1 million is 10 times smaller.

Let's count up in 1 million now, shall we? Watch out, make sure you count with me.

Are you ready? Zero, 1 million, 2 million, 3 million.

Wait for it.

4 million, 5 million.

Wait for it.

6 million, 7 million.

Ooh, did you notice we've counted down now 6 million, 5 million, 4 million and back up 5 million, 6 million, 7 million, 8 million, 9 million and 10 million.

10 one millions are equal to 10 million.

And we can say 10 million is 10 times the size of 1 million.

And that 1 million is one-tenth times the size of 10 million.

We can also count up in steps of 1 million using a number line.

Are you ready to count with me? So zero, 1 million, 2 million, 3 million, 4 million, 5 million.

Wait for it, 6 million, 7 million, 8 million and back down 7 million, 6 million, 5 million and back up, 6 million, 7 million, 8 million, 9 million, 10 million.

We can also count using the numerals.

Are you ready to count with me? Zero, 1 million, 2 million.

Wait for it.

3 million, 4 million, (gasps) back down, 3 million, 2 million, 1 million, back up, 2 million, 3 million, 4 million, 5 million, 6 million.

Wait for it.

7 million, 8 million, 9 million, 10 million.

We can also use a Gattegno chart to help us count in multiples of powers of 10.

So our powers of 10 are shaded in green on the left hand side and the multiples of the powers of 10 are the other numbers as we count up in the steps of the powers of 10.

So let's start with 0.

1.

The next multiple of 0.

1 is 0.

2.

The next multiple of 0.

1 would be 0.

3.

Count with me, 0.

4, 0.

5, 0.

6, 0.

7, 0.

8, 0.

9.

They're all multiples of the power of 10, 0.

1.

Let's count up in multiples of 1 million.

Are you ready to count with me? 1 million, 2 million, 3 million, 4 million, 5 million, 6 million, 7 million, 8 million, 9 million.

So we can use this Gattegno chart to help us count up in multiples of our powers of 10.

Let's check your understanding with this.

If we count up in 10 millions, what number will we say after 50 million? Pause the video while you have a think about that.

Maybe confirm your answer with somebody else.

When you are ready to hear the answer, press play.

Did you say that it would be 60 million? Because if we count in 10 millions, 10 million more than 50 million is 60 million.

Because 10 more than 50 is 60, isn't it? So 10 million more than 50 million must be 60 million.

How did you get on with that? Brilliant.

Jacob and Laura use place value counters.

Laura is telling us that she has 18 one hundred thousand place value counters.

Can you visualise that? Having 18 counters? Each worth 100,000? And Jacob is saying then that she must have 18 hundred thousands because she's got 18 lots of 100,000.

Good question, Laura.

How would we write 18 hundred thousands as a numeral? Ah, good idea.

Let's use some partitioning to help us.

We can partition 18 hundred thousand.

We can partition 18 hundred thousand into 10 hundred thousand and 800,000 and we know 1,000 thousands are the same for the next power of 10 or 1 million and we would then have another 800,000.

So we can say that 1800 thousand is written as 1,800,000 and Laura summarises that for us.

If we have more than 10 of a given power of 10, we need to restate the quantity and the appropriate power of 10 because we don't normally have more than the value of nine of any given digit, do we before we then move to the next power of 10? So 18 hundred thousand is equivalent to 1,800,000.

We have restated the 18 hundred thousand in the power of 10, 1 million and 800,000.

Let's check your understanding with that.

Could you use partitioning to support you and write 16 hundred thousand in the appropriate power of 10? Pause the video while you have a go.

Maybe compare your answers to somebody else.

And when you are ready to go through the answer, press play.

How did you get on? Did you use partitioning to partition 16 hundred thousand into 10 hundred thousand, which is equal to 1 million and you had another 600,000 left? 16 hundred thousand is is equivalent to 1,600,000 or a one and a six and then five more zeros.

How did you get on with that? Well done.

We could also use the Gattegno chart to identify relationships between the multiples of the powers of 10.

Remember, the powers of 10 are on the left and they are shaded in green.

If we take a look at one part of the Gattegno chart, Laura and Jacob are asking each other questions about the powers of 10 and their multiples.

Jacob would like Laura to tell him which number is 10 times bigger than 4 million.

And Laura knows she can use the Gattegno chart to help.

10 times bigger than 4 million is 40 million.

Each column in the Gattegno chart, each row above is 10 times the value, 10 times the size.

10 times bigger than 4 million is 40 million.

And we could write that as an equation.

4 million multiplied by 10 is equal to 40 million.

Laura then chooses a number, 30 million, and she wants to know what number is one hundredth times the size of 30 million.

And Jacob knows that he can use the Gattegno chart to help work this out.

One hundredth times the size of 30 million.

Well, he knows he needs to look two rows below.

One, two.

So, 30 million multiplied by 100 is 300,000.

100 times the size of 30 million is 300,000.

Let's check your understanding with that.

Could you use this Gattegno chart to complete the sentences? Mm is 100 times larger than 800,000 and mm is one hundredth times the size of 60 million? Pause the video while you have a go and when you are ready to go through the answers, press play.

How did you get on? Did you say that 80 million is 100 times larger than 800,000 and 600,000 is 100th times the size of 60 million? Well done.

It's your turn to practise now.

For question one, where possible could you work in a pair? I'd like you to use one place value counter for each power of 10.

If you put the counters in a bag, then I would like the first person to pick a counter and count up in those multiples until the next power of 10 is reached.

Then answer the question, how many steps did you count? How many mm are equivalent to the next power of 10? And then take it in turns to repeat this until all your counters have been drawn from the back.

For question two, could you fill in the missing numbers in these sequences? For question three, could you use partitioning to support you and write these values in the appropriate power of 10? 18 hundred, 76 hundred, 13 hundred thousand, 45 hundred thousand, 27 tenths? For question four, could you answer the following questions using a Gattegno chart to support you? A, 50,000 made 1000 times the size is, mm, B, 80 million made one 10th times the size is mm, C, 0.

5 made 1000 times the size is mm, D, 20,000 made 100 times the size is mm.

And a word problem for you.

The distance from Birmingham to London is 160 kilometres.

The distance from Birmingham to Melbourne in Australia is about 100 times as far.

Approximately how far is it from Birmingham to Melbourne? And then to challenge yourself, you could write equations for each of these.

Pause the video while you have a go at these questions and when you are ready to go through the answers, press play.

How did you get on? Let's have a look.

For question one, you needed to work in pairs.

The first person may have picked a count that had 0.

01 on it and counted up in hundredths until they reached the next power of 10.

So 100th, 200th, three hundredths, four hundredths, five hundredths, six hundreds, seven hundredths, eight hundredths, nine hundredths, 10 hundredths, or 0.

1.

And you might have noted that you counted 10 steps each time and that ten one hundredths made the next power of 10 or 0.

1.

The next person may then have picked a counter that had 100,000 on it and repeated the above, counting up though this time in multiples of 100,000 and each time there would've been 10 steps to count up in because each power of 10 is equal to one group of 10 of the previous smaller power of 10.

For question two, you need to fill in the missing numbers in these sequences, 40 million, 50 million, 60 million, 70 million.

For part B, 6 million, 7 million, 8 million, 9 million.

For part C, 19 million, 18 million, 17 million, 16 million.

For part D, four tenths, five tenths, six tenths, seven tenths or 0.

7 and eight tenths.

Nine hundredths, eight hundredths, seven hundredths, six hundredths.

For question three, you needed to use partitioning to support you to write these values in the appropriate power of 10.

1800.

Well, we've got 1,800 because 10 hundreds are equal to 1000 and then you had eight more hundreds.

76 hundred would be equal to 7,600 because 70 hundreds would be equal to 7,000 and then you have six more hundreds left over.

1300 thousand would be equal to 1,300,000 because 1,000 thousands are equal to 1 million.

45 hundred thousand would be 4,500,000 because your 40 hundred thousands will be equivalent to 4 million and you would have 500 thousands left over and 27 tenths, well, this will be equivalent to two ones and seven tenths, so 2.

7.

For question four, you had to answer the following questions using a Gattegno chart to help.

50,000 made 1000 times the size would be 50 million.

80 million made one 10th times the size is 8 million.

0.

5 made 1000 times the size is 500.

20,000 made 100 times the size is 2 million.

And then the word problem, the distance from Birmingham to London is about 160 kilometres.

Well, if we make that 100 times the size, we'd get 16,000.

So it's about 16,000 kilometres from Birmingham to Melbourne.

You then may have challenged yourself to write equations for each of these.

Part A, 50,000 times 1000 is 50 million.

For part B, 80 million times one 10th would be 8 million.

Part C, 0.

5 multiplied by 1000 will be equal to 500.

For part D, 20,000 multiplied by 100 is 2 million.

And then the distance question you would have 160 multiplied by 100 is 16,000.

How did you get on with those questions? Well done.

Fantastic learning.

I'm really impressed with how you have deepened your understanding of the powers of 10 and their multiples.

We now know that 1 million is composed of 1000 thousands and we know that the powers of 10 are the column headings in a place value chart, and each column is 10 times the value of the column to its right.

I have really enjoyed my time learning with you today as I look forward to learning with you again soon.