Lesson video

Hello, how are you today? My name is Dr.

Sharik, and I'm really excited to be learning with you today.

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

Today's lesson is from our unit, "Calculating with decimal fractions." The lesson is called "Explain how to multiply and divide a number by 10, 100, and 1000." As we move through the learning today, we will deepen our understanding of multiplying and dividing by 10 and its powers.

We are going to look at including the use of decimal fractions and those which have got two decimal places.

Throughout the lesson today, we will use place value charts and Gattegno charts to help us make connections in our learning.

Sometimes new learning can be a little bit tricky.

But remember, if we work really hard together, and I am here to guide you, then I know that we can be successful in our learning.

Let's get started, shall we? So how can we explain how to multiply and divide a number by 10, 100, and 1000? These are the key words that we will use in our learning today.

We've got to tenth, hundredth, and thousandth.

You've probably heard those words before, but it's always good to practise them.

So my turn, tenth.

Your turn.

Nice.

My turn, hundredth.

Your turn.

Fantastic.

And my turn, thousandth.

Your turn.

Brilliant.

So when we talk about one-tenth, we mean it's one part in 10 equal parts.

One-hundredth is a part in 100 equal parts.

And one-thousandth is one part in 1000 equal parts.

Look out for those key words as we move through our learning today.

We will start today's learning by looking at how to multiply and divide by 10, 100, and 1000.

And in this lesson, we have Lucas and Sofia to help us.

"Lucas and Sofia are playing a game with a Gattegno chart.

Lucas represents a number by shading two boxes." There we go.

"If Sofia identifies the number, successfully divides it by 100, colours the boxes of her product and writes the matching equation, she will get four points." I wonder if you have already identified the number.

Let's look at that part of the Gattegno chart.

Sofia is telling us, "The number Lucas chose is 25." We can see 20 is shaded and 5 is shaded.

And if we recombine 20 and 5, we get 25.

When we divide by 100, we're making a number 100 times smaller.

So Sofia has formed an equation 25 divided by 100.

And when we make a number 100 times smaller on the Gattegno chart, we move down two rows.

So Sofia needs to move the 20 down and the 5 down two rows.

25 divided by 100, well, Sofia can see then from the Gattegno chart that that is 0.

25.

25 made 100 times smaller is 0.

25.

The 20 made 100 times smaller with 0.

2, two tenths.

The 5 made 100 times smaller with 0.

05, or five hundredths.

If we recombine 0.

2 and 0.

05, we get 0.

25.

Lucas agrees with what Sofia has done, so she gets all four points.

Well done, Sofia.

You could also have proved this on a place value chart.

We started with 25, so 2 tens and five 1s dividing by 100 is equivalent to multiplying by 0.

01, and we could form that as an equation.

And when we multiply by 0.

01, the digits move two places to the right, and so 25 made 100 times smaller is 0.

25.

And we can form an equation there to help us.

We can show the equivalence between 25 divided by 100.

Well that's 25 times 0.

01, which has a value of 0.

25.

The children then change roles, and Sofia represents a number by shading two boxes.

Can you tell what Sofia's number is? If Lucas identifies the number and then multiplies it by 1000, and then colours the boxes of his number and writes the equation, he will get four points this time.

Let's look at that part of the Gattegno chart.

Lucas is saying, "The number Sofia chose is 0.

37." Do you agree? Let's have a look.

Well the 0.

3 is shaded and the 0.

07 is shaded.

We've got 0.

3 and 0.

07.

If we recombine those, we do get 0.

37, and Lucas can form an equation to help him multiply by 1000.

And we know that when we make a number 1000 times larger on the Gattegno chart, we move up three rows.

So Lucas needs to move the 0.

3 and the 0.

07 up three rows, 0.

37 made 1000 times large is 370.

We can see 0.

3 made 1000 times larger is 300, and the 0.

07 made 1000 times larger is 70.

Sofia agrees, so he gets all four points.

Well done, Lucas.

Aha, yes.

He could also have proved this on a place value chart.

We started with 0.

37, so 3 tenths and 7 hundredths.

When multiplying by 1000, the digits move three places to the left.

1, 2, 3, and that would be 370.

So 0.

37 multiplied by 100 is equal to 370.

Let's check your understanding on this.

"Lucas thinks of a number.

His number is highlighted in the Gattegno chart." Can you see which number is highlighted? And then I would like you to look at the equations, A, B, C, and D, and tell me which equation shows dividing his number by 10.

Pause the video, maybe chat to someone about this and compare your thoughts, and when you are ready to go through the answers, press play.

How did you get on? Well it couldn't be A, because A is 7.

04.

We haven't got 7.

04, we've got 7.

4.

We've got 7 ones and 4 tenths.

What about b? Well it can't be b because the answer is the same as the starting number, 7.

4.

We haven't moved the digits.

C? Well, it can't be C.

We are dividing 7.

4 by 10, but when we divide by 10, it's not the same as multiplying by 0.

01.

It should be the same as multiplying as 0.

1 as in equation D.

Did you get equation D? Well done.

Sofia and Lucas then discussed this equation, 90 divided by 10 is equal to 9.

And Lucas is saying, "Well, I've removed the zero from 90 to divide by 10." Can you see why he thinks that? And Sofia is saying, "But does that always work?" Can we always just remove the zero? "Yes!", Lucas says, "Let's look at a different example." Now do you agree with Lucas? Do you think he's right? Can we always just remove the zero? 0.

09 divided by 10 is equal to 0.

9.

Can you see Lucas has just removed the zero from the tenth place, from 0.

09 to divide by 10.

Can he do that? Ah, Sofia is respectfully challenging Lucas.

Sofia is reminding Lucas that when we divide a number by 10, it is equivalent to multiplying by 0.

1.

So the digit will move one place to the right.

The answer should be 0.

009.

So you can't just remove a zero.

You need to make sure that the digit has moved places.

It will have a different value.

Ah, Lucas has seen that now, so he's now supporting Sofia.

His original answer was greater than his starting number.

0.

9 is greater than 0.

09, isn't it? But we were divided by 10, so it should have been smaller, 10 times smaller.

Let's check your understanding.

Look at this equation.

0.

03 divided by 10 is equal to 0.

03.

Is that true or false? Pause the video, and when you're ready to hear, press play.

Did you work out that that was false? But why is it false? Is it because a, "When we divide by 10, we remove a zero, but, in this case, we need to leave the zero in the ones place.

The answer should be 0.

3."? Or should it be, "When we divide by 10, the digits move one place to the right.

The answer should be 0.

003." Pause the video, maybe chat to someone about this.

See what you think, and when you're ready to hear the answer, press play.

How did you get on? Did you work out it must be b? When we divide by 10, the digits move one place to the right.

The answer should be 0.

003.

We can't just remove zeros.

We need to move those digits.

Sofia and Lucas then discuss this equation.

25.

34 multiply by 10 is equal to 25.

340.

Lucas is saying that to work that out, he placed the zero onto the end of the number.

That's how he multiplies by 10, popping a zero on the end.

Ah, Sofia is respectfully challenging Lucas again.

Why is that, Sofia? Sofia knows that when we multiply by 10, all the digits move one place to the left.

You can't just pop a zero on the end.

All the digits have to move.

This is because the number becomes 10 times the size.

If the digits don't move, the number doesn't change value.

So it should be 25.

34 multiplied by 10 should be 253.

4.

And Lucas supports Sofia now.

He can see by just placing a zero in the thousandth place, the number remained the same size.

It didn't get 10 times bigger.

Let's check your understanding on that.

True or false, 9.

08 multiplied by 10 is equal to 98? Pause the video while you think about that.

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

How did you get on? Did you realise that was false? But why? Is it a, "When we multiply by ten, all the digits will move one place to the left.

The answer should be 90.

8."? Or is it b, "When we multiply by ten, we place a zero at the end.

The answer should be 9.

080." Pause the video, maybe chat to someone about this, and when you're ready to hear the answers, press play.

How did you get on? Did you say it's a, "When we multiply by ten, all the digits move one place to the left.

The answer should be 90.

8." If we just place a zero at the end, then the value of the number does not change.

Your turn to practise now.

For question one, could you complete the empty boxes? You can see we started with 19 in the middle, but what should be in the other boxes? Be careful.

It might be a number or it might be an operation.

For question two, could you complete the tables deciding if the calculations are correct or not? If any that are incorrect, could you correct them and give reasons to convince me that you are right? And for question three, could you complete the table by filling in the missing boxes? Pause the video while you have a go at all three questions and when you are ready to go through the answers, press play.

How did you get on? We started with 19, and when we divided by 1000, we should get 0.

019.

When we multiply by 100, we get 1,900.

When we divide by 100, we get 0.

19.

When we multiply by 10, we get 190.

When we divide by 10, we get 1.

9.

And when we multiply by 1000, that is equal to 19,000.

For question two, you had to decide if the calculations were correct or not.

So we had 3020 divided by 10.

Well that is 302.

302 divided by 10, well, that is 30.

2.

The digits have moved one place to the right.

For the third question, ah, that's not correct.

If we divide by 10, all the digits, including the zeros, need to move one place.

We can't just remove a zero.

3.

02 divided by 10, the digits have moved one place to the right, so that is correct.

0.

32 divided by 10, the digits have moved one place to the right, so that is correct.

For the second table, 405 multiplied by 10, that is 4050.

4.

05 multiplied by 10, ah, that's not 4.

050.

We can't just place a zero at the end.

The value of that number has not changed.

40.

5 times 10, is that 405? Yes.

And the last one, 0.

405 multiplied by 10, well, that's incorrect.

We can't just remove that zero.

All the digits have to move.

You were then asked to correct any that were incorrect and give reasons.

So we know that when we divide by 10, all the digits move one place to the right.

30.

2 divided by 10 should be equal to 3.

02.

We can't just remove that zero.

And then we have 4.

05 multiplied by 10.

That's not equal to 4.

050.

We can't just place a zero at the end.

When we multiply by 10, all the digits move one place to the left, and the resulting number is 10 times larger.

4.

05 times 10 is 40.

5.

And then 0.

405 times 10, we can't just remove the zero.

We need to move all the digits one place to the left.

The answer should be 4.

05.

For question three, you needed to complete the table by filling in the missing boxes.

46 multiplied by 1000 is 46,000, and divided by 1000 is 0.

046.

60.

2 multiplied by 1000, 60,200, and divided by 1000, 0.

0602.

Hmm, did you notice something? You might have noticed that when 60.

2 is divided by 1000, we get a number that has four decimal places.

This is correct.

The digits all move three places to the right and so the 0.

2 became.

002.

562 multiplied by 1000 is 562,000, divide by 1000 is 0.

562.

And then 14 multiplied by 1000, 14,000, and divide by 1000, 0.

014.

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

Fantastic learning so far.

You should be really proud of how hard you are trying.

We're going to move on now, and we're going to use what we've learned to solve problems. Let's look at this problem.

"Sofia has zero pounds, 61 pence.

Lucas has 100 times this amount of money." Nice.

Can you visualise that? Can you visualise what 61 pence looks like or 0.

61 pounds? And the fact that Lucas has 100 times this amount of money, it's got to be greater, it's 100 times greater.

What might the question be here do you think? I haven't got a question yet.

Ah, that's right.

"How much money does Lucas have?" We can form an equation from this information.

We know Lucas has 100 times the amount of Sofia has, so we need to multiply Sofia's amount by 100.

We've got 0.

61 multiplied by 100.

"When we multiply by 100, we can place two zeros at the end of the number." So Lucas must have 0.

6100.

Ah, Sofia's challenging him.

He can't do that, can he? "I respectfully challenge you," she says.

Do we just place two zeros at the end when we're multiplying by 100? No.

When we multiply by 100, all the digits move two places to the left.

0.

61 made 100 times greater is 61.

Ah, Lucas understands now.

"By just placing zeros at the end, the number remained the same size." So Lucas has 61 pounds, and, "61 pounds is 100 times the size of 61 pence." Let's look at this different problem.

"Sofia's mum wins 3040 pounds in the lottery." Nice.

I'd like to win that amount in the lottery.

Would you? Yes.

"She decides to give one-thousandth of this amount to charity." That's good of her, isn't it? Can you visualise that? Can you visualise that amount of money? And she gives that money to charity, one-thousandth of the amount.

What might the question be, do you think? Hmm.

Ah, "How much money does she give to charity?" Good question.

And we can use this information to form an equation.

"We know the charity are given one-thousandth times the amount that Sofia's mum won, so we need to divide the whole amount by 1000." When we divide by 1000, it is the same as finding one-thousandth times the amount.

And, "When we divide by 1000, it's also equivalent to multiplying by 0.

001," one-thousandth.

And Sofia is supporting Lucas in that statement.

"When we multiply by 0.

001, all the digits move three places to the right." 3040 multiplied by 0.

001, or finding one-thousandth of it, is 3.

04.

So, "Mum gives 3 pounds, 04 pence to charity." 3.

04, "3 pounds 04 pence, is one-thousandth times the size of 3040." Let's check your understanding on this.

Could you complete these sentences? "To find one-thousandth of a number we need to divide by," mm.

"This is the same as multiplying by," mm.

"When we multiply by," mm, "the digits move," mm, "places to the," mm.

Pause the video, maybe talk to someone about these sentences and when you're ready to go through the answers, press play.

How did you get on? Did you complete the sentences to say that, "To find one-thousandth of a number, we need to divide by 1000," and, "This is the same as multiplying by 0.

001." And, "When we multiply by 0.

001, the digits move 3 places to the right." Your turn to practise now.

For question one, could you solve these problems and form an equation to help you? "Sofia buys a bottle of water every day." Can you visualise that? "One bottle costs zero pounds 65." So, "How much has she spent after 100 days?" Part b, "Lucas's school are getting some new play equipment.

FunPlay has said it will cost 7,499 pounds and SnazzyPlay have said they can do it for one-tenth of the cost.

What does SnazzyPlay charge?" And then can you tell me, "How much cheaper is the cost from SnazzyPlay?" For question two, could you solve these problems? "Lucas has 430 pounds in his savings account.

Sofia has one-hundredth of this amount.

Izzy has ten times as much as Sofia.

How much money do they have in total?" and "How much more money does Lucas have than Sofia?" Pause the video while you have a go at those questions, and when you are ready to go through the answers, press play.

How did you get on? Let's have a look at the first problem.

We know Sofia buys a bottle of water every day and one bottle costs 0.

65 pounds or 65 pence.

And she's buying this for 100 days, so we need to multiply by 100.

When we multiply by 100, the digits move two places to the left.

And we know 0.

65, then move two places to the left, is 65.

So Sofia spends 65 pounds over 100 days.

For part b, Lucas's school are getting some new equipment.

We had to work out what do SnazzyPlay charge, and they charge one-tenth that FunPlay charge.

So 7,499 divided by 10 is the same as 7,499 times 0.

1, or finding one-tenth.

When we multiply by 0.

1, the digits move one place to the right.

So that would give us 749.

9.

So SnazzyPlay charge 749 pounds, 90.

We were then asked to find out how much cheaper does it cost from SnazzyPlay.

And I like to represent these things in a bar model.

I can see the whole is 7,499, and one of the parts is 749 pounds 90.

And I have to find the unknown part.

We can then adjust both numbers to help us subtract.

I'm going to adjust both numbers by one, which means the difference will remain the same.

We can then use partitioning to help us.

I'm going to partition the part 750 pounds 90.

I'm going to partition into 500, 250 and 0.

90.

I can then subtract the 500 from 7,500, and then subtract the 250 and the 0.

90, which gives me 6,749 pounds 10.

So SnazzyPlay is 6,749 pounds 10 cheaper than FunPlay.

For question two, we had to solve a problem about Lucas having 430 pounds in his savings account.

Sofia had one-hundredth of the amount, and Izzy, ten times as much as Sofia.

And we had to work out how much money they had in total.

Well to do that, we need to work out what Sofia has got and what Izzy has got.

Let's look at Sofia.

Sofia has one-hundredth of the amount, so we need to divide by 100.

And dividing by 100 is the same as multiplying by 0.

01.

The digits will move two places to the right, so she has 4 pounds 30.

Izzy has 10 times this amount, so we need to multiply 4.

3 by 10, which is 43, or 43 pounds.

We can then add their totals together to get 477 pounds and 30 pence.

For part b, "How much more money does Lucas have than Sofia?" I can represent this in a bar model.

Lucas has 430 pounds.

Sofia has 4 pound 30.

To find the value of the unknown part, we need to subtract, and we can use partitioning.

I can subtract the 4, then I can subtract the 0.

30, which gives me 425 pounds 70.

So Lucas has 425 pounds 70 more than Sofia.

Fantastic learning today, everybody.

Really impressed with the progress that you have made.

We know that when we multiply by 10, 100, or 1000, the digits move one, two, or three places to the left, respectively.

We also know that when we divide by 10, 100, or 1000, the digits move one, two, or three places to the right, respectively.

I am really impressed with how hard you have worked today.

I've had a lot of fun learning with you, and I look forward to seeing you again soon.