Lesson video

(birds chirping) <v ->Hello, how are you today?</v> My name is Dr.

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

We are gonna have great fun as we move through the learning together.

Today's lesson is from our unit calculating with decimal fractions.

The lesson is called explain the effect of multiplying and dividing a number by 10, 100 and 1000, including bridging 1.

As we move through the learning today, we will deepen our understanding of multiplying and dividing by 10, 100 and 1000 and thinking about what happens when we bridge 1, so when we have to calculate with decimal fractions.

Throughout the lesson, we will use a place value chart and the Gattegno chart to support us to make connections in our learning.

Sometimes new learning can be a little bit tricky, but I know if we work really hard together and I am here to guide you, then we can be successful.

So shall we get started? Let's find out.

How do we explain the effects of multiplying and dividing a number by 10, 100 and 1000 including bridging 1.

These are the key words that we will use in our learning today, tenth, hundredth and thousandth.

I'm sure you've heard those words before, but let's practise them anyway.

My turn tenth, your turn.

Nice.

My turn, hundredth, your turn.

Lovely.

My turn, thousandth, your turn.

Fantastic and really see those tongues when you do the th part at the end.

One-tenth is one part in 10 equal parts.

One-hundredth is one part in 100 equal parts.

And one-thousandth is one part in 1,000 equal parts.

Look out for those keywords as we move through the learning today.

We are going to start our learning today thinking about how we divide by 10, 100 or 1,000.

We have Lucas and Sophia to guide us through the learning.

Right, let's have a look at this then.

Sophia is thinking of a number.

She wants Lucas to guess her number and gives him a clue.

Sophia's clue is, "My number is one-hundredth times the size of eight".

Hmm.

I wonder if you might be able to work out what that is.

Can you visualise what that means? Ah, so Lucas knows that to find the number, he needs to divide eight by 100, because the number Sophia is thinking of is one-hundredth times the size.

So he needs to divide eight by 100.

Lucas is going to use some derived facts to help, he knows one divided by 100 is equal to one-hundredth.

So two divided by 100 must be two hundredths.

Three divided by 100 must be three hundredths.

Four divided by 100 must be four hundredths.

I wonder if you can tell what's coming next.

That's right, five divided by 100 is five hundredths.

Six divided by 100 is six hundredths.

Seven divided by 100 is seven hundredths.

What does that mean? What's next in the pattern? That's right, eight divided by 100 is eight hundredths.

Let's look at this on a Gattegno chart, we can see the starting number is eight and we can divide by 100, which means we need to look down two rows on the Gattegno chart.

Eight divided by 100 is equal to 0.

08.

0.

08 is one-hundredth times the size of eight.

And we can use a place value chart as well to help.

We know when a number is divided by 100 the digits move two places to the right.

One, two.

So eight divided by 100 is equal to 0.

08.

Dividing by 100 makes the number 100 times smaller, so Sophia's number is 0.

08.

Let's look at this equation in more detail.

We've got eight and we're dividing by 100 and it was 0.

08.

What's the value of the eight in eight? Well the value of eight is eight ones or eight.

What about the value of the eight in the answer of 0.

08? Well the value of the eight there is eight hundredths.

We had eight ones, we now have eight hundredths.

We can say that 0.

08 is one-hundredth times the size of eight and we can use that information to form a second equation.

Dividing by 100, well that's the same or equivalent to multiplying by one-hundredth or 0.

01.

So eight divided by 100 is equal to 0.

08 but also, eight multiplied by 0.

01 is equal to 0.

08 because dividing by 100 is the same as multiplying by 0.

01.

These expressions are equivalent to each other and they each have a value of 0.

08.

We can say that eight divided by 100 is equal to eight multiplied by 0.

01, which is equal to 0.

08.

Let's check your understanding with that.

Could you fill in the blanks in the equations? Four divided by 100 equals mm.

Four multiplied by mmh is equal to 0.

04.

And that means four divided by mmh is equal to four times mm which is equal to 0.

04.

Pause the video while you have a go at completing the equations.

Maybe find someone to chat to about this.

And when you are ready for the answers, press play.

How did you get on? Four divided by 100 is 0.

04.

Maybe you use a Gattegno year chart to help, or a place value chart to help.

We've got four multiplied by, hmm, well if we divide it by 100 we must be multiplying by 0.

01 or one-hundredth, that would give us the same answer, 0.

04.

Then we can put the equations together, four divided by 100 is equal to four multiplied by 0.

01, which is equal to 0.

04.

How did you get on? Well done.

Now Lucas' turn to think of a number.

He wants Sofia to guess his number and he gives her a clue.

"My number is one-thousandth times the size of three." So Sophia knows that to find his number she needs to divide three by 1,000.

And Sophia can use some known facts, or derived facts to help.

She knows one divided by 1,000 is the same as one-thousandth.

Two divided by 1,000 would be two thousandths.

Have you spotted the pattern already? What would come next? That's right, three divided by 1,000 is three thousandths.

Let's look at this on a Gattegno chart.

We start with the number three, we divide by 1,000, which means we have to move down three rows.

Three divided by 1,000 we can see is equal to 0.

003.

We can also use a place value chart to help us.

We started off with three ones and when a number is divided by 1,000 the digits move three places to the right.

One, two, three.

We had three ones, we end up with three thousandths.

It makes the number 1,000 times smaller.

So Lucas' number must have been 0.

003.

0.

003, three thousandths is one-thousandth times smaller than three.

Let's look at the equation in more detail.

Three divided by 1,000 is equal to 0.

003.

What's the value of the 3 in three? Ah, thank you Sophia.

The value of 3 is three ones or three.

What about the value of 3 and 0.

003.

That's right, the value of that three is three thousandths.

We have three ones, we now have three thousandths.

We can say that 0.

003 is one-thousandth times the size of three.

We can use that information to form a second equation.

We know dividing by 1,000 is equivalent to multiplying by one-thousandth or 0.

001.

We can say that these expressions are equivalent to each other and they have a value of 0.

003.

So three divided by 100, well that's the same as three multiplied by 0.

001 and they both have an answer or a value of 0.

003, three thousandths.

Let's check your understanding of that.

Could you fill in the blanks in these equations? Nine divided by 1,000 is equal to mm.

Nine multiplied by mm is equal to 0.

009.

Nine divided by mmh is equal to nine times mmh, which is equal to 0.

009.

Pause the video, maybe find someone to chat to about this.

And when you're ready for the answers, press play.

How did you get on? Did you either use a Gattegno chart, or a place value chart to help you? Nine divided by 1,000 is 0.

009 or nine thousandths.

When we divide by 100 it is the same as multiplying by 0.

001.

And those two expressions have the same value so they are equal.

Nine divided by 1,000 is equal to nine multiplied by 0.

001 and they have a value of 0.

009.

We have seen that when we divide by 100 it's equivalent to multiplying by 0.

01, and we know the digits move two places to the right.

And we know dividing by 100 is equivalent to multiplying by 0.

01.

We've seen that when we divide by 1,000 it is equivalent to multiplying by 0.

001, and the digits move three places to the right.

So dividing by 1,000 is equivalent to multiplying by 0.

001.

What about 10? What would divided by 10 be equivalent to? Can you spot a pattern to help? That's right, when we divide by 10, it is equivalent to multiplying by 0.

1 or one-tenth, and the digits move one place to the right.

Dividing by 10 is equal to multiplying by 0.

1 or one-tenth.

Let's look at this equation in more detail then.

Two divided by 10 is equal to two multiplied by 0.

1, which is equal to 0.

2.

Well we know Lucas is reminding us that 0.

1 is equivalent to one-tenth.

So we could also say that two divided by 10, we know it's the same as two multiplied by 0.

1, we know 0.

1 is one-tenth, so that is also the same to two multiplied by one-tenth and they all have the value of 0.

2.

But we know two one-tenths are equivalent to two-tenths.

All of these expressions are equivalent and have a value of 0.

2.

Let's check your understanding.

Could you have a look at these four equations and tell me which equation is correct? Pause the video while you have a look and when you're ready to go through the answers, press play.

How did you get on? Did you say, well it can't be A, because we're dividing by 100 but then we're multiplying by one-hundredth, so that's okay.

But then we've got four multiplied by one-tenth, well this time we're dividing by 100, so it can't be A.

What about B? Well we start with dividing by 100, we've got one-hundredth as our fractions, but ah, we're multiplying by 0.

1, that's the same as one-tenth, so it can't be B.

C is definitely correct, we're dividing by 100.

Dividing by 100 is the same as multiplying by 0.

01.

Dividing by one-hundredth is the same as finding one-hundredth and we've got four of them, which is four hundredths.

And D, D can't be correct because the answer is 0.

4, which is four tenths and we've got four divided by 100, so it should be four hundredths or 0.

04.

I wonder how you got on with those.

Well done.

It's your turn to practise now.

For question one, could you solve this problem? Sophia is thinking of a number.

Her number is one-thousandth times the size of seven.

Could you form two expressions to represent this, and then tell me what Sophia's number is, explaining how you know.

For question two, you've got some equations, could you complete? And then when you finish those, could you form a division equation of your own? But I'd like you to make a mistake and then explain the mistake that you made.

For question three, could you look at the equation, is it true or false? And convince me that you are correct.

Four divided by 1,000, is it equal to four multiplied by 0.

001, is it equal to 0.

04? Pause the video while you have a go at all three questions and when you are ready for the answers, press play.

How did you get on? For question one, we were asked to find what Sophia's number is.

We know it was one-thousandth times the size of seven, so we can form our first equation, seven divided by 1,000.

And we know dividing by 1,000 is the same as multiply by 0.

001.

We then had to work out Sophia's number, maybe you used a Gattegno chart or a place value chart but I worked out that it was 0.

007.

And we might have given me a reason such as, to find a number that is 1,000 times smaller you need to divide by 1,000.

Dividing by 1,000 is the same multiplying by 0.

001.

And the digits will move three places to the right.

This makes the number one-thousandth times the size, so Sofia's number is 0.

007.

For question two you were asked to complete the equations.

We've got three divided by 10 is equal to 0.

3.

Three divided by 100 is 0.

03.

And three divided by 1,000, 0.

003.

Nine times 0.

1 is 0.

9.

Nine times 0.

01 is 0.

09.

And 0.

009 is equal to nine multiplied by 0.

001.

Five divided by 10, well that's equal to five one-tenths or five times 0.

1, which is equal to 0.

5.

Two divided by 10 is equal to two times 0.

01, which is equal to 0.

02.

And then we have a longer equation here, we've got 0.

006, well that's the same as six divided by 1,000, which is the same as six multiplied by 0.

001.

We know that's the same as six times one-thousandth, which is six thousandths.

You were then asked to form an equation of your own but make a mistake.

You might have formed an equation like, nine divided by 100 is equal to 0.

9 and explained that the answer was incorrect.

When we divide by 100, it is the same as multiplying by one-hundredth and the digits move two places to the right.

In this example, the digits were only moved one place to the right.

The answer should have been 0.

09.

For question three you had to tell me whether or not the equation was true or false and convince me.

So you might have said that this was false and convinced me by saying that when we divide by 1,000 it is the same as multiplying by 0.

001, so that part of the equation was correct, but the digits would move three places to the right, not two, as in the given equation.

The answer should be 0.

004.

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

Fantastic learning today so far everybody, really impressed with how hard you are working.

We are now going to move on and look at how we multiply by 10, 100 or 1,000.

Sophia and Lucas are still playing their game and Sophia is thinking of a different number.

She wants Lucas to get her number and gives him a clue.

"My number is one-thousand times the size of 0.

04." Hmm.

Have you noticed something different this time? That's right, her number is one-thousand, so it's not one-thousandth this time, it's a whole number this time, one-thousand the times the size of 0.

04.

So this time the number she's given us for a clue is a decimal fraction, 0.

04.

"To find your number I need to multiply 0.

04 by 1,000." Because we need to find the number that is 1,000 times the size of 0.

04.

And we can use some derived facts to help.

We know 0.

01 or one-hundredth times 1,000 is equal to 10.

So two hundredths multiplied by 1,000 would be 20.

Three hundredths multiplied by 1,000 would be 30.

Hmm.

Can you spot what would come next, have you seen that pattern? That's right, 0.

04 multiplied by 1,000 is equal to 40.

And we can look at this in the Gattegno chart, we've got 0.

04 was the starting number that Sophia gave us and if we multiply it by 1,000, we move up three rows, which would be 40 and we can use that to form an equation.

0.

04 multiplied by 1,000 is equal to 40.

We can also look at this on a place value chart.

We started with four hundredths and we are multiplying by 1,000, so we need to move the digits three places to the left.

This makes the number 1,000 times larger.

0.

04 multiplied by 1,000 is 40, so Sophia's number is 40.

Let's look at this equation in more detail.

0.

04 multiplied by 1,000 is equal to 40.

Well what's the value of the four in 0.

04? Do you know? That's right Lucas, the value of the four is four hundredths.

What about the value of the 4 in 40? The value of the 4 is four tens, or 40.

We had four hundredths, we now have four tens.

40 is 1,000 times the size of 0.

04.

Let's check your understanding.

When we multiply 0.

9 by 1,000 the digits move two places to the left, the product is 90.

Is that true or false? Pause the video while you think about it and when you are ready, press play.

How did you get on? Did you work out that that must be false? But why is it false? Is it because A, 0.

9 is being increased 1,000 times, the digits move three places, 10 times 10 times 10.

The product should be 900.

Or is it B, when we multiply by 1,000 we place three zeros at the end of the number.

The product would be 0.

9000.

Pause the video, maybe chat to someone about this, and when you are ready, press play.

How did you get on? Did you realise it must be A, when 0.

9 is increased 1,000 times, all of the digits move three places.

The product should be 900.

We don't just place three zeros at the end of a number, do we? No, we know that the digits move.

Let's summarise what we've learned so far.

When we multiply by 10, well the digits move one place to the left.

When we multiply by 100, what happens? That's right, the digits move two places to the left.

What about when we multiply by 1,000? What happens? That's right, the digits move three places to the left.

Let's check your understanding on that.

Could you match the expression to its product? Pause the video while you have a look and when you're ready for the answers, press play.

How did you get on? Did you work out that 0.

3 multiplied by 1,000 is 300? 0.

03 multiplied by 1,000, that's 30.

And three thousandth multiplied by 1,000 must be three.

How did you get on? Brilliant.

Your turn to practise now.

For question one, could you complete the equations and then when you finish, could you form an equation of your own but make a mistake? Explain the mistake that you make.

For question two, look at the equation.

Is it true or is it false? Convince me that you are correct by giving some reasons.

We've got 0.

05 multiplied by 1,000 is equal to 50.

Pause the video while you have a go at both questions and when you are ready for the answers, press play.

How did you get on? For question one you had some equations to complete.

We've got 0.

8 multiplied by 10, well that's eight.

0.

8 multiplied by 100 is 80.

0.

8 multiplied by 1,000, that's what would give us 800.

0.

6 times 10 is six.

0.

06 times 100 is six.

And six, well that's the same as or equal to 0.

006 multiplied by 1,000.

0.

5 times 1,000 is 500.

0.

05 times 1,000 would be 50.

And five would be equal to 0.

005 multiplied by 1,000.

You were then asked to form an equation of your own but make a mistake.

You might have formed an equation like 0.

3 multiplied by 1,000 is equal to 0.

3000 and explained that my product was incorrect.

When we multiply by 1,000, the digits moved three places to the right.

In this example, placeholders were just placed at the end of the 0.

3 decimal number, weren't they? I just put three zeros at the end.

We can't do that.

My digits needed to move.

I have three-tenths, I still have three-tenths, nothing moved, so the product should have been 300.

For question two, you were asked to tell me if the equation was true or false and convince me that you were correct.

You might have said that it is true and convinced me by saying that when we multiply by 1,000 the digits move three places to the left.

We had five hundredths, we now have five tens or 50.

How did you get on with those questions? Brilliant.

Fantastic learning today.

I am really proud of how hard you have tried and how much further you have moved your understanding with multiplying, dividing a number by 10, 100 and 1,000.

We know that when a number is divided by 10 or 100 or 1,000, the digits move one, two, or three places to the right, respectively even if it's bridge is one.

We know dividing by 10, 100 or 1,000 is equivalent to multiplying by 0.

1, 0.

01 or 0.

001 respectively.

And this is also equivalent to multiplying by one-tenth, one-hundredth or one-thousandth.

We've also learned that when a decimal number is multiplied by 10, 100 or 1,000, the digits move one, two, or three places (indistinct) Fantastic learning.

I've had great fun today and I really look forward to learning with you again soon.

Goodbye.