Lesson video

Hi there.

My name is Mr. Tilstone.

It's really great to see you today and I hope you're having a wonderful day so far.

Let's see if we can make it even better by having a successful maths lesson.

If you are ready, I'm ready.

Let's begin.

This is the outcome of today's lesson.

I can explain the use of placeholders when multiplying whole numbers by 100.

You might hopefully already be familiar with placeholders.

And that's one of our keywords.

So if I say these words, will you say them back to me please? Are you ready? My turn, placeholder.

Your turn.

And my turn, magnitude.

Your turn.

Those are definitely not common everyday words.

Let's have a little reminder about what they mean.

A placeholder is where we use the digit zero to hold a place in a number and maintain place value.

And the magnitude of a number is its distance from zero.

Our lesson today is split into two cycles.

The first will be one-digit numbers and the second two-digit numbers.

So let's focus on one-digit numbers.

In this lesson, you're going to meet Sofia and Jun, have you met them before? They're here today to give us a helping hand with the maths.

6 multiplied by 100.

Do you know the answer to that? Well, Jun does.

He says, "I know the answer." And Sofia says, "Well, so do I.

It's 600." Did you get that quickly as well? "How did you recall it so quickly?" She wants to know.

"Easy" says Jun, "to multiply by 100, you just add two zeros." Now that might be something you've heard before.

It might be something you've thought before.

It might be something you've said before, but Sofia's not sure.

She says, "Hang on, are you sure" That would look like this." Hmm and then that will give you the answer six.

Hmm.

So it's not about adding two zeros.

"You're right." He says, "So what's happening? Let's explore." The value of six changes in this calculation, the digit six.

"As a factor, the digit six is worth 6 ones." "In the product, the digit 6 is worth 6 hundreds." "Place value must be important here." And indeed it is, Sofia.

Let's have a look at the place value chart.

And maybe you've got one of these in front of you and maybe you've got some counters in front of you.

And if so, you can recreate that as we go.

So here is one.

It's in the ones, one counter in the ones is worth one.

One counter in the tens, it's not worth one anymore.

It's worth 10.

And one counter in the 100s column is not worth 1 or 10 anymore, it's worth 100.

What do you notice? Jun says, "As the counter moves to the left, its value increases." Did you notice that? Did you say something similar? Here we go.

So one's become 10, the value's increased, it's moved left, and it's moved left again, and his value's increased again from 10 to 100.

So Jun is right.

And Sofia says, "The counter's value becomes 10 times the size each time it moves one column to the left." Did you say something like that? So one 10 times the size becomes 10.

10, 10 times the size becomes 100.

So here's one in the ones.

It's worth one.

Here's one in the 100s.

It's worth 100.

How many places did it move there? What do you notice? "This time." Says Jun, "the counter moved two positions to the left on the place value chart." It move one, did it? It move two positions.

"Its value became 100 times the size, from a value of 1 to a value of 100." When it moved those two places to the left.

Label the arrows on the place value chart below with the correct number to show the magnitude of the movement.

So when it goes from the 1s to the 100s, it's mm times the size.

Pause the video.

Did you get that? It's 100 times the size.

Well done if you got that, you're on track.

They represent the equation using Base 10 blocks.

If you've got some Base 10 blocks with you, you could do this too.

So 6 multiply by 100 is equal to 600.

"Let's make 6 ones using Base 10 blocks," say Sofia.

Okay, let's do that.

Can you do that? One, two, three, four, five, six.

Now let's multiply each one block by 100.

What will happen to each of those blocks, each of those ones if we do that, what will they become? This is what will happen.

Each of those ones will become a 100 and again.

And the next one and the next one and the next one.

And finally this one will also become 100.

What have we got now? This shows six groups of 100.

It was six groups of one before and now it's six groups of 100, that's equal to 600.

Here's six place value counters.

Have you got place value counters in front of you? You could use those as we go.

You can also draw place value counters very easily too.

Let's multiply each by 100.

So this is our six.

This is that part of the equation, and we're going to multiply each by 100.

What is going to happen to each of those six counters? What will they become? What can you exchange each one for? "We're going to need a lot of counters." Says Sofia, Not necessarily Sofia, because as Jun recognises, We can exchange 100 ones for 1 one hundred.

That will make the value of each counter 100 times the size." There we go.

Now we've got 6 one hundreds instead of 6 ones.

Let's have a check.

Use place value counters or draw them if you haven't got them to represent them multiplication below.

So five multiply by 100 equals 500.

And if you're drawing, you might want to do like a before and after.

Okay, pause the video.

Let's see.

"Exchange each 1." So you might have drawn five ones like this for 100 to make the value of each counter 100 times the size.

So let's do that.

So that 5 ones were multiplied by 100 becomes 5 one hundreds.

Let's use counters in a place value chart.

Okay, let's do that.

And again, you could draw these if you don't have them.

So six multiplied by 100 equals 600.

What's going to happen to each of those six counters? Each one is multiplied by 100 to become a 100 in the hundreds column.

Mm.

So we can move them two places to the left.

That one, one is now one, 100 and again and again and again and again and again.

So each of those counters has been moved two places to the left and their value has changed from 1 to 100.

"There are still 6 counter." Says Jun, "but now they are hundreds." So instead of having six, we've got 600.

"How about we swap the counters for a digit?" Say Sofia, "starting in the 1s column?" Mm.

So instead of saying six 1s, we can have the digit six.

"Good idea.

6 counters means a digit of six." Let's look at that.

Here we go.

"Let's multiply it by moving it in the same way." So we're going to move it two columns to the left.

It's still going to be a six, but it's not worth six anymore.

Is it? Because it's in the hundreds column.

What's it worth now? We have 6 hundreds shown in the 100s column or 600.

So what about these zeros then? Where did they come from? Hmm? Could you explain that? Maybe you've had some recent experience with placeholder zeros.

Let's take away the place value chart.

Okay? Yes.

Can you see the issue? It doesn't look like 600 anymore, does it? It looks like six.

Without place value, this does read as 6 or 6 ones." So that's why the placeholder zeros are very important.

"We need zeros to show it's 6 hundreds." "There are 0 ones and tens, but 6 hundreds." So there's place value zeros are very, very important.

They're placeholders.

"We had 6 ones, now there are 6 hundreds." And we can see that with or without the place value chart.

Have a look these different representations, four different representations.

What do you notice? What's the same and what's different? "I notice." Says Jun, "that 6 is shown in all of them." You can see six or something in each of them, "but it's 6 hundreds, not 6 ones." Did you notice that? This shows us that all the digits have moved two places to the left.

"And are 100 times the value that they were before." A digit changes value when it moves its place value.

"To multiply a whole number by 100, place two 0s after the final digit of that number." We're not adding two 0s, we're placing two 0s.

They're placeholders.

"That's what I meant by add two zeros.

But I see now that it is not the same." Hopefully you can see the difference too.

Okay, let's do a check.

True or false? To multiply a whole number by 100, you just add two zeros.

Is that true or is that false? And can you explain that? Pause the video.

What do you think true or false? It's false.

Although you are writing two zeros on the page, they are placeholders to show that the digits now have a greater value and to show that they have moved two columns to the left.

Well, I think you are ready for some independent practise.

So let's do that.

Number one, represent each of the following equations using place value charts provided drawing counters that would show the value before and after the multiplication.

And then complete the stem sentence below.

So we've got, first of all, 4 multiply by 100 is equal to 400.

What would that look like before the multiplication? What would it look like after the multiplication? And can you complete the stem sentence? We had mm mm.

Now we have mm mm.

And do the same for B.

That's 5 multiply by 100 is equal to 500.

Then number two, write down the equation being represented below and then complete the sentence describing it.

We had mm mm.

Now we have mm mm.

Number three, which opinion do you agree with and why? Let's have a look.

So Jun says, "In multiples of 100, the placeholder is used in the 1s and 10s column to show that there are no extra ones and tens.

And Sofia says, "The placeholders are used in multiples of 100 to show that there are no ones or tens whatsoever, only hundreds." Hmm, who's right? Is it Jun? Is it Sofia? Is it both or is it neither? And can you explain? Pause the video and I will see you soon for some feedback.

Welcome back.

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

Let's give you some answers.

So number one, 4 multiplied by 100 is equal to 400.

But how can we represent that? Well before it looks like this.

That's 4 ones.

That's our four.

So we had 4 ones and then this is what it looks like.

Now we have 4 hundreds.

And for B, 5 multiplied by 100 is equal to 500.

What does that look like? How can we represent that? By drawing five circles in the ones.

So we had 5 ones, now we have, how can we represent this? We can draw five circles in the 100s because we have 5 hundreds.

And then for number two, here's the equation.

It's 7 multiplied by 100 is equal to 700.

So we had 7 ones, now we have 7 hundreds.

And for the place value counters, here's the equation.

4 multiplied by 100 is equal to 400.

So we had 4 ones, now we have 4 hundreds.

And who did you agree with? Who was right? In this case it was Jun.

There are ones in every whole number, but they can be arranged into the hundreds columns and columns greater so that there are non leftover.

This is when zero is used as a placeholder and appears in the tens and ones column.

So well done if you said something a little bit like that.

You're doing ever so well and you're ready, I think, for the next cycle.

And that's two-digit numbers.

Let's have a look at this equation.

12 multiplied by 100 is equal to 1,200.

Hmm 1,200.

"Why does a product have a comma." Wonders Jun.

Do you know the answer to that? Can you see that comma? Well, Sofia knows.

She says, "It helps us to read the number by separating the thousands from the hundreds, tens, and ones.

Hmm so 1,200.

Yep, that does help.

Let's investigate.

Multiplying two-digit numbers by 100.

"Let's use the representations again", say Sofia "to explore what happens." So if you've got those resources, get them at the ready.

Let's have a check first.

Why is a comma used in a four-digit number? A, it looks neat and more like a number.

Or B, it separates the thousands from the hundreds, tens and ones making it easier to read.

Right really quick, A or B? Pause the video.

Did you say B? That's the right answer.

They represent the equation using Base 10.

So 12 multiply by 100 is equal to 1,200.

Let's make 12 using Base 10.

If you've got Base 10 in front of you, you could do that too.

Then let's multiply by 100.

So here's 12, it's composed of 2 ones and 1 ten.

Now we're going to multiply each part by 100.

Let's start with that 10.

We're going to multiply that 10 by 100 and this is what it becomes.

That 1 ten becomes 1,000.

And let's do the same with the 2 ones.

Let's multiply those by 100.

So that one becomes 100 and the other one also becomes 100.

Now we've got 1 thousand, and two hundreds.

Here we can see 12 groups of 100.

Here's 1 ten and 2 ones as place value counters to represent 12.

And if you've got place value counters, go for it.

Get them out now.

That's what it looks like, that's 12.

Now let's make each part 100 times bigger.

What's the 10 going to become? What's the ones going to become? Let's see.

We can exchange the counters to do that.

'cause you don't want to have 100 lots of 10, but we can exchange for the same value.

Each counters value will become 100 times the size.

So it won't be worth 10 anymore.

It will be worth 1,000.

And it won't be worth one anymore, it will be worth 100 and that happens to the other one as well.

So now what have we got? We've got 1,200.

Let's do a little check, use place value counters or draw them if you haven't got them to represent the multiplication below.

So 13 multiplied by 100 is equal to 1,300.

What does that look like before and after? Pause the video.

Did you manage to do that? Let's have a look.

This is what 13 looks like.

1 ten and 3 ones.

And this is what 1,300 looks like.

So that 13 has been made 100 times bigger.

Here's 12 on a place value chart.

So if you've got a place value chart counters, get them out.

Now let's put 1,200, the product underneath it.

Okay, but different this time.

What do you notice? What's happened? Can you explain what's happened to the counters? Movement is magnitude.

Each of these counters moves two columns to the left.

So they're moving further away from zero.

They're increasing in value.

Each counter's value is now 100 times the size.

So that 1 ten is worth 1,000.

And those 2 ones are worth 2 hundreds.

We had 1 ten and 2 ones.

Now we have 1 thousand and 2 hundreds.

Let's replace counters with the digits that represent them and remove the place value chart.

Okay, so what will it be? 2 ones and that 1 ten.

We use a digit one and the 2 hundreds, the digit two and the 1,000, the digit one.

We need to do something now though, don't we? What comes next? When we take away that place value chart, what do you notice? We've got a little bit of a problem I think, don't you? Both of these look like 12 'cause there aren't any placeholders.

So let's use placeholders.

Here's the placeholders.

Now that looks like 1,200, doesn't it? So to multiply a whole number by 100, place two zeroes after the final digit of the number not adding two zeroes, you're placing two zeros, they're placeholders.

Number one, represent each of the following equations using the place value charts provided, drawing counters that show the value before and after the multiplication.

And then complete the stem sentence below.

So we'll start with 14 multiply by 100 is equal to 1,400.

What does that look like before and after? Draw counters to show that.

And then complete the stem sentence we had.

Mm and mm, now we have mm and mm.

And the same for B.

This time it's 15 multiplied by 100 is equal to 1,500.

Can you draw the counters? Can you finish the stem sentences? And the same for C.

This time we've got 26 multiplied by 100 is equal to 2,600 before and after and stem sentences please.

Number two, complete the ratio chart below by filling in the missing numbers.

And number three, mark the statements true or false.

And you might want to have a guide explaining why.

When a whole number is multiplied by 100, the product is a multiple of 100.

True or false? Only single digit numbers can be multiplied by 100.

True or false? To find 100 times the size, multiply by 100.

True or false? To find 100 times the size, just add two zeros to the number.

True or false.

And digits that move two places to the left on a place value chart become 100 times the size.

True or false and why? Pause the video.

Good luck with that and I'll see you soon for some feedback.

Welcome back.

How are you getting on? Are you feeling confident? Are you feeling successful? Well, number one is this.

That's 14.

Before the multiplication we had 1 ten and 4 ones.

And then this is 14.

After being multiplied by 100, it's 100 times bigger.

Now we have 1 thousand and 4 hundreds.

And this time we've got 15.

This is what that looks like before the multiplication.

So we had 1 ten and 5 ones.

And then after we had 1 thousands and 5 hundreds, 1,500.

And see this is what 26 looks like.

So we had 2 tens and 6 ones.

And then after being multiplied by 100, we have 2 thousands and 6 hundreds, 2,600.

And number two, Sofia says, "To multiply a whole number by 100 placed two 0s after the final digit of that number." So now add place.

That means that we need to place two zeros after six, changing its value from ones to hundreds.

There we go.

So six multiply by 100 becomes six hundreds.

That six has moved two places to the left and the two zeros are placeholders.

13 multiply by 100 is equal to 1,300.

52 multiplied by 100 is equal to 5,200.

67 multiplied by 100 is equal to 6,700 84 multiply by 100 is equal to 8,400.

And 97 multiplied by 100 is equal to 9,700.

And number three, true or false? So maybe you explain why for each one.

When a whole number is multiplied by 100, the product is a multiple of 100, that's true.

Only single-digit numbers can be multiplied by 100.

That's false.

Any number can be multiplied by 100.

And today you've investigated some two-digit examples as well.

You can do it with any number of digits though.

And three, to find 100 times the size, multiply by 100.

That's true.

To find 100 times the size, just add two zeros to the number.

No to multiply whole numbers by 100 you are placing two zeros after the final digit showing that the value of that digit has changed.

And then digits that move two places to the left on in place value chart become 100 times the size.

That's true.

We've come to the end of the lesson and you've been fantastic.

I hope you're proud of yourself and your achievements.

Today you've been explaining the use of placeholders by multiplying whole numbers by 100.

Hopefully you're starting to feel really confident and secure with that concept of placeholder zeros.

In our place value system movement is magnitude.

Moving left, each column is 10 times the size.

To multiply a whole number by 100, place two 0s after the final digit of that number, not add, place.

This makes a number 100 times the size.

The 0s act as placeholders.

It works for single digit, whole numbers or whole numbers with more than one-digit.

And you've investigated both kinds today.

This is not the same as saying add two 0s.

So if anybody says that to you in future, say no, we're not doing that.

We are placing two 0s.

There's a big difference.

I've had a lot of fun today and I hope I get the chance to spend another maths lesson with you at some point in the near future.

But until then, have a great day.

Whatever you've got in store, and be the best version of you that you can possibly be.

Take care and goodbye.