Lesson video

Hello there, my name is Mr. Tilston, I'm a teacher.

It's absolutely lovely to see you today, and I'm really looking forward to spending this math lesson with you.

So if you're ready, let's begin the lesson.

The outcome of today's lesson is this, I can explain the removal of placeholders when dividing whole numbers by 100, and perhaps you've had some recent experience using placeholders, perhaps it's something you are getting more confident with.

We've got some keywords today, if I say them, will you say them back please, are you ready? My turn, scaling, your turn, my turn, inverse, your turn, my turn, placeholder, your turn, my turn, magnitude, your turn.

Now those are definitely not everyday common words, and you may well have forgotten what they mean, so how about a little reminder? Scaling is when a given quantity is made mm times the size, so for example five times the size or one 10th times the size.

Inverse means the opposite in effect, the reverse of.

So for example, multiplication is the inverse of division.

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

You may have had some recent experience of using one placeholder zero or perhaps even two placeholder zeros.

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

We've got two parts, two cycles to our lesson today.

The first will be 100th times the size and the second dividing multiples of 100 by 100.

So let's begin by focusing on 100th times the size.

In today's lesson, you're going to meet Sam and Lucas.

Have you met them before? They're here today to give us a helping hand with the maths.

Let's begin with the question 600 divided by 100.

And Lucas says, "I know the answer." Do you know the answer too? If you know it, shout it out now.

Sam knows the answer too, it's six, well done if you got that, you got that really quickly if you did, but how did you recall it so quickly, she would like to know, hmm.

Well, Lucas says, "Easy, to divide by 100, you just take away two zeros," hmm, you might have heard that before.

You might have said that before, but is that true? Sam's not convinced.

She says, "Hang on, are you sure, "that would look like this," taking away two lots of zero, and that would give you 600.

That's still the same number we started with.

Hmm, that can't be right, can it? "You are right," says Lucas.

So what is happening? Let's explore.

Let's start with thinking about 100th times the size, scaling down is when we find a fraction times the size of a number, making it smaller.

So for example, one 10th times the size.

Lucas and Sam explore scaling down by comparing base 10 blocks.

So here's some base 10 blocks, you may have some of these in your classroom, maybe some right in front of you now, you can explore along with us if you have.

Lucas says "1 hundred is 100 times the size of one." Would you agree with him? Yes, that's true.

So one multiplied by 100 is 100.

What's about comparing 100 to 1? That's 100th times the size, so it's the inverse of that, it's the opposite of that.

We will need to use the inverse, then you are quite right, Lucas.

What's the inverse of multiplied by 100, hmm? We could say divided by 100, that's the opposite.

Define 100th times the size, divide by 100, they are the same thing, so let's say that again, define 100th times the size, divide by 100.

"Let's model finding 100th times the size," says Lucas.

Let's do that.

So this is the 100 block split into 100 parts divided into 100 parts, and this is one of them, so that's 100th.

We had 100 or 100 ones, now there is one one.

So it's 100th times the size.

Let's have a look at another example.

How about starting with a greater multiple of 100? Start with 200, okay, well, let's do that.

This is 200, and we're going to divide by 100.

So we're dividing that 100 by 100 and dividing that 100 by 100.

And this time we've got two.

So two one hundreds divided by 100 equals two or two ones.

We had two hundreds or 200 ones, now we have two ones.

To find 100th times the size, divide by 100, okay, that's really important.

So let's say it again, this time can we say it together please? Are you ready, to find 100th times the size, divide by 100.

Fabulous, now just one more time.

This time I'm not going to say it, I'd like you to say it.

Are you ready, off you go! Very good, let's do a little check.

Describe what will happen to the base 10 blocks if we make them 100th times the size.

And if you've got base 10 blocks in front of you, perhaps you can explore it with your blocks.

Pause the video.

Did you get that? Well, each block becomes 100th times the size.

So each 100 becomes one when we divide it by 100 or make it 100th times the size.

Each 100 block was divided by 100.

Now there three ones instead of three hundreds.

You're doing well, let's move on.

Lucas has one marble, Sam has 100 times as many.

How many marbles does Sam have? "For every one marble I have, you have 100." Here we go, so that's one marble for Lucas, 100 for Sam.

So one multiplied by 100, think of one and make it 100 times the size, that gives you 100.

One marble multiplied by 100 is equal to 100 marbles.

Pretty straightforward so far, hopefully.

"What if we look at the inverse," says Lucas.

Okay, let's turn the arrow around.

What's going to happen when we do that? What can we say this time to go from 100 to one? What's the operation? One is 100th times the size of 100.

So we divide by 100.

True or false? The inverse operation to undo multiply by 100 is divide by 100.

Hmm, pause the video.

What do you think? Was that true or was that false? That is true.

Well done if you said that, multiplication and division are inverse processes.

They undo each other.

Now Sam has 200 marbles in total.

How many marbles does Lucas have? Well, Lucas says, "For every one marble I have, you have 100," like before.

And Sam says, "I have 200, "which is 100 times as many as you." So something multiplied by 100 equals 200.

The inverse of 100 times as many is to divide by 100.

I know that 200 divided by 100 is equal to two.

So you have two marbles.

We've used our inverse there.

This time Sam has 300 marbles in total, you can see that she's got three jars of marbles, so 300 in total.

How many marbles does Lucas have? And remember, "For every one marble I have," he says, "You have 100." So she's got 300, how many has he got? "I have 300," says Sam, "Which is 100 times as many as you." So something multiplied by 100 is equal to 300.

But let's use our inverse.

300 divided by 100 is equal to something.

The inverse of 100 times as many is to divide by 100.

I know that 300 divided by 100 is equal to three.

So you have three marbles.

See what you notice here, have a look.

What is going on, what could you say here? What do you notice? What do you think, could you explain that? Well, Lucas says, "I notice that in each case, "for every one marble I had, you had 100 marbles." So one marble, 100 marbles, two marbles, 200 marbles, three marbles, 300 marbles, yep, that checks out.

And Sam says, "I notice that to find the inverse "of 100 times as many, you have to divide by 100." So they're inverse, they're opposite to each other, they undo each other.

I noticed that to find 100th times the size, you divide by 100, that's correct, well done, Lucas.

It's time for some practise.

I'm confident that you are ready for this.

Well, complete the labels and sentences below.

So for a, mm is mm, mm times the size of mm, what could we say? And then mm is mm, mm times the size of mm, so it's the opposite, it's the inverse.

And the same for b.

Number two, fill in the missing numbers to show the inverse of 100 times as many.

Number three, complete the following ratio table filling in the missing numbers.

Be careful, some of the information is missing from the right hand column and some from the left hand column.

Righteo, pause the video and away you go! Welcome back, How did you get on? Would you like some answers? Let's do that now.

So number one, that's multiplied by 100.

So 100 is 100 times the size of one.

And then the inverse of that, divided by 100, one is 100th times the size of 100.

And for b, 200 is 100 times the size of two, so we're multiplying that by 100 again, and then the opposite, the inverse of multiply by 100 is divided by 100.

So two is 100th times the size of 200.

Number two, fit in the missing numbers to show the inverse of 100 times as many.

So here we've got that's divided by 100, that's the inverse.

So three is equal to 300 divided by 100.

And for b, once again, divided by 100 is the inverse of 100 times as many.

So this time we've got four is equal to 400 divided by 100.

And we see, once again, the inverse of 100 times as many is divided by 100 and we've got five is equal to 500 divided by 100.

And number three, those missing numbers.

So 700, 100th times the size is seven, 500, 100th times the size is five, 400, 100th times the size is four, 300, 100th times the size is three and 100, 100th times the size is one.

You're doing very, very well.

I think we are ready for the next cycle, in fact, we definitely are.

We're going to look at dividing multiples of 100 by 100.

We've got a place value grid.

Maybe you've got one of these in front of you.

Maybe you've got some counters in front of you.

You can represent this along as we go if so.

So we've got a counter in the one hundreds, just one counter, so that one counter is worth 100.

Now one counter is in the tens and that one counter is worth 10.

And now one counter is in the ones and that one counter is worth one.

What do you notice, what was going on there? Could you explain the effect? Well, Sam can, she says, "As the counter moves right, "its value decreases, it goes down, "it's the opposite of increase, it's decreasing." Did you notice that yourself.

And Lucas says, "Another example "that 'movement is magnitude.

'" So it's moving closer to zero.

It's getting smaller, the counters value becomes one 10th times the size each time it moves one column to the right.

Let's see that again, so here's 100, and it's going to be one column to the right, and it's going to become one 10th times the size, it's going to become 10.

This time it's going to move one place to the right, again, it's going to become one 10th times the size again.

Instead of being 10, it is now worth one, here it's worth 100, here it's worth one.

What happened there, what did you notice, that was different, wasn't it? What do you notice, what could you say about that movement, hmm? The counter this time moved two places to the right, not one.

Its value became 100th times the size from 100 to one.

To find 100th times the size we divide by 100.

That's really important.

So let's say that again, this time will you say that with me please, are you ready? To find 100th times the size, we divide by 100.

Fantastic, now can just you say it, off you go.

Fabulous, let's do a little check, label the arrows on the place value chart below with the correct number to show the magnitude of the movement.

So it's moved two places to the right, it's mm times the size, pause the video.

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

And if you've got that, well done, you're on track.

You're ready for the next part of the learning.

Let's use counters in a place value chart.

Have you got to place value chart? Have you got counters? You can represent along with us if you do.

So this time we're looking at 900 divided by 100 is equal to nine.

How can we represent that? Well, we could represent 900 this way with nine counters in the hundreds column, each 100 is divided by 100 to become a one.

Let's look at that, here we go.

Every one of those one hundreds is now worth one.

We've still got nine counters.

They've all moved changing their value from 100 to one when we divided by 100.

There are still nine counters, but now they are ones.

We had nine hundreds, we now have nine ones.

That's what happens when we divide by 100.

How about we change the counters for digits starting with the hundreds? Okay, well, there's nine one hundreds so we can use the digit nine.

Sounds good, let's swap nine hundreds for the digit nine.

Let's do that, here we go.

Now we've got nine one hundreds.

We need to use some placeholder zeros, yes we do.

Why, Lucas isn't sure why you've got to do that.

Maybe you've had some recent experience of this.

Could you explain it do you think, what could you say? Why are those placeholder zeros needed? Hmm, well, if we didn't have that place value chart, how would we know it was nine hundreds? Let's see that.

Yes, we removed the chart, what does it look like now? It just looks like a nine.

When we place those two placeholder zeros in, it becomes 900.

And that is why those placeholder zeros are so important.

Now, let's move that nine digit two places to the right, and here we go.

So instead of being nine one hundreds, it's worth nine ones.

Those zeros are no longer needed as placeholders to show the value of nine.

We don't write nine ones a 009, 9 ones is written as a single digit, just as you've always done.

"That's what I meant by 'takeaway two zeros'" says Lucas, but I see now that it's not the same.

"What if we try starting with a 4-digit multiple of 100?" I like your confidence, Lucas, let's see.

We will need to include a one thousands column in our place value chart.

Well, let's do that.

You might have one of these charts in front of you.

You could draw one very quickly on your whiteboard if not.

And here are our counters.

So this time we've got 2,300.

That's the number being represented.

We've got two in the thousands column and three in the hundreds column, so 2,300.

Let's make it 100th times the size by dividing it by 100.

So the counters and digits will move two places to the right, let's do that.

So we're going to move the counters and the digits this time.

So two places, and this is a new place when we divide them by 100.

We've now got two tens and three ones.

The digits two and three have moved to replace a placeholders is 23.

So 2,300 divided by 100 is equal to 23.

We could say, to divide a multiple 100 by 100, remove the two zeros in the ones and tens and move the digits two places to the right.

That's what's really happening, we're not taking them away.

Okay, it is time for some final practise.

Number one, for each of the following equations, use the place value chart to represent them, drawing counters in for before and after the division.

Then complete the stem sentence below.

So let's start by looking at 400 divided by 100 is equal to four.

How could we represent that drawing circles on that place value grid before and after the division.

And then complete that stem sentence we had, mm mm, now we have mm mm, and the same for b, but this time we're looking at 500 divided by 100 is equal to five.

And number two, whose opinion do you agree with and why? Let's have a look.

Well, Lucas says, "When you divide a multiple of 100 by 100, "you remove the zeros from the ones and tens place "because there are no ones or tens," okay? And Sam says, "The placeholders are removed "from the ones and tens "when dividing a multiple of 100 by 100 "to allow all the digits to become 100th times their size." Hmm, who do you agree with? Do you agree with Lucas, Sam, both, or neither? Can you explain your choice? Okay, pause the video and away you go.

Welcome back, how did you get done? Are you feeling confident? Are you feeling good about this, let's have a look.

So number one, this is 400 divided by 100 is equal to four.

That's how we can represent 400, four in the hundreds column.

So we had four hundreds, and we divided by 100, and this is what we've got.

We've now got four, that's four ones.

And for b, 500 divided by 100 is equal to five.

So that's our 500, that's what we had before.

We had five hundreds, and this is what we've got after.

Now we have five ones, that's the effect of dividing by 100.

And whose opinion did you agree with and why? In this case, Sam was correct.

All whole numbers are made up of ones, but they are arranged into different place value columns.

The zero in the ones and tens column is removed to show that the other digits are now 100th times the size.

And very well done to you if, in your explanation, you said 100th times the size.

We've come to the end of the lesson, and my goodness, haven't you been brilliant today.

Today we've been explaining the removal of placeholders when dividing whole numbers by 100.

Scaling down is when we find a fraction times the size of a number, making it smaller.

And in this case we've been finding 100th times the size.

To find 100th times the size, divide by 100.

To find the inverse of 100 times as many, divide by 100.

To divide a multiple of 100 by 100, remove the two zeros in the ones and tens, this the other digits 100th times the size.

Okay, well, I hope that's crystal clear now.

Well done in your achievements today and your accomplishments, you've been fantastic.

I hope you have a great day, whatever you've got in store.

Take care and goodbye.