Lesson video

Hello there.

My name is Mr. Tilstone.

I'm a teacher and I just love maths.

So, it's a real honour and pleasure to be with you today to teach you this lesson, which is all about multiples of 100.

If you're ready, I'm ready.

Let's begin.

The outcome of today's lesson is this.

I can explain the relationship between multiplying a number by 100 and multiples of 100.

And we've got some keywords.

If I say them, will you say them back please? My turn, multiple.

Your turn.

My turn, digit.

Your turn.

And my turn, placeholder.

Your turn.

What do those words mean? Do you think you could explain them? If not, don't worry, I'm going to give you a little reminder now.

A multiple is the result of multiplying a number by another whole number.

I wonder if you could think of a multiple of 10.

A digit is one of the symbols of a number system.

In our number system, we use the digits zero, one, two, thee, four, five, six seven, eight and nine.

They are digits.

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

Our lesson is split into two parts or two cycles today.

The first will be multiples of 100 and the second, multiplying by 100.

But first, let's focus on multiples of 100.

And in this lesson, you're going to meet Izzy and Andeep.

Have you met Izzy and Andeep before? They're here today to give us a helping hand with the maths, and very good they are too.

Andeep and Izzy count in 100s.

Can you count in 100s? Count along with me.

100.

200.

300.

400.

500, 600, 700.

`800, 900.

Nice and easy? "What's next? Ten-hundred?" asks Izzy.

Hmm, I don't think I've heard people say ten-hundred before.

Do you? I know what she means.

What do you think? What comes next after 900? It's 10 lots of 100, which is 1,000, yes, that's what people say.

900, 1,000.

That's what's next.

"Oh, yes, I remember," said Izzy.

So, let's have a little check.

Can you practise counting in hundreds? If you have a partner, try counting back and forth between you, a bit like Izzy and Andeep did.

Pause the video.

Did you do that? Were you successful? 100, 200, 300, 400, 500, 600, and so on.

We could keep going.

Now, what's the same and what's different? Let's have a look.

We have counted in 100s, so all of these numbers are multiples of 100.

That's what's the same.

And Izzy says, "They all have a different digit in the hundreds column." That's what's different.

So, look at the hundreds column.

Look at the digit.

That's one of our keywords.

So, for the first one, the digit is one.

For the second one, it's two.

For the third one, it's three, and so on.

They are all three-digit numbers except for 1,000.

That's not a three-digit number.

What's that? That's a four-digit number.

They all have a zero in both the ones and tens column.

Did you notice that? That means they all end with two placeholders.

You might have had some recent experience of multiples of 10 where we use one placeholder zero.

These are multiples of 100.

They've got two placeholder zeros.

True or false? All multiples of 100 have both a tens and a ones digit of zero.

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

That's true.

If it is a multiple of 100, then it is made up of hundreds with no additional ones or tens.

So, zeros are placed in the tens and ones columns as placeholders.

So, all multiples of 100 have two zero placeholders at least.

Andeep and Izzy look at a sorting task.

So, they've got a table, it's got two columns, one for multiples of 100, one for not multiples of 100, and we've got four numbers to sort, 1, 10, 200, and 1,001.

Where would you put them? Could you explain why? Andeep says, "We have to place these numbers in the correct column in the table." Yes, you do.

1 and 10 are less than 100, so can't be multiples of 100.

That's correct.

Any number that's less than 100 cannot possibly be a multiple of 100.

The first multiple of 100 is 100.

So, we can put those in not a multiple of 100.

I wonder if you could think of any other numbers that would go there for that same reason because they're less than 100.

And, "All multiples of 100 have both a tens and ones digit of zero," says Izzy.

Yes, that's correct.

200 has both a tens and ones digit of zero.

It's a multiple of 100.

Do you agree with her? Yeah, she's right.

That is a multiple of 100.

"I think 1,001 is not a multiple of 100," says Andeep.

Hmm.

And Izzy says, "I think that it is a multiple of 100 because it's got two zeroes." Hmm.

Who do you agree with? I can see where they're both coming from, but only one of them is right.

What do you think? Well, as Andeep correctly says, it has two zeroes as placeholders, but in different columns, not in the tens and ones.

"I see now.

The zeroes must be in the ones and tens column.

The zeros in 1001 are in the hundreds and tens column." So, therefore, it's not a multiple of 100.

Let's have some practise.

Number one, sort these numbers into their correct column according to whether each are a multiple of 100 or not, just like we did there.

Number two, complete the table by deciding true or false.

And can you explain why? Number three, using all four cards each time, how many different multiples of 100 can you make? I wonder if you could be systematic about that.

Maybe start with the lowest possibility and work up.

Number four, do you agree with Andeep? Explain your answer.

Multiples of 100 always have a digit greater than zero in the hundreds column.

Hmm.

You might want to read that again.

Have a good think about that.

Do you agree or disagree? And see if you can explain as clearly as you possibly can.

Pause the video and away you go.

Welcome back.

How did you get on? Are you feeling confident? Number one, sort these numbers into the correct column according to whether each are a multiple of 100 or not.

So, let's start with four, not a multiple of 100.

It's less than 100.

It can't be a multiple of 100.

40, the same reason, it's less than 100.

Remember, the first multiple of 100 is 100.

400 is a multiple of 100.

We could count in 100s to get there.

It's got two zeros as placeholders for the tens and the ones.

420 is not a multiple of 100.

It's only got one placeholder zero for the ones.

402 is not a multiple of 100.

It's got one placeholder zero in the tens.

4,002 is not a multiple of 100.

It has got two placeholder zeros, but not in the tens and ones.

That's in the hundreds and tens.

And then 4,200 is a multiple of 100.

We could count in one hundreds to get there.

It will take a long time.

But what you can notice is that it's got two placeholder zeros, one in the tens and one in the ones, making it a multiple of 100.

All multiples of 100 are both the tens and ones digit of zero.

Yes Izzy, That's correct.

Number two, complete the table by deciding true or false multiple of 100 or not.

And can you explain? So, 30, nope.

And you might have said that it's less than 100, so it can't be a multiple of 100.

You might have said it's only got one placeholder zero.

300 is a multiple of 100.

It is got two placeholder zeros, one for the tens, one for the ones.

450 is not.

It's only got one placeholder zero.

1,020 is not.

It's got two placeholder zeros, but not in the right places.

Not for the tens and ones.

1,800 is, it's got two placeholder zeros, one for the tens, one for the ones.

And using all four cards each time.

How many different multiples of 100 can you make? Did you use a system here I wonder? The two zeros will have to be the ones and tens digit for every number.

That's right, because multiples of 100 always have a ones and tens digit of zero.

Then we can systematically work through the other digit combinations, maybe start with the lowest.

Starting with one in the thousands column and then swapping one and three.

So, we've got 1,300, 3,100.

Do you agree with Andeep? Explain your answer.

Multiples of 100 always have a digit greater than zero in the hundreds column.

True or false? False.

Izzy disagrees.

She says "Multiples of 100 need a ones and tens digit of zero, but they can have a zero in other place value columns too." So, for example, 2,000 is a multiple of a thousand.

It's also a multiple of 100 because the final two digits are zeros.

Below are some other examples of numbers that are multiples of 100 and have a hundreds digit of zero.

1,000, 2,000.

Can you think of any others? 3,000.

Any others? Let's move on to the next cycle that's multiplying by 100 Andeep has one marble.

Izzy has 100 times as many.

How many marbles does Izzy have? For every one marble I have, you have a jar of 100.

So, that's Andeep's one marble.

And this is Izzy's jar of 100 marbles.

Think of one and make it 100 times the size that's what we've done here.

So, one 100 times the size of one is 100.

Think of one and multiply by 100.

So, one multiplied by 100 is equal to 100.

100 marbles is 100 times as many as one marble.

I have 100 marbles.

Now Andeep has two marbles.

Izzy has 100 times as many.

How many marbles does Izzy have? Hmm? Can you picture it? Remember, for every one marble I have, you have a jar of 100 of this.

And there's one, there's two.

So, one jar, two jars of 100.

Think of two and make it 100 times the size.

100 times the size of two is 200.

"Think of two and multiply it by 100," says Andeep.

Two multiplied by 100 is equal to 200.

"200 marbles," says Izzy, "Is 100 times as many as two marbles, I have 200 marbles." What do you notice? Have a look at this.

What's going on? What's happening? What could you say? Andeep says, "I noticed that for every one marble I had, you had 100 marbles.

That means that you had 100 times as many marbles as me." And Izzy says, "I noticed that to find 100 times as many you have to multiply by 100." Let's have a check.

How many marbles are there in three jars? Write an equation to show your calculation.

Pause the video.

Three jars, what can we see? What would the equation be? Hmm, three multiplied by 100 is equal to 300.

So, that's 300 marbles.

That's what the equation looks like.

Well then if you've got that, you are on track and you are ready for the next part of the lesson.

Andeep and Izzy, use a Gattegno chart to multiply by 100.

I really love Gattegno charts.

They're so useful.

You might have had some recent experience of multiplying by 10 using a Gattegno chart.

Can you remember what you discovered? We found that when you multiply by 10, the value moves one place up.

Let's see what happens when we multiply by 100.

Let's model finding 100 times the size using the Gattegno chart.

Okay, let's be systematic.

I like that word.

I like that idea Andeep, and start with one.

So, one multiplied by 100 is equal to 100.

We know that.

And let's add that to the chart.

100 is 100 times the size of one.

So, this is what that looks like.

Okay, what do you notice? Didn't move up one place, did it? Let's do another one.

Two multiplied by 100 is 200.

What happened there? What can you say? What did you notice? Hmm.

Three multiplied by 100 is 300.

300 is 100 times the size of three.

Hmm.

What happened? Four multiplied by 100 is 400.

400 is 100 times the size of four.

Hmm.

What happened on the Gattegno chart? Five multiplied by 100 is 500.

500 is 100 times the size of five.

And that's where that appears on the Gattegno chart.

Complete the Gattegno chart to show six multiplied by 100 is equal to 600 and then fit in the missing numbers in the sentences below.

So, that is mm multiplied by mm is mm.

Mm is mm times the size of mm.

Pause the video and off you go.

Let's see.

This is what it looks like.

And six multiplied by 100 is 600.

600 is 100 times the size of six.

Well done if you got those.

So what did you notice? What's going on here on the Gattegno chart? Moving two rows up in a Gattegno chart is multiplying by 100.

So, one multiplied by 100 is equal to 100.

It's moved two places up, two rows up.

Two multiplied by 100 is equal to 200.

It's moved two places up.

Three multiplied by 100 is equal to 300.

It's moved two places.

Four multiplied by 100 is equal to 400.

It's moved two places up.

Five multiplied by 100 is equal to 500.

It's moved two places up.

Six multiplied by 100 is equal to 600.

It's moved two places up.

Seven multiplied by 100 is equal to 700.

It's moved two places up.

Eight multiply by 100 is equal to 800.

It's moved two places up and you guessed it, nine multiply by 100 is equal to 900.

It's moved how many? Two places up.

when multiplying by 100.

The products are all multiples of 100 because say that of all of those 100, 200, 300, 400, 500, 600, 700, 800 and 900 are all multiples of 100.

They all have ones and 10 digits of zero.

Izzy says, "I'll describe making a number 100 times the size and you can represent it on the Gattegno chart." Okay, three multiplied by 100 is equal to 300.

300 is 100 times the size of three.

Hmm.

What would that look like on the Gattegno chart? I'll draw an arrow from three to represent making it 100 times the size on a Gattegno chart.

So, this is three and then an arrow pointing to the 300 showing that it's moved two places up.

And then let's circle the product.

That's 300.

It's a multiple of 100.

So, three multiply by 100 is equal to 300.

This time I'll draw on the Gattegno chart and you have to describe it.

Okay, what has he done here? Could you describe this? What's the equation? What's happened? Nice challenge," Izzy says, "Is this time you started with a multiple of 10.

So, that's 60 multiplied by 100.

It's equal to 6,000.

So, just like before we've moved two places up on the Gattegno chart, we've still got a multiple of 100 for our product because the tens and the ones are zeros.

And Andeep's notice that too.

Let's do some final practise.

Number one, read the descriptions of making a number 100 times the size and represent each on the Gattegno chart.

Then represent each as an equation.

So, 20 multiplied by 100 is equal to 2,000.

2,000 is 100 times the size of 20.

What does that look like on the Gattegno chart? Could you draw that with arrows and circles? And seven, multiply by 100 is equal to 700.

700 is 100 times the size of seven.

Could you draw that on the Gattegno chart with circles and arrows? Number two, look at the representations of making a number 100 times the size on the Gattegno chart and complete the sentences to describe each.

Then represent each as an equation.

So, mm, multiply by mm is equal to mm.

Mm is times the size of mm.

Can you do that for both of those examples? Number three, complete the table deciding if each statement is true or false.

And you might like to explain why as well.

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

All multiples of 100 have a digit greater than zero in the hundreds.

To find 100 times the size, multiply by 100.

And all multiples of 100 have both the tens and ones digit of zero.

Are those statements true or false? And why? Okay, pause the video and I'll see you soon for some feedback.

Welcome back.

How did you get on? Are you feeling confident? Would you like some answers? Let's do it.

So, 20 multiplied by 100 is equal to 2,000.

2,000 is 100 times the size of 20.

That's what that looks like.

20 multiplied by 100 is equal to 2,000.

And then seven multiplied by 100 is equal to 700.

700 is 100 times the size of seven.

That's what that looks like.

And the equation is this, seven multiplied by 100 is equal to 700.

And let's fill in these stems. We've got four multiplied by 100 is equal to 400.

400 is 100 times the size of four.

And that's the equation.

And 70 multiplied by 100 is equal to 7,000.

7,000 is 100 times the size of 70.

And that's the equation.

And number three, our true or false questions.

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

That's always true.

All multiples of 100 have a digit greater than zero in the hundreds, that's false.

Multiples of 1,000 can have a zero in the hundreds column and they will also be multiples of 100.

To find 100 times the size multiply by 100, that's true.

And all multiples of 100 have both the tens and ones digit of zero.

That's always, always true.

We've come to the end of the lesson.

You've been fantastic.

Today we've been explaining the relationship between multiplying a number by 100 and multiples of 100 and hopefully you are starting to feel really confident about that relationship.

To find 100 times as many of something, you have to multiply it by 100.

All the multiples of 100 have a ones and tens digit of zero.

So, I'm going to think of an example now.

3,200, the ones digit and the tens digit there are both zero.

Can you think of an example? And when a whole number is multiplied by 100, the product is always, always a multiple of 100.

So, let me think of an example.

72 multiplied by 100 is equal to 7,200 and 7,200 is a multiple of 100 because the tens and the ones are both zeros.

Well done in your accomplishments and your achievements today.

I hope you're very proud of yourself and I'm sure your teacher is too.

I hope I get the chance to spend another math lesson with you at some point in the very near future.

But until then, I hope you have a fantastic day filled with smiles and success.

Take care and goodbye.