Lesson video

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Hi there.

My name is Mr. Tilston.

I'm a teacher.

I teach all of the different subjects, but the one I enjoy the most is definitely maths, so it's a real pleasure to be here with you today to teach you this lesson, which is all about multiples of 10.

So 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 10 and multiples of 10.

And we've got two keywords.

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

Scaling.

Your turn.

And my turn.

Multiple.

Your turn.

What do those words mean? Have you heard them before? Let's have a look.

Scaling is when a given quantity is made mm times the size.

So for example, two times the size, or five times the size, or 50 times the size.

And a multiple is a product of a number and an integer.

Could you think of an example of a multiple, let's say a multiple of 10? Our lesson today is split into two cycles, two different parts.

The first will be 10 times the size, and the second, multiplying by 10.

Let's start by looking at 10 times the size.

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.

Have you ever stretched or elongated something? "I make sticky-tack worms by rolling it," says Jun.

Hmm, that sounds fun.

So here's a little piece of sticky-tack and it's rolled out into a worm shape.

Have you ever done that? If you've got a little piece of sticky-tack in front of you now, you could do it now.

Make a little sticky-tack worm.

And he's rolled it again.

And Sofia says, "I like stretching out slinkies." So you got a slinky? So here's a slinky, and they stretch, don't they? You can pull them and they stretch, just like so.

So that's stretching.

What else can you stretch? Make a list of things that you can stretch or elongate like that.

Okay, pause the video and give that a go.

So we're looking for things that can be stretched.

What did you come up with, what kinds of things? Let's have a look.

Well, Jun says, "I thought of elastic in clothing." Yes.

And Sofia says, "I thought of stretchy toys made of rubber." So maybe you've got some toys at home that are stretchy.

Maybe you've got some toys in the classroom that you can stretch.

Scaling up is when a given quantity is multiplied by a number to make it bigger.

So my sticky-tack worm is getting longer.

Is a sticky-tack worm as a sticky-take.

Here's that sticky-tack worm getting longer and longer.

That's an example of scaling up.

And Sofia says "It's four times the length." The length is scaling up.

So I have scaled up the length by a factor of four.

So that original ball of sticky-tack has been scaled up by a factor of four, being made four times the length.

Jun is using a peg board, and if you're lucky enough to have this in your classroom, something like this, you could use one of these, too.

Jun says, "I'm going to put in two pegs and an elastic band." Let's have a look at that.

Here are the two pegs, and he's put an elastic band around them.

Sofia says, "The elastic band covers a length of one centimetre." Okay, got that one centimetre is the length that we can see there.

That's one centimetre.

"Underneath," he says, "I'll stretch another band further." So let's see what he does here.

So he put another peg down, and this time he's put his peg here.

Hmm.

He's put an elastic band around it.

What could we say about that length compared to the original length? Sofia says, "This elastic band covers a length of two centimetres." So the original one was one centimetre; the new one is two centimetres.

It's been scaled up.

The elastic band length scaled up.

It's twice the size.

It was one centimetre; it's now two centimetres.

"We can show this with multiplication," says Jun.

What's the multiplication? What do you think we could write here? Is there an equation that we could write? Well, we are doubling it.

We're multiplying it by two.

So one way that we could express this is one centimetre multiplied by two is equal to two centimetres.

"I'll stretch the second band further this time," he says.

So he's stretching.

Here we go.

Let's put an elastic band around it.

What could we say this time? Remember the original elastic band had a length of one centimetre.

What could we say this time? Well, this elastic band covers a length of four centimetres.

The elastic band length scaled up.

It is four times the size.

So we stretched it out to four times the size.

And once again, we can show that with multiplication.

What's the multiplication? One centimetre multiplied by four is equal to four centimetres.

Let's have a little check.

What is the multiplication that will represent the scaling up from the first elastic band to the second on this peg board? So look very, very carefully.

Okay, pause the video, and give that a go.

Let's have a look.

So the second band covers a length of three centimetres.

It has been scaled up.

It is now three times the size.

One centimetre multiplied by three is equal to three centimetres.

Jun returns to his sticky-tack worms and now he says, "I'm scaling up the length of the sticky-tack to make longer worms." And Sofia says, "I'll record it using equations." "Okay, my sticky-tack blob is one centimetre long to start with." So we can say one centimetre multiplied by one is equal to one centimetre.

What could we say now? This time it's one centimetre multiplied by two is equal to two centimetres.

It has been stretched.

It's been scaled up.

What about now? What can we say now? One centimetre multiplied by four is equal to four centimetres.

What about now? It's been stretched again.

It's been scaled up again.

Could we use an equation to record that? What could we say? That one-centimeter blob that we started with has been multiplied by 10, so it's been stretched with a scale factor of 10, and that's equal to 10 centimetres.

What do you notice here? Have a look at those examples, anything at all.

Jun says, "To find 10 times the size, you multiply by 10." That is exactly what 10 times the size is.

Let's have a check.

How long will the slinky be after Sofia has stretched it? Write an equation to calculate this.

Sofia says, "I'll stretch this slinky out to 10 times the length," and Jun says, "That's longer than the ruler.

You'll have to multiply instead of measure." So how long would it be? Can you write an equation? Pause the video.

Did you manage to write an equation there? Hmm.

Well, it started off at two centimetres.

So two centimetres multiplied by 10 is equal to 20 centimetres.

So if we stretched that two centimetres out 10 times, it would equal 20 centimetres.

Two centimetres multiplied by 10 is equal to 20 centimetres.

Sofia says, "I'm going to show 10 times the size on this pegboard using pegs." So it's a peg.

One peg multiplied by 10 is equal to 10 pegs.

Okay? And Jun says, "I don't think that's correct!" Hmm.

What do you think? Is Sofia correct? Jun says, "You have multiplied by 10 to find 10 times as many, not 10 times the size." They're different.

"Then I'll show it with an elastic band instead." There we go.

"It starts at one centimetre long and then I stretch it to the 10th peg hole." Okay.

And Jun says, "I still don't think that's correct!" What about you? What do you think? What has Jun seen this time? He's right, it's not correct.

What's he noticed? The elastic band is only nine centimetres long because there are 10 peg holes.

So it's not in fact been stretched to 10 times its size.

Jun explains further using pencils.

So there's a pencil.

There's another one,.

Another one.

And again, again, again, again, again, again, again.

We've got 10 pencils, so there's one pencil next to 10 times as many.

This shows one 10 times, or one pencil multiplied by 10 is equal to 10 pencils.

One pencil multiplied by 10 is equal to 10 pencils.

That's our equation.

Here's a pencil again.

This time it's 20 centimetres.

And then we've got this gigantic pencil that's 200 centimetres long.

That's a longer pencil.

That's longer than I am.

Jun says, "Here is one pencil of 20 centimetres next to another pencil 10 times the size, length in this case." So 20 centimetres multiplied by 10 is equal to 200 centimetres.

You can find out both of these by multiplying by 10, but the first is 10 times as many, and the second is 10 times the size, so they're different concepts, 10 times as many versus 10 times the size.

So the second one's a bit more like stretching.

Okay, let's do some practise.

Number one, match the words or phrases with the correct multiplication expression.

So we've got twice the size, 10 times the size, four times the size, and three times the size.

Can you match them up? We've got multiplied by 10, multiplied by two, multiplied by three, multiplied by four.

Are there clues, do you think, in the numbers? I can see some clues.

Number two, match the quantities with the quantities that are 10 times the size.

Can you match them up with the quantities that are 10 times the size? Number three, both the equations feature multiplying by 10, but which is finding 10 times as many, and which is finding 10 times the size? So think about stretching.

Is that 10 times as many or 10 times the size? So we've got one bag of sugar multiplied by 10 is equal to 10 bags of sugar.

One kilogramme multiplied by 10 is equal to 10 kilogrammes.

Number four, complete the ratio table below.

One has been done for you.

So the first column is two times the size, the second one is four times the size, and the third one is 10 times the size.

In the case of one centimetre, two centimetres is two times the size, four centimetres is four times the size, and 10 centimetres is 10 times the size.

Can you finish the rest? Righteo.

Pause the video and away you go.

Welcome back.

How are you getting on? Are you feeling confident? Let's have a look.

Let's give you some answers so you can check.

So number one, match the expression.

So twice the size is this one, multiplied by two, 10 times the size is this one, multiplied by 10, four times the size is this one, multiplied by four, and three times the size is this one, multiplied by three.

And then, match the quantities with the quantities that are 10 times the size.

So 10 times the size of three centimetres is 30 centimetres, 10 times the size of nine kilogrammes is 90 kilogrammes, 10 times the size of 11 centimetres is 110 centimetres, and 10 times the size of six metres is 60 metres.

And number three, both the equations feature multiplying by 10, but which is finding 10 times as many, and which is finding 10 times the size? They're different concepts.

So one bag of sugar multiplied by 10 equals 10 bags of sugar.

That's 10 times as many.

There were 10 times as many bags of sugar.

And then one kilogramme multiplied by 10 equals 10 kilogrammes.

That's 10 times the size.

And number four, complete the ratio table below.

Here are the answers.

Well done if you got those.

I think you're ready for the next part of the lesson, and that's multiplying by 10.

Let's find out.

Jun and Sofia use a Gattegno chart.

I love Gattegno charts.

They're so helpful.

So here we've got one circled, and we've got 20 circled, and we've got 500 circled.

What number have I made? So I'm sure that you've used a Gattegno chart before, so hopefully this is ringing a bell.

What number has been made here by circling those three numbers? It's showing the three parts of that number.

What number is being represented on this Gattegno chart? Sofia says, "You've made 500 plus 20 plus one, and that is equal to 521." Yes, it is.

Let's do another one.

Here's 40, here's six.

"What number have I made?" asks Sofia.

What do you think? What number's being represented on the Gattegno chart? "Well, you didn't use any hundreds," says Jun.

So that's just 40 plus six and that equals 46.

Let's do another one.

I've got four circled, hm.

Just four this time.

What number have I made? What number's being represented on the Gattegno chart? Sofia says, "This is four because there are no other values selected." So that's a Gattegno chart.

That's how that works.

Complete the equation below to show which number is being represented on this Gattegno chart.

Two numbers have been circled.

Can you complete that equation? Okay, pause the video.

Well, let's see how you got on.

That's 300 plus six, and that is equal to 306.

Jun and Sofia use a Gattegno chart and Sofia says, "Let's model finding 10 times the size using the Gattegno chart." Gattegno charts are really, really helpful for finding 10 times the size of a number.

Jun says, "Okay, let's be systematic," one of my favourite words in math, systematic, "and start with one." So we've got one circled.

"One multiplied by 10 is equal to 10." Would you agree? "10 is 10 times the size of one." What about this? "Two multiplied by 10 is equal to 20." "20 is 10 times the size of two." Can you see a pattern? "Three multiplied by 10 is 30." "30 is 10 times the size of three." And we could show that on the Gattegno chart.

So it's the one just above it.

Do you think you're getting the hang of this? Join in with me if you can.

Four multiplied by 10 is 40.

40 is 10 times the size of four.

Again, it's the number straight above it on the Gattegno chart.

Five multiplied by 10 is 50.

50 is 10 times the size of five.

And again, we can see that it's the number straight above it on the Gattegno chart.

Okay, complete the Gattegno chart to show six multiplied by 10 is equal to 60 and then fill in the missing numbers in the sentences below.

So mm multiplied by mm is mm, and mm is mm times the size of mm.

Pause the video.

How'd you get on? So this is six multiplied by 10 is 60.

And we can see that on the Gattegno chart those two numbers have been circled.

And 60 is 10 times the size of six.

Jun and Sofia use a Gattegno chart.

What do you notice? Jun notices moving up in a Gattegno chart is multiplying by 10.

So we've moved up, we've moved up, we've moved up, we've moved up, we've moved up, we've moved up, we've moved up, and we've moved up.

So each time we've multiplied that number by 10 and we moved up one in the Gattegno chart.

When multiplying by 10, the products are all multiples of 10.

Did you spot that? They all have a zero in the ones digit.

True or false, all multiples of 10 have a zero as the ones digit.

Hmm, true or false? Can you explain why? Pause the video.

What do you think? Was that true or false? That's true, but why? This is because 10 has a zero as the ones digit, and then a multiple of 10 is made up of groups of 10 without any extra ones.

So multiples of 10 are simply groups of 10.

Jun and Sofia look at a Gattegno chart and Sofia says, "I'll describe making a number 10 times the size and you can represent it on the Gattegno chart.

Three multiplied by 10 is equal to 30.

30 is 10 times the size of three." How would you represent that on the Gattegno chart? Let's see if Jun can do it.

"I'll draw an arrow from three to represent making it 10 times the size on the Gattegno chart." So here's three, there's an arrow, and there's 30.

"So that's three multiplied by 10 is equal to 30 and the product is 30." And 30 is a multiple of 10.

Three multiplied by 10 is equal to 30.

That's the equation.

This time I'll draw on the Gattegno chart and you have to describe it, and why don't you join in as well? Let's see what Jun's done.

This is what he's drawn.

Hmm, what equation can you see here? A bit different this time, isn't it? Sofia says, "Nice challenge." She likes being challenged in maths.

I hope you do, too.

"You started with a multiple of 10." Yes.

So the first number was a multiple of 10.

"60 multiplied by 10 is equal to 600.

600 is 10 times the size of 60." And again, notice, says Jun, "600 is also a multiple of 10 as it has a zero as the ones digit." So when we multiply a multiple of 10 by 10, we still got a multiple of 10.

Let's do some final practise.

Number one, read the descriptions of making a number 10 times the size and represent both on the Gattegno chart.

Then, represent both as an equation.

So we've got, Jun says, "20 multiplied by 10 is equal to 200.

200 is 10 times the size of 20." And Sofia says, "Seven multiplied by 10 is equal to 70.

70 is 10 times the size of seven." Can you represent those on the chart and with equations? Number two, look at the representations of making a number 10 times the size on the Gattegno chart and complete the sentences to describe them.

Then, describe both as an equation.

And we've got some stem sentences here.

Mm multiplied by mm is equal to mm.

Mm is mm times the size of mm.

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