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Hi there, my name is Mr. Tilstone.
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 key words.
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 (hums) 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 Sophia 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 Sophia says, "I like stretching out Slinkies." Have 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.
OK, 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 Sophia 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.
Here's a sticky-tack worm as a sticky-tack.
Here's that sticky-tack worm getting longer and longer.
That's an example of scaling up.
And Sophia 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.
It's been made four times the length.
Jun returns to his sticky-tack worms. Now he says, "I'm scaling up the length of the sticky-tack to make longer worms." And Sophia 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's been stretched and 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 centimetre 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 Sophia has stretched it? Write an equation to calculate this.
Sophia 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 will it be? Can you write an equation? Pause the video.
Did you manage to write an equation there? Well, it started off at two centimetres, so two centimetres multiplied by 10 is equal to 20 centimetres.
So if we stretch that two centimetres out 10 times, it would equal 20 centimetres.
Two centimetres multiplied by 10 is equal to 20 centimetres.
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.
There's 200 centimetres long.
That's a long 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.
OK, 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? 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's 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? Rightio.
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 Sophia 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 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 has been represented on this Gattegno chart? Sophia says you've made 500 plus 20 plus 1, and that is equal to 521.
Yes, it is.
Let's do another one.
Here's 40, here's 6.
What number have I made, asks Sophia.
What do you think? What number has been represented on the Gattegno chart? Well, you didn't use any hundreds, says Jun, so that's just 40 plus 6, and that equals 46.
Let's do another one.
I've got four circled.
Just four this time.
What number have I made? What number has been represented on the Gattegno chart? Sophia 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? Pause the video.
Well, let's see how you got on.
That's 300 plus 6, and that is equal to 306.
Jun and Sophia use a Gattegno chart.
And Sophia 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, OK, let's be systematic.
One of my favourite words in math, systematic, and start with one.
So we've got one circle.
1 multiplied by 10 is equal to 10.
Would you agree? 10 is 10 times the size of 1.
What about this? 2 multiplied by 10 is equal to 20.
20 is 10 times the size of 2.
Can you see a pattern? 3 multiplied by 10 is 30.
30 is 10 times the size of 3.
And we can show that on the Gattegno chart.
So it's a 1 just above it.
Do you think you're getting the hang of this? Join in with me if you can.
4 multiplied by 10 is 40.
40 is 10 times the size of 4.
Again, it's a number straight above it on the Gattegno chart.
5 multiplied by 10 is 50.
50 is 10 times the size of 5.
And again, we can see that it's a number straight above it on the Gattegno chart.
Okay, complete the Gattegno chart to show 6 multiplied by 10 is equal to 60.
And then fill in the missing numbers in the sentences below.
So (hums) multiplied by (hums) is (hums).
And (hums) is (hums) times the size of (hums).
Pause the video.
How'd you get on? So this is 6 multiplied by 10 is 60.
We can see that on the Gattegno chart, those two numbers have been circled.
And 60 is 10 times the size of 6.
Jun and Sophia 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 multiply 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 a ones digit.
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 a 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 Sophia look at a Gattegno chart.
And Sophia says, I'll describe making a number 10 times the size.
And you can represent it on the Gattegno chart.
3 multiplied by 10 is equal to 30.
30 is 10 times the size of 3.
How would you represent that on the Gattegno chart? Let's see if Jun can do it.
I'll draw an arrow from 3 to represent making it 10 times the size on the Gattegno chart.
So here's 3.
There's an arrow.
And there's 30.
So that's 3 multiplied by 10 is equal to 30.
And the product is 30.
And 30 is a multiple of 10.
3 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.
What equation can you see here? Bit different this time, isn't it? Sophia says, nice challenge.
She likes being challenged in math.
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 this, Jun.
600 is also a multiple of 10, as it has a 0 as the ones digit.
So when we multiply a multiple of 10 by 10, we've 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 Sophia says, 7 multiplied by 10 is equal to 70.
70 is 10 times the size of 7.
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.
(hums) multiplied by (hums) is equal to (hums).
(hums) is (hums) times the size of (hums).
Number three, complete the table by deciding true or false.
You might like to explain why as well.
When a whole number is multiplied by 10, the product is a multiple of 10.
10 times as many and 10 times the size are the same.
True or false? Define 10 times the size multiplied by 10.
True or false? Define 10 times as many multiplied by 10.
True or false? All multiples of 10 have a zero as the ones digit.
True or false? Okay.
Good luck with that.
Pause the video and I'll see you shortly.
Welcome back.
How did you get on? Are you feeling super confident now? Let's have a look.
So read the descriptions of making a number 10 times the size and represent both on the Gattegno chart.
So we've got 20 multiplied by 10 is equal to 200.
200 is 10 times the size of 20.
And that's what that looks like on the Gattegno chart.
And as an equation, we can say 20 multiplied by 10 is equal to 200.
And what about this one? 7 multiplied by 10 is equal to 70.
70 is 10 times the size of 7.
We can show that like this on the Gattegno chart.
And as an equation, 7 multiplied by 10 is equal to 70.
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 represent both as an equation.
So we've got 4 multiplied by 10 is equal to 40.
That's our first example on the left.
And we can also say 40 is 10 times the size of 4.
And as an equation, we write that like this.
4 multiplied by 10 is equal to 40.
And for our second example, 80 multiplied by 10 is equal to 800.
Or 800 is 10 times the size of 80.
And as an equation, 80 multiplied by 10 is equal to 800.
Number three, true or false? When a whole number is multiplied by 10, the product is a multiple of 10.
Yes, that's true.
Even when you start with a two-digit number or a two-digit multiple of 10, when you multiply it by 10, the product is also a multiple of 10.
10 times as many and 10 times the size are the same.
True or false? No, that's not true.
That's false.
10 times as many could be 10 of an object, whereas 10 times the size could be one object but 10 times bigger.
So they're not quite the same.
They're different concepts.
10 times the size is more like that stretching relationship or growing.
And then to find 10 times the size multiplied by 10, that's true.
To find 10 times as many multiplied by 10, that's true.
And all multiples of 10 have a zero as a ones digit.
That's also true.
No matter what the multiple of 10 is, it's got a zero for the ones digit.
And if it hasn't, it's not a multiple of 10.
We've come to the end of the lesson.
You've been amazing.
I've really enjoyed this lesson.
Today, we've been understanding that multiplying by 10 makes a number 10 times the size.
You've done that in lots of different ways, including those examples related to stretching.
Making a number 10 times the size is a form of scaling.
To find 10 times the size of a number or quantity, multiply it by 10.
When a number is multiplied by 10, the product is also a multiple of 10.
You've looked at lots of different examples of that today.
I hope you're very proud of yourself today and I'm sure your teacher is too.
I hope you have an amazing day, whatever you've got in store.
Whatever lessons are coming up, I hope you succeed in them and that you are the best version of you that you could possibly be.
You can't ask for more.
I also hope I get the chance to spend another maths lesson with you in the near future.
But in the meantime, take care and goodbye.
