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Hello there.
My name is Mr. Tilstone.
I'm a teacher.
If I've met you before, it's lovely to see you again and if I haven't met you before, it's nice to meet you.
I hope you are feeling sharp and refreshed and ready for today's math challenge.
I'm looking forward to it.
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 our key words.
We've got two of them.
If I say them, will you say them back? My turn, multiple.
Your turn.
And my turn digit.
Your turn.
You've probably heard those words before, but let's have a little check and a reminder about what they mean.
A multiple is a result of multiplying a number by another whole number.
So can you think of an example of a multiple? And a digit is one of the symbols of a number system.
In our number system we use the digit 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
They are all digits.
Our lesson today is split into two parts or two cycles.
The first is 10 times as many and the second is multiples of 10.
So let's start by thinking about 10 times as many.
And in this lesson you're going to be Izzy and Andeep.
Have you met them before? They're here today to give us a helping hand with the maths.
Andeep and Izzy practised a 10 times table.
How good are you at your 10 times table? 10, 20, thirty, forty, fifty, sixty, 70, 80, 90, 100, 100 and 10, 100 and 20.
You are going to practise the 10 times table by counting in tens, just like Andeep and Izzy did.
If you have a partner, try counting back and forth between you.
Pause the video.
Welcome back.
So this is Andeep and Izzy, and he says 10.
She says 20, 30, 40, 50, 60 70, 80, 90, 100, 110, 120.
That's counting in tens.
That's multiples of 10.
Andeep has one pencil and Izzy has 10 times as many.
How many pencils does Izzy have? Let's have a look at Andeep's one pencil.
He says, for every one pencil I have, you have 10.
His is one and 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
That's Izzy's 10.
Think of one and make it 10 times the size says Izzy.
So one, 10 times the size of one is 10.
Think of one and multiply by 10, says Andeep.
One multiplied by 10 is equal to 10.
10 pencils is 10 times as many as one pencil.
I have 10 pencils.
Now Andeep has two pencils and Izzy has 10 times as many.
How many pencils does Izzy have? Let's have a look.
Andeep says, for every one pencil I have, you have 10.
So here's Andeep, one pencil and here's Izzy's 10 pencils.
Here's another one of Andeep's pencils and another 10 of Izzy's pencils.
So that's two this time.
And Izzy says, think of two and make it 10 times the size.
So two 10 times the size is 20.
Think of two and multiply by 10, says Andeep.
Two multiplied by 10 is equal to 20.
20 pencils is 10 times as many as two pencils.
I have 20 pencils.
Now Andeep has three pencils.
Izzy has 10 times as many.
How many pencils does Izzy have? For every one pencil I have, you have 10.
So there's time one, 10, another one, another 10, another one, another 10.
What have we got? So that's three pencils for Andeep.
Think of three and make it 10 times the size.
10 times the size of three is 30.
Think of three and multiply by 10, say Andeep.
Three multiplied by 10 is equal to 30.
30 pencils is 10 times as many as three pencils.
I have 30 pencils.
So one 10 times as many as equal to 10.
Two, 10 times as many is equal to 20.
Three 10 times as many is equal to 30.
What do you notice? Anything at all? Andeep says, "I noticed that for all of them, for every one pencil I had, you had 10 pencils." That means you had 10 times as many pencils as me.
And Izzy says, I noticed that to find 10 times as many you have to multiply by 10.
One multiplied by 10 is equal to 10.
Two multiplied by 10 is equal to 20.
Can you do the last one with me? Are you ready? Three multiplied by 10 is equal to 30.
Let's do a check.
Complete the missing numbers to finish the equation describing the images.
So do a little count of the pencils on the left and we've got 10 times as many.
And how many pencils have we got on the right? Remember on the right they are in tens.
Pause the video.
How did you get done? Let's have a look.
Six multiplied by 10 is equal to 60.
Let's do some practise.
Number one, complete the missing numbers below and you'll notice a missing part of each equation is in different positions.
And number two, complete the diagrams below that.
Describe the representations of pencils.
And number three, which of the characters below do you agree with? Explain your reasoning.
So let's say, Andeep says to find 10 times as many of something you have to count up in tens that number of times.
And Izzy says to find 10 times as many as something, you have to multiply it by 10.
So do you agree with Andeep? Do you agree with Izzy? Do you agree with neither? Do you agree with both? Whatever your choice, can you explain and justify it? Okay, pause the video and I'll see you soon for some feedback.
How did you get it? Let's have a look.
Let's give you some answers.
So number one, zero multiplied by 10 is equal to zero.
One multiplied by 10 is equal to 10.
Two multiplied by 10 is equal to 20, three multiplied by 10 is equal to 30, four multiplied by 10 is equal to 40, five multiplied by 10 is equal to 50, six multiplied by 10 is equal to 60, seven multiplied by 10 is equal to 70, eight multiplied by 10 is equal to 80, nine multiplied by 10 is equal to 90, 10 multiplied by 10 is equal to 100, 11 multiplied by 10 is equal to 110 and 12 multiplied by 10 is equal to 120.
That's how 10 times tables.
And number two, complete the diagrams below.
So we've got four multiplied by 10 is equal to 40.
Four 10 times the size is 40, and then 10 times as many as four is 40.
And for B five multiplied by 10 is equal to 50.
Five 10 times the size is 50 and 10 times as many as five is 50.
Number three, which of the characters do you agree with? Well actually both characters are saying similar things here.
Andeep is using tens as a group size in a multiplication, whereas Izzy is using 10 as a number of groups.
So they were both right.
So well done, if you said that, you might have given a different explanation to that.
I think you are ready for the next cycle, which is multiples of 10.
You're doing really, really well.
Let's see if you can keep that up.
Andeep and Izzy look at packs of pencils.
In every pack says Andeep, there are 10 pencils.
So one pack is equal to one multiplied by 10, which is equal to 10 pencils.
Now there are two packs of 10 pencils.
We can see that.
And Izzy says, I know two multiplied by 10 is equal to 20.
So there are 20 pencils.
Andeep says, now there are three packs of 10 pencils.
What might Izzy say here? She says, I know three multiplied by 10 is equal to 30.
So there are 30 pencils.
How many pencils are there in four packs? Write an equation to show your calculation.
Pause the video.
Did you get it? That's four multiplied by 10 is equal to 40.
So 40 pencils.
We've got 10, 10 pencils.
20.
20 pencils.
30.
30 pencils.
40.
40 pencils.
What do you notice? Anything at all? Andeep notices.
This is the 10 times tables.
They're all multiples of 10.
And Izzy says, "I notice they all have ones digit of zero." Did you notice that as well? 10 had a ones digit of zero, 20 ones digit of zero, 30 ones digit of zero and 40 the ones digit is zero.
That's true of all four of those examples.
Let's use a different representation to show this.
So Izzy creates a stacked number line as we call them.
So here's a number line that goes from zero to 12 in ones and below it a number line that goes from zero to 120 in tens.
Andeep says this shows the 10 times table two, the bottom line are all multiples of 10.
Izzy says they all have ones digit of zero.
Can you see that? 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120.
The ones digit is zero in all of those examples.
All of those multiples of 10 have got a ones digit of zero.
Andeep and Izzy play a game.
They are shown different two digit numbers.
When they see a multiple of 10, they have to shout "Multiple of 10" to gain a point.
The first to three points wins.
You can play along if you like.
Let's see.
11.
Good, that's not a multiple of 10.
24.
Good, not a multiple of 10.
30.
Did you shout, Izzy did, multiple of 10.
30 is three multiplied by 10 and has a zero in the ones place.
That's how we know it's a multiple of 10.
It's got a zero in the ones place.
Let's keep going.
Izzy gets a point.
65, not a multiple of 10.
70.
Did you shout multiple of 10? Andeep did.
He gets a point.
It's a multiple of 10.
It's a whole number with a zero for the ones digit.
53, 20.
Did you shout? Multiple of 10 says Izzy.
It's a whole number and it's got a zero for the ones digits.
A multiple of 10.
She's got another point.
Shall we keep going? She's getting close.
Who's going to be the winner here? One more for Izzy.
And she's done it.
31, not a multiple of 10.
It hasn't got a zero for the ones digit.
64.
Hmm same.
10, "Multiple of 10," shouts Izzy.
10 is still a multiple of 10.
In fact it's the first multiple of 10.
So well done if you got that.
I win, says Izzy, well done.
Maybe they could have a rematch.
It is time for some final practise.
Number one, sort these numbers into the correct column according to whether they are a multiple of 10 or not.
So we've got 1, 4, 15, 200, 42, 208, and 30.
So think about what it is that makes a number a multiple of 10.
Number two, complete the table by deciding true or false.
So a tick for true across for false are these multiples of 10? Have a think.
You might like to have a think about why as well.
Can you explain that? Number three, using all four cards each time, how many different multiples of 10 can you make? Maybe you could use a system to find all of them.
And number four, do you agree with Andeep? Explain your answer.
Let's see what Andeep says.
Multiples of 10 always have a digit greater than zero in the tens column.
Hmm.
Have a good think about that.
Read it again if you need to, take your time, make sure you've understood it and then see if you agree or disagree and explain why.
Have fun with that.
And I'll see you soon for some feedback.
Welcome back.
How did you get on? Are you feeling confident? Let's compare your answers with ours.
So number one, sort these numbers into the correct column.
So we're looking for the multiples of 10 or not multiples of 10.
Well, one isn't a multiple of 10.
It doesn't have a zero in the ones digit.
Four is not a multiple of 10 for the same reason.
The first multiple of 10 is 10.
And those numbers are less than 10.
15 no, that is a two digit number.
It's not a multiple of 10 though it's got a five in the ones digit, not a zero.
200 is a multiple of 10.
It's got a zero in the ones digit.
42 is not a multiple of 10.
It hasn't got a zero in the ones digit.
208 is not a multiple of 10.
It hasn't got a zero in the ones digit.
And 30 is a multiple of 10.
It has got a zero in the ones digit.
These all have a zero as a ones digit.
Can you think of any other examples? Number two, complete the table by deciding true or false.
Let's have a look.
30.
Yes, that's true.
It's got a zero for the ones digit, and 130 it has got a zero for the ones digit.
103 no, it's got a three in the ones digit.
It's not a multiple of 10.
Multiples of 10 have a zero as a ones digit.
And 1000 is another example of that.
The ones digit is zero.
And finally 1020.
The ones digit is zero.
You don't really need to look at the other digits.
Number three, using all four cards each time, how many different multiples of 10 can you make? Now, did you use a system? Andeep says the zero will have to be the ones digit for every number.
Yes.
Otherwise, it's not a multiple of 10, is it? Multiples of 10 always have a zero as a ones digit? They do always.
And easy to say is then we can work systematically through the other digit combinations.
So starting with the lowest possibility, that's 1,230 and then 1,320, 2,130, 2,310, and 3,120 and 3,210.
That system worked really, really nicely and enabled us to find all of the possibilities.
So well done if you've got one possibility, well done if you've got more than one possibility, but especially well done if you've got all six possibilities there.
And do we agree with Andeep? He says multiples of 10 always have a digit greater than zero in the tens column.
Izzy disagrees and she's right to disagree.
She says numbers only need a zero as a ones digit, but they can have a zero in other place value columns too.
Let's see some examples.
Here are some examples of numbers that are multiples of 10, but also have a zero in the tens column.
So 100, 200, 300, they're all multiples of 10.
You could count in tens and reach those numbers.
Well, we've come to the end of the lesson and you've done really, really well.
I hope you're proud of yourself.
In today's lesson, we've been explaining the relationship between multiplying a number by 10 and multiples of 10.
They are directly linked.
To find 10 times as many of something, you have to multiply it by 10.
And you've done lots of examples of that today.
All multiples of 10 have zero as a ones digit.
So let's think of some examples.
What about 70? That's my multiple of 10.
Let me give another one.
What about let's say 400? That's got a zero for the ones digit and a zero for the tens digit.
But the important part of that is it's got zero for the ones digit.
And what about, let's say 520? Lots of possible examples.
What have you got? Well done on your accomplishments and your achievements today.
You've been fantastic and I think you are ready for the next step in your learning.
Give yourself a pat on the back.
It's very well deserved.
I hope you have a fantastic day, whatever you've got in store.
If you've got any more lessons coming up today, I hope they're successful and that you are the best version of you that you can possibly be.
Take care and goodbye.
