Lesson video

Hello, my name's Mrs. Hopper, and I'm really looking forward to working with you in this lesson on representing the five times table and linking it to the 10 times table.

So are you ready to do some counting in fives and 10s and explore how the five and 10 times table are related to each other? Are you? Excellent.

Let's make a start.

So in this lesson, we're going to be explaining the relationship between multiples of five and 10.

So more counting in fives and 10s for us, I think.

Let's make a start.

We've got two key words in our lesson today and I'm sure they're words you know, they're double and half, but let's just rehearse saying them.

So I'll take my turn and then it'll be your turn.

Are you ready? My turn, double, your turn.

My turn, half, your turn.

Well done.

I'm sure you've come across the words double and half before, but we are going to be using them today in our lesson, so look out for them.

There are two parts to our lesson today.

In the first part, we're going to be looking at the relationship between multiples of five and 10.

And in part two, we're going to be representing that relationship in different ways.

So let's make a start.

And we've got Aisha and Laura helping us in our learning today.

So Aisha and Laura explore the relationship between multiples of five and 10.

Can you see the representation we've got there? How many groups of five are there? How many groups of 10 are there? Well, we can see that there are two groups of five outlined in the purple and there's one group of 10 outlined in the green.

Could you see that? Two groups of five and one group of 10, but the same number of dots.

Aisha adds another frame.

What can you see this time? How many groups of five are there? How many groups of 10 are there? Well, this time there are four groups of five and there are two groups of 10.

There are the four groups of five outlined in purple and the two groups of 10 outlined in green.

Time to check your understanding now, how many groups of five are there and how many groups of 10 are there? Can you complete the stem sentences? Pause the video, have a go.

And when you're ready for some feedback, press play.

How did you get on? Did you spot that there are six groups of five in the purple and there are three groups of 10 outlined in the green? Hmm, now, you're spotting something here.

Miss Coe is counting the number of fingers with some of her class and they've got their hands up.

Can you see? How many groups of five are there? How many groups of 10 are there? Well, there's two fives, and another two fives, and another two fives, and another two fives, and there's a 10 for each of those 'cause we know that we've got 10 fingers altogether on our two hands.

So can we complete those stem sentences? There are eight groups of five and there are four groups of 10.

And you can say that for every one group of 10, there are two groups of five.

So for every one group of 10 fingers, there are two groups of five fingers.

And you can see that in the representation on the screen.

She's counting again.

What can you see this time? There are hmm groups of five.

There are hmm groups of 10.

I wonder how we're going to complete those sentences this time.

Are you ready? How many groups of five can you see? One, two, three, four, five, six, seven, eight, nine, 10 groups of five.

How many groups of 10? There are five groups of 10.

So let's complete the stem sentences.

There are 10 groups of five and there are five groups of 10.

Ooh, can you spot something happening there? And you can also say, for every two groups of five, there is one group of 10.

Every two hands, we've got 10 fingers.

Every two groups of five, we've got one group of 10.

And you can see that with your fingers as well I'm sure.

She's counting again.

What can you see this time? One, two, three, four, five, six, seven, eight groups of five, and one, two, three, four groups of 10.

So you can say if there are eight groups of five, there will be four groups of 10.

And that's because 10 is double five, so you'll need half the number of groups of 10.

So you can see there that we've got eight groups of five and four groups of 10, half the number of groups of 10 or double the number of groups of five.

What's it going to be this time? How many groups of five do you think we're going to need to match this number of groups of 10? Well, you can see it there with the fingers, can't you? One, two, three, four, five, six.

So you can say if there are three groups of 10, there will be six groups of five.

That's because five is half of 10, so you need double the number of groups of five to have the same number of groups of 10.

Time to check your understanding.

Complete the stem sentence and explain how you know.

So our sentence says if there are 12 groups of five, there will be hmm groups of 10.

And explain how you know.

Pause the video, have a think.

And when you're ready for some feedback, press play.

What did you spot? Ah, did you spot? If there are 12 groups of five, there will be six groups of 10.

And you could explain it by saying that's because 10 is double five.

So you'll need half the number of groups.

Well done if you've got that right.

Laura is counting five pence coins.

She found them in mum's purse.

I hope she's gonna put them back afterwards.

So she arranges them into groups of 10 to make it easier for her to count the amount of money she's got.

So she's got two five pences.

She says, "I know two groups of five make one group of 10 so that's 10 pence altogether." Five, 10.

So two fives are equal to one 10.

Laura finds some more coins.

How many groups of five has she got? She's got two groups of 10.

She says, "I know that two groups of 10 is equal to four groups of five." One, two, three, four.

Five is half of 10.

So I'll need double the number of groups of five.

So there are four groups of five and there are two groups of 10.

And we can see that clearly, there are four five p coins, but if we put them into pairs, we'd have a value of 10 ps.

So there are two lots of 10 p.

And it's 20 p altogether.

Four groups of five is equal to 20 and two groups of 10 is equal to 20.

Laura's mum gives her more coins.

So what's she got now? She's got six groups of five, but how many groups of 10 is that worth? Laura says, "I know that six groups of five is equal to three groups of 10." One, two, three.

If we put those fives together, two fives together are the same as 10.

So she says 10 is double five, so I will need half the number of groups of 10.

Six groups of five is the same as three groups of 10.

And how much money has she got? Ah, 30 p altogether, six groups of five is equal to 30 and three groups of 10 is equal to 30.

Time to check your understanding.

Can you use the image below of those five p coins to fill in the gaps? We've given you the number of groups of five, we've got eight groups of five, but it's how many groups of 10? So can you fill in the gaps? Eight groups of five is the same as hmm groups of 10 and that's hmm p all together.

Pause the video, have a go.

And when you're ready for some feedback, press play.

How did you get on? Did you spot that it was four groups of 10 and that it was 40 p altogether? Eight groups of five and four groups of 10 are equal to 40.

And you could explain that by saying that 10 is double five.

So I need half the number of groups of 10, eight groups of five is the same as four groups of 10.

Well done if you've got that.

And it's time for you to do some practise.

Using your knowledge of the relationship between the multiples of five and 10, fill in the blanks.

So for each of the images, you've got hmm groups of five and hmm groups of 10.

And Laura is saying, "Remember 10 is double five, so I'll need half the number of groups of 10." See if you can spot that relationship when you're filling in your answers.

And for question two, again you're going to fill in those blanks.

And in B and C, we've got pictures of five pence coins there.

So pause the video, have a go at your tasks.

And when you're ready for some feedback, press play.

How did you get on? So for A, we could see two groups of five and one group of 10.

And in B, we could see four groups of five and two groups of 10.

What about the hands in C? Well, we could see eight groups of five and four groups of 10.

You might have drawn a ring around the groups of 10 to help you.

And Laura's reminder that 10 is double five, so I'll need half the number of groups of 10.

So can you see that? Two groups of five, half of two is one, one group of 10.

Four groups of five, half of four is two, so two groups of 10.

And in C, eight groups of five, half of eight is four, so four groups of 10.

And can we see that same pattern in the questions for two? So in A, we had 10 groups of five fingers and five groups of 10.

And half of 10 is five so half the number of groups of 10.

And for the coins in B and C.

In B, we had eight groups of five p coins, and so we had four groups of 10, half of eight is equal to four.

And in C, we had 12 groups of five p coins and six groups of 10, and half of 12 is equal to six.

I hope you spotted those relationships between the multiples of five and 10 in your answers there.

And on into part two of our lesson, we're going to be representing that relationship between the multiples of five and 10.

Aisha has 10 counters and she wants to find out how many groups of 10 this is.

Do you know? She says, "I know for every two groups of five, there is one group of 10." And can you see her counters are in two groups of five? You can put two groups of five together to make one group of 10.

So let's do that.

There we go.

Our two groups of five have merged to make one group of 10.

Aisha now has 30 counters.

She wants to find out how many 10s this is.

She's arranged them into groups of five.

But she says, "I know for every two groups of five, there is one group of 10." Two groups of five makes one group of 10.

So you can put six groups of five together to make three groups of 10.

Should we see that happen? There we go.

Our six groups of five have become three groups of 10, the same number of counters, we've still got 30 counters there.

Time to check your understanding.

Can you gather 10 counters and can you show that for every two groups of five, there is one group of 10 using your 10 counters? Collect your counters, pause the video.

And when you're ready for some feedback, press play.

How did you get on? So with your 10 counters, you can make two groups of five and then you can put the two groups of five together to make one group of 10.

So for every two groups of five counters, we have one group of 10 counters.

Laura's thinking the other way around.

She wants to find out how many groups of five she's got.

She's got 10 counters.

She says, "I know for every one group of 10, there are two groups of five." So can she show this with her counters? You can split one group of 10 into two groups of five.

And there they go, one group of 10 split into two groups of five, the same number of counters, 10 is equal to two groups of five.

Laura now has 30 counters, and she wants to find out how many groups of five this is.

She's got them arranged in groups of 10 at the moment, but she says, "I know for every one group of 10, there are two groups of five." So can she split her groups of 10 counters up? Let's see.

Haha, you can split three groups of 10 to make six groups of five.

Let's watch that happen.

And our three groups of 10 have split themselves up to become six groups of five.

The same number of counters, six groups of five is equal to 30 and three groups of 10 is equal to 30.

Time to check your understanding.

Can you gather 10 counters again and can you show that one group of 10 is two groups of five? Pause the video, gather your counters.

And when you are ready for some feedback, press play.

How did you get on? So there's our group of 10 counters, but we needed to show that it was two groups of five.

And there we go.

You can split one group of 10 to make two groups of five.

Two groups of five is equal to 10.

Aisha is counting the fingers she can see and she records the groups of fives and 10s as times tables.

Ah, so she's thinking about her times tables.

And she says there are two groups of five and there is one group of 10.

She says, "I'm going to use my knowledge of grouping to help me." She can see the two sets of five fingers and she says two times five is equal to 10.

She's got two lots of five fingers, two times five, and she's got 10 fingers altogether.

But she can also see one group of 10 and one times 10 is equal to 10.

Another friend joins.

There are four groups of five now.

And those two groups of 10, how can we record that as our times table facts? So we've got one, two, three, four groups of five.

Four multiplied by five is equal to 20.

We've got four groups and we've got five in each group.

This equation is in the five times table.

It says Aisha because one factor is five.

That's right.

Five fingers on one hand gives us our factor of five.

And we've got four hands there.

Four groups of five is equal to 20.

What about the 10s? Ah, we can see that we've got two groups of 10 there, haven't we? Two multiplied by 10 is also equal to 20.

We've got the same number of fingers there.

We are just thinking about them in groups of 10 this time.

And Aisha says, "This equation is in the 10 times table because one factor is a 10." Two groups of 10 fingers is equal to 20 fingers.

Aisha's joining in two as well.

So now we've got six groups of five and three groups of 10.

Can you think what that's going to look like as our times tables? We've got one, two, three, four, five, six groups of five.

Six multiplied by five is equal to 30.

30 fingers altogether.

10, 20, 30.

Three groups of 10.

So we can represent that as three multiplied by 10 is equal to 30.

No wonder what you notice.

Aisha's noticed something.

She says, "The product is the number of fingers and it's the same." That 30 represents how many fingers there are altogether.

And it's the same if we count in fives or if we count in 10s.

Is there anything else you've noticed? Aisha says, "The factors are different.

The number of groups and the value of the group are different." We've got six groups of five fingers and we've got three groups of 10 fingers, but our product is the same.

Six times five is equal to 30 and three times 10 is equal to 30.

Well, Aisha has also noticed that double three is six and double five is 10.

And the product remains the same.

So we've got three groups of 10.

Well, if we double the number of groups, we get six groups, but that's six groups of five.

We could think of half of 10 is five, or we could think of that doubling of five to equal 10.

Time to check your understanding.

Can you fill in the blanks here? So there are hmm groups of hmm and hmm groups of hmm.

And can you fill in those times table calculations as well? Thinking about the number of groups and how many are in each group.

Pause the video, have a go.

And when you're ready for some feedback, press play.

How did you get on? So we had one, two, three, four, five, six, seven, eight groups of five.

So there are eight groups of five and we can represent that with eight multiplied by five.

There are eight groups and there are five in each group.

And altogether we've got 40.

What about 10s? One, two, three, four groups of 10.

So we can represent that with the multiplication four multiplied by 10 and it's also equal to 40.

We've got the same number of fingers, we've just counted them in a different way.

This time, our four represents four groups and our 10 represents 10 in each group.

And our stem sentences say there are eight groups of five and there are four groups of 10.

And you can think about all those doublings and halvings.

We've got double the number of groups of five and we've got half the number of groups of 10.

And we know that 10 is double five and five is half of 10.

Aisha compares the five and 10 times tables.

What patterns do you notice? Is there anything you've spotted? Ooh, she spotted lots of things.

She says, "Multiples of 10 appear in both the five times table and the 10 times table." Can you see we've got 20 highlighted there? It's in the five times table and it's in the 10 times table.

20 is two groups of 10 and it's also four groups of five.

Five is half of 10.

So you'll need double the number of groups.

So we had two groups of 10 to equal 20, but we've got four groups of five to equal 20 and double two is equal to four.

Double the number of groups of five.

Time to check your understanding now.

Can you use four times 10 is equal to 40 to find the gap for something times five is equal to 40? And can you explain why? Pause the video, have a go.

And when you're ready for some feedback, press play.

What did you think? So you may have said four groups of 10 are equal to 40.

So eight groups of five are equal to 40.

This is because five is half of 10.

So you need double the number of groups and you might have thought about fingers and hands perhaps.

So if you could picture four groups of 10, four people standing next to each other with their hands up, you'd have known that there were eight groups of five because five is half of 10.

So we need double the number of groups.

Well done if you work that out.

Time for you to do some practise now.

So for question one, you're going to write multiplication equations to describe the groups of five and 10 that you can see.

And we've got hands and we've got five p coins there.

And then for question two, you are going to gather 20 counters and you're going to group them into fives and group them into 10s.

How many groups of five are there? How many groups of 10 are there? And for question three, Alex has 60 counters.

He's grouped them into 12 groups of five.

How many groups of 10 is this? And Aisha had 35 counters.

She groups them into seven groups of five.

Can she make groups of 10? How do you know? So pause the video, have a go at your tasks.

And when you're ready for some feedback, press play.

How did you get on? So here are the multiplication equations.

So for A, we could see two groups of five and one group of 10.

So two multiplied by five is equal to 10 and one multiplied by 10 is equal to 10.

In B, we've got four groups of five equal to 20.

And we can also see that that's two groups of 10, but we can see 20 fingers altogether.

In C, we had eight groups of five equals 40 and four groups of 10.

And we can represent that with eight multiplied by five is equal to 40, and four multiplied by 10 is equal to 40.

We can see eight lots of five fingers and four lots of 10 fingers.

And indeed these were five p coins, and we had 12 lots of five p coins.

So 12 multiplied by five is equal to 60.

And we could think of that as six groups of 10 p coins.

Six multiplied by 10 is equal to 60.

So question two, you are going to gather 20 counters, group them into fives and then into 10s.

So how many groups of five were there? Well, there were four groups of five.

And how many groups of 10? There are two groups of 10.

We know that 10 is double five, so we'll need half the number of groups of 10 as we need of groups of five for our 20 counters.

And there you can see it moving between four groups of five and two groups of 10.

So for question three, Alex has 60 counters and he grouped them into 12 groups of five.

How many groups of 10 is this? Well, if there are 12 groups of five, if we imagine for every two groups of five, we've got one group of 10.

And we know that 10 is double five, so we'll need half the number of groups.

So we'll need six groups of 10.

And you might have done that by counting as well.

How many 10s are there in 60? We can count 10, 20, 30, 40, 50, 60.

So we've got six groups of 10.

And in question four, Aisha has 35 counters.

She groups them into seven groups of five.

Can she make groups of 10? Well, she can't, can't she? She can't make groups of 10 because 35 is not a multiple of 10.

The ones digit is a five and not a zero.

And if we imagined our seven groups of five being turned into groups of 10, we wouldn't be able to make a full group of 10 with our seventh group of five.

So there we can see it.

We can make three groups of 10, but we'll have one group of five left over.

And we've come to the end of our lesson.

We've been explaining the relationship between multiples of five and 10.

So we can understand that multiples of five are half the value of multiples of 10 and multiples of 10 are double the value of multiples of five.

Thank you for all your hard work and your mathematical thinking today.

I hope you've enjoyed the lesson and I hope I get to work with you again soon.

Bye-bye.