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 tens 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 how a multiplication equation with two as a factor is related to doubling.

I expect you've done some doubling in the past, so it'll be useful to remember those doubling facts and see how we can write them as multiplications with two as a factor.

We've got one or two keywords today.

We've got double and doubling, so I'll take my turn and then it'll be your turn.

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

My turn, doubling, your turn.

Well done.

As I say, I'm sure you've done some doubling before, so look out for it as we go through our lesson and relate it to our multiplication.

There are two parts to our lesson.

In the first part we're going to be exploring two as a factor, and in the second part we're going to be solving some problems. So let's make a start on part one.

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

Aisha and Laura are exploring doubles.

Here we can see two groups of four.

Can you make the two groups of four with your fingers? One group of four, two groups of four.

So there is four two times, and that's the same as double four.

And we can write it with a multiplication.

In two times four, the four represents the number of fingers in each group and the two represents the number of groups.

So we've got two groups of four fingers.

Aisha says, "So that's two times four.

That's in the two times table," she says.

And we can say that two times four is the same as four plus four.

We can represent it with an addition as well.

Four plus four is the same as two groups of four.

Let's have a look at this one.

What have we got this time? Well here we've got two groups of three.

Can you make that with your fingers? Two groups of three.

There's three, two times and that's the same as double three.

And Laura says, "In two times three, the three represents the number of fingers in each group and the two represents the number of groups." We've got two groups of three fingers, two times three.

So we can see that when two is a factor, we had two times three, we can think about doubling the other factor.

So when we see two in a multiplication, we can think about doubling.

Two times three is the same as three plus three and that's equal to six.

Time to check your understanding.

Can you complete the sentences below? There are two groups of hmm.

There is hmm two times and this is the same as double hmm.

Okay, so have a look at the picture.

Complete the stem sentences.

Pause the video, and when you're ready for the answers and feedback, press play.

How did you get on? Did you make the two groups there? What did we have this time? There are two groups of five, aren't there? So our stem sentences say there are two groups of five, there is five two times, and this is the same as double five.

I hope you got that right and maybe you used your fingers to show it as well.

Two groups of five, double five.

Aisha is using 10 frames to explore doubles.

Oh, she's put in a red counter and a blue counter.

She says one, two times is the same as double one.

One plus one is equal to two.

She says that's two times one is equal to two.

That's the same as two groups of one.

It's double one isn't it? Can you see we've got that factor of two.

So when the factor is two, we can double the other factor.

And we know that double one is equal to two.

And we can represent that with multiplications in both ways, can't we? Two groups of one is equal to two and one two times is equal to two.

Two times one is equal to one times two.

Do you remember? Multiplication is commutative.

We can change the order of the factors and the product stays the same.

Ah, this time she's got two red counters and two blue counters.

Two plus two is equal to four, she says.

And two, two times is the same as double two.

As a multiplication, she says that's two times two is equal to four.

That's the same as two groups of two.

Two times two is equal to four.

Oh and two times two is equal to four.

Two, two times.

The factors are the same here, aren't they? Because we've got two groups of two.

So both our factors are two, our product double two is equal to four.

Let's have a look at some more doubles then.

What have we got here? Oh, we've got three red counters and three blue counters.

Can you think about how we can fill in that stem sentence? We've got something two times and it's the same as double something.

So how are we going to complete that stem sentence? Well, let's write our multiplications to help us.

We've got two groups of three counters, two times three, and we can see that it's equal to six.

But we can also say we've got three, two times because we know that we can record the multiplication factors in any order and the product stays the same.

So two times three is equal to three times two, and we can think of that as three, two times.

So let's complete our stem sentence.

Three, two times is the same as double three.

And we've got it there with the digits and also with the words.

What about this next one? What have we got here? We've got four red counters and four blue counters.

Four plus four is equal to eight.

Can you think of how we're going to record that as a double? Well we can say that two groups of four is equal to eight, and four, two times is equal to eight, two times four is equal to eight and four times two is equal to eight.

And what about our stem sentence? That's right, four two times is the same as double four.

What do you think our last one's going to be? We've got five red counters and five blue counters.

What's the addition going to be? That's right, five plus five is equal to 10.

How are we going to record that with multiplication? Yes, we've got two groups of five, two times five is equal to 10 and we've also got five, two times.

Five times two is equal to 10.

So can we complete our stem sentence? Five, two times is the same as double five.

Well done.

And Aisha says, "Remember, multiplication is commutative." We can change the order of the factors and the product stays the same.

So here are three examples on 10 frames.

Can you look and see what's the same? Well Aisha says two is always a factor in the multiplications.

In all of them we've got a two, sometimes we've got two twos, but that's because we've got a group size of two as well.

But because we've got two groups of counters, two is always a factor.

Ah, she's noticed that the total number of counters is always even.

We've got four in our first 10 frames, six in our second, and eight in our third 10 frame.

So they're all even numbers.

The equations we've written down are all in the two times table.

Two times two, two times three, two times four, or two times two, three times two and four times two.

But they're all in the two times table.

And when two is a factor, we think of doubling.

That's right, isn't it? That two represents the double of each of our 10 frames.

Double two, double three and double four.

And we can see that the two is representing doubling.

So can you look at this 10 frame and fill in the gaps? What can you see? Pause the video, have a go, and when you're ready for the answers and some feedback, press play.

How did you get on? Did you spot that we had five red and five blue counters? Five plus five is equal to 10.

And we can represent that with our multiplications.

Two times five is equal to 10 and five two times is the same as double five.

Five times two is also equal to 10.

Time for you to do some practise.

So in question one, you're going to look at the representations and fill in the blanks.

So you've got some pictures of fingers, two groups in each case.

Does that give you a hint? And in question two you're going to use your knowledge of doubles.

You've got in A and B, the equations to complete.

And in C, you've got some equations to complete and also fill in the 10 frame to represent what the equations are saying.

So pause the video, have a go, and when you're ready for some answers and feedback, press play.

How did you get on? Well, let's have a look at question one.

In A, we had two groups of two fingers.

So we've got two, two times and that's the same as double two.

And we can represent that with two plus two is equal to four or two times two is equal to four.

In B, there are two groups of six fingers.

So there's six, two times and that's the same as double six.

So we can represent that with an addition.

Six plus six is equal to 12 and also as a multiplication two times six is equal to 12.

And we could have six times two, six, two times as well.

And in C there are two groups of nine fingers, so there's nine two times and that's the same as double nine.

And we can represent that as nine plus nine is equal to 18, or two times nine is equal to 18, two groups of nine fingers.

So for question two, A was showing us two times six.

Six red counters and six blue counters.

Two times six is equal to 12 and six times two is equal to 12.

Six, two times.

Six plus six is equal to 12.

In B, we had eight red counters and eight blue counters.

So we were representing double eight.

Two times eight is equal to 16 or eight, two times eight times two is equal to 16 and we had eight plus eight is equal to 16.

In C we knew that we had two times 10, two groups of 10 is equal to 20.

So we must have had two full 10 frames, 10 red counters and 10 blue counters.

And you might have put all the red counters in one 10 frame and all the blue ones in another, but we've got two times 10 or 10, two times.

10 times two is equal to 20 and 10 plus 10 is equal to 20.

Well done if you've got all of those right.

And on into the second part of our lesson we're going to be solving problems. And Laura's going to use a bar model to explore doubling as well.

So what can you see here? Well Laura says, "I can see that there are two parts." We've got one part of three and another part of three.

So our bar model can represent parts and a whole.

She says, "The parts are equal." They're both equal to three aren't they? And the whole at the top is double one of the parts.

We know that when we've got two of something we are doubling.

So the whole is double one of the parts and that's what we can see in our equation.

Two times three is equal to six, one of our parts was three and there are two parts.

So when one factor is two, we know we can think about doubling.

Two times three is equal to six.

Aisha says the bar model shows two groups of three or three, two times.

Double three.

And we can represent that with our equation as well.

She says, "Each part is a group, so there are two groups." Two groups of three.

The value of the part is the number inside and the value here is three.

The product, so the result of multiplying our two factors is represented by the bar at the top and it has a value of six.

Two times three is equal to six.

So we can represent a bar model using multiplication as well if the parts are the same size.

Laura continues to use a bar model to explore doubling.

Can you see what she's got in her bar model this time? Laura says, I can see two parts and we can see those highlighted in the green and they're two equal parts.

They both have the same value.

The parts are equal and the whole is double one of the parts.

When the parts are equal, we can think about multiplication to represent our whole.

So we've got two groups of two and that's equal to four.

We know that when one of the factors is two, we can think about doubling.

In this case both our factors are two because we've got two groups and we've got two in each group.

So two times two is equal to four.

Laura says, "This time there are two groups of two.

Two, two times and double two." What do you notice this time? Ah, Aisha says, "This time the product is at the bottom and the parts are at the top.

It still shows that there are two groups of four." We've got two equal parts of four and we've got a whole of eight.

The value of each part is four.

This represents the group size and is one of our factors.

The two parts are equal and represent the number of groups.

So two is the other factor.

And the whole is double one of the parts and it represents our product.

So we've got two groups of four and we've got eight as our whole.

Two times four is equal to eight.

Four, two times is equal to eight.

And Aisha says, "When two is a factor you can double the other factor." So we can think of two times four, but because we know two is a factor, we can think double four and we might know already that double four is equal to eight.

So look at the bar model, what equation does it represent? It's a multiplication equation.

Pause the video, have a go, and when you're ready for the answers and some feedback, press play.

How did you get on? Well Laura says, I can see that there are two parts with the value of six and that is equal to 12.

So we've got two equal parts.

So one of our factors can be two, can't it? So our equation is two times six is equal to 12 and we can read that as two groups of six or two, six times, or we can think double six because one of our factors is two.

Well done if you've got that.

Aisha's stuck, what advice would you give her here? Hmm, she's got a bar model and she's got a missing value in her equation.

What's the missing value? Well Laura says, "We can see that something multiplied by seven is equal to 14." So we are thinking about those sevens.

We know that our product is 14 and we know that one factor is seven.

What can we see in that bar model? She says, well you know that two groups of seven is equal to 14 if you know about your counting in twos or about your doubling maybe.

So two groups of seven is equal to 14 and you also know that the whole is double one of the parts.

When we've got two parts and they're the same, the whole is double one of the parts and that's giving us a clue.

What do we know about doubling? What's one of our factors when we double? Ah, the missing factor must be two because two times seven is the same as saying double seven.

So our missing factor is two.

Two times seven is equal to 14.

Two groups of seven or seven, two times.

Now Laura's stuck, what advice would you give her? This time she knows her product and she knows that it's something times nine.

So what about those two parts? Aisha says, "We can see that something multiplied by nine is equal to 18." What about the two parts though? Well Aisha says, "You know that two groups of nine is equal to 18." Oh, there's that two again, isn't it? And we can see we've got two equal parts there.

You also know that when the parts are the same, the whole is double one of the parts.

So if we know that two lots of nine are equal to 18, so the missing parts must be nine because two times nine is the same as saying double nine and that's equal to 18.

So our parts are nine and our missing factor is two because we are doubling.

Time to check your understanding now.

Aisha has filled in the bar model with the given equation.

Is she correct? Have a look carefully at the bar model and the equation.

Do they represent the same thing? What needs to change? Pause the video, have a go, and when you're ready for the answer and some feedback, press play.

How did you get on? Did you spot that there was a mistake in one of the parts? The missing part must be 10 and not two.

This is because two groups of 10, two times 10 is the same as saying double 10.

When one of our factors is two, we can think about doubling.

10 plus 10 is equal to 20.

10, two times is equal to 20.

So our missing part has to be 10.

Well done if you spotted that.

Aisha and Laura are playing a card game.

They pick a card and have to multiply it by two.

So they pick the card three.

So Aisha says, "There are two groups of three.

There's three, two times.

So this is the same as double three." And Laura's made double three with her counters so they can see how many counters they've got altogether.

So they're going to fill in their equation.

Two times three is equal to six.

Two groups of three or three, two times.

So they've double three and it's equal to six.

They play another round.

This time they picked four.

Aisha says, "There are two groups of four.

There are four, two times.

This is the same as double four." And Laura's made double four with her counters.

So it's the same as saying two times four.

Two groups of four.

When two is a factor, we can think doubling.

And when it's doubling, we know that two is a factor.

Two times four is equal to eight or four, two times.

Time to check your understanding.

Aisha picked another card and multiplied it by two.

Can you find the correct representation? Is it A, B or C? Pause the video, have a think, and when you're ready for the answer and some feedback, press play.

What did you think? Was it A, B or C? Oh, it was A wasn't it? We've picked the card five.

So we've got to have two groups of five.

So five, two times and it's the same as double five and A represents double five.

B and C both represent double four, don't they? One of them upright and one of them on its side.

So A was the correct answer.

Well done if you spotted that.

Time for you to do some practise now.

In question one, you're going to use your knowledge of the two times table and doubling to complete the questions below.

You've got some bar models and you've got some equations and you've got to fill in the gaps in the equations and in the bar models.

And there's a couple more for question one.

And then in question two, Aisha has filled in the bar model with the given equation.

Is she correct? Can you help her out? And for question three, you're going to continue playing the card game.

You'll need a pack of cards from one to 12.

Partner A will choose a card, partner B will then multiply this card by two, and then you're going to draw and write an equation to represent this.

And I think if you get it right, maybe you can keep the card.

You've got some stem sentences there that Aisha's giving you to help you and an equation to fill in.

And their example is double 10.

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? Let's have a look at question one.

So in part A, we had a bar model with a whole of 10 and two parts of five, two equal parts.

So we can think about multiplying, we've got two times five is equal to 10 or five, two times is equal to 10.

In B, we had a bar model with 12 and we had a factor of two.

So we know we are doubling here, don't we? So our parts must be the same size and they must both be worth six.

So two times six is equal to 12, six times two is equal to 12.

We can think of that as six, two times.

In C, we had two equal parts of seven.

So we know that the other factor is going to be two because we are doubling and we know that double seven is 14.

So two times seven is equal to 14 and seven, two times is equal to 14.

And indeed we had two eights and then we had a missing whole.

So if we know that there are two equal parts, we know that we can be doubling.

So our other factor must be two.

So two times eight is equal to 16 and eight times two is equal to 16.

In E we had two equal parts of six, so our whole had to be double six.

So our other factor was two.

Two times six is equal to 12, six times two is equal to 12.

And in F all we knew was that we had a factor of two and a whole of 24.

So 24 is double something isn't it? And we know from our two times table and our doubles that two times 12 is 24.

24 is double 12.

So our equations are two times 12 and 12 times two and our missing parts were both worth 12.

So Aisha had filled in her bar model with a given equation.

Is she right? She's not right, is she? There are two equal parts and we know that this is representing two times nine, nine doubled is 18.

So the missing part must be nine and not two.

Well done if you spotted that.

And for three you were carrying on playing their card game, you might have got a 12.

Wow, that would be a lot of counters to represent two groups of 12 because you were doubling.

So there are two groups of 12, there are 12, two times, and this is the same as double 12, and two groups of 12.

Two times 12 is equal to 24.

Double 12 is 24.

Well done with all that doubling, you've worked really hard.

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

We've been explaining how a multiplication equation with two as a factor is related to doubling.

So we now understand that if two is a factor, you can use double facts to solve problems and doubling a number is the same as multiplying it by two.

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.