Lesson video

Hello there.

How are you today? I hope you're having a really good day.

My name is Ms. Coe.

I am really, really excited to be learning with you today in this math lesson where we are thinking about doubling and halving.

Now, you may have had some recent experience looking at the two times table, and if you can recall or remember any of those two times tables facts, that's gonna be really helpful in your learning today.

So if you are ready, let's get started.

This lesson is part of the unit focusing on multiples of two, doubling and halving, and by the end of this lesson you'll be able to say that you can double two digit numbers and record this as a multiplication equation where one of the factors is two, and you may have had some recent experience thinking about factors and the two times table.

We have a few keywords in our learning today.

I'm going to say them and I'd like you to say them back to me.

Are you ready? My turn.

Double.

Your turn.

My turn, doubling.

Your turn.

My turn, partition.

Your turn.

My turn, factor.

Your turn.

My turn, product.

Your turn.

Excellent work.

Keep an ear out for these words in your learning today and see if you can use them yourself in your explanations.

In this lesson today we're going to be doubling two digit numbers and recording them as multiplication where one of the factors is two.

We have two cycles in our learning today.

In the first cycle we're going to be doubling two digit numbers and in the second cycle we're going to be recording doubling as a multiplication equation.

If you are ready to get going, let's get started with the first lesson cycle.

In this lesson today, you're going to meet Aisha and Alex.

They're going to be helping us with our learning.

So let's start here.

Alex and Aisha are revisiting their doubling skills.

Now you might have some experience with doubling.

You might know some doubling facts or have a strategy that you can use to double.

Let's see what Alex and Aisha do.

Alex is solving double eight.

We can see eight fingers there.

He says "I'm trying to solve double eight, but I don't have enough fingers." He's only got 10 fingers.

He doesn't really want to get his toes out as well.

What could he do? Aisha's giving him a really good strategy.

She says, "Remember, eight is equal to five, add three, so double five, add double three is equal to double eight." Now we can see that eight is five and three by looking at the fingers.

We have one group of five and one group of three and we can see that eight is made of five and three.

Aisha's saying if we double the five and double the three, that's the same as doubling eight.

That's a really good strategy I think.

Alex uses Aisha's strategy and 10 frames to double eight.

So first he's going to partition eight into five and three on his frames.

We know that eight can be partitioned in five and three like so.

Then we can double each of the parts.

That's double five.

Double five is 10, that's double three.

Double three is six.

How many counters do we have altogether? Is there an efficient way that we can find out? Well we can see that we have 10 and six.

10 plus six is equal to 16, so that means that double eight is 16.

Great use of that strategy, Alex, well done.

Time to check your understanding.

Use your 10 frames and Alex's stem sentences to double nine.

So we can say nine can be partitioned into mm and mm.

Think about an efficient way to partition.

Think about how you can double those two parts and if we double those two parts, then we know what nine doubled is.

Pause the video here and have a go.

(no audio) Welcome back.

How did you get on? Well there are lots of ways that you can partition nine but to do it efficiently when doubling.

So we can see a part of five and a part of four.

We know that nine is equal to five plus four.

Then we can double those parts.

So double five is 10 and double four is eight.

Now we can think about how many counters we've got altogether.

Now remember we you think about these groups to calculate efficiently.

We have 10 plus eight which is 18.

So I know that double nine is a 18.

Well done if you talked through it and partitioned nine efficiently in order to double.

Aisha notices another way that she could double nine.

Let's see what she says.

Aisha says that nine is one less than 10, so double 10 subtract double one will also be equal to double nine.

Oh I think that's quite hard to think about.

Should we see what that looks like on 10 frames? Here we can see 10.

If we double 10, we know double 10 is 20.

That's quite an easy fact to remember but we don't want to double 10.

We want to double nine.

We know that nine is one less than 10, so double one is two.

So we can subtract that, 20 subtract two, is equal to 18, that means that double nine is 18.

That's an excellent strategy, Aisha, and it might be one you want to use yourself.

Aisha explores the idea of doubling 10 further.

She knows that she could use a 10 pence coin to represent 10.

There's a 10 pence coin.

It has a value of 10 pence.

It's worth 10.

One 10 is 10.

Well what is two 10s? I wonder.

Well here are two 10s.

I can say double one 10 is two 10s.

Can you say that with me? Double one 10 is two 10s.

We can also say double 10 is 20.

10 plus 10 is equal to 20.

These all mean the same thing.

So what if Aisha doubled two 10s? Can you visualise that? Can you imagine what would happen? There we go.

We've doubled two 10s.

What do we have now? How could we write it? Well, we can say that double two 10s is four 10s.

We had two 10s, we doubled it and we now have four 10s.

We could say that double 20 is 40.

20 plus 20 is equal to 40.

They all mean the same thing.

They all mean that double 20 is 40.

So what would happen then if she doubled three 10s? Again, can you visualise that? Can you start to think about the different ways that you might say that? Aisha notices something.

She says that when she doubles 10s it is 10 times the size of the doubling facts that she already knows.

So if we double three 10s, how many 10s do we have now? That's right, we have six 10s.

Double three 10s is six 10s.

Double 30 is 60.

30 plus 30 is 60.

What's the fact that Aisha could know? You might know a doubling fact that looks very similar to 30 plus 30 is equal to 60.

We can use the stem sentence if I know mm then I know mm to help us think about this.

Double one is two, so therefore double 10 is 20.

I can say if I know double one is two then I know double 10 is 20.

Double two is four.

I wonder if you can complete the sentence.

If I know double two is four, then I know, that's right.

Double 20 is 40.

Can we say that whole sentence together? If I know double two is four then I know double 20 is 40.

Great job.

What about double three? If I know double three is six then I know double 30 is 60.

I can definitely see a pattern in some of these numbers.

Can you? Aisha and Alex now apply their doubling knowledge to help them double 13? Oh that's quite tricky I think.

I wonder how they're going to tackle it.

Alex says he thinks he can use partitioning to double 13.

So like we partitioned nine for example earlier we can do the same and partition 13.

How would it be best to partition 13 to double efficiently? I should suggest it might be easier to use base 10 blocks to represent 13 rather than counters because she thinks we'll end up with a lot of counters.

I agree.

So let's think about what double 13 is.

Well we can think about 13 as one 10 and three ones and we can show that using our base 10 blocks.

One 10 and three ones is 13 so we can partition 13 into 10 and three.

Here it is doubled.

What is the total amount that we have now? How can we think about it? Well we can see that as double 10 and double three and we've moved the base 10 blocks around here but we've still got 13 twice.

We've just moved them around.

So double 10 plus double three is the same as double 13.

I can see that double 10 is 20.

Double three is six and then we can add them together to find out what double 13 is.

20 plus six is equal to 26, therefore double 13 is 26.

Time to check your understanding.

Use your base 10 blocks and send sentences to double 14 and then double 15, pause the video here and have a go.

(no audio) Welcome back.

How did you get on? If we double 14 we can think about it as double 10 and double four.

10 and four makes 14.

Double 10 is 20 and double four is eight.

20 plus eight is equal to 28.

If we apply the same partitioning structure to 15, we can say that double 15 is the same as saying double 10 plus double five.

Double 10 is 20, double five is 10, 20 plus 10 is 30, so double 15 is 30.

Well done If you've got both of those and well done if you represented that using your base 10 blocks.

Aisha and Alex explore the doubles that they've just solved.

So they found double 13 is 26, double 14 is 28, double 15 is 30.

Is there anything that you notice about those? Is there a pattern or something that you can see? Alex notices that all of his doubles are even numbers.

26, 28 and 30 other doubles and they're all even.

So Aisha says, Well, well that's true," and she wonders whether this is always true.

What do you think? Are doubles always even numbers? I wonder.

Let's think about a different context.

Alex has 25 pence.

Aisha has double the amount that Alex has.

How much money does Aisha have? Here we can clearly see the 10s and ones.

We've represented 25 pence with two 10 pence coins and one five pence coin and we can think about the five pence as five one pennies.

So we've got two 10s and five ones.

Aisha has double so we need to double 25 pence.

I wonder how we're going to do it.

Here we are, we've represented 25 pence twice, so we've doubled it.

Remember we can partition to work out the double.

We can think about double 20 and double five.

Double 20 is 40, so double 20 pence is 40 pence, double five pence is 10 pence.

What do we need to do now? That's right, we need to add them together.

40 plus 10 is equal to 50.

So that means that Aisha has 50 pence altogether.

Double 25 pence is 50 pence.

Time to check your understanding.

Alex gets another 10 pence.

So now he has 35 pence altogether and you can see that represented in the coins.

His mom comes along and doubles his money.

How much money does Alex have now? Pause the video and have a think.

(no audio) welcome back.

How did you get on? If you had coins you could use those to double it yourself.

We can think about this as 35 plus 35 and we can think about doubling 30 and doubling five.

Aisha has used her known doubling facts.

If she knows that double three is six, then she knows that double 30 is 60.

So double 30 pence is 60 pence and double five is 10.

So double five pence is 10 pence.

Remember we need to add those bits together to find out what double 35 is.

60 plus 10 is equal to 70, therefore Alex now has 70 pence.

Double 35 pence is 70 pence.

Time for your first practise task.

Practise doubling two digit numbers, you're going to turn over a card and double the number.

So Aisha has turned over 14.

Use base 10 blocks, coins or known double facts.

Double the number that you've got.

Remember that you can partition and you can use your doubles up to five and they can both help you to double the number.

Good luck with that task.

Have a few goes each and I'll see you shortly for some feedback.

(no audio) Welcome back.

How did you get on? Now remember you may have turned over different cards to Aisha and Alex, but let's see how Aisha doubled 14, which is a two digit number.

She partitioned 14 into 10 and four.

She knew that double one is two, so double 10 is 20 and then she doubled four, which is eight.

She then knew that she needed to add those together so she needed to add together 20 and eight.

20 plus eight is equal to 28, so double 14 is 28.

Alex says, "Wow, you didn't need any resources, you just used the double facts you already knew." Well done if you did that, but it's also absolutely fine to use base 10 blocks if you needed to to think carefully about how to partition and double a two digit number.

Let's move on to the second part of our learning where we're recording doubling as a multiplication equation.

Let's look at this problem.

Aisha and Alex have two packets of biscuits.

There are six biscuits in each pack.

How many biscuits do they have altogether? So we can see Aisha and Alex's packets of biscuits there.

We can see that they have the same amounts in each pack.

There are six biscuits in each pack.

Aisha suggests that we represent this as a bar model.

Can you visualise what that will look like? There's one group of six and there's another group of six and we are trying to find out how many biscuits they have altogether.

Alex has noticed that he can see two groups of six and he can write an equation.

Two multiplied by six is equal to mm.

Now you may have recently seen this as your two times table.

You may have written an equation like this before, but Alex has noticed, well we can also say this as six plus six.

Two groups of six is the same as six plus six, which is double six.

So that must mean that two groups of six is the same as double six.

Two multiplied by six is the same as writing double six.

So double six is equal to 12, so that must mean that two groups of six is equal to 12.

So we can see that Aisha and Alex have 12 biscuits altogether.

This relationship between two groups and doubling means that we can use doubling facts and strategies to solve problems involving two equal groups.

Aisha and Alex both have 15 pence each.

How much do they have altogether? We can see that they've both represented their 15 pence with coins.

Aisha suggest we represent it as a bar model again.

I wonder if you can imagine what that bar model will look like.

That's right, we have one group of 15 and another group of 15.

They have 15 pence each.

We don't know how much they have altogether.

Alex is reminding us that he can see two groups of 15.

That's the same as writing, two multiply by 15 is equal to mm.

We don't know yet.

And we know that if there are two equal groups we can say that's doubling.

So we can use the doubling facts and strategies that we know to work out two multiply by 15 we need to double 15.

Remember we can partition a number in order to double it.

Double 15 can be thought of as double 10 plus double five.

Double 10 is 20, double five is 10.

20 plus 10 is equal to 30.

So double 15 is 30, which means that two groups of 15 or 15 twice is also 30.

We can complete our bar model.

We can say that Alex and Aisha have 30 P altogether.

Time to check your understanding.

Which of these would we be able to use doubling facts to solve? A, two multiply by 12 is equal to mm.

B, three multiplied by five is equal to mm.

Or C, two multiply by three is equal to mm.

Think carefully about each equation.

Pause the video here and have a think.

(no audio) A could be solved using a doubling fact.

Alex explains that that's because two multiplied by 12 can be thought of as two groups of 12, which is the same as double 12.

So we can use a doubling fact to solve that.

Any of the others? That's right.

C can also be solved using a double fact.

Here, two multiplied by three is two groups of three or double three.

Well done if you spotted both of those.

Alex and Aisha take a look at some other multiplication equations.

What do you notice? Take a really good look at the equations that you can see here.

You may have seen them before.

What do you notice about them? What's the same? What's different? Alex notices that all of the multiplications have two as one of the factors.

Here's an example.

In both these equations, two is one of the factors, one of the numbers that is multiplied together.

The same here and here and here.

Two appears as a factor in all of these multiplication equations.

Aisha noticed that in each pair of equations the position of the factors has been swapped over.

Even though they've been swapped, the product is still the same.

So if we look at the first pair, we have two and one and then we have one and two.

The factors are one and two, it doesn't matter which order they go in.

So whether two is the group size or the number of groups, the product will still be double the other factor.

So we can still use our doubling facts to help us solve and multiply by two problem.

So we can say that when two is a factor, the product is double the other factor.

Two multiplied by one or two is one of our factors.

So the product will be double the other factor, the product has to be double one.

Double one is two.

What about this one? Well two is a factor.

So the product is double two this time because that's the other factor, two doubled is four.

What about this one? What are we doubling this time? That's right, two is a factor.

So the project is double three.

Double three is? That's right, double three is six.

And finally, this one? That's right, two is a factor.

So the product is double four.

Double four is eight.

Alex is going to use this knowledge to solve this problem.

Aisha sorts through her sock drawer, she has 13 pairs of socks.

How many socks is that all together? Alex says he can see that there are 13 groups of two.

Remember a pair is a group of two, so he can record that as 13 multiplied by two is equal to mm, we don't know yet.

That's the equation that we can write.

He can see that one factor is two.

So remember that if one factor is two, then the product is double the other factor.

The product has to be double 13 and we have strategies for doubling 13.

We know that double 13 can be thought of as double 10, plus double three.

Double 10 is 20, double three is six.

20 plus six is equal to 26.

Double 13 is 26, so therefore 13 multiplied by two is 26.

That means that Aisha has 26 socks all together.

Time to check your understanding.

Think really carefully about this one.

What is 45 multiplied by two? Remember you can use your doubling understanding to help you.

Pause the video here and have a go.

(no audio) Welcome back.

How did you get on? Well, we know that because one of the factors is two, the product is going to be double the other factor, which is 45.

We can think about strategies to double 45.

We can partition 45 into 40 and five in order to double it.

Double 40 is 80 because double four is eight.

So double 40 is 80, double five is 10, 80 plus 10 is 90, so the product is 90.

Well done if that's what you got.

Time for your second practise task.

For question one, I'd like to fill in the missing numbers from the bar models.

Let's take a closer look at A.

We know the whole or product is 10, we have two equal parts.

What is the value of those equal parts? For B, this time we know the value of those two equal parts is three, but we don't know the product or the total.

For question two, you have some equations to complete.

Look really carefully at what you know about the factors and therefore what you know the product will be.

For question three, I'd like you to fill in the missing numbers to complete the statements.

Let's look at A.

Double seven is equal to mm, two groups of seven is equal to mm.

I think I know something about those answers that will make it super efficient and super quick to fill in.

For question four, I'd like you to tick the examples that represent double five.

So look carefully at those six options.

Which of those represent double five? Tick the ones that do.

Good luck with those four tasks.

Pause the video here and come back when you're ready for some feedback.

(no audio) Welcome back.

How did you get on? Let's take a closer look.

For question one, you had some bar models to complete.

For A, we knew the product was 10 and we knew that there were two equal groups.

Well I know that double five is 10.

So the missing number in that one was five.

For B, we knew the two groups had a value of three, so we can think about this as double three.

I know that double three is six, so the missing number was six.

For C, well we can see that there are two groups, so there are two groups and they're equal in size.

If one has a value of six, the other one must have a value of six.

Then we can think about this as two groups of six, which we know is double six.

Double six is equal to 12.

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

For question two, we're going to complete the equations.

Now you may have noticed that in the first two equations, two multiply by seven and seven multiply by two, we have the same factors.

We've just swapped them around so the product is going to be the same both times.

You might just want to have a quick check to make sure that your product is the same for A and B.

You also may have noticed that one of the factors is two.

Remember if one of the factors is two, then the product will be double the other factor.

So for A, the product is double seven.

I know that double seven is 14.

So 14 is the product for both of those equations.

Remember, it doesn't matter which way around the factors are presented.

For B, we also have another factor of two, but this time the other factor is nine.

So my product is double nine.

I know that double nine is 18.

So the answer is 18.

Aisha's reminding us of that word, commutative.

Multiplication is commutative.

The factors have just been swapped over.

Well done if you spotted that.

For question three we had to fill in the missing numbers to complete the statements.

Double seven is equal to 14.

Now you may have just known that or you may have partitioned seven into five and two.

Double five is 10.

Double two is four.

Add them together.

If we know that double seven is 14, then we also know that two groups of seven is equal to 14.

For B, we can write six twice as two multiplied by something.

Well, we've got six twice, so it's two multiplied by six.

Double six is equal to 12.

And for C, Aisha is reminding us that when two is a factor we can double the other factor.

So we can say that if we write double three as two multiplied by three, this is the same as three multiplied by two.

Two multiplied by three, three multiplied by two is the same as double three.

So double three is equal to six.

And for question four we were looking for examples that represent double five.

Remember, double five can be thought of as two groups of five or five twice.

Here are the ones that represent double five.

Let's take a closer look.

B is five multiplied by two.

I can say that as five two times.

So I know that that is two groups of five.

It's double five.

For D, I have two groups of five there.

I've represented double five with the spots on the dice.

What's wrong with A and F then? Well, for A, doubling means two groups of five and for A there are four groups of five.

So that does not represent double five.

It might represent double 10, but it doesn't represent double five.

And for F we do have two groups, but the value of each group is two and not five.

So this represents double two and not double five.

Well done if you spotted those four that represented double five.

We've come to the end of the lesson where we've been doubling two digit numbers and recording them as multiplications where one of the factors is two.

Let's summarise our learning.

Double facts to five can help us double two digit numbers.

So there are different ways that we can double two digit numbers.

We can partition the two digit number so we can double the 10s digit and then double the ones digit and we can recombine that to find the double two digit number.

Doubling can be written as a multiplication equation where one of the factors is two, and when one of the factors is two, the product is double the other factor.

Thank you so much for all of your hard work today and I look forward to seeing you in another maths lesson soon.