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 maths lesson where we're thinking about doubling and halving.

Now, you may have had some recent experience looking at the 2 times table, and if you can recall or remember any of those 2 times tables facts, that's gonna be really helpful in your learning today.

If you're ready, let's get started.

In this lesson, we are going to be thinking about multiplying by 2 and factors of 2, and you may have had some recent experience multiplying by 2 and doubling.

By the end of this lesson, you will be able to say that you can identify missing factors when one of the factors is 2.

We have some keywords in this lesson today.

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

Are you ready? My turn, half.

Your turn.

My turn, halving.

Your turn.

My turn, double.

Your turn.

My turn, doubling.

Your turn.

My turn, factor.

Your turn.

My turn, product.

Your turn.

Excellent work.

Now, hopefully, you're familiar with some of these words.

Keep an eye out for them in the lesson today and try and use them in your own explanations.

In today's lesson, we're going to be identifying missing factors when one factor is 2, and we have two parts to our lesson today.

In the first part, we're going to be reviewing the relationship between product and factor, so you're going to be really thinking about what those two words mean.

And for the second part of our learning, we're going to be finding a missing factor.

If you're ready, let's get started with the first cycle of our learning.

In this lesson today, you're going to meet Alex and Aisha, and they're going to be helping us with some of the questions along the way.

Let's start here.

This morning, there were 6 felt-tip pens on the table, but now there are half that number.

How many felt tip pens are there now? Well, Aisha says she knows that half is the same as two equal groups.

Remember, thinking about halving, we're thinking about splitting something into two equal groups.

She's going to use a bar model to help us visualise this problem, and I think that's a good idea.

When you're not sure about what a problem will look like, it can always help to draw a sketch.

We can think about 6 being the whole as the total number of felt-tip pens, and she can see this as 2 groups of something is equal to 6, because there are half that number.

So, it's 2 groups of something makes 6.

What is the missing value? We can also represent this as multiplication equations.

Remember that because halving and doubling are inverse, or opposite relationships, we can write this as 2 multiplied by something is equal to 6, or something 2 times is equal to 6.

We can think about this as 2 groups of something is equal to 6, and Aisha knows that 2 times by 3 is equal to 6, or 3 twice is equal to 6.

That means half of 6 is equal to 3.

So, if there were half the number of felt-tip pens, that means there were 3 felt tip pens left on the table.

Time to check your understanding.

There are 2 packets of biscuits.

Each packet has the same number of biscuits.

There are 12 biscuits altogether.

How many biscuits are there in each packet? Use the bar model in the equations to help you find the answer to this problem.

Pause the video here.

Welcome back.

How did you get on? Well, we can see this as 2 groups of something is equal to 12, so we can think about this as 2 packets of 6, or 2 times 6, because I know that 2 multiplied by 6 is equal to 12.

That means we can see it as 6 biscuits twice, which is equal to 12.

That means that there are 6 biscuits in each packet.

We can write 2 multiplied by 6 is equal to 12, or 6 multiplied by 2 is equal to 12.

Well done if you identified that there were 6 biscuits in each packet if there were 12 biscuits altogether.

Let's move on to thinking about a different problem.

This time, we're thinking about money.

Alex earns 20 pounds for washing his family's cars.

How much will he put in each piggy bank? You can see here that he only has one note, but he wants to put an equal amount in each piggy bank, and he has two piggy banks.

So, Aisha has suggested that if you split the whole into two equal parts, each piggy bank will have half the amount of money.

Alex represents this as a bar model to help him solve it.

Remember, we're finding half of 20, but we can think about this as 2 multiplied by something is equal to 20.

Half of 20 will go in each piggy bank.

He says he can see 20 as 2 tens.

He knows that half of 2 tens is 1 ten, or 10.

1 ten is equal to 10, so he's going to put 10 pounds in each piggy bank.

We can see that half of 20 is equal to 10.

So, what can we write in our multiplication equations? Well, I should notice that when 2 is a factor, we can see the other factor as half of the product.

At the moment in the first equation, one of the factors is 2 and the product is 20.

So, if one of the factors is 2, Aisha is saying that we can see the other factor, the missing number, here, as half of the product.

If the product is 20, that means the missing factor must be 10 in both equations.

Let's take a closer look at what she means.

We know that when 2 is a factor, the product is double the other factor.

So, in this equation, 2 multiplied by 10 is equal to 20.

One of the factors is 2 and the other factor is 10, so we know the product is double that other factor.

Double 10 is 20.

But we can also see this as, when one of the factors is 2, the other factor is half of the product.

Again, in this case, we can say that the product is 20 and half of that is 10, which is the other factor, and we can say that half of 20 is equal to 10.

Even if we change the order of the factors, this is still true.

2 is one of our factors, so double 10 is equal to 20 and half of 20 is equal to 10.

The product is still the same 20 and the missing factor, the other factor, is still 10.

Time to check your understanding.

Use the bar model to complete the equations below.

The whole is 10 and one of our factors is 2.

What is the missing number? Pause the video here and have a think.

Welcome back.

How did you get on? Well, 2 is a factor in both of the equations, so the other factor must be half of the product.

"I know that half of 10 is equal to 5," says Aisha, "So 5 is the missing factor in both equations." and we can double-check that.

If we know that one of the factors is 2, then the missing factor is half of 10, which is the product.

Half of 10 is 5, so the missing number had to be 5.

Well done if you said that.

Time for your first practise task.

For question one, I'd like you to tick the examples that represent half of 10.

You've got a, b, c, and d.

a and c are pictures, so look really carefully at what's being circled or identified, and b and d are numbers.

Which of them represent half of 10? For question 2, I'd like you to complete the statements.

You're given a multiplication equation.

Let's look at a, 2 multiplied by 7 is equal to 14.

And then, you have two statements to complete.

Double 7 is equal to mm, half of mm is equal to 7.

Think carefully about what you know about the factors and the products to help you answer that.

For question three, you have some missing numbers to fill out in equations, a, b, and c.

c has two equations to fill in, but you might notice something about them.

Pause the video here, have a go at those three tasks, and I'll see you shortly for some feedback.

Welcome back.

How did you get on? For question 1, I asked you to tick the examples that represent half of 10.

Let's look at a.

I can see that the whole is 10 spots or dots and I can see that it's been split into two equal groups, and one of those groups has been shown.

That means a does represent half of 10.

What about b? Well, I can see the number 5.

I know that half of 10 is 5, so a and b both represent half of 10.

Let's take a look at c.

Hmm.

Well, I can see 10 bottles all together, but I can see that 6 of them have been circled and 4 of them are uncircled.

Now, I know that half is 2 equal-size groups.

6 and 4 are not equal, so they are not equal.

And what about d? Well, I know that half of 10 is five.

20 is not 5.

20 is, in fact, double 10, so c and d do not represent half of 10.

Well done if you spotted that.

For question 2, I asked you to complete the statements.

2 multiplied by 7 is equal to 14.

Well, one of the factors is 2, so when one of the factors is 2, I know that the product is double the other factor.

So, I can say that double 7 is equal to 14, and I can say, therefore, that half of 14 is equal to 7 because it works the opposite way 'round.

If I know the product, then the other factor is half that of the product.

For b, we can say that double 6 is 12 and we can say that half of 12 is equal to 6.

For question 3, you have to fill in the missing numbers.

For a, 2 multiplied by something is equal to 8.

Well, I know if one of the factors is 2, then the missing factor is half the product.

The product is 8.

I know that half of 8 is equal to 4, so the missing factor there is 4.

For b, 2 multiplied by something is equal to 10.

Again, the missing factor here is half that of the product.

Half of 10 is equal to 5.

And for c, 2 multiplied by something is equal to 4.

Well, I know that the missing factor is half the product, so 2 multiplied by 2 is equal to 4.

And I know as well it doesn't matter which order the factors go in, so I can also say that 2 multiplied by 2 is equal to 4.

Really well done if you got all of those correct.

Let's move on to the second cycle of our learning, where we are finding a missing factor.

Alex and Aisha are using their knowledge of factors and products to fill in the missing numbers.

We have 2 multiplied by something is equal to 16, something multiplied by 2 is equal to 12, and 2 multiplied by something is equal to 40.

What do you notice about them? Is there anything you can spot? That's right, 2 is one of the factors in all of them.

The product is different in each equation.

Alex is reminding us that when 2 is a factor, you can see the missing factor as half of the product.

So, we can think about this first one as half of 16 will give us the missing factor.

Double mm is equal to 16.

I know that double 8 is equal to 16, so half of 16 is equal to 8.

2 multiplied by 8 is equal to 16.

Remember, it doesn't matter which of the factors it is.

In this case, in the second one, the factor is the first factor, but it doesn't matter, because the other factor is 2.

Half of 12 is equal to mm.

Well, I know that double 6 is 12, so half of 12 is equal to 6.

And Alex is reminding us that this strategy works for any factor when the other factor is 2.

So, half of 40 is mm.

Well, 40 is 4 tens.

I know that half of 4 tens is 2 tens, so half of 40 is 20.

Time to check your understanding.

Which of these problems could I use halving to find the missing factor? You have a, b, and c.

Take a really careful and close look at the missing factors and the information that you know.

Pause the video here.

Welcome back.

How did you get on? Well, a has one of the factors of 2, and we know that if 2 is a factor, we can use our halving to find the missing other factor.

When we're missing a factor, the other factor is 2, we can see the missing factor as half of the product.

So, half of 20 is equal to 10.

What about the other two? In the other two problems, 2 is not a factor, so we'd have to use other strategies to find those missing factors.

Well done if you recognised that a was the only one that we could use halving to find the missing factor.

What is the missing factor here? Something multiplied by 2 is equal to 24.

Hmm, I wonder how we're going to work that out.

Well, that's right, Alex.

Here we can see that 2 is a factor and 24 is one of our products.

The missing factor is going to be half of the product, so the missing factor will be half of 24.

I wonder if you can work out what half of 24 is.

Remember, we can always partition if we're not sure.

Alex says he can partition 24 into 20 and 4 to help us find the answer.

Half of 20 is equal to 10, half of 4 is equal to 2, and we can combine those bits to make half of 24.

10 plus 2 is equal to 12, so half of 24 is equal to 12.

12 is the missing factor, and Aisha now knows that 12 times 2 is equal to 24.

Alex now uses this knowledge to solve this problem.

Listen carefully.

Aisha sorts through her sock drawer.

She has 28 socks.

How many pairs of socks is that? Hmm.

Well, we can write that as something multiplied by 2 is 28.

How do we know that 2 is one of the factors? Well, that's right, because we have a pair of something.

A pair means 2 of something, and we have 28 socks altogether, so we know that 28 is our product.

The missing factor is going to be half of the product, remember, so the missing factor is going to be half of 28.

We can partition 28 in order to find out what half of 28 is.

Half of 20 is equal to 10.

Half of 8 is equal to 4.

Now, we need to combine those bits together.

10 plus 4 is equal to 14, so half of 28 is equal to 14.

This means that Aisha has 14 pairs of socks, because 14 groups of 2 is equal to 28.

Well done, Alex, for using your halving and doubling knowledge to solve this problem.

Time to check your understanding.

What if Aisha had 26 socks? How many pairs does she have now? How would you show this as an equation? Pause the video and have a think.

Welcome back.

Well, we could write something multiplied by 2 is equal to 26 because there are 26 socks, and they come in pairs, or groups of 2.

Remember, if one of the factors is 2, we can halve the product to find out what the missing factor is.

We can find half of 26.

We can partition 26 into 20 and 6.

Half of 20 is 10.

Half of 6 is equal to 3.

10 plus 3 is equal to 13, so half of 26 is equal to 13.

Well done if you said that Aisha has 13 pairs of socks if she has 26 socks, because 13 groups of 2 is equal to 26.

Time for your second practise task.

For question 1, I'd like to fill in the missing numbers.

So, a, something multiplied by 2 is equal to 26.

If you look at b, c, d, e, and f, I can see that one of the factors is always 2.

Remember, if that's the case, you need to halve the product in order to find the missing factor.

Remember, you can use partitioning or you can use base 10 or 10 frames to help you with that halving if you need to.

For question 2, I would like you to record each of these problems as a bar model and an equation to help you solve the problem.

For a, there are 22 shoes in a shoe cupboard.

How many pairs of shoes are there altogether? Remember, pairs are a group of 2.

For b, Sam has double the number of marbles that Andeep has.

Sam has 40 marbles.

How many does Andeep have? Think carefully about what that question is asking you.

Good luck with those two tasks.

Pause the video here and I'll see you shortly for some feedback.

Welcome back.

How did you get on? For question 1, I asked you to fill in the missing numbers.

Now, remember that when one of the factors is 2, we can halve the product to find the missing factor.

And Alex is reminding us that if we need to partition a 2-digit number to find half of it, then that's absolutely fine.

For example, with 26, half of 20 is equal to 10, half of 6 is equal to 3, so that means if we add 10 and 3 together, half of 26 is equal to 13.

For b, we had 12.

Half of 12 is equal to 6.

For c, now, this one might have been a little bit trickier, because the product was first, 14 is equal to 2 multiplied by something.

But remember, it doesn't matter where the product of the factors are.

We can still find half.

Half of 14 is 7 because double 7 is 14.

For d, remember, it doesn't matter where the missing factor is.

Half of 28 is equal to 14, so 14 is the missing factor.

For d, we had a multiple of 10.

60, you can think about as 6 tens.

Half of 6 is 3, so half of 6 tens is 3 tens, which means that half of 60 is 30.

For f, we have an odd number of tens, which is 70, so Alex is reminding us that we can partition it into 60 and 10.

Half of 60 is equal to 30.

Half of 10 is equal to 5.

30 plus 5 is 35, which means that half of 70 is equal to 35.

Well done if you used your halving and doubling knowledge to find those missing factors For 2a, there were 22 shoes in a shoe cupboard.

How many pairs of shoes are there altogether? Well, something multiplied by 2 is equal to 22, and that's the equation that we could have written.

We have a missing factor, and we know that because one of the factors is 2, the other factor is half of the product.

We can find half of 22 to find the missing factor.

Half of 20 is equal to 10.

Half of 2 is equal to 1.

10 plus 1 is equal to 11, so the missing factor is 11, which means there will be 11 pairs of shoes in the cupboard.

b think was a little bit tricky.

Sam has double the number of marbles that Andeep has.

Sam had 30 marbles.

How many does Andeep have? This is the bar model that you could have drawn.

We know that Sam has double the number of marbles that Andeep has, so Andeep has half the number of marbles that Sam has.

We know that 40 is the whole, and we're doing 2 multiplied by something is equal to 40.

So, we can say that half of 40 will give us our missing factor.

We know that half of 4 is equal to 2, so half of 40 is equal to 20.

Our missing factor is 20, so that means that Andeep has 20 marbles.

Well done if you worked that out.

We've come to the end of the lesson where we've been identifying missing factors when one factor is 2.

Let's summarise our learning.

When one of the factors is 2, the other factor is half of the product.

We can use our knowledge of doubling and halving to help us find a missing factor when the other factor is 2.

Thank you so much for all of your hard work in this lesson today, and I hope to see you in another maths lesson soon.