Lesson video

Hello there.

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

My name is Ms. Co.

I am really, really excited to be learning with you today in this maths 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're ready, let's get started.

By the end of this unit, you'll be able to say that you can explain how doubling and halving are related.

In this lesson today we have some keywords.

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

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

My turn, half, your turn.

My turn, halving your turn.

Great job, though you may be familiar with some of these words, keep an eye out for them in our lesson today and see if you can use them in your explanations.

In today's lesson we'll be explaining how doubling and halving are related, and we have two cycles to our learning.

In the first cycle, we're going to be exploring doubling and halving facts, and then in the second cycle we'll be solving problems involving doubling and halving.

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

In today's lesson, you are going to meet Aisha and Alex and they're going to be helping us with our maths along the way.

So let's start here.

Alex and Aisha are enjoying sharing their lunch with each other.

I can see they've got some pizza there.

Pizza is one of my favourite foods.

What toppings do you like? I like ham and pineapple.

Today Alex had a pizza to share with Aisha and that's very kind of him, sharing is a really nice thing to do.

He says we can see this pizza as the whole, so that's the whole, it's one whole pizza and we can cut the whole into two equal parts.

Let's see what happens, there we go.

The whole has been cut into two equal parts, so that means says Alex, each of them will get one half of the whole and you can see there that Alex and Aisha both have half of the whole pizza.

Aisha now returns the favour and shares her grapes with Alex.

She says, I have six grapes.

So what would half of six grapes be? Remember she wants to share fairly so they each get the same amount.

We can think about that as a bar model.

We have six grapes and we want to know what half of six is.

We want to know what it would be divided into two equal parts.

Alex says that we know that two equal groups will be equal to the whole, so we know that these two groups will be equal to six.

If we split the grapes into two equal groups says Aisha, there are three in each and we can see that in the bar model, we've split the grapes into two equal parts.

Half of six is equal to three.

That's right Alex.

That means each of you will get three grapes.

Let's keep thinking about halving using counters and a bar model.

What is half of two? Alex says we can split the counters into two equal groups like we can see on the bar model.

There we go, that is showing half of the whole, which is two.

Half of two is equal to one and that's right Aisha.

We can now see that two equal groups of one or double one is equal to two.

So we can also say that double one is equal to two.

What about four then? Our whole is four.

What is half of four? Well again, we can split the counters into two equal groups.

There we go.

Each of those groups is half, so half of four is equal to two.

What doubling fact can we see here asks Aisha.

I wonder.

Well that's right Alex.

I know that half of four is equal to two.

If I know that, then I know that double two is equal to four.

Time to check your understanding, using your own bar model encounters, find half of six and fill in the missing numbers.

So remember your hole is six counters and you're going to find half of those six counters and then you're going to fill in the sentences.

Half of six is equal to mm and double mm is equal to six.

Pause the video here.

Welcome back, how did you get on? Well, hopefully you started with six counters as your whole and then you split them into two equal groups to find half like so.

And now we can see that half of six is equal to three because there are three counters in each part and we can also see that two groups of three is double three, which is also equal to six.

Let's say those two sentences together, are you ready? Half of six is equal to three.

Double three is equal to six.

Great job, we can now see the three doubling and halving facts that we've looked at so far.

For example, we can see that half of two is equal to one and double one is equal to two.

What do you notice about our bar models? Is there anything you can spot? Are there any patterns? Well Alex has noticed that we can also record this as multiplication equations because he can see two equal groups and he may have had some recent experience thinking about multiplying by two.

So he can see two equal groups of one in the first bar model.

So the bar model also shows two multiply by one is equal to two.

We can say that as two groups of one is equal to two.

Can you say the next equation? Well that's right.

We can see two equal groups of two.

So this shows two multiplied by two is equal to four.

What about the third example? That's right.

We can see two equal groups of three.

So that shows two multiplied by three is equal to six.

All of those representations mean the same thing.

When we have two equal groups, we can see this as the two times table facts.

So what happens when we halve a number? Well, when we halve, we split a number into two equal parts and you can see that shown on the bar models.

If we look at the middle one, we can see that four has been split into two equal parts and each part has a value of two.

When we double, we add together the two equal parts and again, if we look at that bar model, we can see that two plus two is equal to four.

If we combine those two parts, we get the whole, which is four.

So why is it that we can see doubling and halving fat in those bar models? Well that's because doubling is the inverse or the opposites of halving and vice versa.

So that means that we can see halving and doubling fat in these bar models.

Time to check your understanding.

Use the bar models to fill in the missing numbers and complete the facts.

So take a close look at the bar model, think about what is the whole, what are the two equal parts and we have half of eight is equal to mm, double mm is equal to eight and then we have a multiplication equation with the two factors missing.

Pause the video here.

Welcome back, how did you get on? Well, I can see that the whole is eight and I can see that it has been split into two equal parts, which is the same as halving.

The value of those two equal parts is four, so I can say that half of eight is equal to four.

When I know that, I know that if I combine those two parts, I get the double fact because the parts are equal.

So I can say that double four is equal to eight.

What about our factors then? Well we know the whole or the product is eight and we know that one of the factors is four because that's the value of the part.

There are two parts, so the other part is two.

There are two parts, so the other factor is two, we can write two multiplied by four is equal to eight.

Well done if you've got all of those.

Time for your first practise task.

For question one, I'd like you to fill in the missing numbers using your knowledge of doubling and halving.

Let's take a closer look at A.

For A, we have all the values filled in in the bar model and we are missing the values in the sentences.

Double is equal to and half of is equal to.

For B and C, some of the values in the bar models are missing, so check really carefully and use what you know to find the missing parts.

For question two, I'd like to fill in the missing numbers again using your knowledge of doubling and halving.

This time I'd like you to record each bar model as an equation within the two times tables.

So let's look at A, we can see the whole is eight and I can see there are two parts with a value of four.

What's are the missing numbers in the equations? For B and C you have some missing numbers in the bar models as well.

Good luck with those two tasks.

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

Welcome back, how did you get on? For question one, I asked you to fill in the missing numbers using your knowledge of doubling and halving.

If we look at A, we can see that the whole is 10 and we can see 10 has been split into two equal parts, which is halving.

So I can say that double five is equal to 10 or half of 10 is equal to five.

For B, the numbers in the bar model are missing.

How can I work them out? Well, I can see the sentence double three is equal to six, which means I know the whole is six and the two parts are each three.

Well I can say that half of six is equal to three.

What about C? Well, we knew one of the parts was one and so that meant because we're halving and they're two equal parts, the other missing parts had to be one as well.

To find the whole we could combine those parts.

One plus one is equal to two, so we can say that double one is equal to two and half of two is equal to one.

Well done if you filled all those in correctly.

Let's take a look at question two.

This time we had to fill in the equations.

Remember they're all two times stable facts, so one of the factors is going to be two.

For A, the whole was eight and there were two parts with the value of four.

We could say that two multiplied by four is equal to eight or four multiplied by two is equal to eight.

Remember, multiplication is commutative and that means the factors two and four can be written in either order.

For B, we knew the two parts but we didn't know the value of the whole.

Now because there are two equal parts, we can multiply two by two to find that the whole is four, two multiplied by two is equal to four and two multiply by two is equal to four.

In this case the multiplication are the same.

For C, all of the numbers in the bar model were missing, but I know that I can see the equation, two multiplied by five is equal to 10.

I can say that as two groups of five is equal to 10.

So that means the two parts had a value of five and the whole was 10 and the other equation is five multiplied by two is equal to 10.

Well done if you correctly filled in those bar models and equations.

Let's move on to the second cycle of our learning where we are solving problems involving doubling and halving.

Alex and Aisha are back sharing their sweets.

Alex ate nine of his sweets after giving the other half to Aisha.

How many suites must there have been to begin with? Now that sounds like a tricky problem.

Think carefully about what it means.

So Alex says that he knows that he had nine sweets because that's how many he ate and he knew that that was half of the whole because he gave half to Aisha.

So we can see that as one of the two equal groups and he's shown that on the bar model, we can see that we don't yet know the whole but we know one of the two equal groups is nine because that's the number of sweets that Alex ate.

When we half we know that there are two equal parts, so the other parts must also be nine.

So we know that Alex ate nine sweets and he gave half of his original amount of sweets to Aisha, so she had nine sweets as well.

If we double nine, it will be equal to the whole.

So Alex knows that double nine is 18, so he must have had 18 sweets to begin with.

Double nine is equal to 18, so the whole is 18 and we can also say that half of 18 is equal to nine.

This time Aisha had four pancakes, she ate half of them and saved the rest for Alex, how many pancakes did she save for Alex? I wonder what we need to do for this.

Do we know the whole, do we know the parts? Well this time, Aisha says that we know that she had four pancakes and we can see this as the whole.

So we know the whole, the total number of pancakes was four.

What happened next? Well that's right.

Half is partitioning into two equal groups, but we can also think about this as double is equal to four.

What is doubled to make four? Well that's right, double two is equal to four.

So that means half of four must be equal to two.

We can complete our part whole model with two equal parts for the value of two.

So that means that Aisha must have eaten two pancakes and save for Alex.

Time to check your understanding, represent this problem as a bar model and complete the stem sentences to help you find the answer.

Listen carefully to the problem.

There were six children on the playground, half of them were called back into class.

How many children were left on the playground? So you have a bar model there to complete and then two sentences, double is equal to, half of is equal to.

Think carefully, does the problem tell you the whole or the value of one of the parts? Pause the video here and have a think.

Welcome back.

Well we know that there were six children in the beginning, so that is the whole so well done if you put that as the whole in your bar model.

We know this is a halving problem because we're told that half of the children were called back into class.

So Alex knows that double three is equal to six, which means that half of six is equal to three.

That must mean there were three children left on the playground after half of them went back to class.

Well done if you found the correct answer, but extra well done if you completed that bar model correctly.

Now uses his doubling and halving knowledge to solve some missing number of problems. We have two equations here.

Two multiplied by is equal to 10 and multiplied by two is equal to 10.

What do you notice about them? What's the same, what's different? Well, I've spotted that the product, 10, is the same in both equations and I've spotted that the known factor is two in both equations.

I think we might be missing the same number in each equation here.

Let's see what Alex does.

Well, Alex says, I know double five is equal to 10 and half of 10 is equal to five.

So he's remembered that when we have a multiplied by two problem, it's the same as a doubling fact.

Alex says that he knows double five is equal to 10 and half of 10 is equal to five.

So he's right.

Double five is equal to 10 and half of 10 is equal to five.

So perhaps five has something to do with these equations, but we have multiplying by two equations.

Where has doubling and halving come from? Ah, that's right Alex.

Thank you.

He can use this knowledge to complete the equations because when two is a factor like it is in our problems here, he can see this as a double.

Double five is equal to 10.

So two times five is also equal to 10, and if two multiplied by five is equal to 10, then he knows that five multiplied by two is equal to 10.

So he can fill in the missing numbers in his equation.

Well done Alex.

Great way to use doubling and halving knowledge.

We can also represent this as a bar model.

We can see that the whole is 10 and we have two equal parts of five.

So for this problem, Aisha thinks that she can use doubling and halving knowledge.

Do you agree? Let's think about the problem carefully.

There were eight wheels in the bike shed.

Each bike has two wheels.

How many bikes are in the shed? So what do you think, do you agree with Aisha? Can she use her doubling and halving knowledge? Hmm, I wonder.

Well she says, although this isn't two equal groups, two is one of the factors, so we can still use doubling and halving to solve it.

Alex says that he can see eight, the number of wheels is the whole.

So we know that each bike has two wheels, so we can see this as something multiplied by two is equal to eight.

Hmm, what do we know about doubling and halving and eight that can help us? That's right Aisha.

Double four is equal to eight.

So two multiplied by four is equal to eight.

That means that there must be four bikes in the shed because four multiplied by two is equal to eight.

Great use of doubling and halving there Aisha.

Time to check your understanding.

Complete the equations to help you find the answer to this problem.

I can see six wheels in the bike shed.

I know each bike has two wheels.

How many bikes are in the bike shed? Pause the video here.

Welcome back, how did you get on? Well, Alex has noticed that because there are six wheels in the bike shed and each bike has two wheels, we can write the equation.

Something multiplied by two is equal to six.

We can use our doubling and halving facts here.

Two times is the same as double and Alex knows that double three is six, therefore the missing number is three.

If two multiplied by three is equal to six or double three is equal to six, then there must be three bikes in the shed because three multiplied by two is equal to six.

Well done if you use those equations to help you find that there were three bikes in the shed.

Time for your second practise task.

For question one, I'd like to represent each of the problems as a bar model and show the facts you have used to solve them.

So for A, the question is, Aisha had two sweets, she gave half to Alex.

How many sweets did Aisha have left? So I would like you to complete the bar model and complete the sentences.

Double is equal to, and half of is equal to.

B, the word problem is, Aisha cut an eight metre piece of ribbon into two equal pieces.

How long will each piece of ribbon be? This time you also have two equations to complete.

This is the problem for C.

Alex had eight grapes, Jacob had twice as many grapes.

How many grapes does Jacob have? Hmm, that question seems a little bit different to me.

I wonder if you can spot anything.

Jacob's giving you a handy hint here.

He says, I can see twice as many so I can use my two times table facts and doubling and halving to help me.

So the wording of this question may look a little bit different, but don't worry, you can still use those doubling and halving facts.

Good luck with those tasks.

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

Welcome back, how did you get on? For 1A, Aisha had two sweets.

She gave half to Alex so I know the whole is two and she gave half of them to Alex.

I need to find out how many she had left.

Alex uses doubling and halving facts to solve this.

Two is the number of sweets that Aisha had and that's the whole and he knows that double one is equal to two, so therefore half of two is equal to one.

That means she gave one sweet to Alex and so she had one sweet left.

This one, Aisha cut an eight metre piece of ribbon into two equal pieces.

How long will each piece of ribbon be? So we can see the length of the ribbon at the start as the whole, which is eight or eight metres and we know that double four is equal to eight.

So that means that two four metre lengths of ribbon will be equal to an eight metre length.

We can say that double four is equal to eight, which means that two groups of four or two multiplied by four is equal to eight.

You might have used the knowledge that two times or two groups of four is equal to eight as well.

So that means that each ribbon would be four metres long.

Well done if that's what you got.

For C, Alex had eight grapes.

Jacob had twice as many grapes.

How many grapes does Jacob have? Well, I should notice the words twice as many and she knows that that means the same as two times.

So we can think about this as two groups of eight.

Alex had eight grapes.

Jacob had twice as many, so he had two times as many.

Two groups of eight is the same as double eight.

Aisha knew that double eight was 16, so that meant that Jacob had 16 grapes.

16 is our whole, well done if we spotted that and spotted the word twice in that question.

We've come to the end of the lesson where we've been exploring how doubling and halving are related.

Let's summarise our learning.

If double four is eight, then half of eight is four.

Halving means to partition the number or split the number into two equal groups.

Halving is the inverse of the opposite of doubling.

Whether we are doubling or halving, we can also see these as our two times table facts.

So we can think about half of two is equal to one, double one is equal to two, and from that we can write two multiplication facts.

Two multiplied by one is equal to two and one multiplied by two is equal to two.

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