Lesson video

Hello.

How are you today? My name is Dr.

Shorrock, and I'm here to guide you through your learning today.

You have made a great choice to learn maths with me, and I know we are gonna work really hard together.

Welcome to today's lesson.

This lesson is from our unit Calculate the value of a part, fractions as operators.

The lesson is called "Calculate the value of a part and a whole using understanding of division." And we will also look at using your knowledge of division facts.

Throughout the learning today, we will deepen our understanding of how we can work out the value of a part or a whole or how many parts there are.

We're also going to think about how really important it is to represent things visually.

In particular, in a bar model.

Now, sometimes new learning can be a little bit difficult, but it is okay.

I am here to guide you, and I know if we work really hard together, then we can be successful.

So, how do we calculate the value of a part and a whole using our division facts? Shall we find out? Let's go.

The keyword that you will hear throughout the learning today is divide.

And I am sure you have heard that word before, but it's always useful to practise.

So, let's practise together.

My turn, divide.

Your turn.

Well done.

So what do we mean to divide? Well, when we divide, we mean to split something into equal parts or groups.

And there is a symbol that you can see there that means divide.

So look out for that symbol and that keyword throughout our learning today.

Let's start by thinking about how we calculate the value of a part.

To help us in our lesson today, we have got Lucas, Sofia, Izzy, and Alex.

Let's look at a problem.

Lucas has found 15 marbles.

Can you visualise that? Can you see that in your head? Can you see Lucas and 15 marbles? He decides to share them between himself and four friends.

Can you visualise that? Can you see Lucas, and can you see his four friends? And what do we need to do first with this information, do you think? Well, what could we do? That's right.

Thank you, Lucas.

We could represent this as a bar model.

And bar models are a really important way of helping us represent the information to make sure that we understand the problem, and they can then support us to know how to solve the problem.

We have 15 marbles, and this is our known whole.

We don't get any more, do we? We are sharing those 15 marbles.

So we have 15 marbles, and this is our known whole.

Hmm.

How many parts did we have? Can you remember? Well, we had Lucas, and he shared the marbles between himself and four friends.

How many parts is that? That's right, there are five equal parts altogether.

But we don't know the size of each part yet, do we? We haven't worked that out.

We need to calculate the value of each part, and we can do this using our knowledge of division.

We know that the whole is 15, and there are five equal parts, and we can use, then, this bar model to help us form an equation.

15 is our whole, and we know there are five equal parts.

So if we divide 15 by 5, we will know the value of each part.

And we can use our five times table to help us, can't we? We know three 5s are 15, so 15 divided by 5 must be 3.

The value of each part is three.

And Lucas is telling us that his four friends and himself, they will get three marbles each.

The whole is 15, the whole was divided into five equal parts, and we formed a division equation from knowing that there were five equal parts and from knowing that the whole was 15.

Each part is worth three.

Let's check your understanding.

Look at this representation, and could you complete the sentences? So take a look at that bar model, think about what the whole is and how many parts there are, and then complete the sentences.

The whole is, mm.

The whole is divided into, mm, equal parts.

12 divided by, mm, is equal to 3.

Each part is worth, mm.

Pause the video while you do that.

You might want to talk to somebody about it and compare your answers.

And when you're ready to go through the answers, press play.

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

So the whole is 12.

We can see that because it's the whole amount on our bar.

The whole is divided into four equal parts, and we can see the equal parts in our bar.

So we know the whole is 12, and we are going to divide by how many parts we've got.

12 divided by 4, and that is 3.

Each part must be worth three.

How did you get on with those sentences? Brilliant.

It's your turn to practise now.

Could you solve these problems? Represent each of them as a bar model, and form an equation to solve them.

For problem A, Sofia has 36 pounds.

She decides to share this money between herself and three sisters.

How much money do they each get? So have a think.

What is the whole amount, and how many parts are there? For question B, Lucas has 32 marbles.

He decides to share these marbles between himself and seven friends.

How many marbles do they each get? Again, visualise the problem.

What do you see? What is the whole amount? How many parts are there? For question two, could you solve these problems, representing each of them as a bar model and forming an equation to solve? Sofia has 40 sweets.

She shares them between herself and four friends.

How many sweets do they each get? How many more sweets would she have got if she had shared them between herself and three friends rather than herself and four friends? Have a go at both questions.

Pause the video, and when you are ready for the answers, press play.

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

For question A, Sofia had 36 pounds, so that is our whole amount, and that's the whole amount she's got.

And she decides to share it between herself and three sisters, herself and three more, so that is four.

There are four parts.

So my bar model looks like this.

36 pounds is my whole, and there are four equal parts.

And we know the whole is 36 pounds, and we know the whole is divided into four equal parts.

And using that information, we can form an equation.

36 divided by 4 is equal to 9.

They each get 9 pounds.

Each part is worth 9 pounds.

For part B, Lucas has 32 marbles.

Well, he decides to share these marbles between himself and seven friends.

How many marbles do they get each? Well, 32 marbles, that's the whole amount.

That's what I'm visualising.

And it's shared between himself and seven friends, so that's one more than seven, so that's eight.

There are eight equal parts.

I've got my 32 as my whole, and there are eight equal parts.

The whole is divided into eight equal parts.

Then I can form an equation.

32 divided by 8.

Well, I know my eight times tables, so that must be four.

Each part is worth four, and they get four marbles each.

For question two, Sofia has 40 sweets, and she shares them between herself and four friends.

So 40 sweets must be our whole.

Herself and four friends, there must be five equal parts.

There's my bar model with 40 being the whole and five equal parts.

From that, I can form an equation.

40 is my whole, and I am dividing the whole amount into five equal parts.

40 divided by 5 is equal to 8.

Each part is worth eight.

They get eight sweets each.

For part B, though, how many more sweets would she have got if she had shared them between herself and just three friends? Well, in that case, there will be four parts.

So we've got 40 as our whole, and this time, it's divided into four equal parts.

The whole is 40.

The whole is divided into four equal parts.

We can use that to form an equation.

40 divided by 4 is 10.

Each part is worth 10, so they would have got 10 sweets each if she shared between herself and three friends.

So she would have had two more sweets.

When she shared between herself and four friends, they got eight each.

This time, she's sharing between herself and three friends, they get 10 each.

That is two more sweets.

How did you get on with both of those questions? Brilliant.

Fantastic learning so far.

I can see how hard you have worked to help yourself understand and deepen your understanding of how we can calculate the value of a part.

We're going to move on now and look at how we can calculate the whole and the number of parts in the whole.

Let's look at this problem.

Lucas, Sofia, Izzy, and Alex have each been given nine strawberries.

Can you visualise that? How many children are there? And they've each been given nine strawberries.

Hmm, and Alex is wondering how many strawberries we have in total.

Good idea, Izzy.

It's always a very good idea to represent word problems visually, and in this case, in a bar model.

We want to know how many strawberries there are in total, so that's our unknown whole.

We don't know that yet, do we? But we know it will be our whole.

And there are four children, so there must be four equal parts.

And they each have nine strawberries, so those four parts each have a value of nine, so there are four equal parts of nine.

And we can use the bar model, then, to form an equation.

The whole is unknown, and it's divided into four equal parts.

Each part is worth nine.

Something, then, is the same as four 9s.

And we can use our known facts to solve the equation.

We know our four times tables, don't we? 4 times 9 is 36.

Four 9s are 36.

So there must be 36 strawberries in total.

Let's check your understanding.

Could you have a look at these three equations and tell me which equation we should use to solve this problem? Alex and seven friends had four pounds each.

How much money do they have in total? Is it A, 8 divided by 4 is equal to 2? Is it B, seven 4s are 28? Or is it C, eight 4s are 32? Pause the video, maybe talk to somebody about this, and when you are ready to have a look at the answer, press play.

How did you get on? Well, Alex and seven friends had four pound each.

How much money do they have in total? So if we had eight, which is the number of parts, and dividing it by four, well, we would be sharing it.

And we're not sharing it, we want to know how much money they have in total.

So it can't be A.

B, seven 4s.

Hmm.

Well, they've each got four pound, but there are not seven parts, are there? There are eight parts because it's Alex and seven friends, so that's eight in total.

So the answer must be C, eight 4s are 32.

We could represent this in a bar model.

The whole is 32, and there are eight equal parts, each with four pounds in them.

Let's move on and have a look at this problem.

Izzy has been baking a birthday cake for her mum, and she needs 40 candles to go on the cake.

Candles are sold in packs of 10.

Right, can we visualise that? So can you visualise a birthday cake? It needs 40 candles.

So Izzy's gonna have to go and find them, but they're only sold in packs of 10.

Can you imagine what a pack of 10 candles looks like? We need to think about how many packs of candles does she need to buy? Can you visualise this? I wonder if you know how many packs of candles she needs to buy.

That's what I'm visualising.

There's my cake, and my cake needs some candles on it, and I've got one pack of 10 candles there.

But that's only 10 candles.

I need 40 of them.

So how many packs do we need to buy? Good idea, Izzy.

Let's start by representing this as a bar model.

We need 40 candles, so this must be our known whole.

We know how many we need.

We don't need any more or any less than 40, do we? So 40 is our known whole.

We want to know how many packs of candles Izzy has to buy.

And this is our unknown number of parts.

We know each pack has 10 candles.

So one part is 10 candles, and we can form an equation now to help us.

The whole is known, and it is 40.

The whole is divided into an unknown amount of equal parts.

How many packs do we need? We don't know, do we? But we do know that each pack is worth 10.

And we can divide the whole by the value of each part, and that will tell us how many packs we need.

40 divided by 10.

Well, we know our 10 times tables, don't we? 40 divided by 10 is equal to 4.

So Izzy needs to buy four packs of 10 candles.

So we knew the whole in this problem, but we didn't know how many parts there were.

But we knew the value of one part, and if we know the value of one part, well, we can divide the whole by the value of that part, and that will tell us how many parts there are in total, and in this case, how many packs we needed to buy.

So we needed to buy four packs.

Each had 10 candles in them, and that would have given us our whole amount of 40 candles that we needed for that cake.

Let's check your understanding with that.

Could you use the bar model to complete the sentences and then form an equation to find how many parts make up the whole? So we can see the whole is known and is, mm.

The whole is divided into an unknown amount of equal parts.

We don't know how many parts there are.

Each part is worth, mm.

Pause the video, have a go at completing the sentences, and then form an equation to find out how many parts make up the whole.

When you have figured that out, press play.

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

So the whole is known and is 60.

We can see that's the whole amount.

The whole is divided into an unknown amount of parts, and that's what we are trying to find out.

But we know each part is worth five.

We can use that information to form an equation.

The whole divided by that value of one part, in this case, five, that will tell us how many parts there are.

60 divided by 5.

Well, we know our five times tables.

Five 12s are 60, so 60 divided by 5 must be 12.

So I have got my 12 equal parts.

Each has a value of five.

There are 12 equal parts of five in the whole.

It's your turn to practise now.

For question one, could you solve these problems to calculate the value of the whole, representing each of them as a bar model and forming an equation to solve them? Question A, Alex has five pots.

He plants six seeds in each pot.

Hmm, so he must be like plant pots, mustn't he? Can you visualise that? He's got five pots, and he plants six seeds in each pot.

How many seeds does he plant in total? For part B, Izzy has eight bags.

She puts four apples in each bag.

Can you visualise that? She's got eight bags, and she puts four apples in each bag.

How many apples does she have altogether? So have a go at representing these so you see if you can calculate the value of the whole.

For question two, this time, I want you to solve these problems to calculate the number of parts, the number of equal parts, in the whole.

Represent these as a bar model, and form an equation to solve them.

For question A, Alex needs to buy 45 balloons, and balloons are sold in packs of five.

Can you visualise that? Can you think about 45 balloons? But one pack is five.

How many packs does he need to buy? And for part B, Izzy needs to plant 48 seeds.

Seeds are sold in packs of eight.

How many packs does she need to buy? Can you visualise that? She needs 48 seeds.

Is that a whole? Is that a part? And seeds are sold in packs of eight.

Is that the whole? Is that a part? And we need to know how many packs she needs to buy.

Pause the video while you have a go at those questions, and when you're ready for the answers, press play.

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

Our first question, Alex has five pots, and he plants six seeds in each pot.

How many seeds does he plant in total? Well, straight away, I've done my bar model.

I don't know the total, so that is our unknown whole.

But I do know there are five pots, so five parts, and he plants six seeds in each pot.

So the value of each part is six.

And from my bar model, I can form an equation.

The whole is unknown.

This is what we are trying to find.

The whole is divided into five equal parts, and each part is worth six.

I've got five parts each worth six, five 6s, and we can use our five times tables to help us.

Five 6s are 30.

Alex plants 30 seeds in total.

For part B, this time Izzy had eight bags, and she puts five apples in each.

We can represent this in a bar model.

We've got eight bags, so there must be eight parts, and each part must have a value of five.

The whole is unknown.

This is what we are trying to find out.

But we do know that it's been divided into eight equal parts, and the value of each part is five.

And we can use that to form an equation.

Eight parts, five in each part, eight parts of five, eight 5s are 40.

Izzy has 40 apples altogether.

I wonder how you got on with finding the value of the whole.

Well done.

For question two, we needed to find the number of parts in the whole.

Our first question, Alex needed to buy 45 balloons, and balloons are sold in packs of five, and we needed to work out how many parts, how many packs he would need to buy to get 45 balloons.

So our whole is 45.

We only know the value of one part, which is five, but we don't how many parts there are.

So the whole is known and is 45, and it's divided into an unknown amount of equal parts, which is what we are trying to find.

But we do know each part is worth five, and we can use that to form an equation.

45 divided by 5.

Well, we know five 9s are 45, so 45 divided by 5 must be 9.

So Alex needs to buy nine packs of five balloons.

For part B, Izzy needs to plant 48 seeds.

Seeds are sold in packs of eight.

So we know the whole, we know it's 48, and we know it's divided into an unknown amount of equal parts.

That's what we've got to find out, how many packs she needs.

And we know each part is worth eight.

We can use this information to form an equation.

The whole is 48, and we're going to divide by 8, the value of one part.

We know six 8s are 48, so 48 divided by 8 must be 6.

So Izzy needs to buy six packs of eight seeds.

How did you get on with those questions? Brilliant, well done.

Fantastic learning today, everybody.

I can see how hard you have tried, and that's what's important.

The harder we try, the more successful that we will be.

I can see how you have deepened your understanding at calculating the value of a part using understanding of division.

We've learned, to calculate the value of a part, we need to divide the whole by the number of equal parts.

We've also learned that to calculate the number of equal parts, we need to divide the whole by the value of each part.

And we also know that we can calculate the whole, and to do that, we need to multiply the number of equal parts by the value of each part.

We've also learned how important it is to draw a bar model to help us visualise the problem.

And once we've drawn our bar model, it helps us to form an equation to determine how to solve the problem.

Well done for all your hard work and effort today.

It has been a pleasure learning with you, and I look forward to learning with you again soon.