Lesson video

Hello, how are you today? My name is Dr.

Shorrock and I'm really excited to be learning with you today.

You've made a great choice to learn maths with me and I know that we are going to be successful as we move through the learning.

Today's lesson is from our unit, calculate the value of a part, fractions as operators.

This lesson is called connect division with finding a fraction of a quantity to find parts and wholes.

As we move through the learning today, we will deepen our understanding of how we can work out the value of a part or a whole or how we can find a fraction of a whole.

Now, sometimes new learning can be tricky, but I know we can work really hard together and I'm here to guide you and if we do that, then we will be successful in this learning.

Shall we get started then? Let's find out how can we calculate the value of a part in a whole and how do we connect with division knowledge, with finding a fraction of a quantity? Today, the keyword that we will be using, throughout the learning is divide.

I'm sure you've heard that word before, but let's practise together.

My turn, divide, your turn.

Brilliant, well done.

And when we say divide, we mean to split something into equal parts or groups and there is a symbol that we use to mean divide.

Look out for that as we move through the learning today.

We are going to start today by thinking about how we can calculate the value of a part.

In our lesson today we've got Lucas, Sophia, Izzy and Alex to help us.

Let's look at this problem.

Alex has been collecting conkers.

Can you visualise that? I wonder if you've ever collected some conkers.

He has found 15 so far.

Wow, he's been good at collecting, hasn't he? He plans to share the conkers between himself and four friends.

That's kind of him, isn't it? What do we need to do first do you think? Good idea, Alex.

Let's represent this in a bar model.

Bar models are really excellent ways of representing words to help us know what we need to do and to help us form an equation to solve a problem.

We know we have 15 conkers, so 15 is our whole and it is known and we are sharing those conkers between Alex and four friends.

How many parts is that in total? That's right, it's five equal parts in total.

We can show those parts on our bar model and we can use then this bar model to form an equation.

Our whole is 15 and we are dividing the whole into five equal parts and then we can use our known five times table facts to help us.

Five multiplied by three is 15.

What does that mean? That's right.

It means that 15 divided by five must be three.

Each part is worth three.

Alex and his four friends will get three conkers each.

Five times three is 15.

Aha, Sofia is going to help us deepen our understanding here.

Did we know that dividing a whole amount into five equal parts, which is what we've done and that's the same as finding one fifth of the whole.

Each part is one fifth of the whole.

We have divided the whole 15 into five equal parts and that is the same as finding one fifth of the whole.

One fifth he 15 conkers is three conkers.

To find one fifth of the 15 then, we need to divide 15 into five equal parts.

15 divided by five is equal to three.

So one fifth of 15 is also equal to three.

And we can write it like this.

We can write it with a fraction replacing the word one fifth, we can write it with our unit fraction.

One fifth or 15 is equal to three.

Do you notice anything here? Anything that is the same? Anything that is different? That's right.

Thank you Sophia.

The denominator of the fraction, tells us how many equal parts we have and therefore what to divide by.

So, our fraction is one fifth, that's one fifth, a fifth is a five.

And therefore we need to divide into five equal parts.

Let's check your understanding.

Could you use the bar model to complete the sentences? So, you can see the bar model and the sentences are, defined one quarter of 28.

We divide um into um equal parts.

Um divided by um is equal to um.

One quarter of um is equal to um and um of um is equal to um.

Pause the video, while you have a go at completing those sentences, maybe compare your answers with somebody else if you can.

And when you're ready to go through them, press Play.

Shall we see how you got on? So, to find one quarter of 28, we divide 28 into four equal parts and that was shown on the bar model, wasn't it? 28 divided by four.

Well we know when we divide by four we can halve and halve again.

28 halved is 14, halve again at seven.

So, 28 divided by four is equal to seven.

One quarter of 28 is equal to seven.

Remember, if we are dividing by four, it must be the same as finding one quarter of the whole amount.

So, one quarter of 28 is equal to seven.

Your turn to practise this now.

Could you use your division facts to solve this problem? Alex has been collecting one pence coins.

He has found 32 so far.

He plans to share the coins equally, between himself and three friends.

And knows this means that he has to find one quarter of 32.

How many coins will they each get? And so fear is given as a bit of a hint there.

We might want to represent this as a bar model.

For question two, could you use your division facts to find the given fractions of quantities? Then starting with the smallest, put the quantities in order.

So, A, you've got one half of 16, B, one quarter of 40, and C one eighth of 24.

And question three.

Sofia prefers to have the greater amount.

Don't we all? Would she rather have one quarter 44 pounds or one eighth of 80 pounds? What do you think? Could you give me some reasons for your answer? Pause the video while you have a go.

All three questions and when you are ready to go through the answers, press Play.

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

For question one, you had to use your division facts to solve a problem.

We had 32 pence as our whole amount and we needed to find one quarter of it.

Finding one quarter, well the denominator of that fraction is four, so we need to divide 32 into four equal parts.

32 divided by four is equal to eight.

When we divide by four, we can halve and halve again, can't we? 32 halved is 16.

16 halved is eight.

So, one quarter of 32 is equal to eight.

They each get eight one pence coins.

For part A of the second question.

We had to find one half of 16.

Well to find one half, well the denominator is a two, so we must need to divide 16 to two equal parts.

16 divided by two is equal to eight, so one half of 16 is equal to eight.

For part B, we had to find one quarter of 40.

To find one quarter of 40, we need to divide 40 into four equal parts.

The denominator for the fraction one quarter is four, isn't it? That's why we need to divide into four equal parts.

40 divided by four.

Well we now divide two divide by four we can halve and halve again.

So, 40 halved 20.

20 halve is 10.

So, 40 divided by four is 10.

So, one quarter of 40 is equal to 10.

For part C, we had to find one eighth of 24.

To find one eighth of 24, we divide 24 into eight equal parts.

The denominator of the fraction one eighth is eight and that tells us how many equal parts we need to divide by.

24 divided by eight, well we know our eight times tables, 24 divided by eight is equal to three.

So, one eighth of 24 is equal to three.

You were then asked to put those quantities in order.

So, one eighth of 24 is only three.

One half of 16 was eight and then one quarter of 40 was 10.

So, three is less than eight, which is less than 10.

For question three you had to work out the amount and Sofia prefers the greater amount.

So, which one would she prefer? And we had to give some reasons for our answers.

Let's work out one quarter of 44.

Well the denominator is four, so we know we need to divide 44 into four equal parts.

44 divided by four.

Well we can halve 22 and then halve again 11.

So, 44 divided by four is equal to 11.

One quarter of 44 is equal to 11.

Now, let's have a think about 80.

We had to find one eighth of 80, the denomination of one eighth is eight.

So, we know we will be dividing 80 into eight equal parts.

80 divided by eight is equal to 10.

So, one eighth of 80 is also equal to 10.

So, which amount would Sofia prefer, do you think? That's right, she would prefer to have one quarter of 44, because that's 11 pounds.

If she had one eighth of 80, that would only be 10 pounds.

So, I think she would prefer 11 pounds, because it's one pound more.

How did you get on with those three questions? Brilliant.

Fantastic learning so far.

You're making a lot of progress and working really hard I can see.

We're going to move on now to think about how we calculate the whole and the fraction of the whole.

Let's look at this problem.

Lucas has been given five pounds by his mom.

It's very kind of her, isn't it? She told him that it was one quarter of the amount that she had won in a lottery.

So, Lucas wants to know naturally the amount of money that his mom did win.

What do we need to do first do you think to help us? That's right Izzy, thank you.

We need to represent this as a bar model.

We want to find out how much money his mom won.

So, that's our whole and we don't know that at the moment, so that's what we're trying to work out.

It is our unknown whole.

We know the value of one part is five pounds and that this part is one quarter of the whole.

So, there must be four equal parts, because the denominator of that fraction one quarter is a four and that tells us the number of parts we are dividing by.

The whole is divided into four equal parts and we have one of those parts.

Each part is worth five pounds.

So, we can represent that on our bar model.

Four equal parts, each part is worth five pounds.

We can then use that, can't we? To work out the whole.

We can form an equation.

We've got four parts and each is worth five pounds, four times five pounds.

And we know our five times tables, so we can use them to solve this problem.

Four fives are 20.

Lucas' mum won 20 pounds in the lottery.

We can say that five pound is one quarter of 20 or that one quarter of 20 is equal to five pound.

Let's check your understanding.

Could you use this bar model and complete the statements to find, then describe the part-part-whole relationship.

So, we've got a picture of a bar model.

Have a look at it there.

What do we know, what don't we know? How many parts are there? And use that to complete these statements.

Um times six is um, six pound is one um of um and then um of something pounds is equal to six pound.

Pause the video while you do that.

Well when you are ready for the answers, press Play.

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

So, using the bar model, we could see that there were five equal parts and each part had to be six pounds.

We know our five times table, so five sixes are 30 and each of those is one fifth of the whole.

So, six pound is one fifth of 30 pound.

One fifth of 30 pound is equal to six pound.

How did you get on with that? Well done.

Let's have a look at this problem.

Izzy collects stickers, can you visualise that? I wonder if there's something that you collect.

But Izzy collects stickers and she wants to collect 72 stickers.

At the moment, Izzy has eight stickers.

What fraction of the whole does she have? So, this time, what do you notice? And think about what do we need to do first to help us? That's right, thank you Lucas.

Let's represent this as a bar model to really help us make sense of those words.

The whole is known and it's 72.

She wants 72 stickers and at the moment she only has a part of that.

She only has eight stickers.

We don't know what the whole has been divided into, so that's an unknown amount of equal parts.

But we do know that each part is worth eight, because that's what she has at the moment.

She has one part and that's worth eight.

So, we can use this information and the bar model to form an equation.

We've got the whole is 72 and we know the value of one part is eight.

So, if we do 72 divided by eight, we can find how many parts there are in total and we know our eight times table, so we can use our division facts to solve this.

72 divided by eight is equal to nine.

So, we've got nine equal parts each are worth eight.

So, there must be nine equal parts of eight in the whole.

Let's have a look at this more closely.

We know 72 divided by eight is equal to nine.

There are nine equal parts and Izzy has one of these parts.

Izzy has won ninth of the whole amount that she wants.

So, one part that was worth eight is worth one ninth of the whole.

And we work that out by dividing the whole by the value of one part.

Eight stickers is one ninth of 72 stickers.

Do you notice something about all of that information? That's right.

There are nine equal parts and each part is worth one ninth of the whole.

You can see that number nine there in both of those statements.

Let's check your understanding.

Could you look at the bar model and complete these sentences? You can see the bar model there.

Have a think about what is the whole, what else have you got? Have you got a part? What's the value of that part? How many parts are there? And let's complete the sentences.

One um of the whole.

There are um equal parts and Izzy has one of these parts.

Izzy has one um of the whole amount.

Pause the video, maybe go and chat to someone about this and when you are ready to go through the answers, press Play.

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

Did you work out that three, must be one quarter of the whole, because there are four equal parts.

There are four equal parts and Izzy has one of those parts and Izzy has one quarter of the whole amount.

Three is one quarter of 12.

How did you get on? Brilliant.

It's your turn to practise now.

For question one, could you solve these problems? Have a go at visualising them first and representing them in a bar model.

It will help you make sense of the words.

For part A, Izzy has 13 stickers.

Can you visualise that? This is one half of the whole set.

How many stickers are in the whole set? Part B, Jacob spends three pound, this is one eighth of his whole amount of money.

How much money does he have left? For question two, a fifth of a quantity is eight.

What is the whole? It might be worth trying to represent that somehow, bar model would be good.

For question three, could you solve this problem? Sofia is making party bags with an equal number of sweets in each.

In total she has 80 suites to share.

She has already made one bag with eight sweets.

What fraction of sweets has she used so far? A good idea there again would be to visualise this, what do you see? And then have a go at representing it in a bar model to help you form an equation.

Pause the video while you have a go at all three questions and when you are ready to go through the answers, press play.

Let's see how you got on.

Question one, part A, Izzy has 13 stickers and this was one half of the whole set, so we didn't know how many were in the whole set.

That was unknown, but we do know that finding one half is the same as dividing by two, because the denominator of that fraction one half is a two.

So, finding one half of a whole is the same as dividing the whole into two equal parts.

Each part is worth 13.

And we can represent this in a bar model.

We have two equal parts.

Each part is worth 13 and then we know we can find the whole by forming an equation.

And two parts each are worth 13, two thirteens.

Well, I'm going to double 13, which is 26.

There are 26 stickers in the whole set.

Part B, you had Jacob spending three pounds, which is one eighth of his whole amount of money.

And how much money does he have left? So, we don't know the whole, we dunno how much money he's got.

We just know he spends three pounds, but we do know we have to find one eighth of the whole and that fraction one eighth, well the denominator is eight, so we must be dividing into eight equal parts and we know the value of the parts, don't we? One part is worth three pounds, so we can represent this in a bar model.

We've got the whole amount, which is unknown and we've got eight equal parts, each part worth three pounds, so we can find the value of the whole then.

We've got eight parts, each is worth three.

Eight threes or we can use our eight times table facts to help us there.

Eight threes are 24, so we had 24 pound, but actually he spent three of it, didn't he? So, he's got 21 pounds left.

For question two, we had a fifth of a quantity is eight and you needed to find out what the whole was.

Well the hole is unknown.

Finding one fifth of a whole is the same as dividing into five equal parts that fraction one fifth the denominator is five, isn't it? So, we know that's how why we know we have to divide into five equal parts.

We have one of those parts.

Each part is worth eight.

Five eights, well we know our five times table and we know our eight times table.

Five eights are 40, so the whole is 40.

For question three, question about Sofia making party bags.

We know the whole it was 80 sweets that she had to share and we don't know how many equal parts though, that's what we had to work out.

But we do know each part is worth eight.

80 divided by eight when we know our eight times tables is 10.

So, there are 10 equal parts and Izzy has one of those parts.

Izzy has used one 10th of the whole amount.

Eight sweets is one 10th of 80 sweets, so she has used one 10th of the sweets so far.

How did you get on with all those questions? Brilliant.

Fantastic learning today.

Really impressed with the progress that you have made.

You have tried really hard and that's what's really important when we learn maths.

We have deepened our understanding of how we can connect division with finding a fraction of a quantity to find parts and wholes.

We know that calculating the value of a part is the same as dividing the whole by the number of equal parts and the denominator of the fraction, tells us the number of equal parts in the whole.

We know that drawing a bar model supports us to visualise the problem and we know to use our times table and division facts to find a fraction of a quantity.

I'm really proud of the work you have done today and you should be really proud of yourselves.

I've had a lot of fun and I look forward to learning with you again soon.

Goodbye for now.