Lesson video

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

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

We are gonna have great fun as we move through the learning together.

Welcome to today's lesson.

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

This lesson is called use knowledge of the relationship between parts and wholes to solve problems. Throughout the learning today, we will deepen our understanding of this relationship between parts and wholes.

We look at the same part, different fraction, different parts, same fraction, and then different part, different fraction, and really deepen our understanding and consolidate our learning on this relationship.

Sometimes new learning can be tricky, but I know, if we work really hard together and I'm here to guide you, we will be successful in our learning.

So, let's get started, shall we? How do we use this knowledge of the relationship between parts and wholes to solve problems? This is our key phrase for the lesson today, times as much.

Let's practise that together.

My turn, times as much.

Your turn.

Brilliant.

Well done.

So when we say times as much, it's a phrase that we are going to use to compare and describe objects.

Today's learning is split up into three learning cycles.

We're going to start by looking at the same size part but a different fraction.

In this lesson we've got Lucas and Sofia to help us.

So Sofia and Lucas are trying to solve a problem to determine which line is longer.

Have a look.

What do you think? We've got line A, and half of line A is shaded purple, and we've got line B, and one third of line B is shaded.

Which whole line do you think is longer? And what do you notice about these lines that might help us solve this problem? Ah, Lucas has noticed that the two given parts are the same length.

Can you see the shaded part, it's the same length, isn't it? Ah, but Lucas has also noticed each part is a different fraction of the whole.

Line A, the part is one half of the whole, and line B, the part is one third of the whole.

Let's look at line A first.

As Sofia is telling us, we know that if one half is a part, then the whole is two times as much.

So we need to take two of those parts and combine them to make one whole.

And you can see that must be the length of line A.

We have got two one half parts and that makes that whole of line A.

And then if we look line B, Lucas is telling us that if we know one third is a part, then the whole is three times as much.

We need to take three parts this time and combine them to make one whole.

So we can see now that line B is longer.

Both parts were the same size, but they had a different fraction.

Let's check your understanding.

Which line is longer.

Is it line A or line B? Line A, I've shown you one quarter of the whole line, and line B, you can see what one third of the whole line looks like.

Pause the video, maybe have a chat to somebody about this.

See if you agree.

And when you are ready to hear the answers, press play.

How did you get on? Did you work out that it must be line A, but why is it line A? Well, both line segments given to you were the same size, but they were both a different fraction.

Line A, you were given one quarter of the whole and line B, you were given one third of the whole.

The parts were the same size, but line A is made up of more of those parts.

We needed four parts to combine to make the whole, but for line B, we only needed three of those parts to combine to make the whole.

So the whole of line A will be longer.

How did you get on with that? Well done.

Let's now look at these groups of children from Lucas' and Sofia's classes.

What do you notice? Is there something you notice? What is the same? What is different? Ah, what's Lucas noticed? Lucas has noticed that the two given parts are the same size.

So the part that we are being shown of Lucas' class is four children, and the part that we are being shown of Sofia's class is four children.

So that is the same.

Ah, Lucas has noticed that each part is a different fraction of the whole class.

Those four children are one fifth of Lucas' class, but they are one sixth of Sofia's class.

So the part is the same size, but it is a different fraction.

This is similar to that line problem, isn't it? But this is now with a group of children, which class has more children? Let's look at Lucas' class first.

If one fifth is apart, then the whole is five times as much.

We need to take five parts and combine them to make one whole.

And remember, each one of those parts is four children.

There's one part, two parts, three parts, four parts, and five parts.

Each part has four children.

So there are five groups of four children in Lucas' class.

We know our four times tables, don't we? So we can save five fours are 20.

There are 20 children in Lucas' class.

Let's look at Sofia's class.

This time, the part was one sixth of the whole.

So if one sixth is apart, then the whole is six times as much.

And remember each part is composed of four children.

So we need to take six parts this time and combine them to make one whole.

One part, two parts, three parts, four parts, five parts, six parts.

Each part has four children.

So there are six groups of four children in Sofia's class.

So we know our four times tables, don't we? So we can say six fours are 24.

There are 24 children in Sofia's class.

So which class has more children? We know Lucas' class has 20 children, and Sofia's class has 24 children.

So Sofia's class has more children.

But why? That's because the parts were the same size.

So the part that we were given was four children from each class, but, Sofia's class is made up of more of these parts.

She had six of those parts, whereas Lucas' class was just five of those parts.

Let's check your understanding.

Can you have a look at these representations of some cherries and tell me which bag has more cherries? Is it bag A or bag B? What do you notice? What's the same and what is different? Pause the video, maybe find someone to chat to about this.

And when you are ready for the answers, press play.

How did you get on? Did you work out that it must be bag B? But why is it bag B? Well, bag B has got more cherries because the parts are the same size.

There were four cherries that we were told was one part, but, bag B is made up of more of those parts.

Bag B, we needed six of those parts.

Six fours.

And bag A, we had one half already, so we only needed two of those parts.

Two fours.

So the whole of bag B will be greater.

How did you get on with that? Well done.

You're turn to practise now.

For question one, could you use this information to tell me who has more marbles and by how many? So the representation, the first representation shows one quarter of Lucas' marbles, and the second representation shows one fifth of Sofia's marbles.

Remember, have a think what is the same and what is different.

Then for question two, could you complete this table? Have a go at both questions when you are ready to hear the answers, press play.

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

So for question one, you are asked to determine who has more marbles and by how many.

Let's start by looking at Lucas' marbles.

We are told that four marbles is one quarter of Lucas' marbles.

If one quarter is a part, then the whole is four times as much.

So we need to take four parts and combine them to make one whole.

One part is four, so we've got four parts each with four in them, and four fours are 16.

So Lucas has 16 marbles.

Let's look at Sofia's marbles.

We are told that four marbles is one fifth of Sofia's marbles.

If one fifth is a part, then the whole is five times as much.

So we need to take five parts and combine them to make one whole.

Five fours are 20.

So Sofia has 20 marbles, but then we were asked to find out who has more marbles and by how many.

So we can see Sofia has more marbles, and by how many? Well, 20 subtract 16 is four.

So Sofia has four more marbles than Lucas.

But did we need to calculate to find out who had more? I wonder if some of you noticed that we didn't need to calculate.

The parts were the same size, they were both four.

And Sofia's marbles were made up of more of those parts so her whole would be greater.

I wonder if you got that.

For question two you were asked to complete the table.

So for the triangle, if the triangle is a part, and it's one third of the whole, then there must be three of those equal parts in the whole.

If the rectangle was a part and we are told that the number of equal parts in the whole are five, so the part as a fraction of the whole must be one fifth, and you might have drawn a representation that looks something like that.

And for the marbles we are shown that four marbles is a part and that part is one half of the whole.

So we must need two equal parts in the whole, and you might have drawn a representation like that with two equal parts of four, or eight marbles in total.

Then, we were given the whole, and we could see that there were three equal parts in the whole.

So that means one part must look like that, just one part of the line and that is equivalent to one third as a fraction of the whole.

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

Let's move on now and look at a different size part but same fraction.

Let's revisit the line problem and look at some different lines.

What do you notice about the parts of the lines this time? Let's look at line A and line B.

Hmm, what's the same? What's different? Lucas has noticed that each part is the same fraction of the whole.

This time, both parts of the lines are one fifth of their whole.

But the two given parts are different lengths this time, aren't they? Good spot Lucas.

Which whole line would be longer then do you think? Well we know that if one fifth is a part then the whole is five times as much.

Now this time, the parts are different sizes but the fraction is the same.

So we need five times as much for each of those lines.

So we need to take five parts and combine them to make one whole.

And if we do that, we can see that line B is longer.

This is because each part is longer in line B than line A, so the whole of line B will be longer.

Let's check your understanding.

Which box contains more toy cars? Is it box A or box B? And you can see from the representation you've been given one fifth of the toys in box A, and in the second representation you've been given one fifth of the toys in box B.

So have a look.

What do you notice is the same, and what is different? Maybe try representing what the whole would look like.

Pause the video while you have a go.

And when you are ready for the answers, press play.

How did you get on? Did you work out that the number of toys in box A must be 25? We had five toy cars in one part and we needed five of those parts, five fives are 25.

And for box B that was still one fifth, so we needed five parts, but this time each had three cars in them, five threes are 15.

So box A contained more toy cars.

The size of the parts are different.

We were given a part of five toy cars, and a part of three toy cars.

And the size of the part in box A is greater.

It was one fifth.

We needed five of those parts to make the whole.

So that whole will be greater.

You're turn to practise now.

Using this information, can you determine whose classroom has more pens and by how many? In the first representation of pens, that is one quarter of the pens in Lucas' classroom, and in the second representation you've got one quarter of the pens in Sofia's classroom.

So have a think carefully about what is the same and what is different.

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

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

Let's start by thinking about Lucas' classroom.

So we know one quarter is a part, so the whole must be four times as much.

We need to take four of those parts and combine them to make one whole.

So there are six pens in one part, so we need four sixes.

Four sixes are 24, 4 parts of six.

So Lucas' classroom has got 24 pens.

Let's now look at Sofia's classroom.

We were told we have one quarter of the pens in Sofia's classroom and that is seven in that one quarter part.

If one quarter is apart, then the whole is four times as much.

We need to take four of those parts and combine them to make one whole.

Four parts of seven.

Four sevens are 28.

So Sofia's classroom has 28 pens.

We needed to work out whose classroom had the most pens and by how many.

So we know Sofia's classroom has 28 pens and Lucas' classroom has 24 pens.

So Sofia's classroom is the one with more pens than Lucas' classroom, but by how many? That's right, we need to subtract.

So Sofia's classroom has four more pens.

But did we need to calculate to find out which classroom had more? You might have noticed we did not need to calculate.

The fractions of the wholes were the same.

They were both one quarter of the whole.

So the greater whole would be the one with a greater number in their part.

The size of Sofia's classroom part was greater than Lucas'.

There were seven pens in that part and Sofia's classroom, but only six in Lucas'.

So that whole would be greater.

Well done if you spotted that.

Let's move on to our third learning cycle.

We're now going to look at what happens if we've got a different size part and a different fraction.

Lucas has some cherries in a bag.

This is one seventh of his cherries.

Can you see how many cherries there are? Can you see that without counting? That's right.

There are four cherries in that one seventh part.

Sofia has some strawberries in a bag and this is one sixth of her strawberries.

Can you see how many there are there without counting? That's right, there are five, aren't there? What do you notice about these? Ah, Lucas has noticed that each part is a different fraction of the whole.

We've got one seventh and we've got one sixth.

And the two given parts are different.

We've got four cherries and five strawberries.

So this time we are looking at a problem where we've got a different size part, and a different fraction.

So who has the most pieces of fruit? Well let's look at Lucas' piece of fruit first.

We are told that four cherries are one seventh of his cherries.

If one seventh is apart, then the whole is seven times as much.

So we need to take seven parts and combine them to make one whole.

One part, two parts, three parts, four parts, five parts, six parts, seven parts.

So each part has four cherries.

So there are seven parts with four cherries in them.

Seven fours are 28.

So there are 28 cherries in Lucas' bag.

Now let's look at Sofia's fruit.

We were told that five strawberries is one sixth of the whole.

So if one sixth is part, then the whole is six times as much.

We need to take six of those parts and combine them to make one whole.

One part two part three parts, four parts, five parts, six parts.

Each part has five strawberries.

So there are six parts each with five strawberries, six fives are 30.

There are 30 strawberries in Sofia's bag.

So who has the most pieces of fruit? We know Lucas has 28 cherries and Sofia has 30 cherries.

So Sofia has more pieces of fruit.

Did you spot that? Let's check your understanding.

Can you tell me who has the most stationary? So first representation is one quarter of Sofia's stationary, and the second representation shows one half of Lucas' stationary.

So just have a think what is the same here and what is different.

Pause the video while you have a go and when you are ready for the answers, press play.

How did you get on? Let's look at Sofia's stationary first.

We are told that her four items are one quarter, so we know we have four equal parts to combine to make the whole, and there are four in each part.

So four fours are 16.

If we look at Lucas' stationery, we are told that this is one half.

So we know there must be two parts in the whole and there are five items in each part.

Two fives are 10.

So we can see that Sofia has the most stationery, both the size of the parts and the fractions were different here, we had four items of stationary and five items of stationary.

We had one quarter and we had one half.

So because both the parts and the fractions are different, we needed to calculate to find the whole before we could then compare.

How did you get on? Well done.

It's your turn to practise now.

For question one, could you use this information and determine who has more marbles and by how many? You can see the representation shows one 10th of Lucas' marbles and one ninth of Sofia's marbles.

So maybe have a think what is the same and what is different and what do I need to do.

You could try representing this drawing something, drawing this visually or representing as a bar model to help you.

Pause a video while you do this, and when you are ready to go through the answers, press play.

How did you get on? Let's start by looking at Lucas' marbles.

We are told four marbles are one 10th of his marbles.

If one 10th is apart, then the whole is 10 times as much.

We need to take 10 parts and combine them to make one whole.

10 parts each with four in them, 10 fours are 40, so Lucas has 40 marbles.

Let's look at Sofia's marbles.

We can see there are five marbles and that is equivalent to one ninth of her whole amount of marble.

If one ninth is apart, then the whole is nine times as much.

We need to take nine parts this time and combine them to make one whole.

We've got nine parts each with five in them, nine fives are 45.

So Sofia has 45 marbles.

We were asked to determine who has more marbles.

So Sofia has 45 marbles and Lucas 40 marbles.

So we co see that Sofia has more marbles than Lucas, but by how many? That's right.

For that we need to subtract.

45 subtract 40 is five.

So Sofia has five more marbles than Lucas.

But, did we need to calculate to find out who had more? Yes, this time we did.

We needed to calculate because both the size of the parts and the fractions were different.

So there was no other way that we could compare them without working out the whole for each.

How did you get on with that question? Well done, fantastic learning today everybody.

I'm really impressed with the progress that you have made about using your knowledge of the relationship between parts and wholes to solve problems. We know that if two parts are the same size but a different fraction of the whole, then the whole with the most parts will be greater.

We know if two parts are a different size, but are the same fraction of the whole, then the whole with a larger part will be greater.

And we know that if both the size of the part and the fraction of the whole are different, we need to calculate the whole to determine which is greater.

You should be really proud of the progress that you have made today and how hard you have tried.

I look forward to learning with you again soon.

Bye for now.