Lesson video

Hello, how are you today? My name's Dr.

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

You have made a great choice to learn maths with me and I am here to guide you through the learning.

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

This lesson is called constructing a whole.

We are going to look at context when we are given one part and the fraction of the whole that it represents and we need to construct the whole.

Sometimes new learning can be a little bit tricky, but don't worry, I know if we work really hard together and I'm here to guide you, then we will be successful in our learning.

So then let's go, shall we? Let's find out how can we construct a whole when given one part and the fraction that it represents? This is the keyword that we will be using in our learning today.

Construct.

Let's practise that together, shall we? My turn, construct, your turn.

Fantastic.

Well done.

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

So if we construct something, it means to make or build something.

Maybe in the past, you have constructed something with LEGO bricks.

In the context of this lesson though, it means to make or build a whole from its equal parts.

Today we are going to look at how we construct a whole, and that is where we will start the learning, constructing a whole.

In this lesson, we have Lucas and Sofia to help us.

Lucas and Sofia are playing a game called what is the whole? They use a red rod as part of the whole and Lucas is thinking of a whole and he's telling us that this red rod is 1/3 of his whole and he wants us to try and work out what is the whole? What do you think? Sophie's going to construct the whole using rods? Great idea.

Great idea to actually use rods, Sofia.

And Lucas has told us that the red rod is 1/3 of the whole.

What does that mean? How will that help us? That's right, thank you, Sofia.

This means that the whole has been divided into three equal parts and this rod is one of those parts.

So there must be three of these parts in the whole.

Here we go.

We've now got three of those parts.

So we can now see what the whole looks like.

Oh, what have you noticed, Sofia? Ah, that's right, you found another rod.

Sofia has found a green rod and Sofia has noticed that the green rod is the same length as the three red rods.

So we can say that the green rod is three times the length of one red rod.

The children have another go at the game and this time, Sofia chooses the fraction that is represented by the red rod and it is Lucas' turn to construct the whole.

So Sofia is thinking of the whole this time and Sofia tells us the red rod is now 1/5 of the whole.

What is the whole? Do you know? Can you visualise that? So Lucas is going to construct the whole using rods.

Great idea.

Sofia told us that the red rod is 1/5 of the whole.

What does that mean? How many parts do you think we need? That's right.

The whole has been divided into five equal parts and this rod is one of those parts.

So there must be five of these parts in the whole.

Ah, what have you noticed, Lucas? Ah yes, he's found a rod that matches.

The orange rod is the same length as five red rods.

We can say that the orange rod is five times the length of the red rod.

Let's check your understanding.

I've shown you a picture of a red rod and I'm telling you that that red rod is 1/4 of the whole.

Could you look at the representations and tell me which representations shows the whole if the red rod is 1/4 of the whole? Maybe find someone to chat to about this and compare your thoughts.

Pause the video while you do that.

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

How did you get on? Did you realise that the red rod is 1/4 of the whole and that means that the whole has been divided into four equal parts and the red rod is one of those parts? So there must be four of those parts in the whole.

So it can't be option A because there are only two parts.

Same for B.

There can't be option B because there are only three parts.

Option C, that's the one with four equal parts and it can't be option D because there are five equal parts.

How did you get on? Well done.

Let's check your understanding with this.

Could you look at the statements and tell me which statement describes the relationship between the red bars and the purple bar? So there might be more than one because I've said which statements.

So there might be more than one.

Is it option A? The red rod is two times the length of the purple rod.

Is it option B? The purple rod is two times the length of the red rod.

Option C, the length of the purple rod is twice the length of the red rod.

Or is it option D? The length of the red rod is double the length of the purple rod.

Pause the video while you have a think about which statement or statements it is.

And when you're ready for the answers, press play.

How did you get on? Did you realise it can't be option A because the red rod is not two times the length of the purple rod.

If that were the case, the red rod would be longer and it is not.

Option B is correct because the purple rod is two times the length of the red rod.

Two of the red rods are the same as the length of the purple rod.

Are there any others correct? That's right, option C is also correct.

The length of the purple rod is twice the length of the red rod, twice means two times.

What about option D? It can't be option D, can it? Because the length of the red rod is not double the length of the purple rod.

The red rod is shorter.

How did you get on? Well done.

It's your turn to practise now.

For question one, could you use some rods to construct wholes using the given information? Draw a picture of your rods and give reasons for the length of your wholes.

If you can, find another rod that is equal in length to your whole.

So for part A, one rod is 1/2 of the whole.

And for part B, one rod is 1/6 of the whole.

For question two, could you solve this problem? The red bar is 1/3 of a whole.

The same red bar is also 1/4 of a different whole.

Which whole is longer? Could you give some reasons for your answer? Pause the video while you have a go at both those 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 were asked to construct some wholes and for part A, one rod needed to be 1/2 of the whole.

So you might have done something like this.

I had two purple rods and I found a brown rod and my whole rod had been divided into two equal parts and the purple rod is one of those parts.

So there must be two of those parts in the whole.

The brown rod is twice the length of a purple rod.

For part B, one rod was meant to be 1/6 of the whole.

So you might have done something like this.

My whole has been divided into six equal parts and the white rod is one of those parts and there must be six of those parts in the whole.

The green rod I found is six times the length of a white rod.

For question two, you had a problem to solve about the red bar being 1/3 of a whole and the same red bar being 1/4 of a different whole and you had to determine which whole was longer.

So you might have made or drawn something like this to support your reasoning.

That's my first image where the red bar is 1/3 of a whole.

So I need three of the red bar parts to make a whole.

And then for the second option where the red bar is 1/4 of a different whole, I needed four of those parts.

So I can see that my whole B is longer.

This is because it is constructed from more of the same size equal parts than whole A is.

I needed four of the parts for option B, but only three of the parts for option A.

So option B must be longer.

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

Well done on your learning so far.

I can see how much progress you are making.

We are going to move on now to think about the part-whole relationship.

Let's remind ourselves of the wholes that Sofia and Lucas were thinking of in their game.

Those were the two wholes that they were thinking of.

Have we noticed something with the examples that we have looked at? Have you noticed anything? Ah, Sofia has.

I wonder if you noticed this.

Yes, the red rod has been the same size.

It was.

They used the same part, didn't they? For both of their examples.

But the wholes that were constructed were different.

Do we know why this is? Ah, that's right.

This is because the red rod is a different fraction of the whole each time.

In the first example, the red rod was 1/3 of the whole.

There we go, we've got 1/3 of the whole.

So we needed three equal parts to make the whole, or I should say to construct the whole.

And in the second example, the red rod is 1/5 of the whole.

And because the part was the same size both times, but a different fraction of the whole, the whole was different.

Does that make sense? The part was the same size.

We used the same red rod both times, but the fraction of the whole was different.

We had 1/3 of the whole and 1/5 of the whole.

So the whole would be different.

Let's summarise what we have discovered so far in a table.

You can see we've got our red rod as a part.

And if we think about the part as a fraction of the whole, so the part is half of the whole, then the whole is twice as much.

There are two equal parts in the whole.

So to construct the whole, we needed to take two parts and combine them.

If the rod is 1/3 of the whole, then the whole is three times as much.

So we have three equal parts in the whole.

And to construct the whole, we need to take three parts and put them together.

Ah, Lucas remembers the relationship between the part and the whole.

Let's have a think about that now, shall we, Lucas? Ah, the denominator is the same as the number of equal parts in the whole.

So when the part was 1/2 of the whole, the number of equal parts in the whole was two.

And the denominator for 1/2 is two.

What about 1/3? Well, the denominator is three and there are three equal parts in the whole.

I wonder if you had spotted that.

Let's check your understanding.

If a rod is 1/10 of the whole, how many times larger will the whole be? 1, 9, 10, or 11? Pause the video while you have a think.

Maybe chat to somebody about this.

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

How did you get on? Well, if the rod is 1/10 of the whole, well, the denominator will be 10.

So the whole will be 10 times the size.

We need 10 of those parts to construct the whole.

And how about this one? Could you complete the stem sentence? If 1/9 is a part, then the whole is mm times as much.

Take mm parts and combine them to make one whole.

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

How did you get on? So if 1/9 is a part, then the whole must be nine times as much.

We're gonna take nine parts and combine them to make one whole and 1/9, what's its denominator? That's right, the denominator of 1/9 is nine.

It's your turn to practise now.

Could you construct two of your own examples? Draw representations and write the stem sentence for each.

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

Take mm parts and put 'em together to make one whole.

For question two, could you complete the table? Use the stem sentence to help.

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

Take mm parts and put 'em together to make one whole.

This is the table to complete where you see the missing parts of the table.

Pause the video while you have a go at both questions and when you are ready for the answer, press play.

How did you get on? For question one, you were asked to construct two of your own examples and draw the representations.

You might have made an example like this.

I found my part and my whole and then I wrote the stem sentence.

If 1/5 is a part, then the whole is five times as much.

Take five parts and put them together to make one whole.

For question two, you are asked to complete the table.

You can see the part was the same, but the part as a fraction of the whole was different.

So the whole needed to look different.

And you can see the number of equal parts in the whole.

Well, that's the same as the denominator of the fraction.

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

Brilliant learning today, everyone.

So proud of the progress you have made at constructing a whole.

We now know that if we know a part and the fraction that it represents, we can construct the whole.

We know to use the stem sentence if one mm is a part, then the whole is mm times as much.

Take mm parts and combine them to make one whole.

And this supports us to construct the whole.

So really well done.

You should be proud of the learning that you have done today.

I know you have tried really hard and I look forward to learning with you again soon.