Lesson video

Hello, how are you today? My name is 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.

Welcome to today's math lesson.

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

And this lesson is called: Use knowledge of parts and hold to find unit fractions of a set of objects.

Throughout the learning today, we will deepen our understanding of how we can work out the value of a part or of the whole, and how important it is to use visualisations to support our understanding.

Now new learning can be a little bit tricky, but I know if we work really hard together, then we can be successful.

And I'm here to guide you through the learning.

Let's get started, shall we? Let's find out how can we use knowledge of parts and wholes to find a unit fraction of a set of objects? These are the keywords that we will be using throughout our learning today.

We have set and unit fraction.

Let's practise those words together.

My turn.

Set.

Your turn.

Nice.

My turn.

Unit fraction.

Your turn.

Well done.

When we talk about a set, we mean a collection of things, objects, or numbers.

Here is a set of crayons.

You might have sets of things at home that you collect.

A unit fraction is any fraction where the numerator is one.

So I've given some examples there.

1/2, 1/4, 1/10, 1/6.

You might be able to think of some more, but the important thing is that the numerator is always one in a unit fraction.

Today, we are going to start our learning thinking about how we can identify the size of each part.

And to help us, we've got Lucas and Sofia.

Sofia's been to the supermarket and has bought a bag of apples.

I wonder if you've ever done something like that, been to the supermarket and bought a bag of something.

And she plans to share them between herself and three friends.

Can you visualise that? That's one of the things I'm going to be doing throughout the course of this lesson today, is really think about visualising what do you see in your head.

So when I say you've been to the supermarket and bought a bag of apples, can you see that in your head, and can you see herself and three friends that she plans to share between? But what do we need to do first then? And Lucas is going to tell us.

First, we need to represent this visually by drawing what we have.

So there's the amount of apples that Sofia has in her bag.

And then, we need to determine how many apples are in the whole set.

Set, that's one of our key words today, isn't it? Remember, it means a collection of things.

So here we've got a collection of apples.

And we can, that's right, Lucas, we can determine how many apples there are here by counting.

We could count all of the apples, couldn't we? But is there an easier way? Can you see? Ah, yes, we can see there are four rows, each with three apples in them.

So we can form an equation: four threes, and then we can use our four times table to help us.

Four threes are 12.

12 apples make up the whole.

Let's check your understanding.

Can you tell me how many lemons are in the whole set? Can you do this without counting? Is there an easier way? Pause the video while you do that, and when you are ready, press play.

How did you get on? Did you notice that there are two rows? Each row has five lemons in them.

Two fives are 10.

So there are 10 lemons in the whole set.

Brilliant.

Let's go back to Sofia's apples.

We know we have 12 apples that need to be shared, but we need to determine the number of parts that we are sharing the apples between.

Can you remember? What did Sofia say? Sofia wants to share the apples between herself and three friends.

Hmm, how many parts is that then? Sofia is going to be one of those parts, and there will be three more parts.

So you can see there will be four parts in total.

The whole is 12 apples, and the whole will be divided into four equal parts.

Let's check your understanding.

How many equal parts has the whole set of lemons been divided into? Pause the video.

When you think you know, press play.

How did you get on? Could you see there that the lemons have been divided into two equal parts? We've got two groups, haven't we? Let's revisit our apples.

So we know we have 12 apples, and we know there are four parts, Sofia and three friends, that's four parts in total.

Dividing a whole amount into four equal parts, well, that's the same as finding 1/4 of the whole.

So each part is 1/4 of the whole.

So three apples is 1/4 of the whole.

Each part is 1/4 of the whole.

And together, we would have 4/4, which would be the whole, that would be one.

And we can see 1/4 of 12 apples is three apples.

Let's check your understanding.

What fraction of the whole is each part? We know there are 10 lemons in total, and we know there are two parts.

What fraction of the whole is each part? 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 see that there are two equal parts? So each part must be 1/2 of the whole.

Well done.

Let's revisit our apples.

We know 1/4 of 12 apples is three apples.

Let's have a go at forming some equations from this, shall we? And we can form two equations from this.

I wonder if you know what they are.

Ah, yes, we had 12 apples, and we divided them into four equal parts.

12 divided by 4 is equal to 3.

Hmm, I wonder what the other equation could be.

Ah, yes, we were finding 1/4 of the whole 12 apples, weren't we? 1/4 of 12 equals 3.

So those are two equations that we could form from our problem related to sharing 12 apples between four people.

Let's check your understanding on this revisiting the lemons problem.

How many lemons are in each equal part? Could you write two equations to represent this? Pause the video while you do that, and when you are ready to see the answers, press play.

How did you get on? Did you manage to form those two equations? We had 10 lemons in the whole set, and we shared them into two equal parts.

So our first equation is 10 divided by 2, and that equals 5.

Our other equation, well, we know divided by 2 is the same as finding 1/2.

1/2 of 10 is equal to 5.

So there are five lemons in each part.

How did you get on with that? Well done.

Time for you to practise now.

For question 1, could you, for each set of objects, complete the stem sentence identifying the fraction of the whole that is circled? So you've got red bags as one set of objects, and blue bears as the second set of objects.

And the stem sentence: The whole is divided into hmm equal parts.

Each equal part is hmm of the whole.

For question 2, use your stem sentences from question 1.

Could you then form two equations for each set of objects? One will be a division, and one will have a fraction and the word of in it.

And then you can use those to identify the amount of objects in each part.

For question 3, could you find 1/5 of a set of 30 marbles? It might be helpful if you've started by drawing those marbles to show that you can visualise, and that will help you to solve the problem.

Then maybe think about what else could you do after you visualised.

You could form equations, couldn't you? Pause the video while you have a go to all three questions, and when you are ready for the answers, press play.

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

For question 1, you had to complete the stem sentence, identifying the fraction of the whole that is circled.

So for our red bags, the whole is divided into two equal parts.

Each equal part is 1/2 of the whole.

For the blue bears, the whole is divided into three equal parts.

Each equal part is 1/3 of the whole.

For question 2, you are asked to use your stem sentence from question 1 to form two equations to help you identify the amount of objects in each part.

We know the whole is six, and we were dividing into two equal parts.

6 divided by 2 is equal to 3.

And our second equation is a fraction equation.

We know divided by two is the same as finding 1/2.

1/2 of 6 is also 3.

For the second part with the blue bears, let's form our two equations.

We can see there are 12 bears is our whole, and we are dividing into three equal parts.

12 divided by 3 is equal to 4.

1/3 of 12 is equal to 4.

For question 3, you're asked to find 1/5 of a set of 30 marbles, and I suggested that you started by drawing the marbles.

So you might have drawn something like this.

The whole is divided into five equal parts because we are finding 1/5.

So each part is 1/5 of the whole.

We can then form our equation.

The whole is 30, and we are dividing into five equal parts.

30 divided by 5 is 6.

Our second equation, well, we know if we're dividing by 5 it's the same as finding 1/5.

So 1/5 of 30 must also be 6.

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

Fantastic learning so far.

Let's now move on and think about how we find the whole.

Lucas gave Sofia and three other friends an equal amount of marbles and kept the same for himself.

Can you visualise that? Can you see Lucas giving Sofia and three other friends an equal amount of marbles? Let's draw the marbles that Lucas gave Sofia, shall we? There we go.

How many marbles is that? That's right, it's three, isn't it? So Lucas gave Sofia and three other friends an equal amount of marbles, so they must all have received three marbles.

And he kept the same for himself, so he must have kept himself three as well.

Sofia wants to know how many marbles Lucas had in his set to start with.

So first we need to determine how many parts there are.

Well, Lucas shared the marbles equally between himself, Sofia, and three other friends.

So how many parts is that? That's five equal parts.

We can represent this as a bar model.

There's my bar model, got five equal parts, each with three marbles.

The whole set of marbles has been divided into five equal parts.

Each part is 1/5 of the whole.

We know that dividing by 5 is the same as finding 1/5.

We've got Sofia's part, Lucas's part, and then the three other friends' parts.

To find whole, then what do we need to do? That's right, because the parts are equal, we can multiply the value of one part by the total number of parts.

We can see that each part of three marbles is one 1/5 of the whole.

There are five equal parts, or groups.

There are three marbles in each part.

There are five groups of three.

So we can form an equation from this, can we? Five threes.

We know our five times tables.

Five threes are 15.

So the whole set of marbles is 15.

So if we want to summarise that, we know to find the whole, well, the whole is divided into five equal parts, and each part is 1/5 of the whole.

1/5 of the whole is three marbles.

So to find the whole, we need to multiply the number of equal parts, five, by the number of marbles in each part, three, five threes.

The whole is 15 marbles.

Let's check your understanding.

Sofia has shared some cherries equally between herself, Lucas, and two friends.

I wonder if you can tell me how many equal parts is that? Do you know? Maybe pause the video, talk to someone, and when you are ready to hear the answers, press play.

How did you get on? Did you say, well, there must be four equal parts.

We've got Sofia, Lucas, and two friends.

That's four parts in total.

Well done.

Another check for you.

Sofia shares those cherries equally between herself, Lucas, and two friends.

We now know that's four parts.

Each child received 12 cherries.

Can you tell me which equation represents how many cherries were in the whole set? Is it A, 3/12 of 36? B, 4/12 of 48? C, 12 divided by 3 is four? Or D, 12 divided by 4 is 3? Pause the video, chat to somebody about this, see if you agree.

When you are ready to hear the answer, press play.

How did you get on? Did you say it must be equation B? Because there are four parts, Sofia, Lucas, and two friends, that's four parts, and each child receive 12 cherries, four 12s, and four 12s are 48.

It can't be A, 'cause that would be three parts, and we've got four parts.

It can't be C, because that would be sharing 12 cherries, and it can't be D for the same reason.

So we didn't share those 12 cherries, each child got 12 cherries.

So we needed to multiply to find the whole.

So the 4 represents the number of parts, there are four children.

The 12 represents the size of each part, there are 12 cherries in each part.

And the 48, that represents the number of cherries in the whole set.

How did you get on with that? Brilliant.

Your turn to practise now.

For this task, I would like you to take four objects, such as counters, and that is 1/2 of a whole set.

Could you draw the objects that you have, such as the counters, and then draw what the whole set would look like? Can you represent it as a bar model? Then form an equation to work out the number of counters in the whole set.

For question 2, could you solve this problem? Sofia has 5 pens.

This is 1/10 of the packet of pens.

How many pens are in the whole packet? Start by representing this as a bar model, then form an equation to work out the number of pens in the whole packet.

Pause the video while you have a go at both of those questions.

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

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

For question 1, you were asked to take four objects, such as counters, and I'm telling you that that is 1/2 of the whole set.

You were asked to draw the counters that you have and what the whole set would then look like.

So there are the counters that I had, and I said that was 1/2, so there must be two equal parts to combine to make the whole.

For part B, you were asked to represent this as a bar model.

So that's my bar model.

I got my two equal parts of four, and I'm not sure what the whole is.

And then we were asked to form an equation to work out the number of counters in the whole set.

We know we've got two equal parts of four.

two fours, well, that's eight.

So there are 8 counters in the whole set.

For question 2, you were asked to solve a problem.

Sofia has 5 pens, which was 1/10 of the packet of pens.

Hmm, if we're finding 1/10, what's that the same as? Dividing by? Hmm? So first, we had to represent this as a bar model, didn't we? So I know I've got 10 equal parts, because we are finding 1/10.

So the whole must have been divided into 10 equal parts, and each part is worth five.

So you can see, I've written five in each of those 10 parts.

Then we can form an equation to work out the number of pens in the whole packet.

We know we've got 10 equal parts, each part is worth five.

Ten fives are 50.

So there are 50 pens in the whole packet.

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

Fantastic learning today, everybody.

You have made good progress in your ability to use parts and wholes to find a unit fraction of a set of objects.

We know that a whole can be a set of objects.

And we know to identify the size of a part, we can divide the whole amount by the number of parts.

And to identify the size of the whole, we can multiply the number of equal parts by the size of each part.

And we can use that stem sentence to help us: The whole is divided into hmm equal parts.

Each equal part is hmm of the whole, and that can support our reasoning.

So really impressed with how hard you have worked today.

It is always much easier to be successful when you work hard.

And it's been a pleasure learning with you, and I look forward to learning with you again soon.

Goodbye for now.