Lesson video

Hello, I'm Mr. Tazzyman and I'm gonna be helping you to learn about fractions today.

I'm looking forward to it and I hope you are too.

So sit back, get ready to listen and think, and let's get started.

Here's the outcome for today's lesson.

By the end, we want you to be able to say, I can identify parts and wholes in different contexts.

Here are the keywords.

I'll say them first and you can repeat them back to me.

I'll say my turn, say the word and you can say it back.

My turn, whole, your turn.

My turn, part, your turn.

My turn, equal or unequal, your turn.

My turn, set, your turn.

Okay, let's look at what each of these words means.

The whole is all of a group or number.

A part is a section of the whole.

You can see a bar model at the bottom there showing that relationship.

We say that two or more things are equal if they have the same quantity or value.

We say that two or more things are unequal if they do not have the same quantity or value.

A set is a collection of items. Here's the outline for today's lesson.

We're gonna start by looking at fractions in sets and then we're gonna look at some examples and non-examples.

And that will hopefully help you to identify parts and wholes in different contexts.

Fractions in sets to begin with.

Ready, let's do it.

You are gonna meet Aisha and Sam throughout these slides and they're gonna help us by discussing some of the prompts that you'll see on screen, revealing some of their own thoughts and also helping with some feedback to give you some answers so you know whether you've been successful or not.

Aisha and Sam have 12 cupcakes in a set.

"Let's divide them into three equal parts using the plates," says Aisha.

There they go.

"We have three plates and each of them has four cakes," says Sam.

"What fraction of the whole is one plate of cupcakes?" "There are 12 cakes altogether, so I think the denominator is 12," says Sam.

"I disagree," says Aisha.

"There are three equal parts- the plates." What do you think? Do you think the denominator should be the cupcakes or the plates? Let's see what conclusion they both come to.

"Yes, you are right," says Sam.

"The denominator is three." "One plate gives a numerator of one" "So one plate is 1/3 of the cupcakes." And they've used fraction notation as a label on one of those plates.

Let's check your understanding of what we've just thought about.

What fraction of the whole is one plate of cupcakes? You might wanna start by counting the number of cakes on each plate to check that they're equal parts.

Okay, I'll leave it over to you.

Pause the video here and I'll be back in a moment to give you an answer.

Welcome back.

Let's see what fraction one of these plates was.

Well, Sam helps us out and says, "There are two plates which means the whole has been divided into two equal parts.

So one plate is 1/2 of the cupcakes." And you can see the fraction notation next to the first plate there.

It could have gone next to the second plate.

Both plates are 1/2 of the whole.

Aisha and Sam have a set of 12 counters.

"I'm going to rearrange them and you can describe the fraction," says Aisha.

There they go.

"I'll put a ring around the parts to make it clear." "The whole has been divided into three equal parts so the denominator is three.

That means that one of these parts is 1/3 of the whole." And there's that fraction notation as a label again.

They put the counters back into a line.

"I'll rearrange them this time," says Sam.

"The whole has been divided into two equal parts." You can see the two rings there.

"That means that one of these parts is 1/2 of the whole." And you can see the fraction notation label again.

Aisha tries one more arrangement.

"How about this?" "But you haven't changed anything," says Sam.

"There are still equal parts though." "Yes.

The whole has been divided into 12 equal parts, so the denominator is 12.

One of these parts is 1/12." There's that label.

Okay, let's check your understanding.

Here's a statement.

The denominator is the number of objects in the set.

Is that always true, sometimes true or never true? Have a discussion with somebody if you can, have a think, pause the video and I'll be back in a moment to reveal the answer.

Welcome back, what did you think? a, b or c? It was b, it's sometimes true.

As Aisha says, "This is sometimes true.

There are 12 counters in this set.

Here they have been rearranged into two equal parts so the denominator is two." Here they have been rearranged into 12 equal parts, so the denominator is 12.

Okay, some of Aisha and Sam's friends stand together.

They're instructed to get into pairs.

There they go.

"There are six of our friends here and they have split up into three groups of two children.

So if the number of children is the whole, which is six, then, the whole has been divided into three equal parts." "But they're all beautifully different," says Aisha.

"Can they be equal parts?" "Yes," says Sam, "because we are counting children.

They are each one child even though they are unique." "So each pair is 1/3 of the whole." Okay, it's time for you to complete your first practise.

For each of these, complete the sentences and write the numerator and denominator.

So you've got some sensors there with some gaps in ready to put some numerals in, and the numerals can also go into the fraction notation on the right hand side.

Have a good look at those images and think about them before you commit to choosing one particular numeral.

There's c, slightly different context, but the same idea.

Number two, what mistake has Aisha made below? Explain your answer.

Remember explanation is what really good mathematicians do.

Aisha says, "There are three plates so the denominator is three." Have a close look at those plates.

Pause the video here and I'll be back in a little while for some feedback.

Okay, ready for some feedback? Let's start with one a.

Here's how it should have been filled in.

The denominator was three because the whole had been divided into three equal parts.

Although there were nine cakes there, there were three plates and those nine cakes had been divided into three equal groups.

One of those parts was 1/3 of the whole.

For b, the denominator was two and the numerator was one, which meant that one of those parts was 1/2 of the whole.

For c, the denominator was four because the whole had been divided into four equal parts.

One of these parts is 1/4 of the whole.

Okay, let's look at number two.

Aisha said there are three plates, so the denominator is three.

Sam explained her mistake.

"The number of cupcakes on each plate is unequal which means the parts aren't equal so we don't know the denominator." It's time for us to move to the second part of the lesson where we look at some examples and non-examples.

Aisha and Sam look at a shape that is partly shaded.

They both describe the shaded part.

"There are two parts and one is shaded.

This is 1/2," says Aisha.

Sam disagrees.

"I think that the shaded part is greater than 1/2." What do you think? Look closely at these two parts making up a whole.

Are they the same? Are they different? Who's correct here? "Let's see," says Aisha.

"We can separate the parts." There they are separated.

"Then we can lay them on top of one another to compare the size." "They aren't equal size.

The shaded part is bigger so this is not 1/2." Really good proof there.

Well done Aisha and Sam.

It's a non-example of 1/2.

Sam decides to create a puzzle.

Sam creates two shapes for shaded parts.

Aisha has to say which is an example and which is a non example.

Those are the two shapes.

"Which of these shows 1/4 of the whole shaded in?" "Both of them have been divided into four parts," Aisha observes.

You can see that both shapes have been divided into four parts.

"I can see that the cross shape is made up of four identical oblongs." "The second shape has parts differently shaped and sized.

The cross shape is the example and the other shape is the non-example." Aisha makes a puzzle for Sam but uses sets of 12 counters instead of shapes.

There are two sets of 12 counters and each of them has been divided up into parts.

"Which of these arrangements shows 1/3 of the whole in each group?" "Both of them have been divided into three groups or parts.

In the first arrangement, each part has a different number of counters.

In the second arrangement there are four counters in each part.

So the second arrangement is showing 1/3." Sam creates another puzzle for Aisha using lines.

Two lines there and they've been separated into different parts.

Now Sam has highlighted one of those parts in each line.

"Which of these lines shows 1/5 of the whole shaded in?" Aisha says, "Both of them have been divided into five parts.

Neither is horizontal but the orientation doesn't matter.

The highlighted part on the second line is smaller than the other parts.

On the first line, the parts have been divided equally.

The first line is the example and the second line is the non-example." Aisha goes on.

She says, "I think some of the parts of the second line are 1/5." "Really? Which part has been divided into unequal parts?" "Well, let's match up the two lines to show equal length." There they are matched together and placed horizontally.

You can see they're the same length.

"Then we can choose a different part of the second line." So watch closely.

Aisha's gonna select a different part on the second line.

"Both highlighted parts and the wholes are the same length." "Exactly! It works for some of the other parts too." There we go, and there we go.

"So even with unequal parts you can create a fraction?" "Yes, as long as the highlighted part fits into the whole." "And it will fit the number of times the denominator says." Alright, your turn to check your understanding on what we've learned so far.

Look at both of these representations.

Which one is an example of 1/4 and which is a non-example.

Look closely at them.

Pause the video here and I'll be back in a minute to reveal the answer.

Welcome back.

Did you choose one of the representations? Well, the left hand one did represent 1/4 because all of the parts were equal, but the second representation featured unequal parts both in terms of shape and in terms of size.

So that couldn't have been 1/4, that was a non example.

Aisha says, "The shaded part and the second shape is differently shaped in size, so the parts are unequal." Sam looks at a Venn diagram using the learning about examples and non-examples to complete it.

You can see the conditions of the Venn diagram there.

The left hand oval is equal parts and the right hand one is 1/3.

"Anything with equal parts goes into the left oval.

Anything that shows 1/3 goes into the right oval." There's that cross shape, again.

This has been divided into four equal parts.

"One equal part is shaded so it is 1/4.

It's equal parts but not 1/3 so it goes into the left oval.

This has been been divided into three equal parts." And you can see there we've got a set that has been divided up.

"One part will be 1/3.

It is equal parts on 1/3 so it goes in the middle." Here's a line.

"This has been divided into three unequal parts.

One part is shaded.

Three of the shaded parts could fit into the whole." You can see three of those parts connected together there and they are the same length as the whole.

"So even though there are unequal parts, the shaded part is 1/3.

It goes into the right oval." Alright, it's time for practise task B.

For each pair of representations, tick the examples of the fraction and cross the non-examples.

For a, we've got each part is 1/3, for b, each part is 1/4.

For number two, you are gonna create your own example and non-examples for each of the following fractions.

Use line, sets or shapes, make sure you label them to show which is which.

For a, you're gonna do an example and non-example of 1/2, and for B, an example and non-example of 1/5.

For number three, you need to complete the Venn diagram below by drawing a representation for each of the three parts.

The left oval is equal parts and the right oval is 1/4.

You've got a, b, and c there to complete.

Okay, pause the video here and have a go at those tasks.

Enjoy them, think carefully about them and I'll be back in a little while for some feedback.

Welcome back.

Let's give you some feedback so you can see whether or not you've understood the learning.

Here's the answers for one a.

The top set was divided into three parts, so that meant that was the example of 1/3.

The bottom set wasn't, and that's because there were different number of counters in each group.

For b, the first shape represented 1/4, the second shape was a non-example.

In the second shape, although the shapes were equally shaped, they were differently sized, which meant that they were unequal parts.

Here's number two then.

I'll show you what Sam came up with.

There's the example for 1/2 at the top and the non-example below you can see they're unequal parts.

Sam's examples for two b used lines.

The top line had been separated into five equal parts, meaning that each part was worth 1/5.

That was the example.

On the second line there were five parts, but they were unequal, so this was the non-example.

Here's number three and Aisha's efforts for each of these sections.

She started with a, a shape that featured 1/3 shaded in equal parts.

For b, she used a line.

There was 1/4 highlighted and the line had been separated into four equal parts.

For c, Aisha showed 1/4, but it was on its own in the whole.

The other part was differently shaped, making up the whole, but it was still 1/4 of the shape.

Okay, here's a summary of today's learning.

A whole is made up of many parts.

Parts can be equal or unequal.

This is true in different contexts such as sets, lines or shapes.

We can describe a whole by counting the number of parts it has and stating whether they are equal or unequal.

If the parts are equal, we can use fraction names and notation.

I've really enjoyed that learning today.

I hope you did too and I hope to see you again in another maths lesson.

My name is Mr. Taziman and goodbye for now.