Lesson video

Hello, my name is Mr. Tazzyman and I'm really looking forward to learning with you today.

I hope you're sat comfortably because we're ready to start.

Here's the outcome for today's lesson.

By the end, we want you to be able to say, "I can use fraction notation to describe an equal part of the whole." Here are the key words that you'll need to consider today in your learning.

I'm gonna say them and I want you to repeat them back to me.

I'll say my turn, say the word, and then your turn, and that's when you will say them back.

My turn, fraction, your turn.

My turn, division bar, your turn.

My turn, numerator, your turn.

My turn, denominator, your turn.

There were some tricky words to say there.

Let's see what each of them means.

A fraction shows us how many equal parts in a whole.

The division bar is the horizontal line separating the two values in a fraction.

A denominator is the bottom number in a fraction.

It shows how many parts a whole has been divided into.

A numerator is the top number in a fraction.

It shows how many parts we have.

Now, you may not understand all of those just yet, but that's partly what today's lesson is about, so please don't worry if that seems confusing at this point.

Here's the outline for the lesson.

The first part, we're gonna talk about describing the wholes and the parts, and in the second part we're gonna look at the numerator and denominator.

Are you ready to start? Let's go for it.

Here's two friends who are helping us to go through these slides and understand them.

They'll be talking to us in response to some of the prompts that you'll see on screen.

We've got Lucas and Laura.

Alex and Lucas look at a range of shapes that have been divided into parts and they describe them.

Lucas starts by saying "The irregular shape is the whole and it has been divided into three equal parts." Laura says "The cross is the whole and it has been divided into five equal parts." Then Laura says, "The hexagon is the whole and it has been divided into six equal parts." So they've described those wholes and parts that you can see on screen.

Each of the shapes has a part shaded in and they describe them differently this time.

Laura says, "The cross has been divided into five equal parts.

One of the parts has been shaded." Lucas says "The irregular shape has been divided into three equal parts.

One of the parts has been shaded." and Laura finishes with "The hexagon has been divided into six equal parts.

One of the parts has been shaded." Okay, let's check your understanding of what we've looked at so far.

Describe the whole and the equal parts by completing the sentence below.

You can see there the triangle and it has been split up into parts.

Parts that are equal.

The sentence to complete is below "The something has been divided into something equal parts.

Something of the parts has been shaded." Okay, pause the video here and have a go at completing those sentences.

Welcome back, let's see whether or not you've got the right idea.

The triangle has been divided into two equal parts.

One of the parts has been shaded.

Did you get that? Okay, let's keep going.

They look at something different.

They each describe what they see.

Laura says "The whole has been divided into zero equal parts.

One of the parts has been shaded." Lucas says "The whole has been divided into two parts.

One of the parts has been shaded." What do you think? Has Laura got it right or has Lucas got it right? Hmm, well, I can see two hexagons there, but what's the whole I wonder? Lucas says "The hexagons have been joined together to make a whole." "Oh, I see," says Laura, "I was treating one of the hexagons as a whole, you're right." Let's check your understanding again.

Describe the whole and the equal parts by completing the sentence below.

You can see we've got another image in the middle of the screen of a whole.

Can you complete the sentences below to describe it? Pause the video and I'll be back in a moment.

Welcome back.

Let's see whether or not you've got the right idea.

"The whole has been divided into two parts.

One of the parts has been shaded." This whole was both of those squares joined together and one of those squares was shaded in.

They look back at a shape they have already described.

You can see that irregular shape there.

Laura says "The whole has been divided into three equal parts.

One of the parts has been shaded." Lucas says, "That's how to say it, but it would be hard to write that down every time." Imagine if every time you wanted to describe this fraction we had to say or indeed write what Laura has said.

Laura agrees, she says "That's true.

How can we write it then? Then Lucas has the idea of breaking up what we say into three stages.

He explains what he means.

Let's divide up what we say into three parts.

The whole has been divided into three equal parts.

One of the parts has been shaded.

The whole has been divided into three equal parts.

One of the parts has been shaded.

Laura replies, "So what we say is the whole, and these are three parts." "I suppose so, yes," says Lucas.

Lucas turns the parts into notation, something he can write down.

The whole has been divided into, "I'll write a division bar to show that the whole has been divided into parts." So you can see for that first part of what we say, he's drawn a division bar in.

Three equal parts.

"I'll write the numeral 3 underneath the division bar to show how many parts the whole has been divided up into." There it goes.

"One of the parts has been shaded.

Then," says Lucas, "I'll write the numeral 1 at the top to show how many parts have been shaded in." Hmm, that might look familiar to some of you.

They look back again at a shape they have already described.

"So I would still describe this aloud in the same way?" says Laura.

"Yes, absolutely," says Lucas "Use the same descriptions, but each part has a written version.

I'll write it down as you say each stage, if you like?" I think that's gonna help us to understand "The whole has been divided into," and there's that division bar being drawn in, "Three equal parts," there's the numeral 3, "One of the parts has been shaded." There's the numeral 1, "All done.

What I've written is a symbolic version of what you've said." I'll tell you what Lucas, that looks like a much quicker way of writing down what Laura has said.

Laura tries it by herself.

"The whole has been divided into four equal parts.

One of the parts has been shaded." Again, that might look familiar to some of you as well.

Lucas has another go.

"The whole has been divided into six equal parts.

One of the parts has been shaded." Okay, it's time to check your understanding of what we've just been learning about.

Turn the description below into a fraction.

So we're asking you to write down, symbolically, what this fraction is.

"The whole has been divided into two equal parts.

One of the parts has been shaded." Okay, pause the video and have a go at writing that down in notation.

Welcome back, let's see how you got on.

The whole has been divided into, you should have drawn a division bar for that, two equal parts, so the two went underneath the division bar.

One of the parts has been shaded, so you should have had the one at the top.

Hopefully you managed to get that.

Ready to move on? Let's go.

These written fractions are called fraction notation.

They describe the special relationship between part and whole.

You can see them there.

They're the examples that we've already looked at.

Laura says, "I have seen them before I'm sure of it." Lucas says, "Yeah, I have.

I use them to see my score in a spelling test." All right, time for you to have a think.

Discuss with some of your learning buddies.

Where else have you seen fractions written down? Share your examples with one another right now.

Pause the video and I'll be back in a moment.

Okay, let's see what Laura and Lucas came up with.

Might be similar to what you came up with.

Laura says, "I've seen them written for time, a quarter of an hour." Lucas says, "I've seen them in baking, half a cup of flour, for example." Were they similar to some of the things that you came up with? Okay, let's move on.

Here's your first practise task.

Below are some wholes divided into equal parts.

For each, complete the sentence to describe it by filling in the blanks.

You can see the wholes as images there and the sentences read as follows.

"The whole has been divided into something equal parts.

Something of the parts has been shaded in." So you've got to put in some numerals there.

There's A, there's B, there's C, and there's D.

Here's number two, you need to tick the whole that matches the description.

Laura says, "The whole has been divided into four equal parts.

One of the parts has been shaded." Here's number three, tick the whole that matches the fraction.

You can see there the fraction has been written down as notation.

We've got a division bar, two underneath and a one at the top.

Which of these wholes matches that? Okay, pause the video here and have a go at those tasks.

I'll be back in a little while for some feedback.

Welcome back, let's mark number one to begin with.

A, the whole has been divided into six equal parts.

One of the parts has been shaded in.

B, the whole has been divided into four equal parts.

One of the parts has been shaded in.

C, the whole has been divided into four equal parts.

One of the parts has been shaded in.

D, the whole has been divided into five equal parts.

One of the parts has been shaded in.

For number two, the whole that you needed to tick was this one, four equal parts and one of them has been shaded in.

For number three, "Tick the whole that matches the fraction." It was this one.

The whole has been divided into two equal parts and one of them has been shaded in.

Okay, I hope that you were successful during that.

Let's move on.

It's time for the second part of the lesson.

The numerator and denominator.

Laura and Lucas look at one of their wholes divided into parts and the fraction that represents it.

Laura says, "Do the three parts of the written fraction have names?" "Yes, they must have" says Lucas.

Lucas looks closely at a written fraction.

The whole has been divided into.

That's a division bar, we've named that one already.

"So the line used to show that a whole has been divided into parts is called a division bar." Three equal parts, there's the numeral 3 written underneath the division bar.

That's called a denominator.

"The numeral at the bottom that tells us how many parts the whole has been divided into is called the denominator." One of the parts has been shaded, so there's the numeral 1 above the division bar.

That's the numerator.

"The numeral at the top that tells us how many parts of the whole have been shaded in or selected is called the numerator." There are the names in the middle.

Laura looks again at the shape and writes at the fraction using the names of the parts.

"We write the division bar," "The whole has been divided into three equal parts." That's the denominator, "So the denominator is 3." "One of the equal parts has been shaded in." "So the numerator is 1." Laura challenges Lucas, "What's the denominator here then?" Lucas replies, "The denominator is 6 because the whole is divided into six equal parts." It's quite a strange looking whole that, I think whoever created it started with the part and then just replicated it five more times to make six parts in total, six equal parts.

Lucas challenges Laura, using a range of wholes.

Wow, look at those.

"Find all the wholes with a denominator of three," says Lucas.

Laura says "That means that the whole has been divided into three equal parts.

I'll tick them if they have a denominator of three and cross them if they don't." She crosses this one, ticks the next, ticks the next, ticks the next, ticks the next and crosses the last one.

Lucas says, "I think one of these is incorrect." Can you spot the mistake? Work through systematically.

The two that she's crossed already have a different number of parts.

They don't have three parts, so it can't be them.

Maybe it's one of the ticks.

What could be wrong with one of those ticks? It's this one, and Lucas explains his reasoning.

"This one has been split into three parts," he says.

Laura says "Yes, so the denominator is 3." "But the parts aren't equal, the denominator is the number of equal parts." That's really important, so it's a cross.

"Ah, of course," says Laura, "So we must look for equal parts when thinking about the denominator." Okay, let's check your understanding of that.

Which of these wholes doesn't have a denominator of 3? Pause the video, maybe chat about it with somebody else and I'll be back in a moment to reveal the answer.

Welcome back, "This one has been split into three parts, but they are unequal, so the denominator isn't 3" says Lewis.

Is that what you thought? Okay, let's go to the next bit.

They look at the wholes again.

"What's the numerator for all of these?" says, Laura.

The numerator is 1 because one equal part is shaded.

"What about the whole split into unequal parts?" says Laura.

It's that one again.

Lucas replies, "You're right.

We can't say that the numerator is 1 because the shaded part is unequal." Let's check your understanding.

Why can't we work out the numerator for this whole? See if you can explain that.

Pause the video here and have a go.

Welcome back, what did you think? Here's what Lucas says.

"This has one shaded part, but the parts are unequal, so we don't know the numerator." Laura and Lucas look at a line divided into equal parts.

"Let's start with the division bar says Lucas," there it is.

Laura says, "If the line is the whole, then what has it been divided into?" "Let's count the intervals, not the ticks," says Lucas and the ticks are the little marks you can see that are separating the parts in the line.

one, two, three, four.

"The denominator is 4 because the whole has been divided into four equal parts." "What's the numerator?" says Lucas, "Nothing can be shaded." "I'll make a numerator of 1 using a highlighter," says Laura.

Very resourceful, there it is.

"Doesn't it have to be the first interval?" says Lucas.

"No, I don't think so.

I can still say the numerator is 1 because one equal part is shaded." And there it is 1 is the numerator.

Laura and Lucas look at their friends standing in pairs during dance.

Aisha and Jacob are selected, we'll put a box around them to show that.

"Let's start with the division bar again," says Lucas.

Laura says "The denominator is 6 because the whole has been divided into six equal parts." Lucas says, "I think the denominator is 3 because the number of children has been divided into three equal parts." "Ah, you're right, we are counting the number of pairs here.

There are three pairs, the denominator is 3." "The numerator is 1 because one equal part has been selected.

Aisha and Jacob were chosen to perform." It's time for your second practise task now.

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

You can see the wholes on the left as images and in the middle there are some sentences that are incomplete.

On the right you can see that the division bar's been drawn in, but the numerator and denominator are just question marks at the moment.

Here's C and D, same thing.

For number two, you need to tick all the objects showing this fraction.

There's a division bar.

The denominator is 3 and the numerator is 1.

Okay, pause the video here and have a go at those practise tasks and I'll be back in a little while to give you some feedback.

Good luck.

Welcome back, let's mark these to see how you got on.

1, A, the denominator is 4 because the whole is divided into four equal parts.

The numerator is 1, because one equal part is shaded.

That's what your notation should have looked like.

The denominator was 4 and the numerator was 1.

B, the denominator is 8 because the whole is divided into eight equal parts.

The numerator is 1, because one equal part is shaded, and remember, it doesn't have to be the first part, it just has to be one of the parts, so the numerator is 1 and the denominator was 8.

C, the denominator is 8 because the whole is divided into eight equal parts.

The numerator is 1, because one equal part is shaded.

There's the fraction notation.

Doesn't it look similar to B? In fact, it's the same.

It's just that the representation was different.

D, the denominator is 2, because the whole is divided into two equal parts.

The numerator is 1, because one equal part is shaded.

That was our fraction notation, denominator of 2 and a numerator of 1.

Now it's possible here, you might have tried to use six because there were six children as your denominator, but actually the children had been split into two equal parts.

The two groups of three that you can see.

Here are the objects that were showing us this fraction with three as a denominator and one as a numerator.

Did you get those? I hope so.

That brings us to the end of today's learning.

Here's a summary of the things that we discussed and learned.

A fraction describes the special relationship between a part and a whole.

Fraction notation is a way of writing down this special relationship.

The division bar tells us that a whole is being divided up.

The denominator tells us how many equal parts the whole is divided into, and the numerator tells us how many of those equal parts have been shaded or selected.

My name is Mr. Tazzyman and I've loved learning with you today.

I hope to see you again soon in another maths lesson.

Bye-Bye.