Lesson video

Hi.

My name is Mr. Tazzyman, and I'm really excited to be learning with you today.

Fractions, sometimes, can be considered quite tricky, but I hope that we can have some fun with it, and we can boost your understanding.

Okay.

Let's get going.

Here's the outcome for the lesson today.

By the end, we want you to be able to say I can identify parts and wholes in the contexts of lines and 3D objects.

These are the key words that you are going to see, and we need you to be able to say them, and to understand them, so that you can engage in the slides.

I'm gonna say each of these words by saying, "My turn," and I'll say it, and then I want you to respond by saying the word back to me when I say, "Your turn." Ready? My turn.

Whole.

Your turn.

My turn.

Part.

Your turn.

My turn.

Equal or unequal.

Your turn.

Okay.

So that's how to say them.

Let's move on and look at what each of them means.

The whole is all of a group or number.

A part is a section of the whole.

Below, you can see a bar model that shows this 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.

Here's the outline for today's lesson.

First of all, we're gonna look at identifying parts and wholes in the context of lines.

Once we've done that, we're gonna move on to looking at 3D objects.

Okay.

Sit back, get ready, and let's get thinking.

Here's two characters that we're gonna meet, Lucas and Jacob.

And they're gonna help us in today's lesson by discussing some of the maths, giving us some clues, and revealing some of the answers.

Hi, Lucas.

Hi, Jacob.

Jacob and Lucas are cutting paper strips into parts.

Jacob says, "I'll divide this strip into equal parts." And he does that.

You can see them there on the screen.

Lucas says, "I'll cut out one of the equal parts." He gets some scissors and cuts out one of the parts.

The whole has been divided into four equal parts.

One of the parts has been cut out.

That's one quarter, then.

Jacob writes the fraction notation.

He starts by saying the whole has been divided in two, and he draws a division bar to represent this.

Four equal parts, so the whole has been divided into four equal parts.

He writes the denominator of four.

Then he says, "One of the parts has been cut out." So he writes in the numerator, which will be one, because one of the parts is being cut out.

It's one quarter, and that is how you write it using fraction notation.

They cut out another part from a strip of paper.

Jacob says, "I think one fifth has been cut out." I wonder why he might have said that.

Look at the number of parts that the paper was folded into originally.

But Lucas disagrees.

He says, "I don't think we know what this fraction is." What do you think? Can you see why Lucas might have disagreed? What is it about each of those parts that means that he thinks it can't be one fifth like Jacob says? Jacob says, "Oh, I see.

"You're right.

"They have to be equal parts, don't they?" And Lucas agrees.

"These are unequal parts, so we don't know "what the denominator or numerator is." Now it's time to check your understanding of what we've learned so far.

Which of the following cut out parts of a strip of paper show one third of the strip of paper? So you've got two strips there.

They both have part cut out.

Which of them shows one third? I wonder if you could explain why as well.

Pause the video, and I'll be back in a moment to reveal the answer.

Welcome back.

How did your discussions go? Well let's have a look and see which of these strips of paper was one third.

Jacob says, "The bottom strip is one third "because the parts are equal." Well done, Jacob.

You can see there, that the parts on the second strip were all the same size.

This time, Jacob folds the paper instead of cutting.

He says, "I'll unfold it again to see the parts." The whole has been divided into eight equal parts.

Yeah.

So each of the equal parts is one eighth of the whole.

They've labelled it using fraction notation.

Remember? They've got a division bar to show the whole has been divided.

They've put down eight because the whole has been divided into eight equal parts, and each of those is one selected part, so each has a numerator of one.

Okay.

Again, let's check your understanding.

I'd like you to take a paper strip and fold it into four equal parts, and then label each part correctly using fraction notation.

Hopefully you've got some strips there ready.

Good luck.

I'll be back in a moment, so pause the video.

Welcome back.

Have you got your strips ready? You can give them a wave if you want.

Okay.

Let's see whether your strip looks similar to the one on the screen.

There it is folded in half.

There it is folded in half again.

And here it is unfolded.

Does yours look something like this? Well let's get the notation on there.

There it is.

Each equal part is one quarter of the whole.

Okay.

Are we ready to move onto something else? Let's go for it.

This time, Lucas draws a line and divides it into equal parts.

"I have divided the whole into five equal parts," he says.

Lucas says, "I think it's four equal parts." What do you think? Why might Lucas have said five, and why might Jacob have said four? And who's correct? They're obviously both counting something different.

Let's see how they resolve it.

"Yes, you're right," says Lucas.

"I was counting the marks on the line, "not the intervals." Jacob says, "I'll highlight one equal part." And there it is, highlighted.

That one equal part is an interval, because it lies between two of the marks on the line.

The marks are what Lucas was counting, but you must count intervals when we're thinking about fractions and lines.

Lucas correctly identifies that the highlighted equal part is worth one quarter.

They compare the line with the strip that has an equal part cut out.

So you've got the line on one side, with the fraction notation of one quarter, and then you've got the paper strip, which has one quarter cut away from the rest of the whole.

What's the same? And what's different? Hmm.

Have a little think.

And let's see what Lucas and Jacob came up with.

Jacob says, "Both have been divided "into four equal parts with one equal part selected." Lucas says, "Yes, they both show one quarter." Jacob replies, "The line is like a squashed version "of the paper strip." "That's true.

"The way we've separated one quarter is different, too." So Jacob there is saying that if we squashed that folded strip right down, it would become a line.

And Lucas is saying that there's definitely a difference in the way that the quarter has been selected.

On the first one, it's a highlighted part, and on the second one, it's been cut away, because it's a folded paper strip.

Lucas redraws his line, but this time, he highlights a different equal part.

"Let's compare this to the last line "that you highlighted an equal part of," he says.

There it is.

What's the same? What's different? Compare those two.

What do you think? Lucas says, "Both of these lines have been divided "into four equal parts." "Yes, they both have a denominator of four." You can see that in those two lines.

There are four intervals making both of those lines up.

"Are both still one quarter, "even though the highlighted part is in a different place?" What a good question from Jacob.

What do you think? Are they still both a quarter? Yes, because only one part has been highlighted, which is a numerator of one.

Lucas rotates one of his lines so that it is vertical.

There it is.

And there's the highlighted part.

"I think it's still one quarter," says Jacob.

"I agree," says Lucas.

"It doesn't matter how it is oriented." And that means the way that you put it on the page.

If it's the same object, it's still showing a quarter.

"I can rotate it a different way," says Jacob.

"Yes, it's still one quarter because the parts "haven't changed at all," says Lucas.

This time, Jacob draws a line.

He traces along two sides of a triangle.

There's the triangle.

And there's his line.

Then he repeats this three times to construct a whole.

"I repeated what I'd drawn three times.

"I started with the part to construct the whole." Well done, Jacob.

"So this line has been divided into three equal parts.

"The denominator is three." "I'll highlight one equal part," says Jacob.

There it is.

"So the numerator is one.

"This is one third." Lucas has a go at making a whole by starting with an equal part and constructing a line.

He's drawn round a semi circle here, and that's given him one part.

Then he repeats it.

Same again.

And same again.

"This is a curved line, "so we can't use fractions here," says Jacob.

"I think we still can," says Lucas.

What do you think? Curved lines.

Can you still use them to show fractions? "Each of the parts I drew were from the same shape, "so they were equal," says Lucas.

"That's true.

"So we can describe a part as a fraction." "There were four equal parts, "and I'll highlight one of those." There it goes.

"That's one quarter then," says Jacob.

All right.

It's time for your practise task now.

For number one, you need to complete the sentences and write the numerator and denominator as numerals on the right hand side in those boxes.

You've got some lines here for A and B, and you've got some highlighted parts.

For number two, you've got to tick the lines or strips of paper that have a denominator of five.

Think about what denominator means.

Remind yourselves.

And for number three, I'd like you to have a go at creating some wholes that are lines yourself, by drawing a round part of a shape.

A, create a line showing one third.

B, create a line showing one quarter.

And C, create a line showing one fifth.

For each of them, can you create one that no one else has? Don't forget.

They've got to have equal parts.

Okay.

Good luck.

Enjoy the practise.

Pause the video here, and I'll be back after you've finished for some feedback.

Okay, let's get marking.

So, are you ready? For A.

The denominator was four, because the whole was divided into four equal parts.

The sentence's been completed, and the denominator's been written into the notation.

And the numerator was one, because one equal part was shaded.

Let's look at B.

The denominator was three, because the whole was divided into three equal parts, and the numerator was one, because one equal part was shaded.

For numerator two, we had to tick the lines or strips of paper that had a denominator of five.

This folded piece of paper had five equal parts, so it had a denominator of five.

So too did this folded strip.

So too did this line.

This one was a bit of an imposter.

This had five unequal parts, so we didn't know what the denominator was.

Okay, for number three, here's Jacob's examples, and I hope you've come up with some really good ones as well.

He's created a line showing one third and highlighted the third.

He's created a line showing one quarter, by highlighting one part out of four.

And he's created a line showing one fifth.

That's a really good one, because it's got curves.

How did you get on? Okay.

We're ready now to move onto the second part of the lesson.

Let's get going.

3D objects.

Jacob draws a line divided into six equal parts.

"I'm going to create a 3D object "using this line," says Jacob.

"I'll match each part of the line "with a multi-link cube." "The whole has been divided into six equal parts." "Now I will swap one of the green cubes "for a different colour." So he's swapped the end cube on the right for a different colour.

"There are still equal parts, "so the denominator is six." Jacob says, "One of them is purple, "so the numerator is one." Can you think of what the fraction notation might be? And what's the name of that fraction? The purple cube is one sixth.

Lucas and Jacob make some different shapes using six connecting cubes.

You can see they've labelled the fraction notation on each of the selected cubes.

"Are these all still one sixth, "even though they are differently shaped wholes?" "Let's describe them to see.

"Each of these wholes is divided "into six equal parts." "So the denominator is six." "Each shape has one equal part that is purple." "So the numerator is one.

"They're all representing one sixth." Lucas decides to add more cubes to one of the shapes.

"I've added three more cubes.

"How does that change the fraction being represented?" What do you think? They were each one sixth.

And we'd selected one of the cubes.

But now, Lucas has added three more cubes.

How will that change the fraction? "Well now the whole is greater, "so the purple cube is a smaller part of the whole." "Yes, you're right.

"There are nine equal parts now, "which means the denominator is nine." "There's still only one purple cube, "so the numerator is one." Which of these two wholes represents one eighth? I'd like you to answer that to be able to check your understanding.

Pause the video here, and I'll reveal the answer in a moment.

Welcome back.

Did you manage to find out which one was one eighth? It was this one.

And Lucas explains, "This one has eight equal parts, "and one of them is a different colour.

"That's one eighth." If you look at the other one, it only had seven cubes, which meant it only contained seven equal parts within the whole.

It couldn't have been one eight.

Lucas and Jacob have a look at a big box of A4 paper.

You've probably seen some of those around.

It's got a label on it that says, "A big box "of smaller boxes of A4 paper." Let's look inside, and you can see it there.

There's a box of A4 paper.

"If the big box is the whole, "then the box of paper is part of the whole." "I agree, but what fraction is one of the boxes of paper?" "Let's work it out.

"We have our first part all ready." "We will need to visualise "the rest of the boxes of paper "to fill up the big box." "I'm going to imagine lines "leading to the edge of the box." There they go.

They might help us.

"Then I'm going to imagine placing more boxes inside "and count as I go." Are you ready to help? Here we go.

Two.

Three.

Four.

Five.

Six.

Seven.

Eight.

"Eight boxes of paper fit inside the big box, "so the denominator is eight." "The box of paper we already have "is one part of the whole, "so the numerator is one." "The box of paper is one eighth of the big box." Lucas and Jacob solve some similar problems looking at pictures of 3D objects.

"What fraction does this represent?" "I'm going to imagine the cubes "filling up the cuboid.

"The whole has been divided into three equal parts "so the denominator is three." "One equal part is shaded in "so the numerator is one." "It's one third." Here's another one.

Slightly trickier, this one.

"I'll have a go at visualising this time," says Jacob.

Two, three, four, five, six.

So there's six equal parts.

The denominator is six.

"We started with one part shaded, "so the numerator is one." "That's one sixth." Here's another one.

"Let's visualise the rest of the parts "needed to make the whole," says Lucas.

Two, three, four.

"There are four equal parts, so the denominator is four." "We started with one part shaded "so the numerator is one." There it is.

One quarter.

Okay, let's check your understanding of that.

Tick the correct fraction being represented.

So have a look at that shaded part, and use your visualisation.

How many of those shaded parts do you think could fit inside the entire cuboid? The whole? Pause the video here.

Have a go at visualising, maybe discuss it, and I'll reveal the answer in a moment.

Welcome back.

Let's see.

Was it one third, or was it one quarter? It was one third.

You can see the visualised parts there.

And Jacob says, "Three parts make up the whole, "so it's one third." It's important to note that there are three equal parts, too.

All right.

It's time for you to practise.

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

Bit like you did in Task A.

You've got a shape at the bottom there made up of many cubes.

That's our whole.

And there's one of those selected.

What fraction does that make? Here's B.

And this is one of our 3D objects that you're going to need to visualise in order to answer this.

Number two, have a go at creating some wholes using multi-link cubes.

Create a whole showing one fifth, one showing one ninth, and one showing one tenth.

Again, for each of them, can you create one that no one else has? Enjoy the tasks.

Good luck.

Make sure you do plenty of thinking, and pause the video here.

I'll be back with some feedback shortly.

Welcome back.

It's time to reveal some of the answers to see how much learning you did today, and how successful you were.

So, here's 1A.

The denominator was 12, because the wholes divided into 12 equal parts.

If you count all of those multi-link cubes, there are 12 altogether.

And the numerator is one, because one equal part was purple.

Here's B.

You needed to visualise for this one.

That's how many parts could fit into the whole, and that was six, so the denominator was six.

And the numerator was one, because we started with one shaded.

Okay.

Here's number two.

These were Lucas' efforts.

There's his multi-link cube showing one fifth.

There's one ninth, and there's one tenth.

How did you get on? Did you manage to create some completely unique ones that nobody else could? Well done for giving that a really good go.

I hope that you enjoyed it.

Okay.

Here's a summary of all the things that we've learned today.

A whole is made up of many parts, and parts can be equal or unequal.

This is true in different contexts, such as lines and 3D objects.

We can describe a whole by counting the number of parts it has.

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

My name is Mr. Tazzyman.

I've really enjoyed learning with you today, and I hope that I'll be able to learn with you again in the future on more maths lessons.

Bye-bye.