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 then.

By the end, I want you to be able to say, "I can identify equal parts in a whole when they do not look the same in 3D contexts." Here are the keywords.

I'll say them and I want you to repeat them back to me, so when I say your turn, say the word.

My turn, whole, your turn.

My turn, part, your turn.

My turn, equal or unequal, your turn.

Okay, let's see what each of those words means.

The whole is all the parts or everything, the total amount.

A part is some of the whole.

You can see the bar model at the bottom of the page there that shows this relationship.

The top bar is the whole, and it's made up of two parts there, but it could be two or more.

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 then.

Identify equal parts in a whole when they do not look the same in 3D context.

We're gonna start by thinking about the fact that equal parts can look different and then we're gonna look at identifying differently shaped equal parts.

Okay, sit comfortably, be ready to think and learn.

In this lesson, you're gonna meet Alex and Andeep and both of these are gonna help us in responding to some of the prompts on screen, discussing problems, and giving us some hints and tips in the feedback.

Alex, Andeep, and four other friends are playing a game with plasticine.

Their teacher divides up a large quantity of plasticine into equal parts and rolls each part into a sphere ready to use.

There they are.

Nice balls of plasticine ready for use.

Their teacher tells each child to make one part of a robot without looking at each other's.

The head is made by Andeep.

Alex makes arm one.

Lucas makes arm two.

Sam makes leg one.

Sophia makes leg two.

And Jun makes the torso.

Each part is joined together to make a robot.

There we go.

Andeep and Alex split the robot back into parts.

"They can't all be equally-sized.

They are different shapes," says Andeep.

"I disagree," says Alex.

"They are the same size, because they were made from the same amount of plasticine." What do you think? Do you think Andeep's right? That they can't be equally-sized? Or do you think Alex is right? They were made from the same starting amount, so they must be equally-sized.

Well, Andeep and Alex agree and justify their thinking.

Andeep says, "You're right.

Each part we created was equally-sized, because the plasticine was divided up equally." Alex says, "Let's write the fraction that describes what one part of the whole is." "Let's start with the division bar," says Andeep.

"The whole was divided into six equal parts, so the denominator is six." "If we look at one part on its own, then the numerator is one," says Andeep, one sixth.

"Each part we created must be one sixth of the whole." "That makes sense, because our teacher split the pack into six equal parts to begin with." Remember the spheres? There were six of them.

Okay, let's check your understanding of what we've learned about so far.

Parts of a 3D object can be differently shaped of equal size, true or false? Pause the video, have a think, and decide whether you think that that statement is true or false.

Welcome back.

Parts of a 3D object can be differently shaped of equal size.

That is true.

Now I'm gonna show you two justifications.

I want you to listen to them carefully and decide which of these justifications proves that that statement is true.

A says, "The amount or quantity is what's important rather than the eventual shape." B says, "Because there are lots of different 3D shapes." So which of those is the best justification? Pause the video, have a think, choose one, and I'll be back in a moment to reveal the answer.

Welcome back.

A was the most appropriate justification.

There are lots of different 3D shapes, but actually the amount or quantity is what's important rather than the eventual shape.

That justification proves that parts of a 3D object can be differently shaped of equal size.

Okay, let's see what's next.

Andeep investigates differently shaped containers.

"I'm going to fill each container from my bottle filled with water." You can see Andeep's bottle there and it's full of water.

He fills up the first container.

He fills up the second container.

And he fills up the third container.

What do you notice? Hmm.

Have a look at all three of those.

Andeep says, "I noticed that the quantity of water in each container is the same." He filled them all up from his bottle.

"I know this because I filled them using the same bottle." I also noticed that each part of water was differently shaped." And you can see that.

The first container, the water inside, was differently shaped to the second and to the third.

Okay, time to check your understanding.

Another true or false for you.

These containers must have a different quantity of water in them.

True or false? You can see the containers there.

Okay, pause the video, and decide whether you think that's true or false.

Welcome back.

That is in fact false.

Let's look at the justifications and select one of those now.

A, it might be the same quantity, but the containers are shaped differently.

B, you always pour the same amount into containers like this.

Okay, decide which of those justifications you think is best and pause the video here.

Welcome back.

A was the best justification here.

The same quantity can be poured into a whole range of different containers provided they have the capacity, but the water will always take the shape of the container.

Okay, it's time for your first practise task.

What I'm gonna ask you to do is to find a range of differently shaped containers.

Fill each container with the same quantity of water.

What do you notice? Now take care here.

Make sure that the capacity of each of the containers you find is greater than the amount of water you're gonna pour in them.

Otherwise, there's gonna be a lot of spillage.

Good luck.

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

Welcome back.

Did you enjoy that? I hope you didn't get too wet.

Here's some containers that have been filled on screen.

Andeep noticed that, "All the parts of water were equal in quantity but differently shaped." All right, let's get started on the second part of today's lesson, identifying differently shaped equal parts.

Andeep and Alex each have a cake they're going to fill with jam and cream.

Mm, delicious.

"The next part of the recipe says we need to cut the cake to put the jam in the middle," says Andeep.

Alex says, "So we need to cut the cake into two equal parts.

Each part will be one half." "I'll go first," says Andeep.

"Now I'll cut my cake," says Alex.

"Wait, they look very different.

Are they all parts that are one half of the whole?" "Definitely," says Alex.

"They are both ways of dividing the whole into two equal parts." The problem for Andeep is that I'm not sure you would spread jam on a cake that has been divided into two halves like that.

I think it's more likely that you'd spread it on the cake that Alex has divided into two halves.

All right, let's move on, and look at something that's gonna make me less hungry.

Alex and Andeep each have a cuboid comprised of 16 multilink cubes.

"Let's try and make parts that are one half of the whole but look different." "One half? So that is dividing the whole into two equal parts.

Okay then," says Alex.

There's Andeep's go and there's Alex's go.

Reminds me a little bit of the cake.

What do you notice? Hmm.

Compare them both.

What can you see? Andeep says, "I notice that both my parts and your parts are one half of the whole." "I notice that our equal parts were differently shaped." "I also noticed that each equal part for both of ours was made of eight cubes." "Yes, you're right," says Alex.

"That's because two lots of eight is equal to 16 and we started with 16 cubes." Andeep sets a challenge for Alex.

He makes lots of different 3D objects, which could be parts of the whole.

You could see the whole there on the screen.

There are the parts.

Andeep says, "Which of these parts isn't one quarter of the whole?" What a great challenge.

"One quarter? So that is dividing the whole into four equal parts," says Alex.

"There are 16 cubes making the whole.

16 divided into four equal parts would be four in each part.

I'll count the number of cubes in each part." There's four in that one, four in that one, four in that one, five in that one, four in that one, and four in that one.

Hmm, I think I can see an odd one out.

"It's this one, because it has five cubes, which isn't one quarter of the whole." Andeep changes the whole.

Alex says, "Which of these parts isn't one third of the whole?" So this time, Alex is challenging Andeep.

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

Three lots of eight cubes is equal to 24.

So I need to find parts made up of eight cubes.

I'll label the number of cubes in each." Eight, eight, eight, and nine.

"It's this one because it has nine cubes.

It's not one third of the whole." Okay, it's your turn.

Let's check your understanding.

Which of these parts aren't one quarter of the whole, which is comprised, which means made up of, 16 cubes? So you can see there are three parts there.

Which of those is not one quarter of the whole? Pause the video, have a think, have a discussion if you can and come back in a few minutes so that I can reveal the answers for you.

Welcome back.

Let's start by counting the number of cubes in each of these parts.

There were four cubes in this one, four in this one, but six in this one.

We know that four cubes is one quarter of 16, so the end one made up of six cubes was not a quarter.

Okay, it's time for your practise task.

For the first one, you've got to spot the part below that isn't one quarter of this whole comprised of 24 cubes.

Use your times tables to help you here.

For number two, can you spot the part below that isn't one third of this whole comprised of 15 cubes? Again, make use of your times table facts here.

And number three, I'd like you to use cubes to create your own version of the challenges set up by Andeep and Alex.

Can your partner find the part that isn't the fraction of the whole you've chosen? 24 cubes is a good number for the whole, but you can choose another quantity.

Okay, pause the video here, and I'll be ready to give you some feedback in a little while.

Welcome back.

Ready to mark? Here goes.

Alex is helping us on this one.

He says, "One quarter is a denominator of four.

So the whole has been divided into four equal parts.

There are four lots of six in 24, so each equal part should have six cubes." That's where your knowledge of your times tables might have helped you out.

Let's count the number of cubes in each part.

Six in this one, five here, six here, six here, six here.

"This part is not one quarter of the whole." So that's the one that isn't a quarter.

Okay, similar sort of problem here.

Andeep says, "One third is a denominator of three.

So the whole has been divided into three equal parts." Here's where you can use your multiplication facts.

What do you multiply three by to make 15? There are three lots of five in 15, so each equal part should have five cubes.

Five in this one, five in this one, five in this one, six in this one, and five in this one.

It was this part.

It's not one third of the whole.

Okay, number three, you were creating your own puzzle.

Alex says he got Andeep to find the part that wasn't one half.

And he found that it was that end one, because that end one was one, two, three, four, five, six, seven, eight, 9, 10, 11 cubes.

It needed to be 12 cubes in order to be one half of that whole, because that whole was made up of 24 cubes in total.

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

A whole is made up of many parts in 3D context as well as 2D ones.

Parts can be equal or unequal.

Equal parts can look different but still be equal.

A 3D whole can be divided into equal parts that look different.

An equal quantity of water can take different shapes depending on the container it is in which proves this.

All right, I really hope you had fun today, I did, and I hope to see you again soon in another maths lesson.

My name's Mr. Taziman.

Goodbye for now.