Lesson video

Hello, how are you today? Welcome to today's maths learning.

My name is Dr.

Shorrock and I'm very much looking forward to learning with you today.

Let's get started.

Welcome to today's learning.

Today's lesson is from our unit.

Compare and describe measurements using knowledge of multiplication and division.

This lesson is called Compare and Describe Measurements Involving Mass and Capacity.

During the course of the learning, we are going to look at comparing mass and capacity measures multiplicatively.

And we're going to use these comparisons to calculate unknown values.

Sometimes new learning can be a little bit hard, but I know we can work really hard together and I'm here to help you and I know that we can then be successful.

So let's get started.

How do we compare and describe measurements involving mass and capacity? These are the key words that we will be using in our learning today.

Times the mass/capacity/volume, mass, capacity, and volume.

Let's practise those words.

My turn, "Times the mass," your turn.

Lovely, my turn, "Times the capacity," your turn.

Well done, my turn, "Times the volume," your turn.

Nice, my turn "Mass," your turn.

My turn "Capacity," your turn.

Well done, and then my turn, "Volume," your turn.

Nice.

So when we use the phrase times the mass, capacity or volume, we're using it to compare or describe.

For example, one bear might be three times the mass of another bear.

It's three times as heavy.

And mass is a measure of how much matter something contains, it's commonly measured by how much something weighs.

And mass can be measured in kilogrammes or grammes, so look out for those units today.

Capacity is a measure of the maximum amount of liquid a container can hold when it's full.

And that can be measured in millilitres and litres.

And volume is the amount of space and object takes up.

In this case, we're going to be looking at the specific amount of liquid in a container.

Volume can also be measured in millilitres and litres.

So today we're going to deepen our understanding on how we compare and describe measurements involving mass and capacity.

We're going to start by comparing and describing mass multiplicatively.

In this lesson we have got Lucas, Sam, Jacob, and Izzy to help us.

We've got Lucas and Sam went to a zoo.

I wonder if you've ever been to a zoo.

I wonder what you saw there.

Lucas and Sam saw a mother bear and her cub, aw.

What do you notice, is there anything you notice? I'm thinking here about the bears.

Ah, Lucas is telling us "The cub is lighter than its mother, it has less mass." And Sam is saying "The mother is heavier than her cub, she has more mass." Lucas asks the zookeeper what the mass of the cub is.

Hmm, interesting question Lucas, I'd like to know too.

Ah, there we go, can you read that scale? Well the arrow is pointing halfway in between the 20 and the 30, isn't it? What does that tell us? That's right, the mass of the cub is 25 kilogrammes, 25 bags of sugar, wow.

Sam asked the zookeeper what the mass of the mother bear is.

The mass of the mother bear is four times the mass of her cub.

So how can we determine the mass of the mother bear? We know the mass of the cub is 25 kilogrammes and we know the mother bear is four times as heavy.

"Let's start by representing what we know as a bar model." Great strategy, Lucas, always a good thing to do.

The mother bear has a greater mass, so this will be the whole and that's our unknown whole.

And the mass of the cub will be a part of that whole and we can see that there are four equal parts because the mother bear is four times the mass of her cub.

Now that we've represented the problem, we can form an equation to calculate the mass of the mother bear.

So the mass of the mother bear is four times the mass of her cub.

I wonder if you can tell what the equation will be.

That's right, we've got 25 kilogrammes multiplied by four.

And that would tell us the mass of the mother bear.

25 fours are 100.

So the mass of the mother bear is 100 kilogrammes.

100 kilogrammes is four times the mass of 25 kilogrammes.

Let's check your understanding.

Look at the bar model.

Which equation can be formed from the bar model? Have a look at your options, A, B, C, and D.

Pause the video and when you think you're ready, press play.

How did you get on? Did you notice that 18 grammes was a part and there were five equal parts? So it must be 18 grammes multiplied by five.

So we know that the mass of the mother bear is four times the mass of her cub, but now let's describe the mass of the cub in terms of the mother bear.

How would we do that? Ah, good one Lucas.

Let's start by representing what we know as a bar model and forming that equation.

So we know the mass of the cub must be one-quarter times the mass of its mother.

So there's my bar model.

The whole, the mass of the mother bear is 100 kilogrammes and the whole has been divided into four equal parts and the mass of the cub is equal to one of those parts.

We can form an equation to represent this.

We know that the mass of the mother bear, our whole, is 100 kilogrammes and we know the mass of the cub is one-quarter times the mass of its mother.

So we've got 100 kilogrammes we want to multiply by one-quarter and we know that finding one-quarter times is the same as dividing by four.

So 100 kilogrammes multiplied by one-quarter is the same as 100 kilogrammes divided by four, and that is equal to 25 kilogrammes.

So the mass of the cub is 25 kilogrammes and 25 kilogrammes is one-quarter times the mass of 100 kilogrammes.

Let's check your understanding.

Look at the bar model, which equations can be formed from the bar model.

Pause the video and when you think you're ready to hear the answer press play.

How did you get on? Did you notice that our whole is 350 grammes and there are five equal parts.

So we need to divide the whole by five.

And actually we know that dividing by five is the same as multiplying by one-fifth.

So both options A and B are correct.

Sam is investigating mass using a balance.

She places a stone and a conker on them.

What do you notice? That's right, they're balanced aren't they? So the conker and the stone have the same mass and when something has the same mass, we can say that they are one times the mass of each other.

So the mass of the stone is one times the mass of the conker.

The mass of the conker is one times the mass of the stone.

Lucas finds some objects to investigate.

He places a stone and two cubes on the balance.

What do you notice? That's right, the stone is twice as heavy as a cube because the stone as balance has the same mass as two cubes.

So actually if we only had one cube, the stone will be twice as heavy as a cube.

This is because two cubes are needed to balance one stone.

The mass of each cube must be one-half times the mass of the stone.

Let's check your understanding.

Which statement accurately describe this image? Is it A, "One cube is three times as heavy as the stone?" Is it B, "A stone is three times as heavy as a cube?" Or is it C, "The mass of one cube is one-third times the mass of the stone." Pause the video, maybe find someone to chat to about this.

And when you're ready, press play.

How did you get on? Did you work out that the stone must be three times as heavy as a cube? Because it needs three cubes to balance the one stone.

But also the mass of one cube is one-third times the mass of the stone because you need three of them to balance the stone.

Your turn to practise now.

I'd like you, for question one, to solve this problem.

Could you represent the information as a bar model which will help you form an equation? The mass of an adult penguin is seven times the mass of its chick.

So for part A, can you determine the mass of the chick first by reading the scale? Then for part B, can you calculate the mass of the adult penguin? And for part C, how much heavier is the adult than the chick? For question two, could you solve this problem? Represent the information as a bar model, which will help you form an equation.

The mass of an adult polar bear is 510 kilogrammes.

The mass of the cub is one-tenth times the mass of its parent.

For part A, could you tell me the mass of the cub? And for part B, how much lighter is the cub than its parent? Have a go at both questions, pause the video and when you're ready for the answers, press play.

Let's see how you got on.

First, you were asked to determine the mass of the chick by reading the scale.

What do you notice about the arrow? That's right, it's halfway between 200 and 400.

So the mass of the chick must be 300 grammes.

We then needed to calculate the mass of the adult penguin, and we know the adult penguin is seven times the mass of its chick.

So I've got my bar model with seven parts and one of those parts is worth 300 grammes.

We can form an equation.

I've got 300 grammes, we need to multiply by seven.

Three sevens are 21, 300 sevens must be 21 hundreds, which is the same as 2,100.

So the mass of the adult penguin is 2,100 grammes.

We were then asked to calculate how much heavier the adult is than the chick.

So this is an additive relationship.

So the mass of the adult is 2,100 grammes.

The mass of the chick was 300 grammes.

So I'm going to calculate that by subtracting 100, first to take me to the nearest thousand, so 2000.

Then I'm going to subtract another 200.

So 1,800 grammes.

The adult penguin is 1,800 grammes heavier than its chick.

For question two, we were asked, first, to find the mass of the cub.

We know that the mass of the polar bear was 510 kilogrammes and that is my whole, and the cub was one-tenth.

So I split my whole into 10 equal pars and that then helped me form an equation.

I know I've got 510 as my whole and I'm multiplying by one-tenth.

This is the same as dividing by 10.

This is 51.

So the mass of the cub is 51 kilogrammes.

Then we had to work out how much lighter the cub was than its parent.

510 kilogrammes is the mass of the parent.

Subtract the mass of the cub 51 kilogrammes.

I'm going to do that by adjusting my numbers.

So 500 kilogrammes minus 41 kilogrammes, that's 459 kilogrammes.

So the cub is 459 kilogrammes lighter than its parent.

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

Brilliant work so far.

I love the way you're deepening your understanding on comparing and describing measurements involving mass.

Now we're going to move on and think about comparing and describing measurements involving capacity and volume.

So we've got Jacob and Izzy.

They both want to compare the volume of liquid in their drinks bottles to see who has the most.

I wonder if you ever do that with your friends, see who has the most.

There we go, what do you notice? Ah, Jacob is saying he has a greater volume of liquid, which means Izzy has a smaller volume of liquid, but Izzy wants to be more accurate and calculate how many times the volume Jacob's water is compared to hers.

And we can start by representing this as a bar model, a good place to start, Jacob.

So Jacob is saying that he has a greater volume of liquid, so this must be the whole at 450 millilitres.

You can see the level of liquid in his jug is halfway between 400 and 500, so it's 450 millilitres.

And Izzy has a smaller volume of liquid.

So this is a part, it's 150 millilitres because the level of liquid in the her jug is halfway between 100 and 200 millilitres.

Two 150 volumes is 300 millilitres.

So the 450 millilitre volume that Jacob's got is more than twice what Izzy has, it's more than twice 150 millilitres.

Three 150 millilitre volumes is equal to 450 millilitres.

So that means the volume of liquid in Jacob's drink is three times the volume that Izzy has.

And we can also represent this in an equation.

We've got 150 millilitres.

Well, if we multiply that by three, 'cause there's three times that amount, we get 450 millilitres.

So the volume of liquid in Jacob's bottle is three times the volume of liquid in Izzy's bottle.

Let's check your understanding.

Which bar model represents this statement.

"The capacity of the jug is four times the capacity of the cup." Have a look at all four representations.

Pause the video, maybe find someone to chat to about this and compare your answers.

And when you're ready to hear the answer, press play.

How did you get on? Did you work out that it must be option C? Option C shows four equal parts and we know that the capacity of the jug is four times the capacity of the cup.

Well done.

We can use known multiplicative relationships to determine unknown capacities or volumes of liquids.

"The capacity of the kettle is one litre 800 millilitres," Jacob is telling us, and Izzy is saying, "The capacity of one mug is one-sixth times the capacity of the kettle.

What does that mean? Does that mean that the mug has got a greater or smaller capacity? That's right, it's a fraction.

So it's telling us that the capacity of the mug will be smaller.

So using this information we can calculate the capacity of the mug.

Yes, Jacob, good reminder, let's always start by representing this in a bar model.

So the kettle has the greater capacity, so this will be the whole, the capacity of the mug will be a part and the whole will be divided into six equal parts because the capacity of the mug is one-sixth times the capacity of the kettle.

So we can use the bar model to help form an equation.

We know that finding one-sixth times is the same as dividing by six.

So the capacity of the kettle at one litre, 800 millilitres multiplied by one-sixth will tell us the capacity of the mug.

And we know that multiplying by a unit fraction is the same as dividing by its denominator.

So one litre, 800 millilitres multiplied by one-sixth is the same as one litre, 800 millilitres divided by six.

And how would you solve this equation, I wonder? Yes, that's right Izzy, me too, I would convert from litres and millilitres to just millilitres, definitely, let's do that.

One litre 800 millilitres is the same as 1,800 millilitres, then we can divide that by six.

And then that's right Izzy, we can use our times tables.

We know that six threes are 18.

So 18 divided by six is three.

So 180 divided by six is 30.

That means 1,800 divided by six is 300.

So the capacity of the mug is 300 millilitres.

300 millilitres is one-sixth times the capacity of one litre 800 millilitres.

So we have used the comparison and one known amount to determine an unknown amount.

Let's check your understanding.

Look at the bar model, which statements accurately describe it.

So statement A, "A volume of 140 millilitres is seven times the volume of 20 millilitres." Statement B, "A volume of 20 millilitres is seven times the volume of 140 millilitres." Or part C, "A volume of 20 millilitres is one-seventh times this volume of 140 millilitres." Pause the video and when you're ready to check your answer, press play.

How did you get on? Did you realise that it's statement A, "A volume of 140 millilitres is seven times the volume of 20 millilitres." You can see our 20 millilitre part and there are seven equal parts that are equivalent to 140 millilitres.

And also part C, "A volume of 20 millilitres is one-seventh times the volume of 140 millilitres." Your turn to practise now.

I'd like to use some containers of 200 millilitres, 250 millilitres, 500 millilitres and one litre.

Can you compare their capacities multiplicatively using the stem sentence? The mm has mm times the capacity of the mm.

For question two, could you look at these containers? Could you form three equations to represent the relationship between the volume of liquid in them? And for question three, could you solve this problem? You should represent it as a bar model and form an equation to help you.

Izzy has a 250 millilitre container.

Jacob has a one litre container.

Jacob wants Izzy to help him fill his container using hers.

How many times will they need to fill Izzy's container and pour it into Jacobs? Pause the video while you have a go at questions one to three, and when you are ready for the answers, press play.

How did you get on? So for question one, you were asked to compare some capacities of contain some containers.

So you might have said that the 250 millilitre container has one-half times the capacity of the 500 mil container.

You might have said the one litre container has five times the capacity of the 200 millilitre container, or you might have said that the 200 millilitre container has one-fifth times the capacity of the one litre container.

I wonder if you found any more statements.

For question two, you had to form three equations to represent the relationship between the volume of liquid in these jugs.

You could have had 50 millilitres, which is the volume in the first jug, if we multiply that by six, we get 300 millilitres.

We could have had 300 millilitres, so starting with a larger volume and multiplying it by one-sixth is equal to 50 millilitres.

And we know multiplying by one-sixth would be the same as dividing by six.

So there are your three equations.

For question three, you had a problem to solve and you were asked to start by representing it in a bar model.

Jacob has a one litre container and one litre is the same as 1000 millilitres.

And Izzy has a 250 millilitre container.

And we wanted to work at how many times they would need to fill Izzy's container and pour it into Jacob's to fill Jacob's container.

So if we did it twice, it would be 500 millilitres, three times would be 750 millilitres, and four times would be 1000 millilitres.

So they will need to fill Izzy's container four times.

1000 millilitres is four times the volume of 250 millilitres.

How did you get on with those questions? Brilliant.

Fantastic learning today.

We have learned that mass, capacity and volume can be compared multiplicatively.

We've learned that the stem sentence, "The mm is mm times the mass, capacity or volume of the mm," can be used to compare and describe measures.

And we know that we can represent comparisons of measure as a multiplication equation.

Really impressed with how far you have come in your learning today.

Well done and I look forward to learning again with you soon.