Lesson video

Hello.

Good to see you today.

How are you? My name is Dr.

Shorrock and I'm really excited to be learning with you today.

We are going to have great fun as we move through the learning together.

Welcome to the learning today.

Today's lesson is from our unit Compare and Describe Measurement Using Knowledge of Multiplication and Division.

This lesson is called Use knowledge of multiplication and division to solve comparison and change problems. As we move through the learning today, we will be looking at lots of different measures in different contexts.

So from mass length, volume, including time and money.

And we will be solving problems thinking about how we can compare amounts of measure.

Sometimes new learning can be a little bit tricky, but it's okay because I am here to guide you and I know if we work really hard together then we can be successful.

So let's start, shall we? How can we use our knowledge of multiplication and division to solve comparison and change problems? These are the keywords that we will use in our learning today.

We've got comparison and change and I know you may have heard those words before, but let's practise them together anyway.

My turn comparison, your turn.

Nice.

My turn, change, your turn.

Fantastic.

So when we talk about a comparison we are really thinking about how different two objects are, we're going to look at a lot of measures in this lesson.

So in this case we might think about how many times longer an object is than another.

We can also make a comparison in with one object before and after it changes.

And examples of a change include the change in height of a flower when it's growing.

So today we are really going to deepen our understanding of using multiplication and division to solve comparison and change problems. And we are going to start by looking at comparing measures.

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

So it is important to have a way to compare different measures and we can compare measures mathematically.

And Lucas is asking us, "Can we think of some measures that we could compare?" Can you think of any? Oh that's right Sam.

That's right.

We could compare the mass of two objects.

We could compare the amount of money two people have.

We could compare the length of time it takes two people to run a race.

I wonder if you thought of any others we could compare.

So yes Lucas, let's do that Lucas, let's have a go at comparing something mathematically.

Sam has a football and a cricket ball.

Can you visualise this? So can you see in your head a football and a cricket ball? It's really important when we solve problems that we can visualise the words in our head.

Ah, that's what I see.

There's my cricket ball and my football.

The football has a mass of 450 grammes.

The cricket ball has a mass that is one third times the mass of the football.

Hmm.

What can we determine from this comparison do you think? We've got a cricket ball that's one third times the matter of the football, what could we work out? Ah, that's right.

We could use that information and determine the mass of the cricket ball.

So let's start by representing what we know in a bar model.

It's always good to do a bar model once we visualise to really help us understand what these words in the problem mean.

And Lucas is going to help us with our bar model.

The football has the larger mass, so this must be our whole and we know the mass of the football.

So it is a known whole.

The mass of the cricket ball is one third time to the mass of the football.

So what does that mean? That's right.

It means we need to divide the whole into three equal parts so that each part is one third of the whole and the mass of the cricket ball will be equivalent to one of those parts because the mass of the cricket ball is one third times the mass of the football.

Ah yes.

Thank you Sam.

We can use our bar model to form an equation.

We know the whole is 450 grammes and we know the mass of the cricket ball is one third times the mass of the football.

So our equation is 450 grammes multiplied by 1/3.

And once we formed our equation we can then solve it.

And we know that when we multiply by a unit fraction, it is the same as dividing by the denominator.

And we've also seen this because we have divided the whole bar into three equal parts.

So we know we've got 450 grammes and we need to divide by three.

So let's look at our equation.

We know 450 grammes multiplied by one third is the same as dividing 450 grammes by 3.

But how do we do that? That's right.

We can use our known facts to help us.

It's always worth checking to see if you can use known facts before you rush off into using a written algorithm.

Let's have a look.

Do you think we've got any known facts here that we could use? Ah, that's right.

We could partition 450.

We know 450 is made up of 300 and 150 and 300 divided by 3 is 100 and 150 divided by 3 well, we know 15 divided by 3 is 5.

So 150 divided by 3 must be 50.

We can then recombine those to get 450 divided by 3 is equal to 150.

So the mass of the cricket ball is 150 grammes and we can say that 150 grammes is 1/3 times the mass of 450 grammes.

We can also say the other way round 450 grammes is three times the mass of 150 grammes.

Let's check your understanding on this so far.

Have a look at these equations and could you tell me which equations represent this statement? The jug contains one litre volume of water.

This is five times the 200 millilitre volume of water in the cup.

So maybe find someone to chat to about this.

Pause the video while you think about which equations represent that statement.

And when you are ready to go through the answers, press play.

How did you get on? Equation a is correct because we've got a 200 millilitre volume of water in the cup and the jug contains five times that amount.

So 200 millilitres multiplied by five.

Any other's correct? Well b can't be correct 'cause we would be making 200 millilitres multiplied by 1/5 would be smaller than one litre.

But c is correct because one litre multiplied by 1/5 is the same as dividing by five, which would be 200 millilitres.

Equation d well if we've got one litre we multiply by five, we're going to get five litres, aren't we? So that can't be correct.

I wonder how you got on? Well done.

So in addition to using a comparison of measure to calculate an unknown, which is what we've just done, we can also take two measures and compare them.

And when we compare measures we can use the stem sentence.

The mm is mm times the mm of the mm.

And we will be practising that as we move through this problem.

So we've got a flight to Japan from London, it takes 14 hours.

Wow, that's a long time, isn't it? 14 hours.

That's the time from maybe when you have breakfast to after you've gone to bed.

So that's how long a flight from Japan to London take.

A flight to France though from London takes 120 minutes.

Hmm.

Can you visualise that? Can you see that flight from Japan to London taking 14 hours and the flight from France to London 120 minutes? Hmm, which is shorter, which is longer.

What could we determine from that then do you think? That's right.

We could determine how many times longer the flight to Japan is than the flight to France.

What do you notice though? Is there something you've noticed with this question? It made it a little bit trickier to work out which flight was longer.

That's right.

Thank you Lucas.

We have been given the flight time to Japan in hours but the flight time to France in minutes.

So they are different units.

So let's start by representing what we know in a bar model.

Thank you Lucas.

And I think Lucas is going to help us with our bar model.

So the question tells us that the flight to Japan takes longer.

So this will be our whole and we know how long it takes 14 hours.

So it is a known whole.

Then the length of time of the flight to France is a known part of the whole 120 minutes.

And we can use the bar model to form an equation to help us compare these flight times.

We've got 120 minutes times something is equal to 14 hours and we know we are multiplying because the question has asked us to find how many times longer the flight to Japan is.

So what does 20 minutes represent? Can you remember? That's right.

Thank you Sam.

It represents the flight time to France.

What about the 14 hours? What does that represent? Can you remember? That's right.

The 14 hours represents the flight time to Japan.

And so the question, well what does that represent then? That's what we're trying to find out, isn't it? That represents how many times the length of time the France flight is in comparison to the Japan flight.

And this is unknown to us at the moment.

This is what we are trying to find out.

So we've noticed that our units are different and when we do any sort of calculating, it is much easier if we convert to the same unit.

So we know 60 minutes is equivalent to one hour.

We also know that 120 is composed of two 60s.

So what does that tell us? What does that mean? That's right, it means 120 minutes is the same as two hours.

So now we've got an equation where our units are the same two hours times something is equal to 14 hours.

So now our units are the same.

We can compare 14 hours and two hours and we can start by thinking about are there any known facts that will help us? Ah yes, that's right.

Thank you Lucas.

We know two sevens are 14, so two hours multiplied by seven is 14 hours.

So the question mark must have a value of seven.

So the flight time to Japan is seven times the length of the flight time to France, it's seven times longer.

We could also say that the flight time to France is 1/7 time the length of the flight time to Japan.

Let's check your understanding with this.

Have a look at the statements a, b, c, and d.

Could you tell me which statements accurately describe this equation? Pause the video, maybe find someone to chat to about this and compare your answers.

And when you are ready to go through this press play.

How did you get on? Did you realise that it can't be equation a? 2.

5 kilogrammes can't be four times the mass of 10 kilogrammes because 10 kilogrammes is greater.

So it must be B 10 kilogrammes is four times the mass of 2.

5 kilogrammes.

Were there any other equations that were correct? That's right, c was correct.

2.

5 kilogrammes is 1/4 times the mass of 10 kilogrammes.

B and c are sort of inverse is the opposites to each other.

And what about D? No, 10 kilogrammes can't be 1/4 times the mass of 2.

5 kilogrammes because 10 kilogrammes is larger.

How did you get on? Well done.

It's your turn to practise now.

For question one, could you compare the mass of the bear and her cub? Could you tick which statements could be correct? The mass of the adult bear is four times the mass of the cub.

The cub is four times the mass of the adult bear.

The adult bear is 1/4 times the mass of the cub.

The cub is 1/4 times the mass of the adult bear or the mass of the adult bear times 1/4 equals the mass of the cub.

For question two, could you represent this comparison problem in a bar model, form an equation and then solve it.

A laptop costs 320 pounds, a camera costs 40 pounds.

How many times the cost of the camera is the laptop.

And how many times the cost of the laptop is the camera? So you're doing it both ways around for me there.

And for question three, could you read these statements? Lucas has a two litre volume of water.

Jacob has 1/4 times the volume of water that Lucas has.

Izzy has twice the volume of water that Jacob has.

I'd like you to start by representing these statements in a bar model.

But before that it might be worth thinking about what this looks like, visualising it in your head.

Then can you form and solve equations to determine the volume of water that each child has? And then starting with the smallest volume, could you place the children in order of the volume of water that they have? Pause the video while you have a go all three questions and when you are ready to go through the answers, press play.

How did you get on? Let's have a look.

So which statements could be correct? Well yes, the mass of the adult bear could be four times the mass of the cub 'cause it is larger.

Now the cub, the mass of the cub cannot be four times the mass of the adult bear.

The cub is smaller.

That's right.

The adult bear can't be one-quarter times the mass of the cub because the adult bear is larger.

But the cub, the mass of the cub could be 1/4 times the mass of the adult.

And yes, the mass of the adult bear.

If we multiply that by 1/4 it would be give us the mass of the cup.

For question two, you had to represent this comparison problem in a bar model, form an equation and solve it.

My whole is 320 pounds and we needed to work out how many times the cost of the camera is the laptop.

So 40 pounds is the cost of the camera and we need to multiply that by something and that will give us 320 pounds.

Well we know 4 eights is 32, so 40 eights must be 320.

So the 320 pound laptop is eight times the cost of the 40 pound camera.

For the second part of the question, you ask to determine how many times the cost of the laptop is the camera.

So we're going to form our equation 320 multiplied by something is equal to 40.

And the way we are going to do this is divide.

We're going to do third, 320 divided by 40.

And that will tell us what we need to multiply the 320 by to get 40.

So we can use our known facts here.

We know 32 divided by four is eight.

And so 320 divided by 40 must also be eight.

So there are eight forties in 320.

So 40 must be 1/8 of 320.

So our equation is 320 multiplied by 1/8 is equal to 40.

So the 40 pound camera is one eight times the cost of the 320 pound laptop.

For question three, you had a problem where you needed to represent these statements in a bar model.

So I've got, Lucas has a two litre volume of water.

Jacob has 1/4 times the amount.

So you can see my bar model has been my whole has been split to four equal parts and Jacobs is equivalent to one of those parts.

Izzy has twice the volume of water that Jacob has.

So she has two of those parts.

You'll then ask to form and solve an equation to determine the volume of water that each child has.

So we know Lucas has two litres and we know if we multiply that by 1/4, it is the same as dividing by four and I'm going to convert that two litres to millilitres to help me.

So 2000 millilitres divided by four is 500 millilitres.

So Jacob must have 500 millilitres.

And then we know Izzy has got twice that amount.

Twice 500 is 1000 millilitres.

You were then asked to start with the smallest volume, place the children in order of volume of water that they have.

Jacob had 500 millilitres, Izzy with one litre and then Lucas with two litres.

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

Fantastic learning so far you've really deepened your understanding about how we can compare measures multiplicatively.

We're now going to move on and look at changing measures.

So when one object changes.

And it's important to have a way to compare changes in measure, and we can compare changes in one measure mathematically using the same stem sentence we use when comparing different measures that mm is mm times the mm of the mm.

Let's have a go and look at this problem.

Izzy is doing an experiment for science and measuring the volume of rainfall over one month.

At first, after one day she has collected water to a volume of 50 millilitres.

At the end of the month, water has been collected to a volume of two litres.

Can you visualise that? Can you maybe see a little pot that she might have outside where she's collecting this rain water? And what could we determine from this? Well, what do we know? We know the water was 50 millilitres and we know that it's now two litres.

So yes, thank you Jacob.

We could determine how many times more volume of water there is now than after one day.

And what do you notice? Anything that you notice about this problem? Ah, that's right.

We've got different units, we've got millilitres and we've got litres.

So we know we need to look out for that and take that into account when we are calculating and we can use a table to form an equation to help us compare this change in volume.

It's my table and we know we are starting with 50 millilitres and at the end of the month we have two litres and we've got an arrow there to show the change.

And that's what we are trying to work out how many times more volume we have now than where we started.

So we can use this table to help us form an equation.

So we've got 50 millilitres multiplied by something is equal to two litres.

So our units are different.

We've already noticed this and it would make it easier here if we can convert to the same unit.

One litre is equivalent to 1000 millilitres.

So two litres are equivalent to 2000 millilitres.

So I can now use millilitres in my equation.

So both my units are the same.

And we can use then our known facts to calculate the missing value.

We know 50 fours is a 200.

So 50 times 40 must be 2000.

The two litre volume of water collected at the end of the month is 40 times the 50 millilitre volume collected after day one.

So we can use our stem sentence for describing this change.

The two litre volume is 40 times the volume of 50 millilitres.

Let's check your understanding with this.

Which stem sentence accurately describes this table? Is it a, one pound five pence is one third times the amount of 35 pence? Is it b, the 35 pence amount is one third times the amount of one pound and five? Or is it c, the one pound five amount is three times the 35 pence amount.

Pause the video, maybe chat to somebody about this.

And when you are ready to go through the answers, press play.

How did you get on? Did you identify? Well, it can't be a, one pound and five P is one third times the amount because one pound and 5 p is larger, it's a larger amount than 35 p.

B is correct.

The 35 p amount is one third times the amount of one pound and five pence.

And what about part c? That's also correct though one pound and five pence amount is three times the 35 pence amount.

How did you get on? Brilliant.

It's your turn to practise now.

Could you represent these change problems in a table, form an equation and then solve it? So for part A, Jacob needs to save 320 pounds to buy a laptop.

He has 16 pounds now how many times his current amount does he need to save? And part b Lucas has a two litre volume of water.

He accidentally spills some.

Oh dear.

He has a 200 millilitre volume of water left.

How many times more volume of water did he have at the start? So just take care with that one.

What do you notice about the units? For question two could you solve this problem? Lucas has a 1 kilogramme 800 gramme cake.

He cuts it into slices and hands it out to his friends.

After he hands it out 1/9 times the original mass is left, he then eats one half times the mass of what is left.

What massive cake did his friends eat and what mass of cake did he eat? Might be helpful to visualise this first, what does this look like? Pause the video.

Have a go at both questions and when you are ready for the answers, press play.

How did you get on? Should we have a look? So for the first question, you were asked to represent the change problem in a table.

So we had 16 pounds now and then Jacob needed to save 320 pounds to buy a laptop and we needed to work out how many times the current amount of 16 pounds does he needs to save.

And we can represent this in an equation.

16 pounds multiplied by something is three 20 pounds.

We can use our known facts to help us.

16 twos are 32.

So 16 20s are 320.

So Jacob needs to save 20 times the amount of money that he has now.

For part b, where Lucas spilled some water, we can represent that in a table.

We started with two litres of water, some were spilled and we can represent that by an arrow.

And he has 200 millilitres of water left.

So we can use the table to help us form an equation.

Two litres multiplied by something is 200 millilitres.

And that's right, the units were different.

So it's always useful then to convert to the same unit.

So I know one litre is equivalent to 1000 millilitres.

So two litres is equivalent to 2000 millilitres.

And we can use our known facts to help us.

I know that if I divide 2000 by 10, I get 200 and dividing by 10 is the same as multiplied by 1/10.

So Lucas now has 1/10 times the volume of water that he had at the start.

And for question two, question about a cake, we've had 1 kilogramme 800 grammes to start within our table.

He cuts into slices and after he hands it out 1/9 times the original masses left.

So you can see that's the change.

So it's multiplied by 1/9 and we need to find out the mass of the cake that his friends ate.

So we know we can form an equation, one kilogramme 800 grammes multiplied by 1/9.

Well we know that's the same as divided by nine.

We can also convert 1 kilogramme 800 grammes to 1,800 grammes to help us calculate and we can use our known facts there.

We know 18 divided by nine is two.

So 1,800 divided by nine must be 200.

There was 200 grammes of cake left.

But the question is asking us what massive cake did his friends eat? So we need to do a subtraction.

We need to subtract that 200 grammes from the original amount of 1,800 grammes.

So 1,600 grammes.

His friends ate 1,600 grammes of cake between them.

And then we were asked to find what massive cake did he eat and he ate one half times the mass of what was left, 200 grammes was left.

We can multiply that by our one half, which is the same as dividing by two.

200 divided by two is 100 grammes.

So Lucas ate a mass of 100 grammes of cake.

Fantastic learning today, everybody really impressed with the progress you have made at using your knowledge of multiplication and division to solve comparison and change problems. We know that if the units are different, we should convert that they are the same.

And this supports us when we calculate, we know we can use the stem sentence that mm is mm times the mm of the mm to support our description of a comparison or change.

And we know comparison problems can be represented in a bar model and change problems can be represented in a table.

And whereafter, we have represented them in a bar model or table.

This helps us to form an equation that we can then solve.

So you should be really proud of the learning that you have done today and how far you have come.

I have really enjoyed learning with you and I look forward to learning with you again soon.