Lesson video

Hello, how are you today? My name is Dr.

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

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

Welcome to today's lesson.

Today's lesson is from our unit: Compare and Describe Measurements Using Knowledge Of Multiplication and Division.

This lesson is called, Describe Changes in Measurement Using Knowledge of Multiplication and Division.

As we progress through the lesson today, we will be looking at problems where an object changes, something changes in its mass, its volume, or maybe in the amount of money or time intervals.

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

So shall we get started? Let's find out how can we describe changes in measurement using knowledge of multiplication and division? This is the key word that we will be using in our lesson today, change.

Let's practise that together.

I'm sure you've heard it before, but it's always good to say these words.

My turn, change.

Your turn.

Fantastic, and the problems we are going to be encountering today are all about change.

So what do we mean by change? A comparison can be made between an object at the start of and then after it's changed.

Examples of such changes include a change in mass of an animal if it grows.

You might have noted that your mass changed from when you were baby to the age you are now, or maybe a change in the amount of money if you spend some.

So today we are going to develop our understanding of how we can describe changes in measurement.

We're going to start by looking at how we can describe changes in mass or volume.

These are the children who will help us in our learning today.

Let's meet Lucas, Sam, Jacob and Izzy.

So sometimes the mass or volume of objects change and we need to be able to describe how they have changed mathematically and then solve problems related to that.

I wonder if you can think of anything that changes in mass or volume.

I gave you a bit of a clue, didn't I? When we looked at the key words.

Your mass has changed since you were a baby and it will continue to change as you grow.

Is there anything else you can think of? Let's look at this problem.

An iceberg had an estimated mass of 1,000 kilogrammes and due to climate change, that iceberg has melted and is now estimated to be 1/5 times its original mass.

Can you visualise that? Can you visualise what an iceberg looks like and maybe what it looks like and then that it's smaller now because it's melted.

Can you see that in your head? So this is an example of a change problem.

An object, the iceberg, has changed, it has melted That's what I saw in my head, a picture of an iceberg.

I wonder, what might the question be for this problem? That's right, what is the estimated mass of the iceberg now? We know what it was before it melted, 1,000 kilogrammes, and we know that it's melted and the estimated to be 1/5 times its original mass.

So we can find out what its mass is or its estimated mass is now.

And we can represent this in a table to identify the change, it will support us to understand the vocabulary in this question.

So we've got my iceberg with a mass of 1,000 kilogrammes, that's where it started.

And due to climate change, it's melted, it's now 1/5 times.

So I'm going to represent that with an arrow to show the change, and we are multiplying by 1/5.

And question mark represents the estimated mass of the iceberg now.

Let's check your understanding.

Could you represent this change problem in a table? Izzy is watering some plants in her garden.

She has five litres, 250 millilitres of water in her watering can.

After she finishes, she has 1/10 times the original volume of water left.

How much water is left in her watering can? I've given you an outline of a table there, pause the video while you fill it in, and when you are ready to go through this, press play.

How did you get on? Did you identify that the original volume of water is five litres, 250 millilitres and after she finishes, she has 1/10 times the original volume left? So we are going to multiply by 1/10, we're gonna show that representing that change with an arrow.

Well done.

Let's revisit our iceberg problem.

We've represented the key information in a table and once we have that table we can use it to form an equation.

So we know that the estimated mass of the iceberg at the start was 1,000 kilogrammes and that the estimated mass of the iceberg at the end after it had melted was 1/5 times the original mass.

So we're multiplying by 1/5, we can then solve our equation.

Oh, but we're multiplying by 1/5, aren't we? Can you remember, how do we multiply by a unit fraction? Ah, that's right, thank you Izzy for reminding us.

Multiplying by a unit fraction is the same as dividing by the denominator.

So we are multiplying 1,000 by 1/5, and that's the same as dividing 1,000 by five.

And we can use our known factors to help.

Yes, thank you Lucas.

We know 10 divided by five is two.

So 100 divided by five must be 20.

And I wonder if you can then guess using this pattern, what 1,000 divided by five must be? That's right, 1,000 divided by five must be 200.

So the estimated mass of the iceberg is now 200 kilogrammes and 200 kilogrammes is 1/5 times the mass of 1,000 kilogrammes.

Let's revisit your problem about the watering can and check your understanding.

Using the table you did previously, could you form an equation and solve it? As a reminder, Izzy is watering some plants in her garden.

She has five litres, 250 millilitres of water in her watering can.

After she finishes, she has 1/10 times the original volume of water left.

How much water is left in her watering can? So pause the video while you use the table to form an equation and then have a go at solving it.

When you have done that, press play.

How did you get on? Did you manage to form an equation starting with five litres, 250 millilitres because that's the original volume in the watering can? And then we know after she finished there was 1/10 times the original volume, so we need to multiply by 1/10.

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

So multiplying by 1/10 is the same as dividing by 10.

So we've got five litres, 250 millilitres divided by 10.

Hmm, how are we going to solve that? What should we do? That's right, it's probably easier to convert.

We know five litres, 250 millilitres is the same as 5,250 millilitres and that's a bit easier to divide by 10.

If we divide it by 10, we get 525 millilitres.

So there is 525 millilitres of water left in the watering can.

Well done if you got that.

Let's look at another change problem.

Lucas takes a water bottle to school, maybe you've got one similar to this water bottle.

He has 30 millilitres of water in his bottle, but he knows that he will drink more than this, he definitely should drink more than 30 millilitres, shouldn't he? He fills it up so it has six times the original volume.

What's the volume of the water in the bottle now? Can you visualise this change? Can you see a water bottle in your head with just 30 millilitres in the bottom and he adds more water, he fills it up, so it has six times the original volume.

So can you imagine having more water in your water bottle? And we can represent this change in a table.

So if we think about where do we start, we had 30 millilitres of water in our water bottle, and then we fill it up, or Lucas fills it up, so it has six times the original volume.

So the change is that we are multiplying by six and then we now need to find the volume of water in the bottle now.

We can represent that with a question mark.

And once we have our table, we can form an equation to help us solve the problem.

So we've got 30 millilitres is the volume we started with, and we are multiplying by six because we are filling the bottle up, so it's got six times the original volume, and the question mark represents what we are trying to find.

Once we have the equation, we can solve it, 30 millilitres multiplied by six.

That's right, Izzy, we can use our known factors to help, which known factor would you use? That's right, our knowledge of three sixes, three sixes are 18, three multiplied by six is 18.

So 30 multiplied by six must be 180.

So the volume of water in the bottle is now 180 millilitres.

That's bit of a better amount to drink than 30 millilitres, isn't it? So 180 millilitres we can say is six times the volume of 30 millilitres.

Let's just revisit this problem.

We know Lucas takes the water bottle to school and has 30 millilitres of water in his bottle and he filled it up so it had six times the original volume.

So we know he had 30 millilitres at the start and then by the end he had 180 millilitres of water.

Hmm, there's a question for you.

What could we work out from this information? We could calculate how much water was added to the bottle by Lucas, we would just need to find the difference between the whole amount and the part.

The whole amount was 180 millilitres and we're going to subtract the known part of 30 millilitres, which is 150 millilitres.

So 150 millilitres of water was added to the bottle.

Let's check your understanding.

Could you use your previous solution to determine how much water was poured out of the watering can? So we know Izzy is watering some plants and has five litres, 250 millilitres of water and we worked out that there was 525 millilitres of water left in the watering can.

So pause the video, have a go.

How much water was poured out of the watering can? When you've had a go, press play.

How did you get on? Did you manage to form that equation? We know we had five litres, 250 millilitres of water at the start, and at the end there was 525 millilitres.

So we need to subtract to see how much water was poured out and we know when we calculate it's easier if the units are the same.

So I converted my five litres, 250 millilitres to millilitres, so that's 5,250 millilitres and then I had to subtract 525.

Hmm, how is it best to subtract 525 do you think? Well if I look, I've got 5,250, I think I know that 525, well 500 is made up of two 250s.

So I'm going to subtract 250, then another 250, then 25, because if I subtract 250 from the 5,250, that takes me to 5,000, a nice number to deal with.

Then I can subtract the 250 and then the 25.

At the end of that, I've got 4,725.

That's the amount that is poured out of the watering can.

Well done.

It's your turn to practise now.

Could you solve these change problems, representing them in a table and using this to form your equation? So for question A, a birthday cake was one kilogramme in mass before some of it was eaten by the guests.

At the end of the party, the cake is 1/5 times the original mass.

What is the mass now? And for part B, a penguin chick has a mass of 300 grammes.

Over the course of the next few years, the penguin increases to 11 times its original mass.

What is its mass now? Give your answer in kilogrammes and grammes.

For question two, could you solve these change problems representing them in a table and using this to form your equation? Question A, Izzy has a bottle of water with a volume of 450 millilitres.

She drinks some of the water so that there is now 1/5 times the original volume.

What volume of water did she drink? And for part B, a jug contains 20 millilitres of water.

More water is poured into the jug so that there is now 50 times the original volume.

What volume of water was poured into the jug? Take care with these questions, they are two step questions.

You will first have to find out the unknown amount, then you will have to find the difference between the whole and the known amount.

Pause the video while you have a go at both questions, and when you are ready for the answers, press play.

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

So our first question was about mass.

It was about the mass of a birthday cake.

We know it was one kilogramme before some of it was eaten and then at the end it was 1/5 times the original mass, so we are multiplying by 1/5.

And here it is easier to convert the kilogrammes to grammes, we know one kilogramme is equivalent to 1,000 grammes and we are multiplying by 1/5, multiplying by 1/5 is the same as dividing by five.

We know 10 divided by five is two, so 1,000 divided by five will be 200.

The mass of the cake is now 200 grammes.

For part B, the question about the penguin chick, the mass started at 300 grammes and over the next few years the penguin increases to 11 times, so we know we need to multiply by 11.

We can use our known factors here.

300 grammes multiplied by 10 is 3000, and 300 multiplied by one is 300.

Recombined, we get 3,300 grammes.

So the mass of the penguin is now 3,300 grammes.

But you are asked to give your answer in kilogrammes and grammes, so this is equivalent to three kilogrammes, 300 grammes.

For question two, Izzy has a bottle of water with a volume of 450 millilitres, so that's where we've started.

And she drinks it so that there's now 1/5 times.

So we know we are multiplying by 1/5.

Multiplying by 1/5 is the same as dividing by five.

We know 45 divided by five is nine, so 450 divided by five is 90.

So there is 90 millilitres left in the bottle.

But the question is asking is how much he drank? So we need to subtract the known part of 90 millilitres from the whole, 450 millilitres, this is 360 millilitres.

So Izzy drank 360 millilitres.

For part B, we had a jug with 20 millilitres of water.

And water was poured into the jug so that there is now 50 times the original volume.

So we've got 20 millilitres and we know we are multiplying by 50.

We can do 20 fives, we know are 100, so 20 50s must be 1,000.

So there is 1,000 millilitres in the jug now.

However, the question asked us what volume of water was poured into the jug? So we need to subtract the known part of 20 millilitres from the whole, 1,000 millilitres, which is 980 millilitres.

So 980 millilitres was poured into the jug.

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

Fantastic learning, you are really making progress with describing changes in measurement in particular with mass and volume.

We're going to progress our learning now and we're going to look at describing changes in time intervals or amounts of money.

Sometimes other measures such as time or money change, and we also need to be able to describe how they have changed mathematically and solve problems related to that.

Let's look at this problem.

Sam has a bank account.

When she first opened it, she deposited 32 pounds.

The amount of money in the account is now three times the original amount of money.

How much money is in her account now? Yes, thank you Sam.

First, we ought to add this information to a table because that helps us form an equation.

So we can represent this change in a table, we've deposited 32 pounds at the start and the amount of money is now three times.

So I can signify the change with an arrow and we're multiplying by three.

And we have a question mark to represent how much money is in her account now.

And once we've got our table, we can use this to form an equation.

We know we started with 32 pounds and the amount we've got now is three times the original amount, so we are multiplying by three.

So we can then use our known factors to solve the equation.

Three threes are nine, so 30 threes must be 90.

Two threes are six and then we can recombine that, 32 threes must be 96.

So 96 is the amount of money in the account now.

So 96 must be three times the original amount of 32 pounds.

So Sam has 96 pounds in her bank account.

But she spends some of it now and there is 1/4 times the amount of money left in her account.

So this time, the amount of money is changing by 1/4 times.

So we know we are multiplying by 1/4, and we want to find out how much money is left in her account now, so we will represent that with a question mark.

Once we've represented the information in a table, we can use it to form an equation.

We know we are starting with 96 pounds and we are multiplying by 1/4, because we have 1/4 times the amount of money left.

Let's look at this equation.

We've got 96 pounds and we are multiplying by 1/4.

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

So 96 multiplied by 1/4 is the same as 96 divided by four.

And then we can use known factors to solve the equation.

We know to divide by four, we can halve and halve again.

So 96 divided by four is the same as 96 divided by two, so halving it, and dividing by two, so halving it again.

96 divided by two is 48 and then half of 48 is 24.

So Sam now has 24 pounds left in her account, and 24 pounds is 1/4 times the original amount of 96 pounds.

Let's check your understanding.

Have a look at options A, B, C, and D, and which of those equations can be formed from this information? Sam had 20.

50 in her bank account, she spends some of the money and now has 1/2 times the original amount left.

How much money is left in her account? So maybe find someone to have a chat with about this, see if you agree.

Pause the video while you do that.

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

How did you get on? Did you identify that it's option B? Because we are starting with 20.

50 pounds and we are multiplying by 1/2, and then the amount we end up with is 1/2 times the original amount.

It can't then be option A can it? Because the amount then at the end is larger.

What about option C? That's correct, it could be option C, because when we multiply by 1/2, it is the same as dividing by two.

And it can't be option D, because we haven't got two times as many, we've got 1/2 times the amount.

Well done.

So we've looked at money, but we can also describe changes in time intervals.

So Jacob has been practising hard to improve the time in which he can run one kilometre.

When he first tried it took him 10 minutes, that's good.

Now it takes him five minutes.

Wow, he's really improved the time in which he runs, hasn't he? So using this information we can determine how much faster that he is now.

So let's represent this as a bar model.

So the original time is longer and it is our known whole and the new time is shorter, so it's a known part.

And we can see there are two equal parts of five minutes in the 10 minute time interval.

So five minutes must be 1/2 times the original time that Jacob took to run one kilometre.

We can also say that 10 minutes is twice the five minutes time interval.

Let's check your understanding of that.

Could you draw a bar model to represent this statement and then complete the given sentences describing the relationship? Sam used to swim for 90 minutes, now he swims for 30 minutes.

Pause the video while you draw the bar model and write the sentences out.

And when you are ready for the answers, press play.

How did you get on? That's my bar model, I've got the whole is 90 minutes and I have divided it into three equal parts and 30 minutes is equivalent to one of those parts.

So I've got 30 minutes is 1/3 times the time of 90 minutes, and 90 minutes is three times the time of 30 minutes.

How did you get on? Brilliant.

Your turn to practise now.

For question one, could you solve these change problems, representing them in a table or bar model and using the representations to form an equation? So for part A, Jacob was given some money by his family for his birthday and he now has 48 pounds in his account.

This is four times the amount that he had before his birthday, how much money was he given? And then part B, Izzy runs a race in three minutes, 18 seconds.

This is twice as fast as she has completed it before.

How long did it take her the previous time? For question two, could you solve this change problem, representing it in a table and using this to form an equation? Izzy had 24 pounds, she now has 72 pounds.

Could you tell me how much more money she has now? And then how many times the original amount of money does she have now? Have a go at both questions, pause the video, and when you are ready for the answers, press play.

How did you get on? Shall we have a look? So for our first question, Jacob was given some money by his family for his birthday and now has 48 pounds in his account.

And we were told that this is four times the amount that he had before his birthday and that's what we have to work out.

So the question mark represents what we have to work out.

We can also represent this as a bar model.

48 pounds is the whole amount we have now and it's four times the amount he had before.

So we have divided the bar into four equal parts.

We can use these representations to form an equation.

We're trying to work out what he had before his birthday and we know whatever it was was multiplied by four to give 48.

We can then use our known factors.

48 divided by four is 12 pounds.

So Jacob had 12 pounds before his birthday, but we need to work out how much money he was given.

So we need to subtract that part from the known whole of 48, which is 36 pounds.

So Jacob was given 36 pounds for his birthday.

For part B.

Izzy ran a race in three minutes, 18 seconds, which is twice as fast as she had completed it before.

How long did it take her the previous time? So we can represent this in the table and as a bar model, we're trying to work out the length of time it took her the previous time.

So we know she ran twice as fast this time, so she must have been twice as slow the time before.

So we are multiplying by two.

Three minutes, 18, multiply by two.

Well that gives us six minutes and 36 seconds.

So previously it took Izzy six minutes, 36 seconds.

For question two, we had a problem about Izzy.

Izzy had 24 pounds and now has 72 pounds.

How much more money does she have now? So that's an additive relationship.

So we can represent the whole of the amount she has now and the part as the amount that she had.

And we know to find how much more, we need to subtract the known part from the whole.

72 subtract 24.

But I'm gonna subtract the 20 first to give me 52, and then I can subtract the four, by subtracting two and two, which is 48.

So she has 48 pounds more now than she did at the start.

But for the second part of the question, we needed to work out how many times the original amount of money she has now.

So we had 24 pounds, what do we multiply that by to get 72 pounds? Well, 24 times one is 24 pounds, times two is 48 pounds, so she has three times the amount of money because 24 multiplied by three is 72.

72 pounds is three times the original amount of 24 pounds.

So Izzy now has three times the original amount of money.

How did you get on with all of those questions? Brilliant, well done.

Fantastic progress in your learning today.

We have really deepened our understanding of how we can describe changes in measurement using knowledge of multiplication and division.

We know many things can change and we need to be able to describe how they change mathematically.

We know that when we compare how something changes, it is useful to represent the change in a table and/or as a bar model.

And we know that we can use the stem sentence, mm is mm times the original mm, and that supports us to describe the change.

So you should be really proud of how hard you have tried today and I look forward to learning with you again soon.