Lesson video

Hello.

My name is Dr.

Shorrock and I am so happy to be learning with you today.

You have made a great choice to learn maths with me.

We are going to have a lot of 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 Compare and Describe Measurements Involving Time and Money.

During the course of this learning, we are going to look at comparing in tools of time and amounts of money and using our comparisons to calculate unknown quantities.

Sometimes new learning can be a little bit tricky, but I'm here to guide you through it.

And I know if we work really hard together, we can be successful.

So, shall we get started? How do we compare and describe measurements involving time and money? These are the keywords that we will be using in our learning today.

We've got times the time, times as long, times the amount of money.

Let's practise those together.

My turn.

Times the time.

Your turn.

Nice.

My turn.

Times as long.

Your term.

Fantastic.

My turn.

Times the amount of money.

Your term.

Brilliant.

Well done.

So when we use those phrases times the time, times as long, times the amount of money, we're using them to compare and describe.

For example, we might say, "One child run a race in two times the time of another child.

So they are half the speed." So today, we are going to start our learning by looking at comparing and describing time multiplicatively.

In the learning today, we've got Lucas, Sam, Jacob, and Izzy to help us.

"Sam and Jacob both walk to school." I wonder if you walk to school.

"It takes Sam nine minutes." If you walk to school, I wonder how long it takes you.

"It takes Jacob four times as long." Hmm.

"How could we compare their journeys," do you think? Well Sam is saying it takes her less time to walk to school.

It takes her nine minutes.

And Jacob's journey is longer, four times as long.

So using that information, we can calculate how long it takes Jacob to walk to school, can't we? And Sam is saying, "Well actually first, we should represent what we know as a bar model." Always a good strategy.

"Jacob's is the longest journey, and so this is the whole and it is unknown." Sam's journey is a nine minute journey and it's shorter, so this is a known part.

And we know that "the time Jacob's journey takes is four times as long, so we need four equal parts." And we can then use that bar model to help us form an equation.

We've got nine minutes is the length of journey of Sam's journey, and we've got four times as long to find Jacob's journey.

So nine fours are 36.

So it takes Jacob 36 minutes to walk to school.

"36 minutes is 4 times as long as 9 minutes." Let's check your understanding.

"Which bar model matches this statement: 120 minutes is four times as long as 30 minutes." Is it A, B, C or D? Pause the video while you have a think about it.

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

How did you get on? Did you choose bar A? Because 120 minutes is four times as long as the 30 minutes, so we need four equal parts of 30.

Let's look at another problem.

"Sam and Jacob both play in a school football match.

Sam plays for the full 90 minutes.

Jacob is injured after 30 minutes and has to stop playing." Oh dear.

"How can we compare the length of time that the boys played?" That's right, Jacob.

We could compare the time that Jahi played to the time Sam played in different ways.

"We could compare the time additively and find out how much longer time Sam plays for.

Let's represent this as a bar model.

Sam plays for the full 90 minutes, and this is the greater amount and it is our known whole." Jacob plays for 30 minutes when he's injured.

"This is a known part." So to compare the difference in how much time the children play, "we need to find the unknown part by subtracting the known part from the whole." So 90 minutes subtract 30 minutes is 60 minutes.

So Jacob plays for 60 minutes less than Sam.

But in this lesson, we want to compare lengths of time multiplicatively.

So we're going to think about "if the whole is divided into three equal parts, each of those parts is one-third of the whole.

So we can see that 30 minutes is equivalent to one-third of the whole 90 minutes." So Jacob plays for one third of the time that Sam plays for.

"Sam plays for three times the time that I play for." We can say it either way.

"We can use our bar model to form an equation." The whole 90 minutes, we know that Jacob plays for one-third times that whole 90 minutes.

We've got 90 minutes multiplied by one-third.

And we know that finding one-third of something is the same as dividing by three.

So let's compare these two statements.

"Jacob plays for 60 minutes less than Sam.

And Jacob plays for one-third times the time that Sam played." Can you spot the difference between those two sentences? "Let's revisit the bar model for both of these statements." This is the bar model for the additive relationship.

And you can see the parts are unequal.

"So when we compare additively, the parts may be unequal so we need to add or subtract." And for the other statement where Jacob plays for one-third times a time that Sam plays for, this is our multiplicative statement.

"The parts will be equal, so we can multiply or divide." Let's look at both of those bar models together.

Can you spot what is the same and what is different about them? That's right.

The wholes are the same, but in the first bar model where we are comparing unequal parts, we have to compare additively.

And in the second bar model, we can compare multiplicatively because the parts are equal.

"Jacob plays for 60 minutes less than Sam or Jacob plays for one-third times the time that Sam plays.

Jacob plays for one-third times the time that Sam plays." Hmm.

"Do you notice something about that statement?" Ah, that's right.

Thank you, Sam.

We've used the word time twice, but for different purposes.

"We use 'times' multiplicatively to mean 'lots of.

'" So Jacob plays for one-third lots of the time that Sam plays.

And the second "'time' is used because we are comparing lengths of time." Let's look at this scenario now.

What do you notice? "Jacob and Sam participate in a swimming gala.

In one race, it takes Sam three times the time that it takes Jacob.

It takes Jacob 240 seconds." We can calculate how long Sam takes using this given information.

I wonder how you would do it.

Yes, that's right.

We can form an equation.

240 seconds multiplied by 3 because it takes Sam three times the time that it took Jacob.

And we can partition the 240 to help us calculate this.

200 seconds multiplied by 3 is 600 seconds.

40 seconds multiplied by 3 is 120 seconds.

Put those together, recombine them, and we get 720 seconds.

So it takes Sam 720 seconds.

"720 seconds is three times the time of 240 seconds.

This is a larger number because we multiplied by three," but it means that Sam is slower, isn't it? Because if you take longer, you are slower.

Let's check your understanding.

"True or false? Jacob runs a race in 30 seconds.

Sam takes two times the time.

Sam is quicker." What do you think? Is that true or false? And then why? Is it A, "Sam will complete the race in a greater time, which means he's quicker," or is it B, "Sam will complete the race in a greater time, which means he took longer." Pause the video.

Maybe discuss this with someone if there's somebody around.

And when you are ready, press play.

How did you get on? Did you say it is false? And it is false because if you complete a race in a greater time, it means you take longer.

You are slower.

It's your turn to practise now.

For question one, I'd like you to work in pairs where it's possible and use a stopwatch.

I'd like you to time each other sketching a picture of a house.

You think you can do that? And then I'd like you to "repeat this, but slow it down so it takes you three times as long.

And then repeat this, but speed it up so it takes you one half times the time." Could you then represent parts A and B as equation? How did you work out what three times the time was going to be or what one-half times the time was going to be? For question two, you've got a problem.

"It takes Jacob 90 seconds to run from the start to end of the school track.

His older brother can run this in one-third of Jacob's time.

Which three equations could represent this situation? Give reasons for your choices." Pause the video whilst you do those two questions, and when you're ready to go through the answers, press play.

Shall we see how you got on? So when you were working in pairs, it might be that you took 81 seconds to sketch a house, and then you had to try and slow it down, so you took three times as long, which would be 243 seconds.

Then "you might have repeated it, but sped it up, so you took one-half times the time." So 81 seconds multiplied by one-half is 40.

5 seconds because we are dividing by two.

We are dividing 81 by 2, we are finding half of 81.

Half of 80 is 40, and half of the 1 would be 0.

5, 0.

5 or one-half.

So 40.

5 seconds.

For question two, you are asked to identify three equations that could represent this situation.

Those are the three equations, and then you are asked to give reasons for your choices.

So for both of these, you might have explained that these represent finding one-third of a time.

"Multiplying by one-third and dividing by three are ways of finding one-third times the time." You might also though have reasoned that "this equation might also be able to represent this situation because 90 is equivalent to three thirties, which is another way of representing one-third of 90." How did you get on with both of those questions? Well done.

We are now going to move on and think about how we can compare and describe money multiplicatively.

So "we can also compare and describe amounts of money.

Lucas and Izzy both win some money at the school fair." Nice.

I wonder how much money they won.

"Lucas receives 15 pounds and Izzy receives 60 pounds." "What could we find out?" Lucas is asking.

Ah, that's right, Izzy.

We could work out how much more money Izzy had.

And "we could do this additively or multiplicatively." So "let's represent this as a bar model." "Izzy has the greater amount, so this is the whole" and we know what that amount is.

And Lucas has the lower amount, so it's a part and it's also known.

"We can see that Izzy has 45 pounds more than me." This is the additive relationship because the parts are unequal.

But we want to compare the amounts multiplicatively.

"If the whole is divided into four equal parts, each of those parts is one-quarter of the whole.

And we can see that 60 pound is equivalent to 4 times 15 pounds." Izzy has four times the amount of money that Lucas has.

Lucas has one-quarter times the amount of money that Izzy has.

We can say it either way around depending if we're comparing the larger amount to the smaller amount or the smaller amount to the larger amount.

"So we can use the bar model to form equations to represent this." 60 multiplied by one-quarter is 15 pounds.

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

So 60 multiplied by one-quarter is the same as 60 divided by 4.

I wonder if you can remember how we can divide by four.

That's right, we can divide by two and divide by two again, so half and half again.

60 halved is 30.

Halved again, we get 15.

And 15 multiplied by 4 is 60.

So we have three different equations representing that bar model.

"So let's revisit our information and summarise.

Lucas and Izzy both win some money at the school fair.

Lucas receives 15 pound, Izzy receives 60 pounds.

And we can compare amounts additively.

Izzy has 45 pounds more than me.

Or we can compare the larger amount to the smaller multiplicatively: Izzy has four times the amount of money that I do.

Or we can compare the smaller amount to the larger amount multiplicatively: Lucas has one-quarter times the amount of money that Izzy does." So it's really important that we take very careful attention to the vocabulary when we're answering these questions to find out what it is that they are looking for.

Let's check your understanding.

"Which statement or statements could be used to compare these amounts?" You can see the whole is 10,000 pounds and one of the parts is 2,000 pounds.

Could it be statement A: 10,000 pounds is four times the amount of 2,000 pounds? Could it be statement B: 10,000 pounds is five times the amount of 20,000 pounds? Could it be C: 2,000 pounds is one-fifth times the amount of 10,000 pounds? Or could it be D: 2,000 pounds multiplied by 5 is equal to 10,000 pounds? Pause the video, and when you are ready to go through the answers, press play.

How did you get on? Did you spot that statement B was correct and C and D? They all say the same thing.

That 10,000 is five times 2,000.

Well done if you've got all three statements.

Your turn to practise now.

So for question one, I'd like you to use some play or real money and make 2 pounds 10.

Then, can you make some new amounts that are twice the amount, one times the amount, and one-third times the amount? And could you form equations to represent each of those? For question two, I'd like you to "represent each of these problems as a bar model and form an equation before solving them.

Part A, Izzy and Lucas both save their pocket money.

Lucas saves double the amount that Izzy saves.

If Lucas has saved 64 pounds, how much money has Izzy saved? For part B, Izzy and Lucas go shopping.

Izzy spends 12 pounds 30.

Lucas spends one-quarter times the amount of money.

How much does Lucas spend? And how much more does Izzy spend than Lucas?" Have a go at both questions, and when you are ready to hear the answers, press play.

Shall we see how you got on? So for question one, you had to use some money to make 2 pounds 10, and then make some amounts that are twice the amount.

So twice 2 pound 10 would be 4 pound 20.

One times the amount, so here we are just multiplying by one, so the amount would be the same, 2 pounds 10.

And one-third times the amount.

2 pounds 10 multiplied by one-third is the same as 2 pound 10 divided by 3.

And we can use our known factor.

We know 21 divided by 3 is 7, so 2 pound 10 divided by 3 would be 70 P.

For question two, you had to represent problems as a bar model and form an equation to solve.

"So Lucas and Izzy both save their pocket money.

Lucas saves double the amount," and that is 64 pounds.

And then we can see that Izzy has half that amount.

So we're multiplying 64 by one-half, which is the same as dividing by two or finding half, which is 32 pounds.

So Izzy has saved 32 pounds.

For part B, it was the question about Izzy and Lucas going shopping.

Izzy spends 12 pound 32, Lucas spends one-quarter time.

So we know that's going to be less.

So I can see in my bar model I've represented the whole amount is 12 pound 32, and Lucas spends one-quarter times the amount.

So we know we have to divide our bar into four equal parts.

So we know we are then multiplying by one quarter.

12 divided by 4 is 3 pounds, and then the 32 pence, or 0 pounds 32 divided by 4 is 8 pence.

Recombine those, we get 3 pounds and 8 pence.

So Lucas must spend 3 pound and 8 pence.

But the question also wanted us to know how much more does Izzy spend? So that is an additive relationship.

So Izzy spends that 12 pound 32, subtract 3 pound 08, which is 9 pound 24.

So she spends 9 pound 24 more than Lucas does.

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

Brilliant learning today.

We have deepened our understanding on time intervals and the amounts of money that can be compared using knowledge of multiplicative relationships.

We know we can use the stem sentence, "The mm is mm times the time, money, or amount of the mm." And this "can be used to compare and describe these measures." We know that "we can represent comparisons of measure as a multiplication or division equation." So really well done, really impressed with the progress that you have made today.

And I look forward to learning with you again soon.