Lesson video

Hello guys and welcome to our next lesson where we're going to be using bar modelling to represent multiplication and division this time.

Now we've worked with addition and subtraction but today we're going to be working on multiplication and division, so let's start.

So, our lesson agenda.

Reviewing multiplicative bar models.

We're going to be matching bar models to the problems which will prepare you for your independent task and then when you're finish, you come back to the slide, so we can go through the answers together.

You will need a pencil and a ruler, a rubber and an exercise book to do your wonderful work in.

So let's begin.

I want you to have a look at these four bar models that represent division and multiplication.

What can you tell me about them? What do you know? What do you not know? What do you think we need to do? Let's have a look at them together.

So the first one, we know that there are four equal parts.

So we have one, two, three, four, four equal parts.

Each part has a value of 12, good, the whole is unknown, that's something that we don't know.

What do you need to do to get to the whole? Well, what do you need to multiply the value of each part by the number of parts to get the whole.

So that's one part, and we need to multiply it by the number of parts.

How many are there? One, two, three, four, so it's 12.

12, 12, 12.

Instead of going 12 plus 12 plus 12 plus 12, we're going to multiply.

We're going to be confident with our four times tables and that should be four times 12 is equal to 48.

So our whole would be 48.

Good, let's go to the next one.

Okay, so having a look at this one, what do we know? Well, we know that the whole is 12, okay? We also know that there are three equal parts that make the whole but one thing that we don't know is the value of each part.

So the value of each part is unknown.

How do we get that then? How do we work that one out? Well, you need to divide the whole by the number of parts to find the value of each part, okay? So in that case it'll be 12 divided by one, two, three which will give you four.

How do I know that? Well, if I know that four times three is equal to 12, then I know that 12 divided by three is equal to four and that's me using my derived facts to get to my answers.

Let's go to the next one guys.

Okay, this one looks a little bit more different.

Let's find out, what do we know? Well, the value of one part is 12.

That's something that we do know.

Well, we know the value of other parts are unknown but it is three times bigger than 12.

So how do I know that we need to multiply by three? Well, because this arrow is pointing to us saying in order to get one part, we need to divide it by three but in order to get the whole, we need to multiply it by three because the inverse of division is multiplication.

Right, we also don't know what the whole is, the whole is unknown.

So how do we get there? Well, you need to multiply the value of the one part by three to find the whole.

So it'll be 12 times by three which is equal to 36.

Right, let's go to the next one.

Okay, slightly different as well.

What do we know? Well, we know that the value of one part is equal to two.

The value of the other parts are unknown, however, we know it's 10 times bigger than two because it says it here, from here to there, okay? It's going to be 10 times bigger.

So the whole is unknown, as we know, but in order to get to the whole what do we need to do? Well, we need to multiply the value of the one part by 10 to find the whole.

In this case, two times by 10 which is equal to 20.

Good work guys.

It's time for you guys to have a go.

So, we have our bar model here, I'd like you to match the bar model with the statements underneath.

You get to pause and then come back to me when you've got your answer.

Okay, let's find out, so your answer should have been, option number two.

Why? Well, let's check.

The whole is 15, is that true? Absolutely, there are three equal parts, one, two, three, good.

The value of each part is unknown, absolutely and what do you need to do to get one part? Well, you need to divide the whole by three and that's something that we've learned, okay? So normally if we have the whole and we want to find out a part, then we need to divide.

If we have a part and we need to find out the whole, then normally we need to multiply.

Right, let's go into matching bar models to their problem.

So let's read it first.

Mr. Slade gave a bag of miniature eggs each to Addy, Melvin and Buttons.

Now Addy, Melvin and Buttons, if there were 50 grammes of eggs in each bag, what was the total mass of the eggs? Okay, so what do we know? Well, we know that there are three people, okay? And we know that they're given an equal amount of 50 grammes.

Right, what do we not know? Well, we don't know the total mass.

So, the total mass would be the whole in this case, okay? And looking at these three, the only one that we don't know the whole to is this one.

Just to make sure though, we need to ask ourselves these questions, are we scaling up a value to find a new value? Is a quantity being shared out equally? Is the quantity being split into equal groups? Is there a whole with equal parts? Well, in this case, our quantities being shared out equally, the quantity is something that we don't know but we know is being shared out equally into three parts.

Therefore, the answer should be that one right there.

Okay, time for you guys to have a go.

So Addy and Melvin measured the mass of their tomatoes.

Addy's tomatoes weighed 60 grammes, Melvin's tomato weighed three times as much.

How heavy was Melvin's Tomato? Well, what do we know? We know that Addy's tomato weighed 60 grammes and we know that Melvin's tomato weighed three times as much, okay? So if it's three times, then we're looking at three equal parts.

What is unknown? Well, we don't know the weight of Melvin's tomato.

So, again, we don't know the whole in this case, okay? But we do the parts is equal to 60 grammes and we know that there are three equal parts.

So having a look at our options, we've either option one or option two.

So, think about those questions.

Are we scaling up a value to find a new value? Is the quantity being shared out equally? Is the quantity being split into equal groups? Is there a whole with equal parts? Well in this case I think we are scaling up to find a new value because we know that one part is equal to 60 and we know that it's three times as heavy, so we timesing it by three, so we're scaling it up to find our whole.

So in this case, it'd be 60 multiplied by three which should give us 180 and that is the one.

Okay, let's move on to the next one.

So Buttons measured how much his sunflower grew in three weeks.

In total, it grew 60 centimetres taller.

If it grew the same amount each week, how much did it grow in one week? All right, so what do we know? Always ask ourselves that.

Well, we know that this was over the space of three weeks, okay? So three equal parts 'cause in each week it grew by 60 centimetres and what do we not know? Well, we don't know the value of the one week, okay? So we need to ask ourselves these questions.

Are we scaling up? Is the quantity being shared out equally? Is the quantity being split into equal groups? Is there a whole with equal parts? All right, so, we know that in total it grew 60 centimetres, that means that our whole is 60 centimetres, okay? We know that it was spaced over three weeks, so there should be three equal parts and we want to find out one week.

So, therefore, our quantity is being split into equal groups and in that case, you are looking at this bar model here.

Why? Because 60 centimetres is our whole, it's being split over three weeks to find out what the one value is.

So in that case it'd be 60 divided by three.

Well, I know that six divided by three is equal to two, so therefore 60 divided by three is equal to 20.

It's your turn guys.

Let's find out.

So Mr. Slater kept a record of the amount of water drunk by the class gerbil.

Every day it drank about 60 millilitres of water.

How much did it drink in three days? I'd like you to pause the video and to complete the question in your book and then come back to find the answer.

Good luck.

Okay, we're back.

So, the answer is, ah, boom, option number three.

Let's find out how we got to the answer.

So Mr. Slater kept a record of the amount of water drunk by the class gerbil.

Every day it drank about 60 millilitres of water.

How much did it drink in three days? Well, what do we know? We know that he drank about 60 millilitres of water every day, okay? And it was over three days.

So we know that there are three equal parts and each part is equal to 60.

What do we not know? Well, we don't know how much it was in total.

We don't know our whole, okay? So, thinking about the questions that we're asking ourselves, I think that it has to go with this bar model right here because we know there is three equal parts, we know that one part is equal to 60 and we don't know our whole.

So the calculation would be 60 times by three.

Well if I know that six times by three is equal to 18, then I know that 60 times by three is equal to 180.

Right, let's go on to the next part of our lesson, which is the independent task.

All right guys, I feel like you're ready to get on with this work.

You've got to match the word problems with the bar models, okay? So you're going to pause the video now and you're going to go to your worksheets and then you're going to come back to get the answers from me.

I can't wait to see them guys.

All right, here we go.

Answer number one, so Pierre and Alex measured the mass of their potatoes.

Pierre's potato weighed 40 grammes.

Alex's potato weighed three times as much.

How heavy was Alex's potato.

Well, what do we know? Well, we know that Pierre's potato weighed 40 grammes and we know that Alex's potato was three times as much.

So that means that one part is going to equal 40 grammes and we're going to have three equal parts.

Right, what is unknown? Well, let's have a look.

We don't know the value or the weight of Alex's potato.

So that is our whole, okay? So, already looking at our bar model, we know that these two are the ones we're looking at because these are the ones with an unknown whole.

Let's figure out what we're going to be doing, are we scaling up? Is the quantity being shared out equally or is it being split into equal groups? Or is there a whole with equal parts? Well, in this case, we are going to be scaling up a value to find a new value because we know that one potato is equal to 40 grammes or Pierre's potato's 40 grammes and Alex is three times bigger, so in that case, we are going to be looking at this bar model.

One potato's 40 grammes, and then we're timesing* by three to get our whole.

Well done.

If it doesn't look like mine, fix it now.

Let's go to the next one.

Okay, Ant kept a record of the amount of water drunk by Dec.

Every day Dec drank about 30 millilitres of water.

How much did it drink in four days? Okay, let's figure this one out then.

So what do we know? We know that Dec drank about 30 millilitres of water and we know that he drank it over four days.

So we know there are four equal parts and in each part is equal to 30 millilitres.

What do we not know? Well, we don't know how much it was in total.

So I know that there's a whole in four equal parts and each one's equal to 30.

Therefore we are looking at this bar model here, okay? So unknown whole, four equal parts representing four days and the 30 millilitres of water drank in every day.

So our calculation would be 30 multiplied by four and if I know four times three is equal to 12, then four times 30 is equal to 120.

Right, let's move on to the next one.

Okay, Jack measured how much his sunflower grew in five weeks.

In total, it grew 50 centimetres taller.

If it grew the same amount each week, how much did it grow in one week? Well, let's have a look.

What do we know? We know that in total it grew 50 centimetres taller and we knew that it grew the same amount each week, okay? So what we need to figure out is, is how much it grew in one week.

So we know our whole, we know our whole is equal to 50 centimetres and we know that we have five equal parts.

So what is unknown? Well, we don't know what our one part is, what our one week is, okay? So in that case, I'm looking at my bar models and I'm thinking to myself, okay, well, only one is where the whole is known, okay? And where the part is unknown.

So in that case, the bar model that I should be choosing is this one because the total is 50 centimetres, okay? And we know that it grew the same amount over five weeks of five equal parts and we need to figure out one week.

So that'll be 50 divided by five.

Well, if I know five times 10 is equal to 50, then that means that 50 divided by five is equal to 10.

So that means that every week it grew 10 centimetres.

All right guys, if it doesn't look like mine, fix it now.

It's been fantastic work today.

I hope that you have now getting into the hang of now working with word problems that include multiplication and division.

Now what we have learned is, is that when you have got the whole and you need to find the part, you normally have to divide and if you have the part and you need to find the whole, then normally you need to multiply by the number of equal parts.

I hope you have a really good day with your learning and I hope to see you guys soon.