Lesson video

Hello everyone, I'm Mrs. Crane and welcome to today's lesson.

In today's lesson, we're going to be applying and consolidating using bar models and solving word problems. I'll run through any equipment you'll need in a moment.

So don't worry about that just yet.

How are you today? I hope you're well, and I hope you're ready for some maths work.

If you can, can you please turn off any notifications that you have on your phone, tablet, or whatever device you're using to access today's lesson, and then if you can try and find somewhere nice and quiet in your home, where you're not going to be disturbed during today's lesson.

When you're ready, let's begin.

Okay then, let's run through today's lesson agenda.

So we're going to start off by looking at different representations.

Then we're going to move on to doing some matching with bar models and word problems. Then we're going to be looking more at bar models and word problems before you have a go at your independent tasks, which we'll be using the bar models to solve some equations.

So, before we get started today, please can you get yourselves a pencil and some paper, and if you can get yourself some counters.

Now they could be counters, they could be multi-unit cubes, they could be Lego, they could be pieces of dried pasta, whatever you've got at home will do.

Please pause your video now to go get those things, if you haven't got them already.

Okay then, let's get started.

So we're going to be thinking about different representations to begin with.

So in order to do that, let's have a look at the following.

I'm just going to move myself here a second, because what we're going to do is consider what's the same and what's different.

Now I can hide that and I can show you here.

What I want you to do is having it really carefully and the different bar models and the equations that you can see both sides of me.

Pause your video now to have a really good look at what you can see.

Can you spot something that's the same? Have you spotted something that's different? Okay, I'm going to go through what I can see.

Now, so I've spotted here.

I've got my first bar model, my whole is eight.

My second bar model, my whole 16.

My third bar model, my whole is 32.

And I can see each time I've times four either by two, by four, by six.

Not six, sorry.

By eight.

Notice, double eight is 16.

So I'm using the word double in my explanation.

Double eight is 16.

Double 16 is 32.

What do you notice within our equation then? Cause our answer has been doubled each time.

So let's see.

Four stayed the same each time.

And then it's been timesed by two.

Two has been doubled to four.

Four has been doubled to eight.

So you can see here, the form remains the same.

So our bars are split into four, but what each part represents has been doubled each time and when it's doubled so is that answer.

Did you spot something different on this side? Let's have a look.

Well this time, four has been timesed by three.

So you can see here that each of these bars represents four and it's been timesed one, two, three, no sorry.

Each of these bars represents three.

It's been timesed one, two, three, four times.

So here you can see our whole is 12 Here you can see our whole is 24.

What do you know about the numbers 12 and 24? I know that doubled 12 is 24.

Let's have a look then.

Three and six.

What do you know about the word.

The word? The numbers three and six? I know that double three is six.

So notice here that when one of our parts has been doubled, our whole has also been doubled by two.

Okay, I'm just going to hide myself for a moment, so you can see this part here.

So what I want you to do for this part is we're going to think about which representations show three times four is equal to 12.

Pause the video now to decide which of these representations accurately shows three times four is equal to 12.

Then we'll discuss it together.

Okay welcome back.

I'm just going to put myself here for a moment over this part whole model.

We'll come back to that in a moment.

So don't worry too much.

Right, let's start off over here.

We're looking for representations that show three times four is equal to 12.

So here I've got one, two, three.

My row, one, two, three, four times.

Is that showing me three times four equals 12? Absolutely it is.

Okay then, let's have a look at our next array.

One, two, three, four, going one, two, three times.

Is that showing me three times four is equal to 12? It is indeed.

12 here and I've been split into one, two, three boxes.

Each box represents four, so I could skip count.

Four, eight, 12.

Does that represent three times four is equal to 12? It does.

Let's have a look here.

One, two, three, yeah.

One, two, three.

Three and three.

Does that show me three times four is equal to 12? No it doesn't.

That shows me three times three and that equals nine.

So nope, not the right representation.

Right then, here we've got our whole, which is 12.

Yes, I know that.

We've got one, two, three parts.

Yes, and each part is worth four.

Yep, that represents three times four is equal to 12.

Let's see what I'm hiding here then.

Now we have 12 and we have one, two, three, four parts.

Okay, and each part is worth three.

Yeah, so that's equals 12.

Let's count together.

Three, six, nine, 12.

Absolutely.

Going to hide that one again for a moment.

Here we have 12, our whole, that's right.

And we have one, two, three, four, yes.

And four represents three.

So here's three, six, nine, 12.

Yep, that represent three times four is equal to 12.

Let's have a look there.

12 is here and we have one, two, three parts.

And each part is worth three.

Let's skip count together.

Three, six, nine.

Oh no, does that part whole model represent three times four is equal to 12? No, it doesn't.

It represents the wrong answer.

That's three times three is equal to nine.

And last but not least, 12 is our whole, yes.

We have one, two, three, four parts.

Each part is worth four.

Let's skip count together.

Four, eight, 12, 16.

Oh no, that definitely isn't correct, and does not represent three times four is equal to 12.

So you can see here, there's lots of different ways we could show three times four is equal to 12.

There's also lots of different ways that we can inaccurately represent it by putting in the wrong numbers, and the wrong parts, or the wrong whole.

Okay then, what we're going to do next is we're going to move on to writing the equation from a bar model.

So here's my bar model.

What information do we know? Well I know, I know the whole is here and I know there are one, two, three, four, five parts, and each part is worth four.

So I could say four times by five is equal to 20 cause each part is worth four and there's one, two, three, four, five of them.

Now, if I needed to write a division equation here, I need to use my whole here, which is 20, and I'm going to say 20 divided into groups which represent four, and you have five groups of them.

So 20 divided by four is equal to five.

Okay, if you're feeling really confident, I'd like you to have a go at pausing the video now to have a go at doing your multiplication and division based on this bar model.

So I'm going to say three times by five because there's one, two, three, four, five here is equal to 15.

Or I could say 15 because it's my whole, divided by three is also equal to five because are five parts.

Okay then, just going to move myself down for a minute.

What I'd like you to do today is we're going to look at matching, bar models, and word problems. So, just going to hide myself for a moment, so you can clearly see the text.

So one of these two word problems matches this bar model.

And one of these two word problems matches this bar model.

I'll read through the word problems for you and then what I'd like to do is pause the video to decide which is the correct word problem for the bar model.

There are five bananas in each pack, there are four packs.

How many bananas altogether? Or there are four bananas in each pack, there are four packs.

How many bananas altogether? That's part one.

Part two is there are three cookies on each tray.

There are four trays.

How many cookies are there altogether? Or it's there are four cookies on each tray.

There are three trays.

How many cookies are there altogether? Pause the video now to decide which of the questions is the accurate question for this bar model and which of these two questions is the accurate question for this bar model.

Okay then, I'm going to put myself back onto the screen.

I'll move myself in a moment.

So let's have look at which one matches.

So here I can see, I don't know my whole and I don't know my parts, but I do know there's one, two, three, four parts.

So I know that each part can be worth four.

So I'm going to say this word problem here four bananas are in an each pack, that I need to work out because there's equally spaced out which are how many bananas that are altogether.

Now I'm going to move myself to this side so you can do this one.

So here, I'm going to match this equ.

Not equation, sorry.

This question with this bar model.

So there are four cookies on each tray.

So there's four cookies in each tray.

There are three trays.

So here's tray one, two, and three.

How many cookies are there altogether? So I'm going to use this question for this equat.

Not equation, bar model.

I'm getting question, equation, and bar model all muddled up today.

Okay, then we're going to look now at some more bar models and word problems. So what we're going to do is have a go at drawing a bar model to represent a word problem.

So my problem is they where five cars driving to the airport with 15 people altogether.

How many people were in each car? So my drawing is going to be here's my bar model.

Here it represents one, two, three, four, five cars.

Now my whole is 15 and I don't know how many are in each.

So I need to work out how many are in each.

Now we don't have to solve it today, but I have drawn my word.

I've drawn my bar model to represent my word problem out here.

So I know 15 divided by five, one, two, three, four, five is three.

Because if I did five, 10, 15, I've got three.

So there are three people in each car.

If you're feeling super confident, I want you to have a go at drawing the next bar model for me.

So a car holds three people and their luggage.

There are five cars driving to the airport.

How many people will go into the airport? Pause your video if you're feeling confident in what to draw out, if you're not don't worry, let's have a look now.

So here we've got five cars.

One, two, three, four, five.

This time we know that our car holds three people.

We don't know this whole part here, so I can do three, six, nine, 12, 15 to work out my whole here.

Okay then, it's now time for your independent task today, which is using bar models to solve equations.

So what I would like you to do for independent task today is I would like you to solve the word problems using bar models to represent them.

Don't forget that you can use counters to help you.

Is this question one, two, and three.

Pause your video now to complete the task.

Don't forget to resume once you're finished, so we can go through the answers together.

Okay then, I'm going to put myself back on the screen so we can go through our answers together then.

So question one, it takes Tess 10 minutes to walk to school.

It takes Tess twice as long to walk to her friend's house.

How long does it take Tess to walk to her friend's house? So we know that one, her walk to school is 10 minutes.

We know that to get to her friend's house, it's twice as long, which is two times that.

So I can put in two times 10.

Now I know that 20 would be my answer.

So I know that it's going to take Tess 20 minutes to walk to her friend's house.

Which is actually not long.

Okay then, Jack has 12 pencils.

He gave a quarter of them to Kev, his friend.

How many pencils did Jack give to Kev? So I can mark on here that he had 12 pencils in total.

I've marked it in that he gets them split into four.

So I can do 12 divided by four because I know that he gave a quarter of them to Kev.

Now, if I needed to do that, I could roll my fours until I get to 12.

Four, eight, 12.

How many pencils did he give to Kev? Oh, he gave him three cause each part represents three.

And question three, there are 12 passengers sitting at the front of the plane.

There are three times as many people sitting at the back of the plane.

How many people are there sitting at the back of the plane? So I'm going to mark on firstly, 12.

I know there's 12 passengers at the front of the plane.

I know there's three times as many at the back of the plane.

So my equation is going to have to be 12 times by three, because I know that there's three times as many.

So 12 times by three, that sounds a bit tricky, but I know that three times by 10 is 30.

So then I just need two more groups of three, which is six.

30 plus six is 36, so my answer is 36.

So my whole here is 36.

If you'd like to please ask your parent or carer to share your work today on Twitter, by tagging @OakNational and using the #LearnwithOak.

Fantastic work today, you've been absolutely amazing.

I've been so, so impressed.

Well done showing off all of your fantastic knowledge.

And don't forget to go and complete your quiz before you finish today's lesson.

Thank you and see you again soon for some more great maths work.

Bye bye.