Lesson video

Hello, everyone.

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

Today's lesson, we'll be looking at part of our unit in multiplication and division, and today's objective is to create bar models that can be used to represent multiplication and division.

For this lesson, you'll need a pencil, some paper, and some counters.

The counters could be Lego, could be pieces of fruit, or you can Google interactive counters.

You don't need any more than 20.

Please pause the video now to go and get these things if you haven't got them already.

Okay, I thought I'd start today with a little hello! And what's an insect's favourite sport? Have a think.

What's an insect's favourite sport? It is in fact cricket.

On that note, let's have a look at our agenda for the lesson.

So, today we're going to be learning how to create bar models that can be used to represent multiplication and division.

So, we'll start with a quiz to test your knowledge.

Then we'll look at today's star words.

Then we're going to be looking at arrays and bar models and how they can help us.

Then it'll be time for your talk task.

Then we're going to be developing our understanding of bar models and how we can create them.

And finally, there'll be a quiz to see what you've remembered.

Please pause the video now to complete your starter quiz.

Okay, then.

Let's get started with today's star words.

We'll do them using my turn, your turn.

So, array, bar model, multiplication, equal parts, division, whole, groups of.

Brilliant! Let's have a look then, at today's new learning.

So, we've got here an array.

And our question says, what equations can you write for this array? So, I want you to have five seconds thinking time.

What is this array showing us? And what equations could we write from this array? Thinking about multiplication and division equations.

Okay, let's have a look then.

So, we could start off by saying that we have three times by two equal six.

So here, we have one, two, three rows, and we have two in each one.

So, you could say three times by two is equal to six, or we could say two, so we have one, two, and we have it one, two, three times.

So, we could say two times by three is equal to six.

Those give us our multiplication equations.

Our division equations then.

We could say, because we know the whole from looking here, our product, our whole is six.

We could say six has been split into three.

One, two, three.

And each box has two, so we could say six divided by three is equal to two, or we could say six has been grouped into twos.

One, two, one, two, one, two.

And we have three of them.

We've got one group here, two groups here, three groups here.

So, we could say six divided by two is equal to three.

There's four different equations that we can make using this array, using multiplication and division.

Okay.

What we're going to do now is we're going to use the same array that we've just looked at, but we're going to alter it to create a bar model.

So, let's have a look at my bar model.

And what I've done here is I've taken each part from my array, and I've stretched it out and I've put them next to each other, rather than down.

So, we can still see that we have one, two, three parts.

Each of these parts has a value of two.

We've got one, two here, one, two here, one, two here.

That means in total, we have a value of six because we know that three times by two is equal to six.

The same array and bar model is showing the same problem, the same equation.

We've just discussed parts of this, but we're going to go through these questions.

So, how many parts are there? We look at this bar model, we can see there's one, two, three parts.

We can see that the value of each part, so what each part is worth, each part of it, so that that jump there is worth two, another jump here is worth two, and another jump here is worth two.

So, if we wanted to work out the whole and we didn't have this number here, we could skip count in our twos to work it out.

Join in with me.

Two, four, six.

That gives me my whole here, and I know that that bar model represents six there.

So, my equation could be three multiply by two is equal to six.

Okay, we're going to look at another example now.

So, we've got a different array to the array we've just been looking at.

I want you to have a look and have a think about what equations we could write for this array.

Pause and give yourself five seconds thinking time.

Equations, multiplication and division, that we could write for this array.

Okay, let's have a look then.

We could say we have three groups of five.

We have one, two, three, four, five here, and each of them is worth three.

Or we could say we have five groups of three.

We've got one, two, three here, and we've got it one, two, three, four, five times.

Now, I know that three times five or five times three is going to give me 15.

If I wasn't sure, I could skip count in my threes.

So, I could say three, six, nine, 12, 15.

That would help me to work out the answer.

Then, I could use my knowledge of the product to know that that's the whole, and I could look at the division equations that it could give me.

So, if I had to say 15 was divided by, into threes, I have them one, two, three, four, five times.

And if I had to say 15 was divided into five groups, each group is worth three because there's three in each group, and there's one, two, three, four, five groups.

So, these are the four equations that I could make using this array.

Now, just like before, we're going to use this array to create a bar model, so it's the same array that we've just looked at.

I'm going to use it to create our bar model.

Now, I want you to have a think, what is the same and what is different about the array and the bar model? Okay, it's showing the same equation, so that's the same.

We've got the three dots in each part, which is the same.

But it's different because in our array, we have that going down here, but in our bar model, we are now stretching it out to show it as a bar model.

So, this time when we're looking at our bar model, we're going to answer those same questions.

How many parts are there? Well, there's one, two, three, four, five parts.

Each part is worth three because I can see there's three dots in each part.

I've also labelled it with three.

My whole, if my 15 wasn't here, I could work that out using skip counting in my threes.

Ready? Three, six, nine, 12, 15.

So, my whole would be 15.

So, my new equation would be five times by three, 'cause I've got five groups of three, is equal to 15.

The same equations that we found from this array here, we can use our bar model to help us solve.

Right then, it's now time for your talk task today.

Using the arrays below, can we make them into bar models and work out the answer to the equations? Remember, you can use your counters to help you.

Going to really quickly show you what I mean by that.

So, if I can just show you here.

I've gathered myself some, sorry, some little blocks that I could use as counters.

So, I could, if I wanted to, put them into an array by holding them like this.

If I wanted to show that array as a bar model, I then have to split it and make it so that it shows lengthways like this.

So, you can use your counters or your Lego blocks or some fruits like some raisins or some blueberries at home to do the same thing, okay? So, using those arrays, you've got two equations here, two questions here, I should say, sorry.

The first one says there are three bags of sweets with three sweets in each bag.

How many sweets are there altogether? The second one says there are three school bags each with five books in them.

How many books are there altogether? My challenge for you today is can you label your bar model with the whole and the parts like we've just done together.

Please pause the video now to have a go at today's talk task.

Okay, welcome back.

What we're going to do is we're going to look at the talk task today, and we're going to have a bit of a discussion based on the two different questions.

So, the first question was there are three bags of sweets with three sweets in each bag.

How many sweets are there altogether? So, here are my bags of sweets.

Imagine this is one bag of sweets with three in it.

This is another bag of sweets with three in it.

And this is another bag of sweets with three in it.

Now, I need to make that into a bar model, so I've done just what we've been doing before, and I've almost stretched it out.

I put them next to each other.

So, I've got one bag of sweets here, two bags of sweets here, and three bags of sweets here to create my bar model.

Now, each of these parts I have to label.

Each of them is worth one, two, three, so I can label them with three.

I know that if I skip count in my threes, I can say three, six, nine, so I know my whole is worth nine.

So, I've not only drawn my bar model here, but I've also labelled it with my parts, so my threes here, and my whole, which is nine here.

So, have a look then at the second example from our talk task today.

There are three school bags.

Each of them have five books in them.

So here, we can imagine this is one bag, there's one, two, three, four, five books in it.

This is another bag with five books in it.

And this is my final bag with five books in it.

How many books are there altogether? So, to do this, I've rotated them so that I can see clearly here, this is one bag, this is another bag, and this is another bag, and make my bar model.

Can I label that bar model with the whole and the parts? Let's have a look then.

I know I've got one, two, three parts.

You see that with my jumps here, and each jump is worth one, two, three, four, five.

There's five, the value of five for each of my parts.

Now, I know that if I skip count in my fives three times, join in with me, five, 10, 15, that my whole is worth 15.

This time, I want you to have a look at what is different about this bar model here? Have a think.

What's different about this bar model here? Let's see, how many does it represent? One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15.

Oh! So, it represents 15, and there's one, two, three, four, there's five parts, and in each part, there is three.

Can I use that bar model to represent this equation? What do you think? No, I can't.

Now, the reason that I can't use that is because my equation says clearly, my question, sorry, says clearly there's three school bags with five books in each one of them.

Here, I have one, two, three, four, five bags with three in each one of them.

So, although I can use the three and the five to work out the same answer, this bar model doesn't represent this equation, so I can't use it.

You can see here, each one is worth three, so I could do three, six, nine, 12, 15.

So, my total is the same, but it doesn't represent this question here.

This bar model represents this question.

Okay then.

Now we're going to develop our learning.

So, there are three people sitting at each table and there are six tables.

How many people are there altogether? So, what we're going to do is create an array and then create a bar model to show this problem.

So firstly, here's our array.

Each of these blocks, I guess you could call them, as part of our array represents a table.

So, we have one, two, three, four, five, six of them.

And we know that at each table, as we can see here, there's three people sitting at it.

So, within our block, we can see one, two, three.

So, I can use that to show this problem.

Now, I'm going to use this array to help me to create my bar model.

So, here I've got one block, one part, which is worth three.

How many parts do you think I need altogether to my bar model? Well done, I'm going to need six so let's keep counting.

Two, three, four, five, six.

So, I've got my bar model here.

I can show that and label it by labelling in my jumps and to show each part is worth three.

So, if I had to skip count up in my threes, I would skip count three, six, nine, 12, 15, 18.

So, I put my whole in here, and it's 18.

So, I know my answer to my problem.

There are 18 people altogether.

I've represented it in two different ways.

Next then.

There are six cows in one field.

How many legs do the cows have altogether? Now, each of these represents a cow.

One, two, three, four, five, six of them.

And my question says, how many legs do the cows have altogether? Now, I know a cow has four legs.

So, here in my array, I've put four dots.

So, each dot represents a leg of a cow.

And I can use that array to represent this equation.

Now, I'm going to use this array to help me to represent it using a bar model.

So, here we've got one cow with its four legs here.

The dots representing each leg.

How many of these blocks do I need to draw to get my bar model? Well done, I need to draw six of them.

So, I've got one, two, three, four, five, six.

So now, I have six there that's showing in my bar model.

Now, I know I've got six parts, each with a value of four, because I've got six cows, each with four legs.

So, I'm going to skip count in my fours up to double-check that my whole is correct.

Join in with me, ready? Four, eight, 12, 16, 20, 24.

So, my whole is 24.

I want you to have a quick look.

What is the same and what is different between this bar model here and this bar model here? You've got five seconds thinking time.

Okay.

You probably noticed the things that are the same first, so I can see I've got one, two, three, four, five, six blocks here, and I've got six blocks at the top.

I've got my jumps of four at the top, and I've got my 24 at the bottom on both of them.

What's different then? The difference is within this first bar model, I've shown the value of each of the parts using the dots from my array.

Here, I haven't.

I've shown it just by writing four down here.

You can imagine four dots here because that's the value of this part, and the same for this part, and this part, and this part, and this part, and this part, but we don't have to show them with our dots if we've got them written at the top with our value, okay? So, what we're going to do next is look at one example where we're going to look at the array, but then we're going to look at bar model without the dots from our array.

A bar model that looks more empty like this bar model.

Okay.

So, we've got four people sitting in each row of a plane.

Here they are, our four people.

There are seven rows in our plane.

How many people are on the plane? So imagine, this is our plane here.

Here are our seven rows.

One, two, three, four, five, six, seven.

And within each row we have one, two, three, four.

Absolutely represents the four people here, represents our seven rows in our plane.

Our array we're happy with.

Let's have a look then, at how we can use this array to create a bar model.

Now, you'll notice here in my bar model, I don't have any of my four marked in, but I do have my fours labelled at the top.

I can imagine I've got four people dotted in here, but I don't have to because that number does that job for me.

So, I'm going to use this bar model to skip count in our fours and double-check we're happy with this number here, the whole.

So, join in with me, ready? Four, eight, 12, 16, 20, 24, 28.

So, my answer would be 28.

Right then, it's now time for you to do today's independent task.

So, your independent task today is to create a bar model before solving the following problems. Remember, you can use the arrays to help you draw your bar models.

So, I've drawn in there those arrays for you to help you.

Read through the questions.

There's two different pages so there's four questions with the arrays all drawn in for you, and then we'll go through the answers together.

Please pause the video now to complete your task.

Okay, we're going to go through the answers then.

So, let's have a look here.

We have got the first equation.

Nigel is baking and needs four eggs to bake a cake.

How many eggs will he need to bake six cakes? So, we can imagine here, each of these is the eggs that he needs, so that's one cake, two cakes, three cakes, four cakes, five cakes, six cakes.

Our equation would be four multiplied by six is equal to 24.

And our bar model would look like this, but it would be all stretched out, so there would be six parts each with a value of four, the whole would be 24.

Next then.

There are three bags of apples with four apples in each bag.

Imagine here, this is bag one, two, three.

Each of them has four in them.

How many apples are there altogether? So, if we did this as a bar model, we'd stretch it out, there would be three parts, each with a value of four.

In total, we could do three multiply it by four, which would equal 12.

Next then, we have five children sitting at a table.

How many children are sitting at six tables? So here, we've got one, two, three, four, five children at a table, and we have one, two, three, four, five, six tables.

We're going to do five multiply by six is equal to 30.

My bar model would look very similar to this, but each of these tables would be stretched out, and I would have six jumps, each worth a value of five.

Last question, then.

There are 20 chips on a plate.

Eva and Ryan divided them equally between them.

How many chips did they get? So, here is our array to show us.

We can imagine Eva and Ryan, and there's two of them, isn't there? So, you can imagine that we've split it into twos.

So, we could say one for Eva, one for Ryan, one for Eva, one for Ryan.

For each of them, I would do that 20 times.

So, our equation would be 20 and we've divided it into twos, and it's equal to 10.

If we wanted to show this as a bar model, we'd stretch it all out and show it as 10 jumps of two.

Well done to everyone for working so hard today.

I've been really, really impressed.

Please pause the video now to have a go at the final quiz and answer a few questions based on what we've been learning today.

Thank you very much, and hopefully see you soon.

Bye-bye!.