Lesson video

Hello.

My name is Miss Sew and today I'm going to be teaching you maths.

How are you doing? I hope you're doing really well and that you're ready to join in with representing two digit by two digit multiplication.

Make sure you're in a comfortable space and let's get ready to learn.

Welcome to today's maths lesson.

We are representing two digit by two digit multiplication.

To represent our multiplication, we'll be using dienes and an area model.

We'll also link this to a formal risk method known as long multiplication later in this lesson.

You might be familiar with some of these strategies and have used them before in previous maths lessons.

If not, don't worry, because I'm going to show you today.

To start with you will need a pencil and some paper.

That's really important for today's lesson because you're going to be doing lots of working out with me.

If you don't have them pause the video and go get them now.

Now that you have all your equipment, make sure you're in a calm, quiet space so that you can focus on your learning.

If you have any apps running, please turn off notifications so that you don't get distracted during this lesson.

To start with, we're going to look at pictorial representations.

Those are pictures to help us.

Then we'll look at our area method.

Then we will link both of these methods to our formal written method and at the end, we'll have time for an independent task and a quiz.

To start with, let's look at dienes.

Dienes, help us represent numbers.

This blue square represents 100.

This green stick represents 10 and this yellow cube represents one.

You might have seen these in other maths lessons and we will be using them today to help us understand and represent long multiplication.

To start with, let's look at this image.

What could this image represent and how do you know? Hmm.

I'm going to start by looking at the dienes vertically.

So that's from top to bottom.

I can see that I have one, two, three, four, five, six, seven, eight, nine, 10.

In every hundred square, I know that one edge will be worth 10.

So this is worth 10, 20, 30, 31 and 32.

So there are 32 dienes down this edge.

Let's look horizontally, left to right.

If I look at the top, I can see once again if I count in my tens 10, 20, 30, 31, 32, 33, 34, 35.

So from looking at just the individual row across the top and across the side, this represents 35 across the horizontal and 32 across the vertical.

Let's look a bit more closely now at the dienes themselves.

If I've got a hundred here, let's count all the hundred squares.

Count with me.

100, 200, 300, 400, 500, 600, 700, 800, 900.

There's 900 across all of our hundred squares.

Let's have a look at some of the other parts of our image.

Pause, and write down what you can see.

Okay, let's have a look.

I have got 150 in tens.

I've got 60 in tens and I've got 10 in ones.

Hmm.

I wonder what this could represent altogether.

If I have 35 along the horizontal and 32 along the vertical then I know that this could represent 35 multiplied by 32.

Let's have a look now at our area model.

We had a look at our pictorial representation of dienes down here, and I have converted it into an area model.

An area model is a simpler way of looking at the same representation and we can use this to help us multiply.

If I know that three multiplied by three is equal to nine, then I know 30 multiplied by 30 is equal to 900 and I have 900 represented in my dienes.

If I add up all these digits, then I can find out the value of 35 multiplied by 32.

Let's start with 900.

Now, if I know that five multiplied by three is 15, then five multiplied by 30 is 150, which is represented by my 10 sticks here.

30 multiplied by two is equal to 60 represented by my 10 sticks here, and then five multiplied by two is equal to 10.

If I add these all up, I can know the answer to 35 multiplied by 32.

The answer is 1,120.

So I could either count all of my dienes here or add up my numbers in my area model.

Let's have a look at converting what we've learned in our area model now to our formal written method.

I'm going to start by writing the equation 35 multiplied by 32 at the top.

Two multiplied by five is equal to 10.

I'm going to put the zero here and the 10 in the tens column.

I have 10 represented in my area model down here.

Next I'm going to do two multiplied by three.

Two multiplied by three is equal to six but this is actually two multiplied by three tens.

Two multiplied by three tens is actually equal to 60 and I have this represented in my area model down here.

I'm going to add the extra 10, which is seven tens.

I have multiplied my five and 30 by two.

And next I'm going to multiply by 30.

If I'm multiplying by 30 I need to add a placeholder.

If I add this placeholder it means I am now multiplying in my tens and not just my ones.

If I multiply three by five, or really what I'm multiplying is 30 by five the answer is 150.

I can put my five tens in my tens column because my placeholder is here, and I'm going to put my 100 in the hundreds column.

Next I'm going to do three multiplied by three.

Really this is 30 multiplied by 30, which we know is 900 and I'm going to add the extra hundred here which is 1000.

I now have 1050, which is 30 multiplied by 35.

I can add these both together to find out the total.

Zero add zero is zero, seven and five is 12, I'm going to regroup and put the two underneath the tens, and the one in the hundreds.

I add my 100 here and my thousand.

The answer is 1,120.

This answer is the same as the answer I worked out in my earlier methods.

So all of these methods that I've shown you, pictorial representation of dienes, area model and formal written method, can all be used to solve the same equation.

Take a look at this new pictorial representation of dienes.

What would our equation be here? Look really carefully at just each individual row or column of dienes.

Pause video and write the equation down.

Let's look at the answers.

Here I have 10, 20, one, two, three, four, I've got 24 in my column and I have 10, 20, 30, 40, 41, two, three, four, five, six, seven, 47 across my rows.

The equation would be 24 multiplied by 47.

How could we work out the answer? One of the ways we could solve the answer is by counting all of the dienes.

Now I think that wouldn't be a very efficient strategy.

It would take us a long time.

So let's look at one of our other methods to help us.

I want you to draw and label your area model.

We are multiplying 47 by 24.

How do I partition 47 multiplied by 24 into my area model? I've helped you by starting to draw it here, can you fill in the grey boxes and tell me what I'd be multiplying in each part of the area model.

To help you I'm going to put the pictorial representation here for you to look at.

Okay, let's look at the answers now.

I could partition 24 into 20 and four, and I can put partition 47 into 40 and seven.

Now that I've partitioned and labelled my area model, I'm ready to start solving my equation.

Now, I have to work out what the value of each part of my area model is.

I have my dienes representation here and my area model here.

Let's take a look together to start with.

I need to multiply 40 by four.

I also need to multiply seven by four.

I also need to multiply 40 multiplied by 20 and seven multiplied by 20.

Using your known facts to help you, I want you to solve each of these equations and put them into your area model.

Remember our known facts such as four multiplied by four can help you solve 40 multiplied by four.

Pause the video and off you go.

Okay, let's look at the answers.

To start with, if I know four multiplied by four is equal to 16, then I know 40 multiplied by four is equal to 160.

Seven multiplied by four is equal to 28, and if I know two multiplied by four is equal to eight then I know 20 multiplied by 40 is equal to 800.

If I know seven multiplied by two is equal to 14, then seven multiplied by 20 is equal to 140.

Now I have all the values of my area model calculated ready for me to add up.

Now, we're going to calculate the answer to 47 multiplied by 24, by adding up the part.

Add up all the parts of your area model to find the answer.

Pause the video and off you go.

Okay, let's look at the answer.

160 add 28 is 188.

800 add 140 is 940, and if we add those together, 940 add 188 is equal to 1,128.

We've solved this equation by using our area model to help us.

Now that we've used our area model, let's look to see if we can use our formal written method.

That was the method I showed you earlier.

If you think you can do this on your own, pause the video now and have a go.

Otherwise, I want you to join in with me, write down what I write down, pause the video in between each step to catch up with me.

Okay, let's start together.

First, four multiplied by seven is equal to 28.

I'm going to put the eight in my ones column, and I'm going to put my two from my tens, in my tens column.

And I have that represented here.

I wrote my two really small so that I know I have to add this on when I'm regrouping.

Next I'm going to do four multiplied by 40.

That is equal to 160, but I have to add my two tens here, which makes it 180.

I'm going to put my eight in my tens column and my hundred in my hundreds column.

Now I've multiplied 47 by four.

I've finished this part of the area model.

Next, I'm going to multiply by 20.

Because I'm multiplying by 20, I need to add a placeholder.

This is very important.

If we forget our place holder, then we would be multiplying by two, but we're multiplying by 20.

I need to move my digits over one place value house, so I am calculating in my tens.

So, 20 multiplied by seven is equal to 140.

And I have this written here.

I'm going to put the four in my tens column and then I'm going to regroup my 100 and put it in my hundreds column, ready to add on.

Two multiplied by four is equal to eight.

So 20 multiplied by 40 is equal to 800, plus this extra hundred I regrouped is 900.

And I'm going to add up both of these sets of numbers to find the answer.

Eight add zero is eight.

Eight add four is equal to 12.

I'm going to regroup the one and put it in the hundreds column.

Nine add one add one is equal to 11, the answer is 1,128.

This is the same answer as earlier, but which method did you think was faster or more efficient for you? For me, I found the formal written method the quickest method.

You might have found some of the other methods easier to use.

You can choose which strategy you use for this lesson.

Now it's time for a quick quiz, which area model represents 45 multiplied by 37? Area model A, or area model B? It's area model A.

Area model A represents 45 multiplied by 37.

This area model represents nine multiplied by nine.

Which area model represents 24 multiplied by 56? Area model A, or area model B? Area model A represents 26 multiplied by 54.

This is not the same as 24 multiplied by 56.

Area model B is the correct answer because area model B shows 24, two tens and four ones, multiplied by 56, five tens and six ones.

Which area model represents 16 multiplied by 84? Area model A represents 16 multiplied by 84.

Area model B represents 64 multiplied by 14.

This is not the same.

Pause the video to complete your task.

Draw an area model of 23 multiplied by 43.

Time to show you the answer.

23 multiplied by 43 would look like this.

I would partition my 23 in two 20 and three and my 43 into 40 and three.

We're going to have a go solving this equation, using our formal written method again.

Pause the video and solve the equation yourself using the formal written method of long multiplication.

Let me show you how I solve this.

Three multiplied by three is equal to nine.

I can put this into my area model as well.

Three multiplied by four is equal to 12.

Or three multiplied by 40 is equal to 120.

I've put this in my area model too.

I need to add my placeholder as I'm now multiplying by 20 and not by two.

20 multiplied by three is equal to 60 and 20 multiplied by 40 is equal to 800.

I now need to add these numbers up.

Nine add zero is nine.

Two add six is equal to eight.

One add eight is equal to nine.

The answer is 989.

Great work joining in with all the equations.

Now it's your turn to draw an area model and have a go checking them using long multiplication.

Pause the video and have a go at both of these equations.

Okay, it's time to show you the answers.

Here are the answers.

Thank you so much for joining in.

It's now time to complete your independent task.

If you're still finding it a little bit tricky, rewind the video and have a go at some of our earlier examples before starting your independent task.

For your independent task, I want you to draw an area model for each of these equations.

Then use the area model to solve each equation.

Here's a support slide, if you need.

I've given you the pictorial representation of dienes to help you.

Well done on finishing your independent work.

It's now time for the answers.

Here are the answers for the independent task.

If you'd like to, please ask your parent or carer to share your work on Twitter tagging at Oak National and hashtag learn with Oak.

Thank you so much for joining of your maths lesson all the way to the end.

You've done an amazing job joining in with any of the tasks and quizzes, and it's now time to finish your final quiz.

So click onto the next page and complete your quiz for the end of this lesson.

Have a fantastic day learning and I'll see you for another maths lesson.

Bye.