Lesson video

Hello, my name is Miss Sew and welcome to today's math lesson.

I'm going to be teaching you maths today and we're going to be multiplying 3-digit by 2-digit numbers using our formal written method of long multiplication.

You've been amazing maths superstars in all your other lessons and I'm so excited to teach you today.

I hope you're feeling really well and let's get started.

Welcome to today's maths lesson.

Today, we are multiplying a 3-digit number by a 2-digit number and we will be using our formal written method of long multiplication.

We will also look to see how dienes can be used to represent these equations and how we can also use an area model as well.

First, we're going to warm up by doing some 2-digit by 2-digit multiplication.

Next, we'll be looking at our pictorial and area method and then we'll be securing our formal written method.

At the end of the lesson, there'll be an independent task and quiz.

For this lesson, you will need a pencil and some paper.

So if you don't have those, pause the video now and go get them.

Now you have all the equipment you need, I want you to just make sure that you are in a calm, quiet space And if you have any apps running on your device, you turn off the notifications so that you can focus during this lesson.

We'll be doing lots of writing today.

So it's really important you're ready with your equipment.

To start with, I want you to get warmed up.

Can you do this 2-digit by 2-digit multiplication? 32 multiplied by 23 using our formal written method, or area method and I'd love it if you could do both.

Before we start, I'm going to give you a clue.

You need to remember your placeholder if we're multiplying by 20, not 2.

Its good to go now Good luck.

Pause the video and off you go.

Let's have a look at the answers.

First 3 multiplied by 2 is equal to 6.

I could put this into my formal written method or my area model here.

Next 3 multiplied by 3 is equal to 9 but this is 3 multiplied by 30 which is equal to 90.

So I'll put my 9 in my tens column Next, I will put in my placeholder, because I'm not multiplying by 2, I'm multiplying by 20.

And I want to make sure that all my digits go into the right place value house.

20 multiplied by 2 is equal to 40.

So I'll put my 4 in my tens column 20 multiplied by 3 by is equal to 600.

And now we need to add these numbers up 6 and 0 is 6 9 and 4 is 13 I will put my 3 in my tens column and regroup my 1 into my hundreds and 6 add my 100 that's been regrouped to the bottom here is equal to 700.

The answer is 736.

Great work.

Today we're doing 3-digit by 2-digit multiplication.

So our 2-digit by 2-digit multiplication really helps us because we are actually using the same strategy and the same methods.

However, when we multiply 3-digits by 2-digits, there's more room for error, it's more likely we'll make mistakes if we are doing more steps in our process.

So it's really important that we feel secure and confident with 2-digit by 2-digit so that we can be successful with our 3-digit by two 3-multiplication.

To start with, these are called dienes This blue square is equal to 100 and represents the value of 100.

This green stick represents 10.

And this yellow key represents 1 you will probably have seen pictures like this in other maths lesson and we are going to use this to help us today.

Firstly, what could this image represent? How do you know? have a look really carefully and think about what this picture below shows you think about what I've just shown you about the value of the dienes Right.

I'm going to show you what I think.

If I look at my vertical column here, each of this is worth 10 1,2,3,4,5,6,7,8,9,10 I can see that there are three groups of 300.

And if I look at just one column, it's worth 10 it's 10, 20 ,30 and then one two, so this entire column is worth 32.

If I look at the horizontal edge of this representation, I can count 10 20 30 40 50 60 70 80 90 100 101, 102, 103, 104, 105 So I have 105, represented across my horizontal edge.

I knew this because I was looking at just one column and one row, and I can see that this represents 105 multiplied by 32.

This image also showed me the value of 105 multiplied by 32.

If I counted all the dienes, all these hundreds, all these tens all these ones, I would know the answer to this equation.

Now even though this does represent the answer, and I can use this to solve the equation, I don't think it's the most efficient strategy.

It's really helpful to understand what the numbers represent.

But I think it'd be really slow counting every single diene.

So I'm going to use my area model instead to help me.

How can I turn this pictorial image of diene into an area model? I want you to pause the video and fill out the box in this area model to help me.

Let's have a look at the answers.

105 can be partitioned into 100 and five and 32 can be partitioned into 30 and two This represents the same values as my dienes pictorial representation.

To solve this equation, I know that 100 multiplied by 30 is 3000.

5 multiplied by 30 is 150.

And 100 multiplied by 2 is 200.

And finally 5 multiplied by 2 is 10.

We've now looked two methods to represent multiplication, we have looked at our dienes pictorial image and we've also looked at our area model.

And now I'm going to make both of these together with our formal written calculation.

Both the pictorial model and our area model are really helpful but I think the formal written method is really efficient when I'm doing 3-digit by 2-digit multiplication.

First, I will start by 2 multiplied by 5 basically put a 10.

Am going to put my zero in my ones column and my 1 in my tens column.

I've now represented 10 in my area model 2 multiply by 0 is 0.

However, if there's 10, I can regroup here and I have 2 multiply by 100 which is 200.

I can put this into my area model here.

Next, I'm going to multiply by 30.

If I multiply my 30 I need my placeholder.

So my placeholder is really important because I'm multiplying by 30.

Not by 3 Now 3 multiply by 5 is equal to 15.

But I'm doing 30 multiply by 5 so its 150 5 goes in my tens column to represent 50.

And my 1 goes into my hundreds column to represent 100.

Like I've put it in my area model here.

Now, 3 multiply by 0 is 0.

Add the 1 I regrouped is 103 multiplied by one is 330, multiplied by 100 is 3000.

So now I can add up both of this numbers to find the total answer.

0 and 0 is 0.

1 and 5 is 6, 2 and 1 is 3 and 3 at the end there the answer is 3,360.

I think this formal written method was probably the quickest way to solve this equation.

If I had counted all these dienes, it would have taken me a long time, especially for numbers over 1000.

And if I'd have done this area model, I have to add off and do lots of steps by the side in my formal written calculation, it's all in one place.

So this is my preferred method.

When I'm doing 3-digit by 2-digit multiplication.

I want you to draw an area model for 24 multiplied by 137.

Pause the video and have a go.

Let's look at the answer.

Here I've partitioned 20 into 20 and 4 and 137 into 130 and 7.

Now I need to solve this equation with my formal written method.

If you know how to do this pause the video and have a go now If you don't know how to do this, that's absolutely fine.

I want you to work together with me.

I'm going to fill out my equation.

So I want you to start and pause the video and do it alongside me together.

So, 4 multiplied by 7 is where I start.

I multiply from my smallest number to my greatest number.

4 multiplied by 7 is equal to 28.

I have in my area model here, I have 8 ones and 2 tens.

4 multiplied by 3 is equal to 12.

So 4 multiplied by 30 is equal to 120 plus the 2 extra tens here, which gives us 140.

I'm going to regroup the 100 into the hundreds column and put the 10 in the tens Column, 4 multiplied by 1 or 4 multiplied by 100 is equal to 400.

Add the extra 100 it's 500.

Next, I need to put in my placeholder, which is very important because I am multiplying by 20, not by 2 20 multiplied by 7 is equal to 140.

My 4 goes in my tens column, my 100 goes in my hundreds column.

If I know 2 multiply by 3 is equal to 6, then I know 20 multiplied by 30 is equal to 600.

Plus the extra 100 here The answer is 700 20 multiplied by 100 is 2000.

So now I'm going to add up all the digits here.

8 add 0 is 8 4 add 4 is eight, 5 add 7 is equal to 12 Am going to regroup into the next column and then 2 add 1 is equal to 3 3,288 Now it's your turn, I've shown you and we've gone through the method together and I want you to have a go now by yourself.

Pause the video and have a go.

Lets have a look at the answers.

6 multiplied by 4 is equal to 24.

My 4 goes here I regroup my 2, 6 multiplied by 3 is equal to 18.

Add the extra 2 is equal to 20 6 multiplied by 4 is equal to 24.

I need to regroup from here and add this on.

To make 26.

Let's look at the next row, and I have to add my placeholder.

3 multiplied by 4 is equal to 12.

I'm going to regroup, 3 multiplied by 3 is equal to 9 plus the extra 1 is 10.

3 multiplied by 4 is equal to 12 plus the extra 1 is 13 and I've shown which numbers I'm multiplying in my area model next to it Now I have to add my numbers up 4 2 6 5 and 1 My answer is 15,624.

Now 15,624 is a huge number and if I represented it with my dienes, it would take up a lot of space.

Using my 3 by 2-digit multiplication method, I'm able to use a much smaller space to solve the same equation Your turn again I want you to solve 612 multiply by 43.

This time I want you to do it just with long multiplication, you don't need to draw the area model.

Have a go and pause your video now.

Lets have a look at the answer.

You should have 6 3 and 18 timesing 612 by 3 And then 0 for our placeholder.

8 4 and 24 for 40 multiplied by 612.

And if we add this together, our answer is 26,326.

Thank you so much for joining in with your math class today.

It's now time for independent tasks and I've got a bit of a problem I want you to solve.

To help you make sure you are feeling really fluent with your long multiplication, we are going to try and hit the target.

Your challenge is to make the number in the pink box.

To do this, you need to choose one number from the orange box and one number from the purple box and multiply them together.

Keep a note of any answer all of your answers, even if they don't reach 20,896 so that we can mark them anyway.

Which two numbers create 20,896 Here are the answers to the independent task.

The two numbers you had to multiply to get 20,896 was 653 multiplied by 32.

If, if you'd like to please ask your parent or carer to share your work on Twitter tagging @OakNational and #learnwithOak Thank you so much for joining in with your math lesson today.

You've been brilliant and trying to learn lots of tricky equations and it's now time to have a go to show what you know by doing the quiz.

Have a wonderful day learning and I'll see you for another math lesson.

Bye.