Lesson video

Hello, I'm Miss Miah and I'm so excited to be a part of your learning journey today.

I hope you enjoy this lesson as much as I do.

In today's lesson, you will be able to multiply a three-digit by a one-digit number using expanded and short multiplication.

These are your keywords.

I'd like you to repeat them after me.

Expanded multiplication.

Short multiplication.

Factors.

Good job.

Let's move on.

So, expanded multiplication is a way of recording the steps of a calculation focusing on partitioning one or more factors and showing the partial products.

Now a way of recording using columns to set out and calculate a multiplication is called short multiplication.

Numbers we can multiply together to get another number are known as factors.

So here in this equation you can see that it's two multiplied by three, which is equal to six.

You can see the factors are two and three.

So for this lesson cycle, you'll be understanding and applying expanded multiplication.

You will also meet Andeep and Izzy.

Let's begin.

Now, you may have seen this type of expanded multiplication.

Today you will explore how to use expanded multiplication when multiplying a three-digit by a one-digit number.

So let's start off with this word problem.

Two laptops cost 322 pounds each.

What is the total cost? Now Andeep's saying that he can use expanded multiplication and Izzy's going to use the base 10 blocks to help her.

What multiplication equation do you think is needed to solve this worded problem? If you got 322 multiplied by 2 or 2 multiplied by 322, you are correct.

Now it can be in any order because multiplication is commutative, which means the answer will always be the same because it doesn't matter which order you're multiplying.

Now, you can record multiplication using expanded multiplication.

This used to be one of my favourite methods, but then of course I came across a more efficient method and we'll talk about that later.

But for now, let's carry on.

So the first thing we have to do is partition 322 into hundreds, tens and ones.

So we can see that it's been done here using the base 10 blocks.

We've got three hundreds, two tens, and two ones.

Now when it comes to expanded multiplication, you must place the largest factor at the top.

Then you place the smallest factor in the ones column.

The smallest factor here is two, and you can see that it's been placed in the ones column.

Now what I want you to take note of is how it's been aligned.

Now, this is super important that you align your digits correctly because if you don't, it could mean that you result in the wrong answer.

Now, because we're multiplying by two, we need two groups of 322.

So let's have a look at our base 10 blocks.

And we can see here now that we've got two groups of 322.

Now we're going to multiply our ones.

We'll do this in both ways.

So 2 multiply by 2 is? If you got 4, you are correct.

What we do is we write the 4 in the ones column directly underneath.

Then we move on to the tens column.

So 2 multiply by two tens is? If you got four tens or 40, you are correct.

Good job.

So what we do now is we place the four under the tens column and the zero as a placeholder in the ones column.

So what do we do next? You've probably guessed it.

We move on to multiplying our hundreds by two.

So 2 multiply by 300 is 600.

How do you think we write that in our expanded multiplication method? Well, we place the six underneath the hundreds column and we put the zero as a placeholder in the tens and the ones.

If you thought that, well done.

What do you think we do next? Yes, we add our partial products.

So in this case we've got 4, 40 and 600.

And then if we look at the base 10 blocks, we are adding our hundred, tens and ones now together.

So this part is very similar to column addition and what makes it easier is that we don't have to regroup.

So what you should get as your product is 644 because 600, add four tens, add four ones is equal to 644.

Over to you.

What I'd like you to do is choose the correct expanded multiplication record for this representation.

Pause the video here.

Off you go.

So how did you do? You should have got B as your answer.

And this is because if we look at our base 10 blocks and we look at one set, which is the top set, we can see that we've got two one hundreds, one ten, and one one, and there are three groups of this.

Now two hundreds, one 10 and one one is the same as 211.

We're multiplying this by three because we've got three groups, which means B is correct.

Andeep and Izzy have used two different ways to record.

What's the same and what's different? Andeep's saying that he's still got the same answer for both.

Okay, well we've got an informal written method here and we've got the expanded multiplication on the right-hand side.

Now let's think about what's the same.

In both the partial products are recorded and they're combined to give you the product.

So what's different? So when you're using the expanded multiplication, we actually begin by multiplying our ones, then our tens, then our hundreds, and it must be done in that order when we're using expanded multiplication because this just makes it easier to calculate.

You're multiplying your ones first, then your tens and then your hundreds.

And then when you're using the informal written method, you begin by multiplying your hundreds, then tens, then ones.

Okay, back to you.

Using Andeep's informal recording, fill in the gaps for Izzy's expanded multiplication recording.

And you can pause the video here.

Off you go.

How did you do? Let's have a look.

So if you got this, give yourself a tick and I'm just going to quickly talk through how you would've got that.

When it comes to expanded multiplication, we always place our largest factor at the top.

In this case it's 323 and we can see that's been placed at the top.

Now we're multiplying by 2.

We make sure we align that correctly.

So it has to go in the ones column and we can see that that's happened there.

We then start multiplying, starting off with our ones.

Now if you think carefully, we didn't actually have to calculate for this at all because all your information was actually given by Andeep.

And what we would've had to do was just look at what he got when he multiplied the ones, then the tens, then the hundreds, and then placed it just like that as you can see on the screen, starting with your ones, then your tens, then your hundreds.

And then when he recombined the partial products, he got 646 so you would've placed 646 at the bottom.

If you got that, good job.

Right, onto our tasks.

For the first part of this task, what you're going to do is label the expanded multiplication examples below.

Think about some of the key words that we've been using within this lesson.

And then for part two, you're going to record the calculation of these multiplication equations using expanded multiplication.

Nothing else, just expanded multiplication.

That's what we're practising today.

So you've got three equations there, 122 multiplied by 4, 3 multiplied by 131 and 323 multiplied by 3.

You can pause the video here.

Off you go.

So how did you do? Let's have a look.

This is what you should have labelled the diagrams as.

So the first part was factors.

644 is your product.

And then let's move across to the right-hand side.

You should have got partial products.

And then for question two, this is what you should have got.

I'm just going to leave this on the screen so you have a few moments to tick off your answers.

If you've got all of those answers correct, well done.

You should be proud of yourself.

Onto lesson cycle two.

So this time you're going to be understanding and applying short multiplication.

It's one of my favourite methods.

So you may have seen this in the past.

Andeep's saying that he can use short multiplication.

So today you will learn how to use short multiplication when multiplying a three-digit by a one-digit number.

Our first question.

So, two laptops cost 322 pounds each.

What is the total cost? Now Andeep's saying he's going to use short multiplication and Izzy's going to use her base 10 blocks to help her.

Before we begin, what is the multiplication equation needed to solve this question? If you got 322 multiplied by 2, you are correct.

We first partition 322 into three hundreds, two tens and two ones.

And we can see that we've got three hundreds represented by our base 10 blocks.

We've got the three placed in our hundreds column.

We then need to place our two tens in the tens column.

And lastly, our two ones in the ones column.

The largest factor goes at the top.

This is very similar to the expanded multiplication method that we looked at before.

So what do you notice? Think about the hundreds.

Because this time you are multiplying by a factor that has three digits, you now have a digit in your hundreds column.

Whereas previously you would've only had a digit in your ones column and in your tens column.

So this is the biggest change so far.

Izzy needs two groups of 322 for her base 10 blocks.

She's got one group there.

Here we have two groups now.

We're going to place the smallest factor underneath the one's column.

Remember, it's super important that you align the digits correctly.

So the two ones have been directly aligned underneath the two ones from your largest factor.

Now multiply starting with the ones.

So two multiply by two as you know is four.

And then you write the four in the ones column.

We then move on to our tens column.

So what is two multiplied by two tens? If you got four tens, you are correct and you write the four in the tens column.

You don't need to write the zero in.

Because we've only got four tens we just put the four in the tens column.

What do you think we're going to do next? If you said multiply our hundreds, you are correct, good job.

So we're going to multiply 2 by 300, which is equal to six hundreds.

So you're going to write the six in the hundreds column.

Now this is equal to 644.

That's our product.

So two laptops cost 644 pounds.

I hope that you also noticed we did not need to combine our partial products.

We just recorded our answer.

Over to you.

The product is 339.

Which short multiplication shows this correctly? Now you've got three options here.

You can pause the video.

How did you do? So the product has to be 339.

So if you got B, you are correct.

And this is because we look at the equations, we can see that in A the three is actually under the tens column.

And on top of that there's no placeholder in the ones column so that cannot be correct.

It is recorded incorrectly.

Whereas B, we can see that the factor three has been aligned correctly in the ones column.

And then if we solve this equation, we know that three multiply by three is nine ones and then three multiplied by one ten is three tens, and three multiplied by one one hundred is three hundreds.

So that is the correct short multiplication.

So Andeep is calculating 113 multiplied by 3.

What is wrong with this calculation? Andeep has not aligned his smaller factor correctly.

Andeep is multiplying by three ones, so he should have placed a three in the ones column.

Let's move on.

One bike costs 122 pounds.

One month later it costs three times as much.

What is the new cost? So in this case, what multiplication equation do you think is needed? The original cost is 122 pounds.

Now one month later it costs three times as much.

This tells me that we need to multiply by a factor of three because the cost is now three times as much.

So our equation is 122 multiplied by 3 or 3 multiplied by 122.

So you start off by placing the largest factor at the top.

And that's 122.

And then you place the smallest factor underneath in the ones column.

What do you think we do next? Well, we start off by multiplying by our ones.

If you got that, good job.

So what is 3 multiply by 2? If you got six ones, you are correct.

And we place that in the ones column.

What do you think we do next? Yes, we move on to the tens column.

And then what we do is we multiply our tens.

So 3 multiply by 2 is six tens.

We place the six in the tens column.

Good job.

And lastly, what do you think we do? Yes, we move on to our hundreds column.

So 3 multiplied by 100 is? If you got three hundreds, you are correct, and we place that in the hundreds column.

Good job.

The product is 366.

The new cost of that laptop is 366 pounds.

Over to you.

If the factors are 130 and 2, which short multiplication method is correct? You can pause the video here.

So how did you do? If you got C, you are correct because 130 is our larger factor.

That should have been placed at the top.

And then two is our smallest factor.

So that should have been placed underneath.

And we can see that between A and C, C is correct because the digits have been aligned correctly.

Let's move on.

Numbers from Sofia's calculations rubbed off.

What could be the missing number? So Andeep's giving us a helpful hint here.

He's saying that he can use his times tables facts to help me.

Now, I don't want you to worry about this question because the more we break it down, the easier it will get.

What I want you to think about is what is known and what is unknown? So in this case, we know that 366 is the product.

We know that one of our factors is three, but part of our factor is missing.

So the first thing I want you to think about is our ones because our ones factor is missing.

So we're going to start off by looking at the ones column.

The question I want you to think about is something multiplied by three gives you six.

And that's exactly what Andeep was thinking as well.

So this is where your times tables facts will really help.

1 multiplied by 3 is 3.

2 multiplied by 3 is 6.

And that matches what we're trying to solve, which ultimately means that we put two in our ones column.

And that works because we know that three multiplied by two ones is six ones.

And the six we would place in the ones column if that was missing.

So that works.

Right, your turn.

What is the missing number? Helpful hint, start by looking at your ones column.

And I'd like you to explain your thinking to your partner.

You can pause the video here.

So how did you do? If you got two as your answer, you are correct because four multiplied by two ones is eight ones.

Back to you again.

So this time there are two numbers missing.

Andeep's given you a hint.

He said he will look at the tens column to help me.

I'd like you to start off by looking at your ones first and then your tens.

You can pause the video here.

So what did you tell your partner? Well, you should have got four in your ones column and two in your tens column.

And this is because 2 multiplied by 4 is 8.

So the missing factor was four for your ones column.

And then 2 multiplied by two tens would've given you four tens.

So the missing factor for the tens column is two.

Well done if you got that correct.

Because at first when you see two missing digit boxes, you may think to yourself, what do I do? But all you have to do is break it down.

Onto our final task.

You've got three tasks you will be completing for this lesson cycle.

So task one, you're going to be using short multiplication to record and calculate these equations.

So A is 442 multiplied by 2.

B is 321 multiplied by 3.

And C is 4 multiplied by 212.

For task two, you'll be filling in the gaps.

And for task, you've got a word problem here and you're going to be completing this using short multiplication.

If all these boxes are the same height, how tall is the stack of boxes? Think about what multiplication equation will be required to solve this question.

You can pause the video here.

Off you go.

Okay, so how did you do? If you got these answers, you can give yourself a tick.

Let's move on.

For task two, if you managed to find the missing digits on the screen, give yourself a tick.

If you got all three correct, massive well done, good job.

And for task three, if you got the total height of the boxes as 884 centimetres, you are correct.

Well done.

You've made it to the end of the lesson.

And I really hope you enjoyed it as much as I did.

So to summarise our learning, today you multiplied a three-digit by a one-digit number with no regroups, and you did this through expanded multiplication and short multiplication.

You now understand that expanded multiplication of a three-digit by a one-digit number will give you three partial products.

You also understand that short multiplication builds the overall product from the ones column to the hundreds with no regrouping.

You know that the partial products can be seen in the expanded and short multiplication strategies.

Thank you for joining me in this lesson and I look forward to seeing you in the next one.