Lesson video

Hello, I'm Ms. 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.

Today, you will be able to multiply a three-digit by a one-digit number using expanded and short multiplication that includes one or two regroups.

So your keywords for today's lesson are regroup or regrouping, expanded multiplication, and short multiplication.

So I'm going to say them again and I'd like you to repeat them after me.

Regroup, expanded multiplication, and short multiplication.

Fantastic.

Let's move on.

So, the process of unitizing and exchanging between place values is known as regrouping.

For example, 10 ones can be regrouped for 1 ten.

One ten can be regrouped for 10 ones.

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

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

So, today, you will be multiplying a three-digit by one-digit number with one or two instances of regrouping.

For our first lesson cycle, you will understand and apply expanded multiplication.

And in this lesson, you will meet Andeep and Izzy.

Let's begin.

Now, you may have seen expanded multiplication in this format, whereby you're multiplying a two-digit by a one-digit number.

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

If one laptop costs 216 pounds, how much do three laptops cost? Andeep's going to be using expanded multiplication, and Izzy will be using her base 10 blocks to help her.

What multiplication equation do you think is needed to solve this problem? If you got 216 multiplied by 3, or 3 multiplied by 216, you are correct.

We're now going to look at how to arrange this as an expanded multiplication.

So, first, we're going to place the largest factor at the top.

So we put 216 at the top.

Then you're going to place the smallest factor at the bottom, and you're going to place this in the ones column.

Make sure you align your ones correctly.

Now, you can see here that Izzy's ran out of base 10 blocks.

This tends to be the case in the classroom especially when we don't have enough equipment to represent our equation.

So you can use place value counters instead, and I'm going to show you how you can do that to help you multiply a three-digit by one-digit number.

So, first of all, we need three groups of 216.

So here's our first group, and we can see that we've got two 100 counters, one 10 counter, and six 1 counters.

And now we've got three groups.

Let's carry on.

You're going to begin by multiplying the ones.

So 3 multiply by 6 is 18 ones.

What do you think we're going to do next? Yes, we're going to place the 1 ten in the tens column, and an 8 in the ones column.

And we can see that that's been represented using our place value counters.

We're now going to move on to our tens column, correct.

So we are going to be multiplying 3 by 1 ten, which is 3 tens.

Now in terms of placement, you're going to place the 3 tens in the tens column and a 0 as a placeholder in the ones column.

Next, you're going to move on to your hundreds column.

So 3 multiply by 2 is 6, and in this case we're multiplying 3 by 200, so you end up with 600.

So you're going to place the 6 in the hundreds column, and you're going to put 0 as a placeholder in the tens column and in the ones column.

So at this point, you're going to be recombining your partial products.

This part is similar to column edition, so you're going to add your ones, and that's 8.

Then you're going to move on to your tens and add your tens, and 1 add 3 tens is 4 tens.

And lastly, you're going to add your hundreds, and we can see we've only got 600 here.

So we're going to place our 6 in the hundreds column underneath.

So the product is 648.

Three laptops would cost 648 pounds.

Over to you.

Which multiplication will need regrouping in the ones column only? I'd like you to explain your thinking to your partner.

You can pause the video here.

How did you do? If you got B as your answer, you are correct.

And you know this, because when looking at your ones, 5 multiplied by 3 ones would give you 15 ones, 15 is greater than 10, so we must regroup.

Let's move on.

Andeep is calculating 152 by 4.

So his calculation is on the screen.

What mistake do you think Andeep has made? Let's have a look together.

We place the larger factor at the top, our smallest factor at the bottom aligned in the ones column, and then we begin to multiply.

So do this with me.

4 multiplied by 2 ones is.

If you've got 8 ones, well done.

4 multiplied by 5 tens is.

If you've got 20 tens, you are correct, but 20 tens regrouped is actually 200, whereas Andeep has written 20.

So Andeep did not regroup correctly.

So when we carry on with the calculation, 4 multiplied by 100 is 400.

If you've got that, good job.

Now, we're going to combine our partial products similar to column edition.

You should get 608, not 428.

And I think you may have noticed that if you do make a mistake when multiplying through your ones, tens, and your hundreds, it does affect your answer, and then you'll end up getting it wrong.

So do pay attention when multiplying each digits.

Over to you.

You're going to be filling in the gaps for this expanded multiplication recording.

Off you go.

How did you do? So we can see here it's partially filled out.

We've got two partial products.

So, from multiplying in our ones and multiplying in our hundreds.

However, we can clearly see that the tens have still not been multiplied.

So, 4 multiplied by 6 tens is 24 tens, which is equivalent to 240.

If you got that, well done.

If all these boxes are the same height, that's key information there, how tall is the stack of boxes? What multiplication equation is needed for you to solve this problem? Have a think.

We can see here that we've got one length of 311 centimetres.

Now, the key information here is that each of the boxes are the same height, so we can assume that we will be multiplying 311 by one, two, three, four, five, 5 would be our factor, 'cause there are five boxes.

So your equation would be 311 multiplied by 5.

Izzy thinks we will need to regroup in our hundreds column.

Do you agree? Let's have a look.

So, first, you're going to begin by placing the largest factor at the top, which is, yes, 311, and then we're multiplying this by our smallest factor, which is, correct, 5.

Now, we're going to begin by multiplying in our ones column.

So 5 multiplied by 1 is 5 ones.

What are we going to do next? Yes, we will be moving onto the tens column.

So 5 multiplied by 1 ten, is 5 tens.

Now, we placed the 5 tens in the tens column, so 5 tens in the tens column followed by 0 as our placeholder in the ones column.

Now, we're going to move on to multiplying in our hundreds.

Now, remember what Izzy said.

She stated that we would have to regroup in our hundreds column.

Let's see if that's the case.

The 5 multiplied by 3 hundreds is equal to 15 hundreds.

15 hundreds can be regrouped as 1 thousand and 5 hundreds.

So you place the 1 in the thousands column.

What do you notice? Regrouping in the hundreds column means that the answer is a four-digit number.

So let's carry on.

You place the 5 in the hundreds column and 0 as a placeholder in the tens and the ones column.

Now, you combine your partial products.

So remember, this part is very similar to column edition, and your product is 1,555.

The total height is 1,555 centimetres.

Onto your task.

Andeep, Jacob, and Izzy are tidying a cupboards.

They have a lot of boxes to put away.

They each have a different amount of boxes stacked on top of each other.

The maximum space available vertically is 1,300 centimetres.

Who do you think can fit their stack of boxes in their cupboard? So you can see here that the length of one box is 218 centimetres.

Jacob has four boxes, Andeep has five boxes, and Izzy has six boxes.

Think about what multiplication equation you will need for each to help solve this problem.

You can pause the video here.

So, how did you do? Now, Jacob has four boxes.

If this is what you've got as your answer, so 872 centimetres, give yourself a tick.

He will be able to stack his boxes in the cupboard because it is less than 1,300 centimetres.

Andeep has five boxes, so this would've been the calculation.

If you got 1090 centimetres, you are correct.

Andeep will also be able to stack his boxes in the cupboard.

Lastly, Izzy had six boxes.

Izzy's total length is 1,308 centimetres.

Now, because this is greater than 1,300 centimetres, she will not be able to stack her boxes in the cupboard.

If you got all three questions correct, really good job.

Well done.

Now, let's move on to lesson cycle two.

You are going to be understanding and applying short multiplication, which also includes one or two instances of regrouping.

A laptop costs 227 pounds.

A newer release costs twice as much.

What is the price of the new laptop? Andeep is going to be using short multiplication.

Now, Izzy states that it will be more efficient.

Before we move on though, what multiplication equation is needed? If you got 227 multiplied by 2, or 2 multiplied by 227, well done, you're correct.

Now, let's get started with this short multiplication equation.

You're going to first partition 227 into 2 hundred, 2 tens, and 7 ones.

And you're going to place that at the top.

Next, you're going to place the smallest factor 2 underneath and it's going to be aligned with the ones column.

Remember, very important, otherwise it will affect your answer.

Now, you're going to multiply starting with the ones.

So, 2 multiplied by 7 ones is 14 ones.

Now, what do we do with this 14? Well, watch this.

So, 14 ones is regrouped as 1 ten and 4 ones.

We record the 1 tens underneath the tens column, because you still have the tens to multiply.

So that's very important.

We record it underneath.

Good job.

Now, you're probably wondering, "Okay, where do I put the 4 ones?" Or you may already know as well.

We put the 4 ones in the ones column.

So what do we do next? We then move on to the tens column, 2 multiplied by 2 tens is equal to 4 tens.

But do we stop there? No, we don't.

We have to add the 1 ten that is underneath.

So 4 tens add 1 ten is 5 tens.

We write the 5 tens in the tens column.

Now, we can move on to our hundreds column.

So, 2 multiplied by 2 hundreds is equal to 4 hundreds.

We place the 4 in the hundreds column, and our product is 454, which means the new cost of the laptop is 454 pounds.

Choose the multiplication which will require one instance of regrouping.

You can pause the video here.

Okay, so how did you do? If you got A as your answer, you are correct.

This is because 2 multiplied by 7 ones is 14 ones.

We must regroup.

Okay, a laptop costs 238 pounds.

What is the total cost of three laptops? So, Andeep states that he thinks he will need to regroup once, whereas Izzy says that she thinks we're going to have to regroup twice.

Who do you agree with? Have a think.

And also, what multiplication equation is required for us to solve this problem? The multiplication equation required is 238 multiplied by 3.

Now, in terms of using the short multiplication method, do remember we always place the larger factor at the top, and then we place the smaller factor underneath in the ones column.

We then start by multiplying our ones.

So 3 multiplied by 8 ones is 24 ones.

Where do you think we will place each digit in the number 24? Have a think.

24 ones is regrouped as 2 tens and 4 ones.

Because we have 2 tens, we must place the 2 tens underneath.

So, record the 2 tens underneath the tens column because you still have the tens to multiply.

Don't forget about your ones.

We place the 4 ones in the ones column.

Now, what do we do? Well, we move on to multiplying our tens.

So 3 multiplied by 3 tens is 9 tens.

If you've got 9 tens, well done.

And where do you think we're going to place the 9 tens? I made a mistake.

We can't just place the 9 tens in the tens column.

We also have to add the remaining 2 tens.

So 9 tens add 2 tens is 11 tens.

And 11 tens is regrouped as 1 hundred and 1 ten.

So where do you think we will have to place the 1 hundred? We're going to place the 1 hundred in the hundreds column, and we have to remember to write it underneath the hundreds column.

Don't forget about your tens.

We still had the 1 ten, and we're going to place that in the tens column.

Now, let's move on to our hundreds column.

So 3 multiplied by 2 hundreds is.

So if you got 6 hundreds, you are correct.

Good job.

So 6 hundreds add 1 hundred, so the product is 714, which means the cost of three laptops is 714 pounds.

Sometimes by adding our regrouped amount we may have to regroup again.

So in this case, there are two instances of regrouping.

Over to you.

I'd like you to fill in the gap, and I'd like you to also explain your thinking to your partner.

You can pause the video here.

How did you do? If you got 2 as your answer, you are correct.

And this is because 3 multiplied by 9 ones is 27 ones.

The 2 in 27 has to be regrouped as 2 tens and placed underneath in the tens column, which shows to us that 2 tens have been regrouped.

Now, let's have a look at this question.

If all these boxes are the same height, key information there, how tall is the stack of boxes? Well, I've got five boxes, and the length of one box is 311 centimetres.

So do remember that.

I want you to think about what multiplication equation is required for this multiplication.

If you got 311 multiplied by 5, you are correct.

So let's calculate this together.

So Izzy's asking, "Do you think we will have to regroup?" Have a look.

Let's start off by multiplying our ones, 5 multiplied by 1 is 5 ones.

Now we're going to move on to our tens column.

5 multiplied by 1 ten is 5 tens.

Well done if you've got that correct.

Now, 5 multiplied by 3 hundreds is 15 hundreds.

So 15 hundreds is regrouped as 1 thousand and 5 hundred.

We're going to have to place the 1 in the thousands column.

So as you can see on the screen here, it's placed all the way to the left, way past the hundreds column, into the thousands column.

I want you to try and imagine that in your head.

Don't forget about the hundreds though.

So, now, you're going to place the 5 hundreds in the hundreds column.

What did you notice? The regrouped 1 thousand has been placed to the left of the hundreds column.

So that's another big change here, because we are quite used to making sure that we've got our digits aligned in the hundreds column, but because we've had to regroup, we've now got our 1 thousand in the thousand column.

So the total length of the boxes is 1,555 centimetres.

Over to you.

I'd like you to fill in the missing gaps.

Begin by looking at the remaining factors which need to be multiplied.

You could pause the video here.

Okay, so how did you do? If you got 2,500 and you regrouped this as two 1 thousands and 5 hundred, and you've placed both digits correctly, you are correct.

Good job.

So, numbers from and Andeep's calculations have rubbed off.

What could the missing number be? Now, Andeep's saying that he can use his timetables facts to help him.

I want you to think about what is known and what is unknown.

So, clearly here, we can see that our factor is known, our largest factor is known, and our product is known.

We also know that there's been one instance of regrouping in the tens.

The unknown part is the factor that we are multiplying by.

So let's have a go together at working what that unknown factor is.

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

Super important.

Something multiplied by 5 ones gives me 15 ones Have a think about your times tables.

Something multiplied by 5 gives me 15.

What could that be? 1 multiplied by 5 is 5.

2 multiplied by 5 is 10.

3 multiplied by 5 is 15.

So, that means the missing factor is 3.

Over to you.

What is the missing number? Remember to look at your ones column first, and I'd like you to explain your thinking to your partner.

Also have a look at the amount that has been regrouped.

You can pause the video here.

So how did you do? If you got 3 as your missing factor, you are correct.

And that's because we can see that the 2 has been regrouped.

So our calculation would've been 9 multiplied by something, gives me a product of 27.

I know that 9 multiplied by 3 is 27.

So 3 is the missing factor.

Onto the tasks.

You're going to be using short multiplication to record and calculate these equations.

You've got 447 multiplied by 2, 252 multiplied by 3, and 4 multiplied by 218.

Do remember to record this in a short multiplication arrangement.

Your second task involves finding the missing numbers by filling in the gaps.

Top hint, start with your ones column first.

And your final task.

The total length of a stack of boxes is 812 centimetres.

If all boxes are the same height, how many different stacks could you have? You could pause the video here.

Off you go.

Good luck.

So how did you do? For the first task, if you got these answers, give yourself a tick.

If you've got all three of them correct, I'm super proud of you.

Well done.

Let's move on to the second task.

So for this task, you should have filled in the gaps.

Now, if you got these answers, give yourself a tick.

Did you get all three correct> If you did, you're a superstar.

Good job.

And lastly, here are some of the solutions you could have had to this question.

So, two boxes at a height of 406 centimetres each, four boxes at a height of 203 centimetres each, or seven boxes at a height of 116 centimetres each.

If you got those, give yourself a tick.

Amazing.

We've reached the end of this lesson.

So, you multiplied a three-digit by a one-digit number with one or two instances of regrouping.

You can now hopefully regroup when using expanded and short multiplication.

You can also select an efficient method when solving multiplication questions.

I tend to find the short multiplication method far more efficient than expanded multiplication.

What do you prefer? Thank you for joining me in this lesson, and I hope to see you in the next one.