Lesson video

Hello, my name is Mister Tazzyman.

Today, I'm gonna be teaching you a lesson from the unit that is all about multiplying and dividing by two digit numbers.

There might be a few procedures to follow today, but it's also important that you understand why we do each step of the procedure as well.

Okay, I hope you're sitting comfortably 'cause we're ready to start learning.

Here's the outcome then.

By the end of the lesson, we want you to be able to say, "I can explain how to use long multiplications to multiply two 2-digit numbers, regrouping ones to tens." The key phrase that you're going to hear today is partial product.

Can you say that back to me? Well done.

Here's what it means then.

Any of the multiplication results we get leading up to an overall multiplication result is a partial product.

You can see a couple of helpful images and jottings there.

16 multiplied by 4 equals 64.

Now, you might know that already, but the important thing here is to understand the process of getting to that answer.

You can see that 16, the factor, has been partitioned into 10 and 6, and each of those parts has been multiplied by 4, giving partial products of 14 and 24, which are then added together to give the overall product of 64.

Here's the outline.

We're gonna start by introducing long multiplication and then we're gonna move on to looking at long multiplication regrouping ones to tens.

Sam and Andeep are going to join us today.

Hi Sam, hi Andeep.

They're gonna help by discussing some of the maths that we see on screen and giving us some hints and tips.

Alright.

Hope you're sitting comfortably 'cause we're ready to start the learning.

Sam and Andeep attend a tennis match.

There are 24 seats in each row.

There are 32 rows.

You could represent the equation using a grid model.

We could also use long multiplication.

Long multiplication combines the steps in one written method.

It is more efficient than separate calculations.

Let's have a quick look and see how it works then.

We start with 4 multiplied by 2 ones, which is equal to 8 ones.

So 8 goes underneath.

Then, we look at 4 multiplied by 3 tens, which is equal to 12 tens, so we write 12 into the correct columns.

Remember, 12 tens is actually 120, so the two needs to go in the tens column and the one needs to go in the a hundreds column.

Are we finished yet? Well, no.

We have to put 0 as a placeholder as we are multiplying by a tens digit.

So that zero goes into the ones column.

We have 2 tens multiplied by 2 ones, which is equal to 4 tens.

Then we have 2 tens multiplied by 3 tens, which is equal to 6 hundreds.

We've now got two partial products.

Now, they need to be added together.

So altogether, we have 768 seats.

Okay, let's look at this one then.

Sam and Andeep attend a local football match.

There are 41 seats in each row and there are 34 rows.

Sam says, "I'm going to use long multiplication to calculate the product." The numbers have been set out correctly.

Here's the first partial product then.

4 multiplied by 1 one is equal to 4 ones, so the 4 goes in the ones column.

Then we've got 4 multiplied by 4 tens, which is equal to 16 tens.

16 tens is equivalent to 160, so that's a 6 in the tens column and a 1 in the hundreds column.

The first partial product has been calculated.

It's time to move on to the second.

What do we need to remember to do to make sure that we signify the fact that the second partial product is going to be multiplying tens, not ones? Well, we need to put 0 as a placeholder as we're multiplying by a tens digit.

3 tens multiplied by 1 ones is equal to 3 tens.

So a 3 goes in the tens column.

Then, we have 3 tens multiplied by 4 tens, which is equal to 12 hundreds.

So we've got 12 hundreds.

Well, that's 1,200, so there's 2 in the hundreds column and a 1 in the thousands column.

We're not finished yet though.

We've got two partial products.

So now what do we need to do? We need to sum the partial products.

We need to add them together.

4 plus 0 is 4.

6 plus 3 is equal to 9.

1 plus 2 is equal to 3.

And 1 added to nothing is 1.

So there are 1,394 seats altogether.

Sam and Andeep are comparing multiplication strategies.

What do you notice? We've got 33 multiplied by 21.

On the left hand side, you can see short multiplication and combining partial products.

So what they've done is they've partitioned 21 into 20 and 1.

Then they've multiplied the 20 by 33, multiplied the 1 by 33, and added those two together.

On the right hand side, you can see long multiplication, 33 multiplied by 21.

They've started by multiplying out the ones then putting a placeholder in to signify the fact that they're moving to tens, they've multiplied out the tens to give two partial products, which are then added together to give the results of 693.

Both answers are the same, but what do you notice about both methods? Hmm.

Well, let's see.

Both show the same factors and product.

The partial products are recorded differently, but they're both there.

Can you see 33 in both of them? Can you see 660 in both of them? And can you see 693 in both of them? Alright, it's time to check your understanding then.

Sam has had three attempts at using long multiplication, which is correct.

Is it A, B, or C? Have a close look at those jottings and I'll be back in a moment to reveal which of those is correct.

Welcome back.

C was the correct answer here.

Let's look at why.

On A, well, multiplied by 2 here and not 2 tens.

B, did not sum the partial products properly.

That meant that C was correct.

One ticket to a local football match cost 23 pounds.

If 121 tickets were sold, how much money was made altogether? But you can see that calculation's been set out below as a long multiplication.

There's space for two partial products and there's also space underneath for the total.

Firstly, let's do the ones.

So 3 multiplied by 1, that equals 3.

Next, we've got 3 multiplied by 2 tens, that's 60.

That means there's a 6 in the tens column.

Now, it's 3 multiplied by 100, which gives us 300.

That's a 3 in the hundreds column.

Are we finished though? No.

That's the first partial product calculated.

Now, we need to put 0 in as a placeholder, and now we look at tens.

So 2 tens multiplied by 1, that equals 20.

That's 2 in the tens column.

2 tens multiplied by 2 tens, well, that equals 400.

So that's a 4 in the hundreds column.

Lastly, 2 tens times 100 is equal to 2000.

That's a 2 in the thousands column.

Now, we need to sum the partial products.

3 plus 0 is 3, 6 plus 2 is 8, 3 plus 4 is 7, 2 added to nothing is two.

So the answer is 2,783.

And because it's pounds, we need to make sure that we put it in the correct unit, 2,783 pounds.

Your turn then, now.

One ticket to a local football match costs 12 pounds.

If 224 tickets were sold, how much money was made altogether? Use the example to help you.

Pause the video here and have a go at that question using long multiplication.

Good luck.

Welcome back.

Let's go through this together then to see if you got it correct.

Here's what it might have looked like.

You have 224 multiplied by 12.

You started with the ones, 4 multiplied by 2 ones is 8 ones.

2 tens multiplied by 2 is 40, so that's 4 in the tens column.

2 hundreds multiplied by 2 ones is 4 hundreds, so that's a 4 in the hundreds column.

That's the first partial product completed.

You then needed to make sure you had a placeholder in to ensure that you were multiplying by tens and not by ones, and you had 1 ten multiplied by 4 ones.

Well, that was 40, so that's a 40 in the tens column.

1 ten multiplied by 2 tens, that gives you 200, that's a 2 in the hundreds column, and 1 ten multiplied by 2 hundreds, well, that gives you 2 thousands, that's a 2 in the thousands column.

Those were the two partial products which were then added together to give a result of 2,688.

That meant that the total amount is 2,688 pounds.

Pause the video here if you need to double check that marking.

Alright, it's your first practise task then.

So for each equation using long multiplication, we've got A, B and C.

And Sam helps us out here to say, "Remember that the larger factor goes at the top." Pause the video here and have a go at those.

Good luck.

It's time for some feedback then.

You can see already one A, the overall answer was 4,623.

You should have got partial products of 603 and 4,020.

Did you remember to put the placeholder in to signify the fact that you were going from ones to tens? I hope so.

The answer for B then: 4,853.

The answer for C: 2,783.

Take some time now to go back through those and double check them if there were any mistakes.

It's time for the second part of the lesson then.

Long multiplication, regrouping, ones to tens, a really key skill.

The following day, ticket prices changed and it is now 16 pounds for one ticket to the local football match.

If 45 tickets were sold, how much money was made altogether? You can see that this has already been set out as a long multiplication.

We've got the larger factor on top of 45 and then we've got 16 underneath, ready to be multiplied into partial products.

So we start with 6 ones multiplied by 5 ones.

That gives us 30, so a zero goes in the ones column, and we have a 3 in the tens column ready to use later on.

Now, we need to do 4 tens multiplied by 6 ones, that gives us 24 tens, But we need to make sure that we add on the 3 tens from the previous calculation.

So we end up with 24 plus 3 is 27, so we end up having 7 in that tens column, and we need to have the 2 in the hundreds column.

Now, we've got our first partial product.

We put a zero in to show this is 10 times the size and we go to the next partial product.

1 ten multiplied by 5 ones, that's 5 tens, so a 5 in the tens column.

Then we have 1 ten multiplied by 4 tens, that gives us 4 hundreds, which is a 4 in the hundreds column.

Now, we can sum them together.

We get 0 plus 0 is equal to 0, 7 plus 5 is equal to 12, so we put a 2 into the tens column and the 1 which is actually 100 goes underneath in the hundreds column, and then we know that we have 2 plus 4 plus the 100 at the bottom gives us 7 hundreds, that's a 7 in the hundreds column.

What did you notice? Did any step change? Hmm, have a look.

Is there anything different here? Sam says, "5 ones, 6 times is greater than 10 ones.

I had to regroup.

I put the 3 tens above so I remembered it.

It didn't get in the way of the rest of my workings." A different football stadium charges 17 pounds per ticket.

Sam's mum buys 12 for a family and friends.

What is the total cost? Well, we start by looking at the ones again to get that first partial product.

2 ones multiplied by 7 ones gives us 14 ones.

Now, we know we need to do some regrouping here because 14 is greater than 9.

So the 4 goes into the ones column and then we make sure that our regrouped 1 ten goes at the top to remind us.

We end up now going on to 1 ten multiplied by 2 ones.

Well, that would be 20.

But we've also got that extra 1 ten at the top there that we need to add on.

So that means that we end up with 3 tens.

And you can see the 3 in the tens column there.

Next, put 0 as a placeholder because we are switching from dealing with ones, to dealing with tens, and we end up starting with 1 ten multiplied by 7 ones, that gives us 7 tens.

So 7 goes in the tens column.

Then we end up with 1 ten multiplied by 1 ten, but that gives us 100, so 1 goes in the hundreds column.

We've got both our partial products and now we need to add them together.

4 plus zero is 4, 3 plus 7 is 10, so we need to make sure that we are regrouping here.

We put a 1 down the bottom to remind us of that in the hundreds column because we're actually signifying 10 tens.

And we end up with 1 plus that extra one at the bottom, giving us 200 in total, so a 2 in the hundreds column.

Sam says, "I had to regroup 10 ones for 1 ten." Sam is trying to calculate the total amount spent on tickets for a basketball game.

23 pounds, amount bought, 18.

Sam says, "I know I'll have to regroup ones from the tens." Do you agree? Justify your thinking to a partner.

Pause a video here and have a go at that.

Welcome back.

What did you think? Well, Sam is correct.

We begin my multiplying the ones.

3 multiplied by 8 is equal to 24.

24 ones is regrouped as 2 tens and 4 ones.

Time to check your understanding then.

Which expressions will require regrouping from the ones to the tens? If you were to solve it using long multiplication, which would require regrouping? Pause the video and have a go.

Welcome back.

A was the one that would require regrouping.

That's because the ones were 4 and 3 and multiplied together, that's equal to 12 ones, which is greater than 9.

If you look at B and C, you can see that the ones were 7 and 1.

Multiply those together as factors and you end up with 7, and it was 5 and 0, and of course, anything multiplied by 0 is equal to 0.

Okay, let's move on.

It costs 14 pounds to go and see the junior basketball team.

If 113 tickets were sold, how much money was made altogether? It's been set out as a long multiplication as you can see.

We know that we're gonna have to do some regrouping because there's a 3 and a 4 in the ones column, and multiplied together, they create a product that is greater than 9.

4 times 3 ones is equal to 12 ones.

So we put a 2 in the ones column, and then we get the regrouped 10, and put it up the top to remind us to add it on later on.

Next, 4 times 1 tens, which is equal to 4 tens, but you've got to add on that extra 1 ten, so you end up with 5 tens.

Now, we've got 4 times 1 hundreds, which is equal to 400, so a 4 goes in the hundreds column at the bottom.

That's the first partial product complete.

Now, we put a 0 in as a placeholder 'cause we're moving from multiplying by ones to multiplying by tens, and we start with 1 ten multiplied by 3 ones.

that gives us 3 tens, so we put a 3 in the tens column.

Now, we do 1 ten multiplied by 1 ten, which is equal to 1 hundred, and then finally, 1 ten multiplied by 1 hundred, which is equal to 1000.

We've got our second partial product.

What's the next step? Well, we've got to add them together.

2 plus 0 is 2, 5 plus 3 is 8, 4 plus 1 is 5, and 1 plus 0 is 1.

The total amount is 1,582 pounds.

Okay, I'm gonna show you my turn.

Multiplying 317 by 12, and then it's gonna be your turn in a moment.

I've set out 317 multiplied by 12, ready for long multiplication.

There's space for two partial products and the sum at the bottom.

I know I'm gonna have to do some regrouping here, so I'll start with 7 ones multiplied by 2 ones.

That's 14.

So a 4 goes in the ones column and then my regrouped 10 needs to go above the other tens digits just to remind me to add it on later on.

Now ,I go to 2 ones multiplied by 1 ten, that gives me 20, but I know I've got an extra 10 to add on as well, so that gives me 30.

To represent 30, I can put a 3 in the tens column.

There it is.

Lastly, I'm gonna be doing 2 ones multiplied by 3 hundreds.

That gives me 600 in total, no regrouping required here.

It's just a 6 in the hundreds column.

Now, I'd be tempting to think, "Oh, I've just done quite a lot of multiplication." That's the question finished, but it's not.

That's just the first partial product.

Now, I've got to move on to using the tens of that small factor.

So I put a placeholder in.

All multiples of ten have a 0 in the ones column, so I write my placeholder there to ensure that all the calculations I do are multiples of ten.

Starting with 1 ten multiplied by 7.

1 ten multiplied by 7 is 70, so there's a 7 in the tens column of the second partial product.

There it is.

Now, I've got to do 1 ten multiplied by 1 ten, that gives me 100.

1 ten multiplied by 3 hundreds, that gives me 3000.

Time to add these two partial products together.

4 plus 0 is 4, 3 plus 7 is 10, that means that I put 0 in the column, and I'm ensuring that I regroup, and I end up with 8 and then a 3 in the thousands column.

My answer is 3,804.

It's your turn.

Can you use long multiplication to multiply 204 multiplied by 24? Pause the video and have a go at that using the calculation you can see on the left to help.

Good luck.

Welcome back.

Did your jottings look like this? The answer was 4,896.

If you didn't get that, it's a good idea to pause the video here and have a go at looking at where you might have made the mistake.

It's time for your second practise task then.

For number one, you need to use long multiplication to answer the following questions.

"A football match is selling tickets at 24 pounds each.

It sells 43 tickets on Monday.

How much money was made on Monday? For B, "It costs 14 pounds to see the junior team.

For their match, 44 tickets were sold.

How much money was made?" And for C, "Swimming tickets cost 13 pounds each.

If 225 tickets were sold, how much money was made altogether?" D, "Swimming tickets for the final are sold at 34 pounds each.

They sell 51 tickets in the first hour.

How much money was made?" And for number two, "Andeep has used long multiplication to solve 214 times 14.

Is he correct? Why? Why not?" Okay, pause the video here and have a go at those.

I'll be back in a little while to give you some feedback.

Welcome back.

Here's number one, A, 1,032 pounds was made in ticket sales on Monday.

For B, it was 616 pounds in ticket sales.

For C, it was 2,925 pounds.

And for D, it was 1,734 pounds.

Pause the video here and go back over those jottings if you've got any incorrect.

Then you'll be able to see where you may have made a mistake in the process.

Here's number two then.

Well, Andeep was actually incorrect.

He forgot to regroup the 1 ten.

So you can see that when he started with 4 ones multiplied by 4 ones, he put 6 in the ones column, that's the 6 from 16, which is the product of those two, but actually, he forgot to write down the regrouped 10 in the correct place to remind him to add that on when he did his next calculation.

Okay, here's a summary then of the lesson.

Long multiplication is a written strategy for multiplication by a two digit number.

Partial products are calculated and the sum is found to find the product.

Regrouping can also occur and should be recorded.

My name is Mr. Tazzyman.

I hope you enjoyed that lesson today, and I hope you found that a useful tool that you can use when you're problem solving in the future or dealing with any long multiplication.

Maybe I'll see you again soon.

Bye for now.