Lesson video

Hello, my name is Mr. 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 for today's lesson then.

By the end, we want you to be able to say, I can explain how to use long multiplication to multiply a four digit by a two digit number.

These are the key words that you might hear during the lesson.

Partial product and regroup.

I'd like you to repeat them back to me, so I'll say my turn, say the word and then I'll say your turn and you can repeat it back.

Ready? My turn.

Partial product.

Your turn.

My turn.

Regroup.

Your turn.

Here's what a partial product actually is.

It's any of the multiplication results we get leading up to an overall multiplication result.

You can see that shown in the representation and the jottings below.

We've got the multiplication 16 multiplied by four, which is equal to 64, but it's the process of calculation we are interested here because along the way, 16 has been partitioned into 10 and six.

Each of those parts has been multiplied by four, giving two partial products, four multiplied by 10, which is equal to 40 and four multiplied by six, which is equal to 24.

Those two products, partial products that is, are added together to give 64, the overall product.

Here's regroup's definition.

The process of unitizing and exchanging between place values is known as regrouping.

For example, 10 ones can be regrouped for one 10.

One 10 can be regrouped for 10 ones.

This is the outline of today's lesson.

We're gonna start with multiple regroupings and then we're gonna look at solving problems. Sam and and Andeep are here to help us in this lesson.

Hi Sam.

Hi Andeep.

They're gonna discuss some of the maths that we might face and help us with some hints and tips along the way.

Alright then, let's get going.

You may have seen this, long multiplication, 489 multiplied by 16 and there is the written method.

Today you will be learning how to multiply a four digit by a two digit number.

Sam and Andeep are estimating the total number of water bottles needed for athletes at the Winter Olympics.

Each of the 3,402 athletes will receive 21 bottles.

How many water bottles are needed in total? What's known? What's unknown? Well, we know that there are 3,402 athletes.

We know that they will receive 21 bottles each.

3,402 and 21 are the factors.

What's unknown is the total number of bottles, so our equation would look like this.

3,402, a four digit number, multiplied by 21, a two digit number.

Long multiplication can be used with a four digit factor.

First multiply by the ones, 3,402 multiplied by one.

Two ones times one equals two.

Place the two in the ones column.

Zero 10s times one equals zero 10s.

Place the zero in the 10s column.

Four hundreds times one equals four hundreds.

Place the four in the hundreds column.

Three thousands times one equals 3000.

Place the three in the thousands column.

Then multiplied by the 10s.

3,402 multiplied by 20.

So we have our first partial product.

We're now going on to work out the second partial product.

Place zero as a placeholder in the ones column.

We do this because we know we're dealing with multiples of 10 now and multiples of 10 always have a zero in the ones column.

Two ones times two 10s equals 40.

Place the four in the 10s column, zero 10s times two 10s equals zero hundreds.

Place the zero in the hundreds column.

Four hundreds times two 10s equals eight thousands.

Place the four in the thousands column.

Three thousands times two 10s equals six thousands.

Place the six in the 10 thousands column.

Now sum the partial products.

Two plus zero is two, zero plus four is four.

Four plus zero is four.

Three plus eight is 11, so we make sure that we do some regrouping.

Six plus the regrouped one is seven.

What did you notice? We've ended up with 71,442.

What did you notice along the way? Andeep says, "I regrouped 10 one thousands into one 10,000 when I summed the partial products.

71,442 bottles are needed in total." Let's check your understanding so far then.

Fill in the missing labels, pause the video and have a go.

(no audio) Welcome back.

The missing labels were as follows.

The top two numbers you could see there were the factors.

In the middle we had the partial products.

There were two of those and at the bottom we had the product.

Did you manage to get that? Okay, let's move on then.

Sam and Andeep are accounting the total number of visitor badges for the Olympic Village.

Each visitor receives a unique badge number.

They have 1,346 visitors per day for 25 days.

How many visitor badges do they need in total? What is known? What's unknown? Well, we know there are 1,346 visitors per day for 25 days.

They are the factors.

What is unknown? The total number of visitor badges that they need.

There's our equation.

1,346 multiplied by 25 is equal to an unknown.

So let's use some long multiplication.

Andeep starts by saying, "I'm going to estimate 1000 times 30 equals 30,000.

My answer will be around this." What a sensible thing to do.

Very often with these written methods, you can make some mistakes that turn your answers completely out of the range that they should be in.

By using an estimate, you can see whether or not your answer is in the right area or not.

First multiply by the ones 1,346 multiplied by five.

Six ones times five equals 30.

Place the zero in the ones column and regroup the three 10s.

Place it at the top of the 10s column.

There we go.

Four 10s multiplied by five equals 20 10s.

20 10s plus three 10s is 23 10s.

Place the three in a 10s column and regroup the 20 10s for two hundreds.

Place the two at the top of the hundreds column.

There we go.

Three hundreds multiplied by five is equal to 15 hundreds.

15 hundreds plus two hundreds equals 17 hundreds.

17 hundreds can be regrouped as 1,700.

Place the seven in the hundreds column and the one on top of the thousands column.

There we go.

One thousands times five equals five thousands, five thousands plus one thousand equals six thousands.

Place the six in the thousands column, there's our first partial product then multiplied by the 10s.

3,402 multiplied by 20.

Place zero as a placeholder in the ones column.

Six ones times two 10s equals 12 10s.

12 10s can be regrouped as 102 10s.

Place the two in the 10s column and place the regrouped 100 in the 10s column.

There we go.

Four 10s times two 10s equals 80 10s.

80 10s add one 10 is 90 10s, nine 10s is equal to 900.

Place nine in the hundreds column Three hundreds times two 10s equals six thousands.

Place the six in the thousands column.

One thousand times two 10s equals two 10 thousands.

Place the two in the 10 thousands column.

Now sum the partial products.

Zero plus zero equals zero ones.

Three 10s plus two 10s equals five 10s, seven hundreds plus nine hundreds equals 16 hundreds, so we need to place a six in the hundreds column and regroup the one thousand by placing it underneath the thousands column.

6,000 plus 6,000 plus 1000 equals 13,000.

13,000 can be regrouped as one 10,000 and three thousands.

Place the 3,000 in the thousands column and the regrouped 10,000 in the 10,000 column.

Two 10,000 plus one 10,000 equals three 10 thousands.

Place the three in the 10,000 column.

We end up with 33,650.

What did you notice though? Well, Andeep said, "You regrouped from thousands into 10,000.

The total number of visitor badges needed is 33,650." Next question then.

In the Olympic stadium, each stand can seat 2,876 spectators.

How many spectators can be seated in 22 stands? Again, what's the known? What's the unknown? Well, we know there are 2,876 spectators and 22 stands and they are the factors.

What's the unknown is the total number of spectators.

There's the equation.

Let's do this as a my turn and then we can do a your turn.

I've set out both the factors, making sure that the largest factor goes on top.

I first multiplied by the ones, 2,876 multiplied by two.

With some regrouping, I get a partial product of 5,752.

Then I multiplied by the 10s.

To do that I ensure that I put a placeholder in to begin with and I end up with a partial product of 57,520.

Once again, you can see there's some regroupings at the top and look where I've placed them.

Now I can sum the partial products.

I get 63,272.

Your turn then.

3,128 multiplied by 29.

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

(no audio) Welcome back.

Here's what your jotting should have looked like.

You should have ended up with the overall product of 90,712.

If you didn't, pause the video here and have a go at comparing your jottings with what's on the screen.

Any mistakes you've made, you can start to try to explain and understand.

Pause the video here.

(no audio) Okay, it's time for your first practise task.

We've got some worded problems here.

You need to complete them using long multiplication.

For A, it says Sam and Andeep are calculating the number of volunteers for the Olympic games.

Each team of volunteers consists of 1,352 members and there are 19 teams. How many volunteers are there in total? For B, the Olympic stadium sells tickets for various events.

Each event has 3,465 tickets available and there are 15 events.

How many tickets are sold in total? For C, there are 2,789 watching the first diving event.

At the final there are 21 times as many spectators.

How many people watch the final diving event? For D, the Olympic gift shop needs to pack merchandise for shipment.

Each box can hold 4,283 items and they have 12 boxes to fill.

How many items are packed in total? For E, the organisers are distributing water bottles to spectators.

Each section of the stadium is given 2,617 bottles and there are 24 sections.

How many water bottles are distributed in total? Pause the video here and have a go at those worded problems. Good luck.

(no audio) Welcome back.

Here's the answer for A, there are 25,688 volunteers in total.

For B, there were 51,975 tickets sold.

For C 58,569 meals being prepared.

For D 51,396 items were packed, and for E 62,808 water bottles were distributed.

I suggest that you pause the video here and go back and have a look at the jottings to compare them to yours if any of those were incorrect.

Pause the video now.

(no audio) Let's move on to the second part of the lesson then.

Solving problems. Andeep is completing missing digit problems. Start with the ones.

"Something multiplied by three is equal to three.

You know one times three is equal to three, so one is the missing digit here.

You can check if you're correct by completing the multiplication." Sam is also completing missing digit problems. Start with the ones.

Something multiplied by two is equal to six.

You know, two multiplied by three is equal to six, so a three is the missing digit in the ones column.

Now move on to the 10s.

Something multiplied by three is equal to 12.

You know three times four is equal to 12, so a four is the missing digit there.

You can check if you're correct by completing the multiplication.

Okay, it's your turn to have a go at some of those then.

Let's check your understanding.

Look at the missing digit problem.

What is the missing digit and how do you know? Pause the video and have a go.

(no audio) Welcome back.

The missing digit was two.

Four multiplied by two is equal to eight and that was the very first multiplication that you started with in the ones column.

Andeep is completing this missing digit problem.

What advice would you give? Andeep says, "Something multiplied by three ones is equal to nine 10s." I know three multiplied by three 10s is equal to nine 10s.

So three is the missing digit in the 10s column of the second factor.

Now we move on to have a look at the other parts.

"The partial product has five 10s.

As I'm multiplying by one, the missing digit is five.

I can use the same logic here.

The partial product has one thousand, so the missing digit is one.

You can check if you're correct by completing the calculation." Okay, let's check your understanding again then.

When solving the problem below, it's best to look at the something column first.

Do you think it's ones, 10s or hundreds? Pause the video and decide.

(no audio) Welcome back.

The ones is the best one to start with.

The next day Sam uses these six digit cards to create a multiplication equation.

What was the equation? So you can see the digit cards there below.

Zero, one, two, three, four, and five, and the product was 46,035.

So what was the equation then? What was the multiplication expression being used? Sam says, "I can use trial and improvement." You know the ones digit ends five, so there can be two possibilities.

One times five or three times five.

The 10 thousands digit is a four.

I know four thousands times one 10 would give me four 10 thousands.

Two digits left.

For now, I'll place them randomly.

Sam uses long multiplication to check the answer.

Starts with three multiplied by five in the ones to get 15.

So five goes in the ones column and then 10 ones are exchanged for one 10 in regrouping.

Two times five is 10, and the added one from regrouping gives 11 with one to regroup.

Zero times five is zero added to the extra 100 that's been regrouped.

You get a one in the hundreds column.

One times five is five, so that's five in the thousands column.

Make sure that a placeholder goes in because now we're dealing with multiples of 10.

We start with four multiplied by three.

That gives us 12, so we need to do some regrouping.

Two multiplied by four is eight with the added regroups one, we end up with nine into the hundreds column, nine hundreds.

Zero times four is zero of course, and one times four is four.

But remember, all of these have different place value.

I was using their unitized values there.

The four, for example, was actually worth 40,000 because it was in the 10 thousands column.

We end up with a second partial product of 40,920.

Time to add them together.

Five add zero is five, one plus two is three.

One plus nine is 10.

That's in the hundreds column, so what we need to do is we need to regroup 10 hundreds as one thousand, five plus zero plus the regrouped one thousand is a six in the thousands column and then we have a four in the 10 thousands column.

46,035, that sounds familiar.

Looks like Sam's managed to work out the puzzle.

Well done, Sam.

"Yes! I got the correct arrangement." Andeep has a go.

He uses these six digit cards to create a multiplication equation.

What was his equation? Well, he's got 63,395 and he's gonna try and use trial and improvement as well.

He knows the ones digit ends in five, so there can only be two possibilities.

One times five or three times five and he's put in five times one here.

The 10 thousands digit is a six.

I know two thousands times three 10s would give me six 10 thousands.

Two visits left, For now I'll place them randomly.

So we end up with 2,045 multiplied by 31.

Andeep now needs to go on and use long multiplication to check that that's the correct arrangement.

He does just that.

No regrouping for the first partial product because it's being multiplied by one one.

Zero goes in as a placeholder because we're dealing with multiples of 10 now.

Now we've got some regrouping.

We've got a second partial product now of 61,350.

Time to add them together.

Five plus zero is five, four 10s plus five 10s is nine 10s, zero hundreds plus three hundreds is three hundreds, two thousands plus one thousand is three thousands and six 10 thousands plus no 10,000 is six 10 thousands.

We end up with 63,395.

Well done, Andeep.

You've got the arrangement correct.

Queue the celebration.

Okay, have a look at this then to check your understanding.

You've got to spot the mistake in this jotting.

There's the arrangement that's been worked out and there's the long multiplication.

Can you spot it? Pause the video here and have a go.

(no audio) Welcome back.

Did you see the mistake? Well, here it is.

Andeep has regrouped incorrectly.

So you can see he started well, he did five multiplied by one, which gave him five.

Then he did four multiplied by one, which gave him four, zero multiplied by one, which gave him zero and two multiplied by one, which gave him two.

The first partial product because it was being multiplied by one one, was the same.

However, when he moved onto the second one, that's when mistakes started to occur.

He placed a zero correctly because we were dealing with multiples of 10, but then when he looked at three multiplied by five, he reversed the digits and ended up with a one in the 10s column and he regrouped by writing a five at the top.

Similar sort of mistake on the next one as well.

Nevermind, Andeep, better luck next time, make sure you're checking carefully as you regroup.

Here's your second practise task then.

You've got to solve the following calculations by finding the missing digit.

Then for number two, Sam uses these six digit cards to create a multiplication equation.

What was the equation? So it was equal to 51,300.

Where would you place those digits? Pause the video here and have a go at those.

I'll be back in a little while with some feedback.

(no audio) Welcome back.

Here are the missing digits for one A, B, and C.

In A, it was four in the ones column and three in the thousands column.

For B, there was a six and a three in the 10s column and then it was a two in the thousands column.

For C, there was a four and a one in the 10s column and a three in the thousands column.

That was for the factors.

For the second partial product, there was a missing digit of three in the thousands column and for the final overall product, you had a missing digit of one in the 10s column and one in the hundreds column.

Pause the video here to catch up with marking if you need.

(no audio) Here's number two then.

This was how the arrangement should have been.

We had 3,420 multiplied by 15.

That was equal to 51,300.

Did you notice the product was a multiple of 100 and try a multiple of 10 for one of the factors? You may well have done.

Okay, we've reached the end of the lesson then.

Here's a summary.

We can use long multiplication to multiply a four digit by a two digit number.

We understand how to regroup when numbers bridge, 10, 100, 1000 and 10,000.

My name's Mr. Tazzyman.

I hope you enjoyed that lesson.

Maybe I'll see you again soon.

Bye for now.