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 two two-digit numbers with regrouping.

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

Partial product and regroup.

I'm gonna say them and I want you to repeat them back to me.

So I'll say my turn, say the word or phrase, 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.

Okay, it's also important that we understand what each of these means.

Here's the definition for partial product, which you may have seen before.

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

So you can see from the grid model below that 16 has been partitioned into 10 and 6, and each of those boxes is a partial product which needs calculation.

Those calculations are involved in the jottings on the right.

4 multiplied by 10 is equal to 40.

4 multiplied by 6 is equal to 24.

Those are the partial products, which are then added together to give the overall product of 64.

Here is our definition of regroup.

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.

The image below shows this more clearly.

You can see there are 10 ones in the ones column, which can then be exchanged for one 10 in the tens column.

Here's the outline for the lesson then, we're gonna start with regrouping tens to hundreds, then it's time for Olympics Bingo.

Sam and Andeep are gonna help us today.

They're going to discuss some of the maths prompts and talk us through some of the learning.

Hi Sam.

Hi Andeep.

Okay, is everyone ready? Let's get learning.

The Olympics is a sporting event that happens every four years.

It happens in a different host city each time.

Countries compete in a huge range of events including athletics, swimming, and team sports such as rugby and basketball.

Sam and Andeep attend an Olympics event.

They're calculating the number of seats in the stadium.

If each of the 35 sections of the stadium has 48 seats, how many seats are there in total? Well, we can write this as a calculation.

And you can see that the template for that calculation has been written down.

Something multiplied by something is equal to something.

What is it that we know and what's the unknown here? Well, what's known? There are 35 sections, each has 48 seats.

These are our factors.

What is unknown? The total number of seats.

35 multiplied by 48 is equal to our unknown, the total number of seats.

Sam and Andeep calculate using long multiplication.

So they're taking that context and they're going to use long multiplication to solve it as a written method.

Andeep says, remember to put the larger number first.

So they write 48 in, followed by the other factor of 35.

Andeep looks at the first step, which is to multiply by the ones, that's 48 multiplied by 5.

They get 240 as their first partial product.

We'll come back and look at how they've managed to calculate that shortly.

They put a zero in as the next placeholder to ensure that all of the bits they work at now are multiples of 10 because all multiples of 10 have a zero in the ones column.

Then they multiply the tens, 48 multiplied by 30.

They get 1,440.

Then they sum the partial products to get 1,680.

There are 1,680 seats altogether.

Now, what did you notice about Andeep's calculation? Have a look back over it.

What did he have to do? He says here, I had to regroup 40 ones for 4 tens.

I recorded this at the top.

So you probably noticed that as we went through.

That's the part I said I'd revisit shortly.

There's a 4 that's been marked down above the 4 in the tens column of the 48, which was the largest factor.

That 4 is actually taken from calculating 8 multiplied by 5, which is 40, but that would be 40 ones.

So they've exchanged those 40 ones for 4 tens.

And Andeep wrote that 4 above to remind himself that he needed to add that on to the next calculation.

Sam and Andeep are now watching a swimming event.

There are 26 stands around the pool.

There are 57 seats in each stand.

How many seats are around the pool? Well, once again, we need to first of all, write down this as an equation.

You've got the template there, but what's known and what's unknown? Well, what's known? There are 26 stands each with 57 seats.

These are our factors.

What is unknown? The total number of seats around the pool.

So we've got 57 multiplied by 26 which is equal to, well, let's work it out.

Andeep's going to use his long multiplication method again to calculate it.

Look carefully at his workings.

Do you notice anything? First, multiply the ones, 57 multiplied by 6.

Then multiply the tens, 57 multiplied by 20.

You can see they put the placeholder in to make sure that they make that transition from multiplying by ones to multiplying by tens.

The partial product is 1,140.

Now they need to sum those and they get 1,482.

There are 1,482 seats all together.

Andeep says I had to regroup twice.

I regrouped when I multiplied by 6, and again when I multiplied by 20.

7 ones multiplied by 6 is 42 ones, so I regrouped 40 ones for 4 tens.

7 ones multiplied by 20 is 140 ones.

So I regrouped 100 ones for 100.

Okay, let's check your understanding so far.

What is the multiplication equation needed to solve the problem? During the Olympics, Sam and Andeep are responsible for distributing brochures.

Each box contains 74 brochures and they have one box for each of the 33 different locations.

How many brochures do they have in total? You can see the question template there.

What do you know? What's unknown? I'll pause the video here so you can get on with that question.

Welcome back.

Here's the answer.

The two known facts that we had were our factors.

74 multiplied by 33 is equal to an unknown.

You know, there was 74 boxes of brochures.

They have to be delivered to 33 locations.

These are the factors and the product is missing.

Sam has used long multiplication to calculate the number of seats at the tennis event.

Is Sam correct? Why? Why not? Hmm.

Have a good look at what Sam has done.

That's right.

If you were thinking it was the regrouping, you were correct.

And you can see where those exchanges have taken place at the top of the calculation.

In Sam's calculation, actually, the regrouping are incorrect.

The digits have been reversed when they've been recorded as exchanges.

Now's your turn to have a look at what you've learned so far.

The factors are 82 and 24.

Select the correct long multiplication.

Is it A, B, or C? Pause the video and have a go.

Welcome back.

C is correct.

The numbers have been multiplied and regrouped from the tens to hundreds correctly.

Let's move on.

It's time for your first practise task.

Number one, which is the only question you're gonna be facing, solve the following problems below using long multiplication.

A, there are 76 torch handlers for each leg of the relay.

If there are 48 legs of the relay, how many torch handlers are involved in total? B, each of the 53 Olympic snack stands sells 67 snack boxes per day.

How many snack boxes are sold each day across all the stands? C, the Olympic village has 82 flagpoles and each flagpole needs 45 feet of rope.

How many feet of rope are required in total? D, each display case at the Olympic museum can hold 96 medals, and there are 34 display cases.

How many medals can be displayed in total? E, a replica Olympic torch costs 87 pounds.

59 torches are sold on Saturday.

How much money is spent on replica torches? Pause the video here and have a go at those.

Good luck.

I'll be back to reveal the answers shortly.

Welcome back.

Here's the answer to A then.

You should have got 3,648 torch handlers.

Did you use long multiplication and did you regroup accurately? Let's look at B.

For B, there were 3,551 snack boxes that were sold.

For C, it was 3,690 feet of rope that was needed.

For D, 3,264 metals can be displayed in total.

And for E, 5,133 souvenir bags are distributed in total.

Now I suggest that you have a good look at the marking there.

Go back, double check it, particularly if you've got any wrong because you might find that you made some errors in your regrouping or other areas of this written method.

Pause the video here to do that.

Okay, let's move on to the second part of the lesson then, Olympic Bingo.

Sam and Andeep are having fun playing bingo in the Olympic Village community hall.

They listen carefully hoping to complete their bingo cards first.

Everyone is excited to win a special Olympic prize.

Yes, I've got that number.

Bingo, says Sam.

But there's a twist.

They must solve the word problems to find the number.

If they manage to get three in a row, they win.

Here is one of the problems. In an Olympic athletics team, each team has 33 members.

If there are 56 teams competing, how many athletes are participating in total? What's known? What's unknown? Well, each team has 33 members and 56 teams are competing and these are our factors.

What's unknown? The number of athletes.

So we've got 33 multiplied by 56 is equal to the number of athletes.

Andeep reminds us, we have to remember to think about regrouping because we're gonna use long multiplication.

The largest factor goes first, 56 multiplied by 33.

First multiply the ones, 56 times 3.

So we've got some regrouping here.

We start with 6 ones multiplied by 3 ones, and that gives us 18.

So we take 10 of those ones and exchange them for one 10, which is marked above the two factors.

Next, we move on to looking at 50 times 3, which we know is 150, but we've also got to add on the exchange 10 that you can see above the factors.

That means that we end up with 160.

So our first partial product is 168.

We put down a placeholder because now we're transitioning to multiplying by tens rather than ones.

And now we're looking at 56 multiplied by 30.

That gives us 1,680.

But again, you can see that there is a regrouping needed here.

We started with 30 multiplied by 6, that gives us 180.

So 10 tens needed to be regrouped to 100 and that's been marked down above the factors.

It's then been added on when we come to do 30 times 50, which we know is 1,500, but we needed to add on that exchanged hundred.

Now we sum the partial products, we end up with 1,848.

There are 1,848 athletes altogether.

So the answer is 1,848.

Yes, I've got that number.

Bingo, says Sam.

Okay, it's your turn to check your understanding then.

Which multiplication is needed to work out the answer? Explain your thinking to your partner.

In the Olympic Village, there are 66 buildings.

Each building has 24 beds.

How many beds are there in total in the Olympic village? Is that modelled by A, B, or C as an equation? Pause the video and consider.

Welcome back.

That was modelled by the equation B, 66 multiplied by 24.

66 buildings is one factor.

24 beds is the other factor.

The product is missing.

If Andeep got the answer, 1,656, what might the problem card have been? Let's read the problem cards carefully.

There are 45 countries participating.

Each country is awarded 62 medals.

How many medals are given out in total? Or, 24 countries participate in a sporting event.

If each country sends 69 athletes to compete, how many athletes are there in total? What advice would you give to Andeep here? Hmm.

Begin by identifying the factors for each card.

For the top card then, 45 and 62 were the factors.

For the bottom card, 24 and 69 were the factors.

When multiplying using long multiplication, you always begin with the ones.

So 4 multiplied by 9 equals 36.

You know the one's digit is 6.

So the first card isn't right.

Andeep's card is the second card.

Okay, let's check your understanding of that then.

Andeep got the answer 2,760, which problem did he answer? And how do you know? We've got A and B and I'll read them both.

During the Olympics, this is A, 30 sports events award medals.

If each event awards 92 medals, how many medals are distributed in total? Or B, at the Olympic marathon event, there are 47 countries participating.

Each country is awarded 62 medals.

How many medals are given out in total? Pause the video here and choose which of those you think is the problem that he answered.

Welcome back.

A was the problem that he answered.

If you start by multiplying the ones, you know anything multiplied by zero is zero.

So the answer must be A because the ones is the digit zero.

So in Andeep's answer you can see it's 2,760.

The ones digit is a zero there.

Okay, it's time for your second task.

You've got to continue playing the Olympic Bingo game in groups of three or four.

Each player gets a bingo card.

One player reads out a problem.

Others solve.

Mark the answer if it's on their card.

Rotate who reads next.

And the first to complete a row, shout bingo.

Here's what the bingo cards look like and here's what the questions look like.

Pause the video here and have a go at that game of bingo.

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

Enjoy.

Welcome back.

Well, this is something you may have got.

During the marathon, there are 36 water stations.

Each station is stocked with 72 bottles of water.

How many bottles of water are distributed in total during the marathon? You can see we've got Andeep's bingo card here and he's got one number left in order to be able to win.

Here's the long multiplication he completed.

He ended up with 2,592.

So what did he shout? He shouted bingo because he managed to get an entire row.

Let's summarise what we've learned today then.

We can calculate the partial products and add the partial products to recombine when using long multiplication.

We can regroup when numbers bridge 10 or 100.

My name is Mr. Tazzyman.

I hope that you've enjoyed that today.

I know I did.

Maybe I'll see you again soon.

Bye for now.