Lesson video

Hi, I'm Mr. Taziman.

Today, I'm gonna teach you a lesson from a unit that's all about multiplying and dividing by two-digit numbers.

There might be lots of steps that you encounter here, but it's really important for you to understand not just the steps, but the maths behind those steps as well.

So sit back, listen well, it's time to learn.

Let's go.

Here's the outcome for today's lesson then.

By the end, we want you to be able to say, "I can solve problems with four digit dividends, using factors and long division." These are the key words that you might expect to hear during the lesson.

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

I'll say my turn, say the word, and then I'll say your turn and you can say it back.

Ready? My turn, factor.

Your turn.

My turn, long division.

Your turn.

My turn, prime number, your turn.

My turn, remainder.

Your turn.

Here's the definitions of each of those words because it's really important for us not just to be able to say them, but to understand them as well.

A factor is a number that exactly divides another whole number.

Long division is a method used for dividing large numbers by breaking the number down into smaller groups.

A prime number is a number with exactly two factors.

A remainder is an amount left after a division.

This is the outline for the lesson then.

We're gonna start by using factors to divide.

Then we're gonna look at four digit number long division.

Okay? Let's introduce some friends of ours.

We've got Sam and Andeep.

They're both gonna help us during this lesson by thinking about some of the maths that you'll see on screen and revealing some hints and tips, so make sure that you concentrate carefully and that you're ready to learn because we're about to start.

Andeep has been reading about our solar system.

Mercury is the planet nearest the sun.

Did you know that Mercury takes 2,112 hours to orbit the sun? Wow.

That means that a year on Mercury lasts for 2,112 hours.

I wonder how many Earth days that is.

Andeep and Sam investigate Mercury's orbit.

They written themselves a calculation there in order to answer the question that Sam just asked about how many earth days there are? 2,112, so that's the number of hours it takes Mercury to orbit the sun divided by 24.

That's how many hours there are in a day is equal to an unknown quotient that we've got to work out.

There are 24 hours in one Earth day.

To work out the number of days for Mercury's orbit, we would divide 2,112 by 24.

That's quite a tricky calculation.

How could we out the answer? We could use the factors of 24 to help us.

What numbers multiply together to equal 24? Do you think you know them? Let's see.

Let's think of the factor pairs for 24.

One multiplied by 24 is equal to 24.

Two multiplied by 12 is equal to 24.

Three multiplied by eight is equal to 24.

Four multiplied by six is equal to 24.

We can also multiply together three or even four numbers to get a product of 24.

Two multiplied by two multiplied by six is equal to 24.

Three multiplied by two, multiplied by four is equal to 24.

Two multiplied by two, multiplied by two, multiplied by three is equal to 24.

Andeep and Sam, think about how to use the factors.

We could divide 2,112 by the factors of 24, instead of dividing by 24.

We could divide 2,112 by two, then divide by 12.

Dividing by two and then 12 is equivalent to dividing by 24.

You can see there are a couple of bar models that have been shown to express this.

The first one has been divided by two and then one half has been divided by 12.

One of those parts is equal to one 24th of the whole bar.

We could also divide 2,112 by four, then divide by six.

How else could 2,112 be divided by 24? That's the question you've got to answer to check your understanding.

Now, we've got three options, A, B, and C, and I'll read them to you now.

Divide 2,112 by three, then divide by eight.

Divide 2,112 by two, then divide by three, then divide by three.

Divide 2,112 by six, then divide by two, then divide by two.

So which of those options do you think is a method to divide 2,112 by 24? Andeep gives us a tip here.

He says, think carefully about the numbers that are being used.

"Do the numbers multiply together to equal 24," says Sam.

Okay, pause the video here and choose which option you think is correct.

Welcome back.

A was an option, B was not, and C was an option.

And you can see that the multiplication has been written above each of these.

Three multiplied by eight is equal to 24.

Two multiplied by three, multiplied by three is equal to 18.

Six multiplied by two, multiplied by two is equal to 24.

Andeep and Sam calculate 2,112 divided by 24.

Let's start by dividing 2,112 by three.

I know 21 divided by three is equal to seven.

2,100 divided by three is equal to 700.

12 divided by three is equal to four.

So 2,112 divided by three is equal to 704.

Excellent multiplicative reasoning from Sam there.

Well done.

Next, we can divide 704 by two.

I know 700 divided by two is equal to 350.

Four divided by two is equal to two.

704 divided by two is equal to 352.

Finally, we can divide 352 by four.

I can partition 352 into 320 and 32.

320 divided by four is equal to 80.

32 divided by four is equal to eight.

352 divided by four is equal to 88.

So 2,112 divided by 24 is equal to 88.

Mercury takes 88 Earth days to orbit the sun.

What a fascinating fact, and we've used division to work it out.

You can see that the divisors that were chosen can be used as factors to equal 24.

3 multiplied by two multiplied by four is equal to 24.

Andeep and Sam calculate 2,112 divided by 24 in a different way.

I wonder how else they can do it.

Let's start by dividing 2,112 by two.

So they've halved it to get 1,056.

Next we can divide 1,056 by two.

I know 1,000 divided by two is equal to 500.

56 divided by two is equal to 28.

1,056 divided by two is equal to 528.

Next, we can divide 528 by two.

I know 500 divided by two is equal to 250.

28 divided by two is equal to 14.

528 divided by two is equal to 264.

Okay, it's time to check your understanding then, and to do that, we need you to complete the calculation.

Remember that the divisors will help you here.

If you turn those into factors, you should be able to get the product to 24.

So we might need some more division done here.

"What do you need to do next?" Says Andeep.

What number do you need to divide 264 by? Okay, pause the video and give it a go.

Welcome back.

How did you get on? Well, we've got two multiplied by two, multiplied by two, multiplied by something that is equal to 24.

To complete the calculation, you need to divide 264 by three.

You could partition 264 into 240 and 24.

Maybe that's what you did.

240 divided by three is equal to 80.

24 divided by three is equal to eight.

So the answer was 88.

This works because if we treat each divisor as a factor, then we get the product of 24.

Okay, I hope you got 88.

Let's move on.

Here's task A.

How many Earth days does Venus take to orbit the sun? Well, we can't work that out straight away.

We need some information here.

Venus takes 5,400 hours to orbit the sun.

How would you use the factor of 24 to help you solve the problem? Think of different ways to solve the problem.

Are some strategies easier than others? For number two, how many days does earth take to orbit the sun? Earth takes 8,760 hours to orbit the sun.

How do you use the factor 24 to help you solve the problem? You might already know this, but think about the best strategy to work it out.

Pause the video here and give those a go.

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

Welcome back.

Here are some possible ways that you could have found the answer.

You could have divided 5,400 by six first, that would've given a quotient of 900.

You could then halve and halve again.

You end up with 225.

You've got that by using the factors six multiplied by two, multiplied by two, which are equal to 24.

So 5,400 divided by 24 is equal to 225.

Here's another way this time using the factors three, four, and two as divisors, and this last one here, you could have used the factors two, three, two and two as divisors and that would've given you 225 as well.

Okay, let's look at number two then.

You could halve 8,760 first, then halve it again.

Then you could have divided 2,190 by three.

2,100 divided by three is equal to 700.

90 divided by three is equal to 30.

That means 2,190 divided by three is equal to 730.

730 divided by two is equal to 365.

That sounds familiar.

So our answer was 365.

We used two, two, three and two as factors of 24 to help us.

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

Four-digit number, long division.

Andeep has more facts about the planet.

Did you know that a day on Mercury lasts for 176 Earth Days? Strange.

Mercury takes 88 Earth days to orbit the sun.

So a day on Mercury lasts as long as two of its years.

That's weird, isn't it? A day on Venus lasts for 243 Earth Days.

Incredible.

Venus takes 225 Earth days to orbit the sun.

So a day on Venus is longer than a year on Venus.

Andeep creates his own planet.

This is the planet Andeepus.

Do you get it? It takes 6,148 hours to orbit its star.

How many days are there in a year on Andeepus? "I can divide 6,148 by 24," says Sam.

"I can use the factors of 24 to help me find the answer.

Wait, I forgot to tell you that there are 29 hours in a day on Andeepus." Of course, of course there are, Andeep.

I need to divide 6,148 by 29.

I can use the factors of 29 to help me find the answer.

Andeep Sam, think of some useful number facts.

I know that one multiplied by 29 is equal to 29, but I can't think of any other numbers.

That's because there aren't any.

29 is a prime number, which means it only has two factors.

We'll have to use long division instead.

I'll start with some useful multiplication facts.

So there's a table there and you can see that they are completing the table to get the first 10 multiples of 29.

We can find four, eight, and five groups using two groups and 10 groups.

I can add and subtract groups of 29 to find the missing multiples and they've got them.

If that's something you might need a little bit more practise with, it's worth doing by yourself sometimes.

To be able to get the first 10 multiples of a number, a two -digit number is really, really useful for long division.

I can use this to estimate how many groups of 29 are in 6,148 hours.

200 multiplied by 29 is equal to 5,800.

So it'll be a bit more than 200 groups.

A good estimate.

Andeep and Sam calculate 6,148 divided by 29 using long division.

Let's start with the thousands.

6,000 divided by 29 is equal to zero thousands.

We look at the hundreds next.

61 hundreds divided by 29 is equal to two hundreds, plus a remainder.

Two hundreds multiplied by 29 is equal to 5,800.

We subtract 5,800 from 6,148 to find the remainder.

You can see there that we put that into the jottings as a five in the thousands column and an eight in the hundreds column.

Once we've done that subtraction, we get 348 as our remainder.

We look at the tens next.

One 10 multiplied by 29 is equal to 290.

We subtract 290 from 348 to find the remainder.

So we've got 58 as our remainder.

We look at the ones next.

58 divided by 29 is equal to two exactly.

There's a remainder of zero, then.

Two is written in the ones column of the answer.

There are 212 days in a year on Andeepus.

Sam creates her own planet.

It's her turn now.

This is the planet Samiter.

Get it? It takes 9,545 hours to orbit its star.

A day on Samiter lasts for 23 hours.

How many days does it take to orbit its star? 23 is a prime number, which means it only has two factors.

Okay, your turn.

Let's check your understanding.

You've got to complete the useful multiplication facts.

You can find four, eight, and five groups using two groups and 10 groups.

You can add and subtract groups of 23 to find the missing multiples.

Pause the video and give that a go.

Welcome back.

Here are the first groups that you might have done.

So four multiplied by 23 is equal to 92.

You can get that by doubling two lots of 23.

5 lots is equal to 115.

You can get that by halving the fact that 10 multiplied by 23 is equal to 230.

Halve that and then eight lots is 184 and that's double four lots.

Then you can add and subtract multiples of 23 to get the others.

Three was 69, six was a 138, seven was 161 and nine was 207.

Did you manage to get those? Hope so.

Let's make use of them now.

Okay, you've gotta use the facts to estimate 9,545 divided by 23.

Pause the video here and give that a go.

Welcome back.

Four multiplied by 23 is equal to 92.

So 400 multiplied by 23 is equal to 9,200.

My estimate is a bit more than 400.

Andeep and Sam calculate 9,545 divided by 23 using long division.

Let's start with the thousands.

Nine thousands divided by 23 is equal to zero thousands.

We look at the hundreds next.

95 hundreds divided by 23 is equal to four hundreds plus a remainder.

Four hundreds multiplied by 23 is equal to 9,200.

We subtract 9,200 from 9,545 to find the remainder.

The remainder is 345.

Okay, it's your turn.

You've got to complete the long division from where we got to.

How many days are there in a year on Samiter? Pause the video here and give that a go.

Welcome back.

Look at the tens next.

One 10 multiplied by 23 is equal to 230.

Subtract 230 from 345 to find the remainder.

The remainder was 115.

Look at the ones next.

Five ones multiplied by 23 is equal to 115.

Subtract 115 from 115, which is equal to zero.

There aren't any remainders left.

9,545 hours is equal to 415 days.

There are 415 days in a year on Samiter.

Okay, it's time for your second practise task then.

How many days are there in a year on Jacobus? Each year is 9,827 hours long.

Each day on Jacobus lasts for 31 hours.

Number two, how many days are there in a year on Alexis? Each year is 7,807 hours long, each day on Lexus lasts for 37 hours.

And lastly, how many days are there in a year on Juncury? Each year is 9,933 hours long, each day on junkie lasts for 43 hours.

Pause the video here and give those three questions a go.

Good luck.

Welcome back.

Here's the answer for number one then.

So be ready to mark.

You can see that through the process of long division, the quotient was 317, so there are 317 days in a year on Jacobus.

What you need to do now is you need to mark carefully, and compare your jottings with the jottings on screen.

So take some time to do that and I'll be back with number two's answer in a moment.

Pause the video here.

Welcome back.

Here's the answer for number two.

211 was the quotient that you needed to get to.

There are 211 days in a year on Alexis.

Again, pause the video here to compare your jottings with those on screen.

Welcome back.

Here's number three, 231.

There are 231 days in a year on Juncury.

Again, pause the video here so you can compare your jottings with those on screen.

Here's number three then.

The answer was 231, which means there are 231 days in a year on Juncury.

Pause the video here to compare your jottings with those on screen again.

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

Here's a summary of the things that we've learned about.

Factors of a divisor can be used to divide a dividend.

Listing multiples of the device improves efficiency and accuracy with written division methods.

Listing multiples helps to reduce the number of steps in the long division.

My name's Mr. Taziman.

Hope you enjoyed the lesson today.

I know I did.

Maybe I'll see you again soon.

Bye for now.