Lesson video

Hi, I'm Mr. Tazzyman.

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.

I can divide by a two-digit divisor and find the remainder.

These are the key words that you might hear today.

We've got long division, and remainder.

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

Long division, your turn.

Remainder, your turn.

Okay, but we need to know what those mean as well.

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

A remainder is an amount left after a division.

This is the outline of today's lesson.

We're gonna start by finding the remainder, then we're gonna move on to solving problems with remainders.

Sam and Andeep are gonna join us today, to think about the maths that we are gonna be learning about.

They're gonna give us some hints and tips along the way, as well as discussing some of the key points.

Hi, Sam, hi Andeep, are you ready to start? Are you ready to start? Okay, let's get learning.

Andeep and Sam are thinking about long division.

What happens if the dividend is not an exact multiple of the divisor? You can see there are some labelled parts in an equation.

We've got 315 divided by 30 is equal to an unknown.

In this example, the dividend is 315, and the divisor is 30.

There's a remainder left, the remainder is always less than the divisor.

300 divided by 30 is equal to 10, so our quotient is 10.

The next multiple of 30 is 330.

300 plus 15 is equal to 315.

The remainder in this equation is 15.

Can you see it's been written there with an R, and then a 15, and it's been labelled in this example.

We represent the remainder with an R.

Andeep and Sam calculate 900 divided by 26.

Let's start off by writing down the first 10 multiples of 26, a really useful skill to develop.

Five groups of 26 is half of 260, which is 130.

Six groups is 26 more than 130, which is 156.

Double four groups is eight groups, so double 104 is 208.

156 plus 26 is equal to 182.

Three groups is 26 more than 52, which is 78.

Nine groups is 26 less than 260, which is 234.

Now they've got those first 10 multiples.

"Now, let's estimate the answer," says Andeep.

780 divided by 26 is equal to 30.

1,040 divided by 26 is equal to 40.

A reasonable estimate for 900 divided by 26 is 35.

They've got a target, they've got somewhere they can go to.

Andeep and Sam calculate, 900 divided by 26 using long division.

We start with the hundreds.

Nine hundreds divided by 26 is equal to zero hundreds.

Zero is written in the hundreds column of the answer.

We look at the tens next.

90 tens divided by 26 is equal to three tens, plus a remainder.

Three tens multiplied by 26 is equal to 780.

We subtract 78 tens from 900 to find the remainder, 120, three is written in the tens column of the answer.

Let's look at the ones.

The largest multiple of 26 we can subtract here, is 104.

We subtract 104 from 120 to get a remainder of 16.

Four is written in the ones column of the answer.

We have 16 ones left.

We cannot make any groups of 26 ones.

900 is equal to 34 groups of 26, with a remainder of 16.

Can you remember how we write that though? Let's see.

34, remainder 16 is very close to our estimate of 35.

Andeep and Sam calculate 5,400 divided by 35.

Let's start off by writing down the first 10 multiples of 35.

Five groups of 35 is half of 350, which is 175.

Six groups is 35 more than 175, which is 210.

Double four groups is eight groups, so double 140 is 280.

210 plus 35 is equal to 245.

Three groups is 35 more than 70, which is 105.

Nine groups is 35 less than 350, which is 315.

Okay, your turn, check your understanding then.

You've got to estimate 5,400 divided by 35.

Use the multiplication facts to help you make an estimation.

Pause the video here, and give that a go.

Welcome back.

3,500 divided by 35 is equal to 100.

7,000 divided by 35 is equal to 200.

A reasonable estimate for 5,400 divided by 35 is 150.

Was that your estimate or something close? I hope so.

Andeep and Sam calculate 5,400 divided by 35 using long division.

Let's start with the thousands.

Five thousands divided by 35 is equal to zero thousands.

We look at the hundreds next.

54 hundreds divided by 35 is equal to 100, plus a remainder.

100 multiplied by 35 is equal to 3,500.

We subtract 3,500 from 5,400 to find the remainder.

It's 1,900.

We look at the tens next.

Five tens multiplied by 35 is equal to 1,750.

We subtract 1,750 from 1,900 to find the remainder.

It's 150.

Okay, let's get you to finish this off then to check your understanding.

You've got to complete the calculation using long division.

Pause the video here, and give that a go.

Welcome back.

Look at the ones next.

150 divided by 35 is equal to four, and a remainder.

Four is written in the ones column of the answer.

150, subtract 140 is equal to 10, so there is a remainder of 10.

The answer is 154, remainder 10.

Did you get that? I hope so.

"That's close to our estimate of 150," says Andeep.

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

Number one, solve this problem using long division.

Write the multiples of 35 to help you.

Find the remainder, remember to make an estimate.

Number two, solve this problem using long division, 6,400 divided by 26.

Write the multiples of 26 to help you, find the remainder.

Remember to make an estimate.

Okay, pause video here and give those a go.

Good luck.

Welcome back.

The answer was 25, remainder 25.

Did you manage to get that? Here's what you might have done for your estimate as well.

700 divided by 35 is equal to 20.

1,050 divided by 35 is equal to 30.

A reasonable estimate for 900 divided by 35 is 25, and you can see that the quotient actually came out to be very close to that.

Alright, if you got anything incorrect there, pause the video now so you can compare your jottings with what's on screen.

Here's number two then.

The answer was 246, remainder four, and your estimate might have been something like 250.

Because 5,200 divided by 26 is equal to 200, 7,800 divided by 26 is equal to 300.

A reasonable estimate for 6,400 divided by 26 then, is 250.

Again, pause the video here, if you need to compare your jottings with what's on screen.

It's time for the second part of the lesson then, solving problems with remainders.

Andeep has 10 pounds.

You can see there, that an apple is 42 pence.

Every day I buy an apple.

An apple costs 42 pence.

How many apples can Andeep buy before he runs out of money? Let's look at some useful facts.

Andeep and Sam find useful multiples of 42.

Double four groups is eight groups so double 168 is 336.

Five groups of 42 is half of 420, which is 210.

Six groups is 42 more than 210, which is 252.

252 added to 42 is equal to 294.

Three groups is 42 more than 84, which is 126.

Nine groups is 42 less than 420, which is 378.

Now, let's estimate the answer.

10 pounds is equal to 1,000 pence.

Great converting, well done, Andeep.

860 divided by 42 is equal to 20.

1,260 divided by 42 is equal to 30.

1,000 is nearer 840 so a reasonable estimate for 1,000 divided by 42 is 23.

Andeep and Sam calculate 1,000 divided by 42 using long division.

Let's start with the thousands.

1,000 divided by 42 is equal to zero thousands.

We look at the hundreds next.

10 hundreds divided by 42 is equal to zero hundreds.

We look at the tens next.

Two tens multiplied by 42 is equal to 840.

We subtract 840 from 1,000 to find the remainder.

Look at the ones next.

160 divided by 42 is equal to three, and a remainder.

Three is written in the ones column of the answer.

160 subtract 126 is equal to 34.

There is a remainder of 34.

23, remainder 34.

That's very close to our estimate of 23.

So 1,000 divided by 42 is equal to 23, remainder 34.

So 23 groups of 42 pence can be made from 1,000 pence or 10 pounds.

So you could buy 23 apples.

If you buy one a day, that's 23 days.

3,600 apples are put into bags.

Each bag contains 28 apples.

How many bags can be filled? Andeep and Sam start with multiples of 28.

It's the same every time, isn't it? Very useful skill this.

Double four groups is eight groups, so double 112 is 224.

Five groups of 28 is half of 280, which is 140.

Six groups is 28 more than 140, which is 168.

168 added to 28 is equal to 196.

Three groups is 28 more than 56, which is 84.

Nine groups is 28 less than 280, which is 252.

Okay, let's check your understanding.

You've got to estimate 3,600 divided by 28.

Use the multiplication facts to help you make an estimation.

Pause the video here, and give that a go.

Okay, welcome back.

Here's what Sam did.

2,800 divided by 28 is equal to 100.

5,600 divided by 28 is equal to 200.

3,600 is nearer 2,800, so a reasonable estimate for 3,600 divided by 28 is 120.

Andeep and Sam calculate 3,600 divided by 28, using long division.

Let's start with the thousands.

Three thousands divided by 28 is equal to zero thousands.

We look at the hundreds next.

36 hundreds divided by 28 is equal to 100, and a remainder.

100 multiplied by 28 is equal to 2,800.

We subtract 2,800 from 3,600 to find the remainder.

It's 800.

We look at the tens next.

Two tens multiplied by 28 is equal to 560.

We subtract 560 from 800 to find the remainder.

It's 240.

Okay, it's your turn again, you've got to complete the calculation using long division.

Pause the video and give it a go.

Welcome back.

So Andeep says, "Look at the ones next." 240 divided by 28 is equal to eight, and a remainder.

Eight is written in the ones column of the answer.

240 subtract 224 is equal to 16.

There is a remainder of 16.

So the answer was 128, remainder 16.

Did you get that? Hope so.

"That's close to our estimate of 120," says Andeep.

3,600 apples are put into bags of 28.

Andeep says, "3,600 divided by 28 is equal to 128, remainder 16." So Sam says, "There are 128 full bags of apples," but remember there's also 16 left over that don't fill a bag.

Okay, it's your turn, second practise task coming up.

Number one, every day Sam buys a banana.

A banana costs 37 pence.

Sam has 20 pounds, how many bananas can she buy? Use the multiples of 37 to help you, remember to make an estimate.

Number two, 5,500 bananas are put into bags of 18.

How many full bags are there? Write the multiples of 18 to help you, find the remainder, remember to make an estimate.

Okay, pause the video there, give it a go, and I'll be back soon with some feedback.

Good luck.

Welcome back, here's the answer for the first one then.

54, remainder two.

"A reasonable estimate would've been a bit more than 50," as Andeep says here.

1,850 divided by 37 is equal to 50.

Okay, pause the video here to compare your jottings with what's on screen if your quotient wasn't 54, remainder two.

That means Sam can buy 54 bananas.

Here's number two then, 305, remainder 10.

Your estimate might have been somewhere near 310 because 5,400 divided by 18 is equal to 300.

7,200 divided by 18 is equal to 400.

So a reasonable estimate for 5,500 divided by 18 is 310.

This was a bit tricky because the tens digit of the answer is zero.

There are 305 full bags of bananas.

Remember, the last bag of bananas has 10 in, so it's not a full bag.

Again, if you didn't get that as a quotient, then pause the video here, and compare your jottings with those on screen.

That brings us to the end of the lesson then, here's a summary of our learning.

A remainder is always less than the divisor.

The remainder, the part left over, is written after the quotient and represented with an R.

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

My name's Mr. Tazzyman.

I enjoyed the lesson today, and I hope you did as well.

I'll see you again soon.

Bye for now.