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 2-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.

Here's the outcome for the lesson then.

By the end, we want you to be able to say, "I can divide by a 2-digit divisor, including using 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 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.

Estimate.

Your turn.

My turn.

Long division.

Your turn.

My turn.

Remainder.

Your turn.

Here's what each of the keywords means.

Estimate means to find a value that is close enough to the right answer, usually with some thought or calculation involved.

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

A remainder is an amount left over after a division.

This is the outline then for today.

We're gonna begin in the first part of the lesson using multiplication facts before moving on to using long division.

Sam and Andeep are gonna join us today, and they are going to be giving us some hints and tips along the way, which will help us in our learning.

Hi, Sam.

Hi, Andeep.

Ready to go? Let's learn! Andeep and Sam are thinking about division methods.

"I'm quite confident using short division," says Andeep.

"I like using multiplication facts to help me answer division problems," says Sam.

What about if you don't know the times table? How would you divide by 17? There's still lots of facts that we can easily work out to help us.

Andeep and Sam work out some multiples of 17.

We can work out some useful facts very quickly.

One times 17 is equal to 17.

Double 17, or 2 times 17, is equal to 34.

We can double 2 times 17 to get four times 17, which is equal to 68.

10 multiplied by 17 is equal to 170.

We can halve 10 multiplied by 17 to get 5 multiplied by 17, which is equal to 85." Andeep and Sam go back to calculate 578 divided by 17.

We can count up in multiples of 17 until we reach 578.

Let's start by counting in steps of 170.

Aha, that's gonna make it a lot quicker! Really efficient, well done, Sam! 10 multiplied by 17 is equal to 170.

20 multiplied by 17 is equal to 340.

30 multiplied by 17 is equal to 510.

40 multiplied by 17 is equal to 680, which is greater than the dividend.

510 plus 68 equals 578.

4 multiplied by 17 is equal to 68.

That means that 34 multiplied by 17 is equal to 578.

578 divided by 17 is equal to 34.

Fantastic reasoning there! Just using some known facts that they managed to develop with their understanding of multiplicative reasoning.

34 was the unknown.

Andeep and Sam calculate 546 divided by 13.

Let's start by working out some useful facts.

Good idea, Sam, helped you out last time.

1 times 13 is equal to 13.

Double 13, or 2 times 13, is equal to 26.

We can double 2 times 13 to get 4 times 13, which is equal to 52.

10 times 13 is equal to 130.

We can halve 10 times 13 to get 5 times 13, which is equal to 65.

How are they gonna use these facts though? Well, let's see.

Which multiple of 13 should we start with? We can work more efficiently by starting with a greater multiple of 13.

4 multiplied by 13 equals 52.

So 40 multiplied by 13 equals 520.

Sam's using understanding of place value to help there.

We know that 4 ones multiplied by 13 equals 52, so four tens multiplied by 13 equals 52 tens.

And remember, 52 tens is equal to 520.

50 times 13 is equal to 650, which is greater than the dividend.

520 plus 26 is equal to 546.

That is our dividend.

2 multiplied by 13 equals 26.

So 42 multiplied by 13 equals 546.

546 divided by 13 is equal to 42.

That is the quotient.

So again, using multiplication facts that they managed to calculate relatively quickly with their understanding of multiplicative reasoning, they've been able to divide 546 by 13.

Let's check your understanding then.

Andeep and Sam calculate 825 divided by 15.

Andeep challenges you, "Work out some useful multiplication facts to help you solve this problem." Complete that table you can see on the right-hand side there and use that to help you find the unknown, to find the quotient, 825 divided by 15.

Pause the video here and give it a go.

Good luck! I'll be back in a little while to reveal the answers.

Welcome back! Let's see how you got on then.

1 times 15 is equal to 15.

Double 15, or 2 multiplied by 15, is equal to 30.

Double 2 multiplied by 15 to get 4 multiplied by 15, which is equal to 60.

10 multiplied by 15 is equal to 150.

Halve 10 multiplied by 15 to get 5 multiplied by 15, which is equal to 75.

Okay, let's go on then to finish off this calculation.

Andeep and Sam are now gonna use those multiplication facts.

What's the greatest multiple of 15 that we use? 5 multiplied by 15 equals 75, so 50 multiplied by 15 equals 750.

One of the factors is 10 times greater, which means that the product is also 10 times greater.

50 times 15 equals 750.

60 times 15 equals 900, which is greater than the dividend of 825.

Time to check your understanding again then.

We're gonna complete the calculation 825 divided by 15.

But here's a couple of helpful hints just before you start.

Andeep says, "What multiple of 15 needs to be used next." And what do you need to add to 750? Pause the video and answer those two questions.

Welcome back! Andeep's answer was this.

750 plus 75 equals 825.

5 multiplied by 15 is 75.

55 multiplied by 15 equals 825.

825 divided by 15 is equal to 55.

There's the quotient.

Is that what you got? I hope so.

Here's your first practise task then.

You're gonna be using all of those skills that you just learned about.

Number 1, complete the multiplication facts.

Use these facts to complete each calculation.

You can see the table on the right there that will help you out.

All of the divisors in A, B, and C are 14, so start with that table of multiplication facts and use those to help you when you're working out the quotients.

"Counting steps of 140 will help you," says Andeep.

"Remember to work efficiently.

What multiple of 14 will you start with?" says Sam.

And don't forget your understanding that if you make one factor 10 times greater, the product will also be 10 times greater.

This will help you to take larger steps towards finding the quotient.

Here's number 2 then.

This time it's 21 as our divisor.

It's the same sort of question though.

Count in steps of 210 to help you.

Remember to work efficiently.

What multiple of 21 will you start with? Okay, pause the video here and have a go at questions 1 and 2.

Good luck, and remember to work through carefully.

It's always worth checking.

Pause the video here.

Welcome back! Let's have a look at the answers then.

Well, in the table, you can see we've got 1 times 14 is 14, 2 times 14 is 28, 4 times 14 is 56, 5 times 14 is 70, and 10 times 14 is 140.

How do we use those to solve A? Well, we've got 448 divided by 14 equals 32.

30 multiplied by 14 was equal to 420.

420 plus 28 equaled 448.

And 2 multiplied by 14 was equal to 28, so that meant, consequently, altogether we had 32 times 14 equaling the quotient.

Okay, let's look at B then.

616 divided by 14 was equal to 44.

You might have used these two multiplication facts to help you out.

40 multiplied by 14 is equal to 560.

And Sam realised that because 4 multiplied by 14 is equal to 56, so that meant that 4 tens multiplied by 14 was equal to 56 10s, which is 560.

That meant that there were 4 lots of 14 to go.

So 44 multiplied by 14 was equal to 616.

For C, 910 divided by 14 was equal to 65.

Here's the multiplication fact that may have been used.

30 multiplied by 14 equals 420.

60 multiplied by 14 equals 840.

840 plus 70 is equal to 910.

And 5 lots of 14 is equal to 70.

So that meant 65 multiplied by 14 was equal to 910, so 910 divided by 14 was equal to 65.

Pause the video here if you need a little bit more time to mark those carefully.

Here's number 2 then.

Similar kind of method, but we had a different divisor.

For A, 462 divided by 21 was equal to 22.

You might have started with this multiplication fact.

20 multiplied by 21 equals 420.

420 plus 42 is equal to 462.

And 2 multiplied by 21 equals 42.

So 22 multiplied by 21 equals 462, and that, using the inverse, gave us our quotient that you can see there.

Let's move on to B then.

714 divided by 21 equals 34.

20 multiplied by 21 equals 420.

So 30 multiplied by 21 equals 630.

630 plus 84 equals 714.

4 lots of 21 is equal to 84.

That meant that 34 multiplied by 21 was equal to 714, and the inverse of that gave us our quotient of 34.

Let's look at C now.

40 multiplied by 21 equals 840.

45 multiplied by 21 equals 945.

Pause the video here if you need some extra time to finish marking those.

Let's move on to the next part of the lesson then, using long division.

Andeep and Sam use long division to divide by 17.

Let's start off by estimating the answer.

Always a good plan, Andeep, because then you know that any answers you get are in the right area.

510 divided by 17 equals 30.

680 divided by 17 equals 40.

A reasonable estimate for 578 divided by 17 is 35.

Okay, let's see.

Sam and Andeep write down the first 10 multiples of 17.

1 time 17 is 17.

I can use doubling to find 2 groups and 4 groups.

So 2 lots of 17 are 34.

4 multiplied by 17 is 68.

10 groups is easy.

I can halve it to find 5 groups.

10 multiplied by 17 is 170.

Then we can halve that to get 5 multiplied by 17, which is 85.

6 groups is 17 more than 85, which is 102.

102 plus 17 equals 119.

That now gives us 7 multiplied by 17.

9 groups is 17 less than 170, which is 153.

Good use of subtraction, Sam.

Three groups is 17 less than 68, which is 51.

Again, great use of subtraction.

Double 4 groups is 8 groups, so double 68 is 136.

Great multiplicative reasoning.

136 is equal to 8 multiplied by 17.

Now we've got the first 10 multiples of 17.

We can return then to our written method.

We start with the hundreds.

5 hundreds divided by 17 is equal to 0 hundreds.

0 is written in the hundreds column of the answer.

There it goes.

We look at the tens next.

57 tens divided by 17 is equal to 3 tens plus a remainder.

3 is written in the tens column of the answer, but what do we do with the remainder? Well, let's see.

3 tens multiplied by 17 equals 510.

We subtract 51 tens from 578 to find the remainder.

We've written it in brackets there.

3 tens multiplied by 17 equals 51 tens.

578 subtract 51 tens is equal to 68.

There it is.

We look at the ones next.

68 divided by 17 is equal to 4 exactly.

4 is written in the ones column of the answer.

4 multiplied by 17 equals 68.

We subtract 68 from 68 and get 0.

578 divided by 17 equals 34.

Sam said it would be about 35.

There's the quotient, 34.

Andeep and Sam use long division to divide by 13.

This time we've got 546 divided by 13 is equal to an unknown.

Let's start off by estimating the answer.

520 divided by 13 equals 40.

650 divided by 13 equals 50.

546 is closer to 520, so a reasonable estimate for 578 divided by 17 is 42.

Sam and Andeep write down the first 10 multiples of 13.

Some have been filled in already.

You can see they've doubled 13 to get 26, and they've multiplied 13 by 10 using their understanding of place value to get 130.

I can find 4, 8, and 5 groups using 2 groups and 10 groups.

There they go.

I can add and subtract groups of 13 to find the missing multiples.

And it's complete.

We've got the first 10 multiples of 13 to help with the long division.

We start with the hundreds.

5 hundreds divided by 13 is equal to 0 hundreds.

0 is written in the hundreds column of the answer.

We look at the tens next.

54 tens divided by 13 is equal to 4 tens plus a remainder.

4 is written in the tens column of the answer.

4 tens multiplied by 13 equals 520.

We subtract 52 tens from 546 to find the remainder.

4 tens multiplied by 13 equals 52 tens.

So we are taking away 52 tens.

546 subtract 52 tens is equal to 26.

We look to the ones next.

26 divided by 13 is equal to 2 exactly.

2 is written in the ones column of the answer.

2 multiplied by 13 equals 26.

We subtract 26 from 26 and get 0.

546 divided by 13 equals 42.

Sam said it would be about 42.

Okay, let's check your understanding then.

What is 825 divided by 15? Andeep says, "Use long division to calculate the answer." Sam says, "You might already know the answer, but that'll help you practise using long division." Okay, pause the video here and have a go.

Welcome back! Let's go over the answer then, but we're also checking that you've understood the process and the jottings.

8 hundreds divided by 15 is equal to 0 hundreds.

5 tens multiplied by 15 equals 750.

We subtract 75 tens from 825 to find the remainder.

75 divided by 15 is equal to 5 exactly.

So the quotient is 55.

Pause the video here if you need to do some extra checking of your answer.

Okay, let's do your second practise task then.

Use long division to complete each calculation.

We've got A, which is 448 divided by 14.

You need to estimate each answer to check it's reasonable.

Remember to write down the multiples of the divisor.

B is 616 divided by 14, and C is 910 divided by 14.

For number 2, you still need to estimate each answer to check it's reasonable, but this time the divisors are 21 rather than 14.

Pause the video here and have a go at those questions.

Good luck, and I'll be back in a little while with some feedback.

Here are the answers.

30 multiplied by 14 is equal to 420, and 40 multiplied by 14 is equal to 560.

That helps us to find an estimate, which Sam says here.

"448 is closer to 420 than 560, so a good estimate is 32," which also happens to be the quotient that 448 divided by 14 gives.

Let's look at how we might have done it using long division, though.

You might have started by doing 4 hundreds divided by 14, which is equal to 0.

Then you would look at the tens.

You can see 44 tens divided by 14 is equal to 3, but with a remainder.

3 tens multiplied by 14 equals 42 tens, so we subtract 42 tens from 448 to find the remainder.

That gives 28.

28 is equal to 2 multiples of 14.

There's no remainder, so 2 goes at the top, and we end up with a quotient of 32.

Here's B and C.

For B, we had 616 divided by 14 is equal to 44, and for C, it was 910 divided by 14 is equal to 65.

Pause the video here if you need some extra time to look carefully through your jottings and compare them to the answers given here.

Let's look at 2 then.

We got multiples of 21.

I'll read them through.

21, 42, 63, 84, 105, 126, 147, 168, 189, and 210.

Did you spot patterns in the tens and ones digit, which helped you find the multiples efficiently? You may well have done.

Here are the answers then for A, B, and C.

We'll start with A.

Here's how the estimate might have looked.

20 multiplied by 21 is equal to 420, and 30 multiplied by 21 is equal to 560.

462 is closer to 420 than 560, so a good estimate is 22.

Okay, you can see there 462 divided by 21 is equal to 22.

You might have reached that by doing the following: 4 hundreds divided by 21 was 0, so 46 tens divided by 21 was 2 with a remainder.

To find the remainder, we needed to subtract 42 tens away from 462.

That gave a remainder of 42.

42 is double 21, so we knew that 2 21s went into 42, and 2 needed to go in the ones column.

That gave you a quotient of 22.

Here's the answer for B.

714 divided by 21 equals 34.

945 divided by 21 equals 45.

Pause the video here if you need some extra time to check your jottings against these answers.

Welcome back! Let's summarise the lesson then.

Different strategies can be used to solve division problems. Multiplication facts are really useful in solving division problems. Known facts and place value can help to estimate the answer to a long division.

My name's Mr. Tazzyman.

I've really enjoyed learning about long division today, and I hope you have as well.

Maybe I'll see you again soon.

Bye for now.