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 use short and long division to divide by a two digit divisor.

Here are the key words that you might expect to hear during this lesson, estimate, long division and remainder.

I'm gonna get you to repeat them back to me.

Estimate.

Your turn.

Long division.

Your turn.

Remainder.

Your turn.

Here's the definition of each of those words.

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 or parts.

A remainder is an amount left after a division.

This is the outline for today's lesson.

We're gonna start dividing by 12 using short division, and then we're gonna move on to dividing by 12 using long division.

Sam and Andeep are gonna join us today.

Hi, Sam.

Hi, Andeep.

They're gonna be really helpful by explaining some of their thoughts and responding to some of the math prompts you can see on screen.

By following along with them, you'll be able to learn loads.

Speaking of which, are you ready to learn? Let's go for it.

Andeep and Sam are thinking about multiples of 12.

Sam, what is two lots of 12? 2 lots of 12 is equal to 24.

I also know the related division fact.

2 times 12 is equal to 24, 24 divided by 12 is equal to 2.

Sam, what is 10 multiplied by 12? 10 multiplied by 12 is equal to 120.

And again, there's the related division fact, 120 divided by 12 is equal to 10.

Sam, what is 5 lots of 12? 5 multiplied by 12 is equal to 60.

I can half 10 multiplied by 12 to calculate 5 multiplied by 12.

5 multiplied by 12 is equal to 60.

60 divided by 12 is equal to 5.

We know the 12 times table pretty well.

Let's use short division to complete this equation.

We've got 288 divided by 12 is equal to an unknown.

It's a quotient, but we don't know its value as yet.

This is how we set out short division.

The dividend is written here.

The divisor is written here.

It's important to remember that.

The quotient is written here, but of course we haven't calculated that yet.

We'll start with the hundreds column.

So we're gonna look and see if we had 2 hundreds, how many groups of 12 hundreds could we make? 2 hundreds divided by 12 is equal to zero hundreds, zero.

You cannot share 2 hundreds between 12 without regrouping.

Zero is written in the hundreds column of the quotient.

It helps to write zero here so that each digit of the quotient is written in the correct column.

It's a placeholder.

The 2 hundreds are regrouped and written to the left of the tens digit.

There are now 28 tens in the tens column.

Andeep and Sam move to the tens column.

28 tens divided by 12 is equal to 2 tens with 4 remaining.

There are 4 tens remaining.

Two is written in the tens column of the quotient.

4 tens are regrouped and written to the left of the ones digit.

There are now 48 ones in the ones column.

Andeep and Sam move to the ones column.

48 ones divided by 12 is equal to 4 ones.

4 is written in the ones column of the quotient.

288 divided by 12 is equal to 24.

24 multiplied by 12 is equal to 288.

That's the related multiplication fact.

Andeep and Sam start with a different dividend, 672 divided by 12.

Let's estimate.

This will help us see if our answer is reasonable.

I know that 60 divided by 12 is equal to 5, so 600 divided by 12 is equal to 50.

672 is greater than 600, so the quotient will be more than 50.

Let's start by dividing 672 by 12.

6 hundreds divided by 12 is equal to zero hundreds, and that's because we are trying to arrange those 6 hundreds into groups of 12, and we would have zero groups of 12.

They'll need regrouping.

So zero is written in the hundreds column of the quotient.

It helps to write zero here, so that each digit of the quotient is written in the correct column.

The 6 hundreds are written to the left of the tens digit.

There are now 67 tens in the tens column.

Andeep and Sam moved to the tens column.

67 tens divided by 12 is equal to 5 tens with 7 remaining.

Again, imagine having 67 tens in front of you.

How many groups of 12 tens could you make? Well, you could make 5 and there would be 7 left over.

50 times 12 is equal to 600.

There are 7 tens remaining.

5 is written in the tens column of the quotient.

7 tens are written to the left of the ones digit.

There are now 72 ones in the ones column.

Andeep and Sam move to the ones column.

72 ones divided by 12 is equal to 6.

6 is written in the ones column of the quotient.

672 divided by 12 is equal to 56.

That's close to our estimate of 50.

We also know related multiplication fact 56 multiplied by 12 is equal to 672.

Okay, it's your turn.

Let's check your understanding.

What is 528 divided by 12? Start by estimating the answer, then use short division to work out the answer starting with the hundreds column.

Pause the video here and give it a go.

Good luck.

Welcome back.

This might be how you started.

480 divided by 12 is equal to 40, 600 divided by 12 is equal to 50.

The quotient is greater than 40 but less than 50.

That's given us a really good estimate.

5 hundreds divided by 12 is equal to zero hundreds.

5 is written in the tens column.

52 tens divided by 12 is equal to 4 tens with 4 remaining, written in the ones column.

48 ones divided by 12 is equal to 4 ones.

44 was the answer.

Did you manage to get that? I hope so, and I hope that it matched your estimate too.

528 divided by 12 is equal to 44.

This is a reasonable answer because it is more than 40 but less than 50.

It's time for your first practise task then.

You've got to use short division to complete each calculation below.

Andeep reminds us we've got to estimate each answer to check that it's reasonable, so make sure you've written down an estimate as well.

Pause the video here and give those a go.

Good luck.

Welcome back.

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

A was 34, B was 67 and C was 81.

Andeep talks about the estimates too.

360 divided by 12 is equal to 30, 480 divided by 12 is equal to 40, so for A, a reasonable estimate would've been 35.

And Sam says that for B, a reasonable estimate would've been 65.

That's because 720 divided by 12 is equal to 60, and 840 divided by 12 is equal to 70.

Okay, pause the video here if you need some more time to really check those answers carefully by comparing your jottings with what's on screen.

Let's move on to the second part of the lesson then, dividing by 12 using long division.

Andeep and Sam have learned about another way to divide by two digit numbers.

We can do something called long division.

They've got their example there, 672 divided by 12 is equal to 56, which they calculated in the first part of the lesson.

Let's do the same calculation using long division and compare.

This looks the same, says Andeep.

Certainly does to begin with.

We're going to write down things we did mentally before.

6 divided by 12 is zero with 6 remaining.

We still have to do 67 divided by 12.

12 multiplied by 5 is equal to 60.

We know that there are 7 tens remaining, but we record it as a subtraction.

You can see there they've written takeaway 60, which is 5 tens multiplied by 12, which is equal to 60 tens, and they've got the answer of 7 tens below.

Recording the quotient is the same.

The remainder is recorded under the subtraction.

This is where it is different.

We still have to divide 72 by 12, but we bring the two ones down.

And finally, there are 6 twelves in 72.

You can see that calculation written in bracket.

The quotient is, of course, 56 again.

In long division, you record the subtraction of the nearest multiple to calculate the remainder to exchange.

The value in the next column is brought down to join the remainder, rather than the remainder being written up.

Andeep and Sam use long division to divide by 12.

792 divided by 12 is equal to an unknown.

We don't know yet.

That's what we've got to calculate.

You can see they've set it out there as long division.

Long division is set out in a similar way to short division.

"Let's start off by estimating the answer." Good idea, Sam.

That way we know whether our answer will be reasonable or not.

720 divided by 12 is equal to 60.

840 divided by 12 is equal to 70.

A reasonable estimate for 792 divided by 12 is 65.

We start with the hundreds.

7 hundreds divided by 12 is equal to zero hundreds.

Again, that's because if we took 7 hundreds and tried to arrange them into groups of 12 hundreds, we wouldn't have any groups, but we would have 7 hundreds left over.

Zero is written in the hundreds column of the answer.

We look at the tens next.

79 tens divided by 12 is equal to 6 tens plus a remainder.

6 is written in the tens column of the answer.

6 tens multiplied by 12 is equal to 720.

We subtract 72 tens from 792 to find the remainder.

792 subtract 72 tens is equal to 72.

We look at the ones next.

72 divided by 12 is equal to 6 exactly.

6 is written in the ones column of the answer.

We subtract 72 from 72 and get zero.

792 divided by 12 is equal to 66.

The answer is very close to our estimate of 65.

Andeep and Sam estimate 924 divided by 12.

840 divided by 12 is equal to 70.

960 divided by 12 is equal to 80.

A reasonable estimate for 924 divided by 12 is 75 because it is between 840 and 960.

Okay, now they use long division to solve it.

We start with the hundreds.

9 hundreds divided by 12 is equal to zero hundreds.

Zero is written in the hundreds column of the answer.

We look at the tens next.

92 tens divided by 12 is equal to 7 tens plus a remainder.

7 is written in the tens column of the answer.

7 tens multiplied by 12 equals 840.

We subtract 84 tens from 924 to find the remainder.

924 subtract 84 tens is equal to 84.

We look at the ones next.

84 divided by 12 is equal to 7 exactly.

7 is written in the ones column of the answer.

We subtract 84 from 84 and get zero.

924 divided by 12 is equal to 77.

The answer is close to our estimate of 75.

Okay, let's check your understanding then.

Andeep and Sam calculate 504 divided by 12.

Andeep says, "Use our workings to find the quotient." So you can see the workings have already been partly written out for you.

Give it a good go.

Pause the video here.

Welcome back.

Let's see what we might have done to finish off this jotting then.

We subtracted 40 multiplied by 12, then we subtracted two multiplied by 12.

42 multiplied by 12 equals 504.

504 divided by 12 is equal to 42.

So the quotient was 42.

Is that what you got? Hope so.

Here's another one to check your understanding.

What is 528 divided by 12? There are fewer jottings laid out for you here.

Use long division to calculate the answer.

You might remember the answer from earlier in the lesson, but it's important to calculate using the long division.

Pause the video and give it a go.

Good luck.

Welcome back.

5 hundreds divided by 12 is equal to zero hundreds.

4 tens multiplied by 12 is equal to 480.

We subtract 48 tens from 528 to find the remainder.

48 divided by 12 is equal to 4 exactly, so the quotient was 44.

Is that what you got? Hope so.

It's time for your second practise task now.

Use long division to complete each calculation.

Estimate each answer to check it's reasonable.

You might recognise the equations from earlier in the lesson.

So for A, we've got 408 divided by 12.

For B, it's 804 divided by 12, and for C, it's 972 divided by 12.

Remember, estimate and use long division.

Pause the video and give it a go.

Welcome back.

Here are the answers then.

Andeep says you needed to start with the hundreds.

4 hundreds divided by 12 is equal to zero hundreds.

You needed to subtract 30 lots of 12 then subtract 4 lots of 12.

That means that the quotient was 34.

Here are the answers for B and C in which we use long division as well.

For B, it was 67, and for C, it was 81.

You might wanna spend a little bit of time now comparing what's on the screen with your jottings.

Pause the video if you need that time.

That brings us to the end of the lesson then, and here's a summary of what we've learned.

Long division records the subtraction as a calculation underneath the dividend.

Long division records the regrouping alongside the subtraction.

There are similarities and differences between long and short division.

My name's Mr. Tazzyman.

Hope you enjoyed the lesson, I did.

Maybe I'll see you again soon.

Bye for now.