Lesson video

Hello, I'm Miss Miah and I'm so excited to be a part of your learning journey today.

I hope you enjoy this lesson as much as I do.

You're going to be using short division when the hundreds digit is smaller than the divisor.

Your keywords are on the screen now, and I'd like you to repeat them after me.

Dividend.

Divisor.

Quotient.

Regroup/regrouping.

It's really important that you know these keywords because this will really help with our explanations and mathematical thinking.

So the dividend is the amount that you want to divide up, and in this case it is six.

A divisor is a number that divides the integer, or in other words, the number that we are dividing by.

A quotient is the result after division has taken place.

So in this case, the quotient of six divided by three is two.

Now, the process of unitizing and exchanging between place values is known as regrouping.

For example, 10 ones can be regrouped for one ten.

One ten can be regrouped for 10 ones.

In our first lesson cycle, we're going to be predicting the number of digits in the quotient.

Let's get started.

In this lesson, you'll meet Andeep and Izzy.

We've got a question here.

We've got 353 divided by 4.

Now, Izzy's asking what to do when the hundreds digit is smaller than the divisor, and here we can see that three is less than four.

So today you'll be learning how to divide using short division when the divisor is greater than the hundreds digit in the dividend.

Now, when I was younger, I used to get stuck on questions like this, up until I was taught how to do it in school.

But my job today is for you to really understand what we do and why we do it, especially when it comes to dividing a question like this.

So a bakery sells in packs of four.

How many packs are required to pack 332 desserts? So we've got our short division on the left-hand side and then we've got our representation using place value counters.

So we're going to start off like normal and divide our hundreds first.

However, there's an issue.

We cannot make one group of four hundreds from the three hundreds in the dividend.

So this part is crucial.

We write zero in the hundreds column.

That's because we cannot carry out the division.

So what did you notice there? Again, because the hundreds digit in the dividend is less than the divisor, it is not divisible.

So that is why you write zero in the hundreds column.

Now what you have to do is regroup the 3 hundreds for 30 tens.

There we are.

So because we've done that, we now write three to the left of the tens digit of the dividend to make 33 tens altogether.

Now we can divide our tens.

You can make eight groups of four tens from the 33 tens in the dividend with a remainder of one ten.

So that's the same as saying 33 tens divided by four is equal to eight tens remainder one ten.

So then you write eight in the tens column.

Now you regroup 1 ten for 10 ones, and you can see that that's happened there.

So altogether we have 12 ones, and we write the one to the left of the ones digit of the dividend to make 12 ones.

Now we can divide our ones.

Now, we know that 12 is a multiple of 4, so there will be no remainder.

So 12 divided by 4 is 3, or in other words, you can make three groups of four ones from the 12 ones in the dividend.

So then we write three in the ones column.

That means 83 packs are needed.

Over to you.

Choose the short division which will require regrouping from the hundred to tens.

You can pause the video here and join us when you're ready.

So how did you do? You should have got b, and this is because the hundreds digit in the dividend is less than the divisor, so you will need to regroup 6 hundreds as 60 tens.

Now, Izzy is solving the calculation below.

She says that she can't make one group of three hundreds, so she'll have to regroup the two hundreds.

So she continues her calculation.

What mistake did Izzy make? Have a think.

You must write the zero in the hundreds column when you're regrouping the hundreds for tens and make sure that the partial quotients are recorded in the correct column.

So the quotient is 73.

Back to you.

You are to choose the correct short division for this equation: 744 by 8 equals 93.

You can pause the video here.

Off you go.

So how did you do? You should have got c as your answer.

The hundreds digit in the dividend is less than the divisor, so you'll need to regroup 7 hundreds are 70 tens.

Andeep and Izzy have both completed this equation.

So the dividend here is 330 and the divisor is 5.

Who is correct and what advice would you give? Andeep did not regroup the three hundreds correctly.

What he did was what I used to do, so he basically took away three from the five and he just put a two next to the ten.

We need to regroup the 3 hundreds as 30 tens and place the digit three next to the tens column to the left to represent this.

Back to you.

You can pause the video here.

Off you go.

So how did you do? Four hundreds can be regrouped as 40 tens.

If you got that, well done.

Now, Andeep is calculating 643 divided by 8.

Sometimes you may have to use zero as a placeholder twice.

Now, this is a good example for this.

Let's have a look.

So you're going to begin by writing the dividend and the divisor.

The divisor is placed outside and the dividend is placed inside the division frame.

So first you're going to divide the hundreds.

Now, you can't make one group of eight hundreds from the six hundreds in the dividend.

So that's where you write zero in the hundreds column, and then you must regroup the 6 hundreds for 60 tens.

You write six to the left of the tens digit in the dividend.

Now you can divide your tens.

You've got 64 tens there.

So you can make eight groups of eight tens from the 64 tens in the dividend.

You also know that 8 multiplied by 8 is 64, so that's where you can use your tables facts to help you.

So then you write the eight in the tens column.

Now you move on to dividing your ones.

You cannot make one group of eight ones from the three ones in the dividend, so ultimately that means that there are three left over.

So you place the zero in the ones column with a remainder of three.

And then you write remainder three on top of the ones.

So Izzy says that she can predict the number of digits in the quotient.

Here are her hints.

"If the 100s digit is greater than the divisor then there will be a 3-digit quotient." I want you to try and remember that.

"If the 100s digit is less than the divisor then there will be a 2-digit quotient." Do you agree? Well, for example, 423 divided by 3.

Here we can see that four is greater than three.

That means the quotient will be a three-digit number.

Now let's look at 123 divided by 3.

The one in the dividend is less than three, so that means the quotient will be a two-digit number.

Now, Andeep asks, "What if the 100s digit is the same as the divisor?" Izzy says, "You'll still have a 3-digit quotient." Over to you.

I'd like you to prove it.

So how did you do? You may have had something like this.

So for example, 323 divided by 3.

Well, three is equal to three.

So three hundreds divided by three is equal to 100, which means we will still have a three-digit quotient.

Your main task for this lesson cycle is to look at the division equations below and complete the table by predicting whether the quotient will be a two-digit or a three-digit number.

One has been done for you.

You can pause the video here.

Off you go, good luck.

So how did you do? Now, it was absolutely key that you looked at your hundreds digit in the dividend.

Now, if the hundreds digit was greater than your divisor, you would've ended up with a three-digit quotient, whereas if it was less than your divisor, you would've ended up with a two-digit quotient.

So I'd like you to pause the video here and mark your work.

Let's move on.

Now, our second lesson cycle is all about recording two-digit quotients.

So we're going to use everything that we've learnt now to apply it.

Andeep has collected 286 guinea cards.

He wants to divide them equally amongst three of his friends.

How many cards does each child get and are there any left over? So let's begin by thinking about what division equation is needed to solve this problem.

Well, I know I'm dividing because one of my keywords is to divide in our question, so that's my operation.

Now, the calculation is 286 divided by 3.

286 is the dividend because that is the amount that we are dividing up.

Three is the divisor because that is the amount that we are dividing by.

And the quotient is unknown.

That is what we are calculating.

So it's my turn.

I'm going to begin by writing the dividend and the divisor.

The divisor is placed outside to the left of the division frame, and as you know, the dividend is placed inside.

So we're going to start off by dividing the hundreds, and straight away I've recognised that the two in the dividend is less than the five, which is our divisor, so I'm going to have to regroup.

So you cannot make one group of five hundreds from the two hundreds in the dividend.

So you write zero in the hundreds column and then you have to regroup.

So 2 hundreds can be regrouped as 20 tens.

So you write the two to the left of the tens digit in the dividend.

Secondly, you divide the tens.

You can make four groups of five tens from the 24 tens in the dividend.

So there is a remainder of four tens.

So you write four in the tens column.

You must regroup.

So 4 tens can be regrouped as 40 ones.

So you then write four to the left of the ones digit in the dividend.

And then lastly, you divide the ones.

So you've got 46 ones altogether.

Now, you can make nine groups of five ones from the 46 ones in the dividend.

There is one left over, and I knew there would be one left over because 46 is not a multiple of 5.

So you write nine in the ones column with a remainder of one.

Your turn.

I'd like you to use short division to calculate the answer to 437 divided by 7.

You can pause the video here.

So how did you do? You should have got zero in your hundreds column, and that is because you cannot make one group of seven hundreds from the four hundreds in the dividend.

You should have got six tens.

You should have got six tens, and that is because you can make 6 groups of 7 tens from the 43 tens with a remainder of one ten.

That one ten then gets regrouped and you end up with 17 ones.

So you can make two groups of seven ones from the 17 ones in your dividend with a remainder of three.

So your quotient is 62 remainder 3.

Back to you.

Describe the quotient in this short division in different ways.

What does it mean? You can pause the video here.

Now, you may have got various answers, so have a look.

You may have written, it means 7 groups of 65 and 2 makes 457.

You may have also got, it means 457 is not a multiple of 7 because there's a remainder of two.

And lastly, it represents six tens and five ones and a remainder of two ones.

Now, Izzy is calculating using her whiteboard, but one of her digits has rubbed off.

What advice would you give to Izzy to find the missing digit? So you're going to begin by looking at the hundreds digit in the dividend.

So again, you have to break this question down.

Ignore the regrouped amount.

So your dividend, your hundreds digit is five.

Right, now we can see that there is a zero that's been placed in the hundreds column, which means our divisor must be greater than five.

So five hundreds divided by something gives Izzy zero hundreds.

50 tens have been regrouped.

As there is a zero recorded as a partial quotient, the divisor must be greater than five.

Now look at the tens column.

55 tens divided by something gives Izzy seven tens remainder six tens.

This is where you can use your tables facts to help you.

So, 55 divided by 7, you're looking for your highest multiple of seven here.

We know that you can make seven groups of seven tens from the 55 with a remainder of six.

So that means the missing digit is seven.

Now, in order to check that you're correct, you can complete the calculation to check 557 divided by 7 is 79 remainder 4.

Back to you.

If the partial quotient written above the hundreds digit is a zero, then the divisor is greater than or less than the hundreds digit in the dividend.

You can pause the video here.

So what did you get? Well, you should have got greater than, because if you end up with a two-digit partial quotient it means that your divisor is greater than your hundreds digit in the dividend.

Onto the main task for lesson cycle two.

So for question 1a, you're going to be completing the division equations that you see on your screen.

For question 2, you're going to be filling in the missing digits.

For question 3, Izzy has set a challenge for Andeep.

She says that this calculation gives a three-digit quotient.

Which digit do we need to change to give us a two-digit quotient? And how many solutions can you come up with? You can pause the video here.

You can pause the video here.

Off you go, good luck.

So how did you do? So for question 1a and 2a, I'd like you to pause the video and mark your work.

If you got all of those correct, well done.

Let's move on.

Let's look more closely at question 3.

So Izzy said that right now, this division equation gives her a three-digit quotient.

and she asked, "Which digit could we change to give us a two-digit quotient?" So thinking about what we know, in order to have a two-digit quotient, the divisor must be greater than the dividend.

And in this example, we can see that the divisor is not greater than the dividend.

So that means we can change the divisor to any digit that is greater than five, so that could be six, seven, eight, or nine.

And this will then result in a two-digit quotient, and there's an example on the screen.

So if you got any of those digits, well done, you are correct.

You've made it to the end of this lesson.

Fantastic work, good job.

So let's summarise our learning.

Today, you used short division when the hundreds digit is smaller than the divisor.

You understand if the hundreds digit is smaller than the divisor, then it is regrouped for tens and included with the tens digit.

You also understand that if the hundreds digit is smaller than the divisor, then no partial quotient is recorded above the hundreds digit of the dividend.

A zero is placed in the hundreds column.

Well done, fantastic work.

I really hope that you enjoyed this lesson, and I look forward to seeing you in the next one.