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.

In this lesson, you will learn to divide a two-digit by a one-digit number using short division with regrouping and remainders.

On the screen now, you can see the keywords and I'd like you to repeat these after me.

Remainder.

Regroup, regrouping.

Fantastic.

Let's move on.

A remainder is an amount left over after division happens when the first number does not divide exactly by the other.

You can also say that you will get a remainder if the dividend is not a multiple of the divisor.

The process of unitizing and exchanging between place values is known as regrouping.

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

So in our first lesson cycle, we are going to be looking at recording regrouping and remainders in short division.

Let's get started.

You will meet Andeep and Izzy in this lesson.

So we've got an equation here, 53 divided by four.

I know that 13 ones divided by four is three ones remainder one.

But what do I do next? And this is exactly what we're going to be exploring today.

So 53 glow sticks are shared equally between four children.

How many glow sticks would each child get? So we're going to begin by dividing the tens.

You can make one group of four tens from the five tens in the dividend with the remainder of one ten.

Five tens divided by four is equal to one ten remainder one ten.

You're going to write one in the tens column to represent that each child will get one bundle of 10 glow sticks each.

Now you have to regroup the one ten for 10 ones, and that's been done there.

So then you're going to write one to the left of the ones digit of the dividend to make 13 ones.

Lastly, you're going to divide the ones.

Now having a look carefully at your ones.

You have 13 ones.

13 is not a multiple of four.

So I can tell straightaway that there will be a remainder.

You can make three groups of four ones from the 13 ones in the dividend.

13 ones divided by four is equal to three ones remainder one.

So you write three in the ones column to represent that each child will also get three singular glow sticks each.

And then because there's one left over, we write "r 1" next to the three ones.

And the r, as you remember, stands for remainder.

So each child will get 13 glow sticks each and there will be one left over.

So what do you notice about the ones? This is key.

If the number of ones, including any regrouped tens, is not a multiple of the divisor, there will be a remainder.

So each child will get 13 glow sticks and there will be one glow stick left over.

Over to you.

I'd like you to label the diagram for the short division below.

You can pause the video here, and when you're ready, click play, so you can see how you've done.

So how did you do? This is what you should have got.

So your divisor is six because that is the number that is placed outside the division frame and that is the number that we're dividing by.

Now, your remainder is expressed by writing an r followed by however much is left over, and then the amount regrouped is usually placed to the left of the ones digit right at the top in small notation.

Or it can be any digit.

Back to you.

I'd like you to describe "r 3" in this short division in different ways.

You can pause the video here.

So how did you do? Now there are many ways to describe r three, or a remainder of three.

So here are some of the ways.

So it means a remainder of three.

It means there are three left over or there's an extra three.

It means 75 is not a multiple of six.

And it represents three ones.

Let's move on.

53 marbles are shared equally between three children.

How many marbles does each child get? So first off, you divide the tens.

You can make one group of three tens from the five tens in the dividend, with a remainder of two tens.

So here we can see we've got that one group of three tens.

So that means we now know that five tens divided by three is equal to one ten remainder two tens.

Now you regroup the two tens for 20 ones.

Now because we regroup that two tens, we write the two to the left of the ones digit in our short division to make 23 ones altogether.

Then we can carry on dividing the ones.

Now what do you notice? There's 23 ones.

Now I know 23 is not a multiple of three.

So there will be a remainder.

The closest multiples of three that we have to 23 are 21 and 24.

So in this case, you can make seven groups of three ones from the 23 ones in the dividend.

So that means 23 ones divided by three equals seven ones remainder two.

So you write the seven in the ones column to represent that each child will also get seven singular marbles.

Then you write "r 2" or remainder of two next to the seven ones to show that there are two marbles left over.

Each child will get 17 marbles and there will be two marbles left over.

Back to you.

Use the information to fill in the gaps.

You can pause the video here.

So how did you do? So you should have got three as your divisor, and that should have been written outside of the division frame.

53 as your dividend.

And then for your quotient, you should have got 17 with a remainder of two, expressed as you can see on the screen.

Lastly, because two tens have been regrouped as 20 ones, you should have placed a two to the left side of the ones digits.

If you got that correct, well done.

You can identify and label the different parts of short division correctly.

Good job.

Now Izzy is solving the calculation below.

So she's got 85 as her dividend and she's dividing that by six.

She says that she can tell that there will be a remainder by looking at her ones.

25 is not a multiple of six, so I know there will be a remainder.

She's going to use her times tables facts to help her.

You can make four groups of six ones in the dividend 25.

So four multiplied by six is 24.

24 can be one part in the part-whole model.

One is the missing part and is also the remainder.

So that means the quotient is 14 remainder one.

Over to you.

If the ones in a dividend are not a multiple of the divisor, there will always be a remainder.

Prove it.

You can pause the video here.

So how did you do? So here are some examples that you may have written down.

So for me, what I've done is I've got 85 as my dividend and six as my divisor.

So 25 is not a multiple.

So that means there is a remainder of one.

And in my second example, with my dividend being 93 and my divisor being eight, if we look at the ones, 13 is not a multiple of eight.

So again, there is a remainder of five.

Let's move on.

Andeep is trying to solve this division problem.

So it's 37 divided by five.

And that's because 37 is our dividend.

Our divisor is five.

So Andeep says that he knows that the multiple of 10 in the dividend is less than the divisor.

So he has to regroup.

And notice because he's had to regroup the tens, he's placed a zero at the top and he's shifted the three tens into 30 ones.

So he has 37 ones altogether now.

But that means he's still dividing the same dividend but it's just been rearranged.

So from there, he's figured out that he can make seven groups of five ones, which is 35, and that there's a remainder of two.

Izzy says that she thinks there's a more efficient way.

Sometimes, short division may not always be helpful, and I actually used to make this mistake all the time.

I used to think, oh, well, I can still use short division, but actually, you realise that there must be an easier way because you're still rearranging your tens into your ones and still dividing into the same dividend.

In this case, other strategies such as partitioning would be a more efficient way.

Your turn.

Which method should Andeep use for both equations? I'd like you to justify your thinking to your partner.

So you've got 92 divided by seven, which is option A, and option B is 57 divided by seven.

You can pause the video here.

So how did you do? So for option A, short division would be best, as the multiple of tens in the dividend will need regrouping.

Now for option B, because the multiple of 10 is less than the divisor, an informal strategy would be best and actually, it would probably be more efficient because I reckon for a question like this, a part-whole model would definitely be quicker, because you can find the highest multiples and then continue to divide.

So onto your task for lesson cycle one.

Question one.

I'd like you to complete the sentences using the short division example you see on the screen there.

And for question two, I'd like for you to complete the table.

You're going to be ticking whether or not there's any regrouping happening from the tens to the ones and whether or not there will be a remainder.

And if so, how many? You can pause the video here.

Off you go.

Good luck.

So how did you do? So for the first question, seven is the divisor, as this is what we are dividing by.

82 is the dividend, as this is what we are dividing up.

Now one ten has been regrouped to make 12 ones, and the quotient is 11 remainder five.

If you've got all of that correct, well done.

Give yourself a tick.

Let's move on.

So for question two, this is what you should have got for your table.

You can pause the video here to mark your work.

Okay, let's move on.

Our second cycle for this lesson consists of us using short division, including remainders.

Let's begin.

Izzy has 89 marbles.

She wants to share them between seven of her friends.

How many marbles does each friend get? And are there any left over? What division equation is needed to calculate this equation? Have a think.

Well, let's highlight the key parts.

There are 89 marbles and we need to share them between seven of her friends.

So that means 89 is the dividend because that is the amount we want to divide up.

Seven is the divisor.

This is the number we are dividing by.

And the quotient is what we are looking for.

We're going to write the divisor and dividend and arrange it in our short division like this.

We're going to start off by dividing the tens.

Now I know there's going to be a remainder straightaway because the eight in the tens column is not a multiple of seven.

So you can make one group of seven tens from the eight tens in the dividend.

So that means eight tens divided by seven is equal to one ten remainder one ten.

We place the one at the top.

We place the regrouped one ten in the ones column.

Which gives us a total of 19 ones.

Now we move on to dividing our ones.

You can make two groups of seven ones from the 19 ones in the dividend.

So that means 19 ones divided by seven is equal to two ones remainder five ones.

So we place the two at the top.

We then write remainder five next to the two ones.

So that means each child will get 12 marbles each and there will be five left over.

Back to you.

Select the correct division equation for this question.

76 marbles are shared equally between three children.

How many marbles does each child get? You can pause the video here.

Off you go.

So how did you do? B is the correct answer because the dividend is 76 and the divisor is three.

Moving on.

Andeep has solved these division questions.

He states that the remainder is never greater than the divisor.

So have a look.

In the first equation, we can see that the remainder is five and the divisor is seven.

And actually, in all the equations, the divisor is seven.

And if we have a look closely, the remainder is never greater than seven.

But do you agree? I'd like you to prove it.

Andeep is correct.

The remainder is less than the divisor.

If the remainder is greater than the divisor, that means an error has been made in the calculation.

Back to you.

I'd like you to calculate the remainder for this equation.

You can use the part-whole model to help you.

Off you go.

You can pause the video here.

So how did you do? You should have got remainder three.

Let's move on.

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? Back when I was in school, again, I really struggled with this type of question because I just felt like there was so much going on, but if we break it down, we will be able to do this.

So if we have a look closely, let's begin by looking at our dividend, and we know that that is 73.

Our quotient is 24 remainder one.

So seven tens divided by something has given Izzy two tens remainder one ten.

You can use your table facts to help you.

We know that three groups of two tens give us six tens.

So seven tens take away six tens is equal to one ten remaining.

So that means the missing digit is three.

So Izzy could complete the calculation to check 13 ones divided by three is four ones remainder one.

Personally, that is the final step that I would take to check that that is the correct divisor.

Back to you.

Fill in the gaps to find the missing number.

You can pause the video here.

How did you do? So seven tens divided by something gives one ten remainder three tens.

I know that one group of four tens gives me four tens with a remainder of three tens.

Seven tens take away four tens equals three tens remaining.

So that means the missing number is four.

If you got that, well done.

Good job.

Onto our final tasks for this lesson.

So for question one, you're going to tick the calculations which will have a remainder.

For question two, you're going to complete the calculations using short division.

For question three, you're going to solve the word problems below using short division.

So Andeep has 73 marbles.

He wants to share them between six of his friends.

How many marbles will each friend get? Three B.

Izzy is making a friendship bracelet for five of her friends.

She has a bundle of thread that is 84 centimetres long in length.

What is the total length she can use for each bracelet? And question four, you're going to fill in the missing digits.

You can pause the video here.

Off you go.

Good luck.

So how did you do? I'm going to leave the rest of the answers on the screen for you to check your work.

Okay, moving on.

Let's have a look at question three A.

So we know that the dividend has to be 73 because there are 73 marbles altogether that are being shared between six friends.

So six is the divisor.

Now, I can make one group of six tens from the seven tens in the dividend with a remainder of one ten.

So that means I will place one at the top and I will regroup the one ten and have 13 ones altogether.

Now, 13 ones divided by six is two ones with a remainder of one one.

So two remainder one.

That means my quotient is 12 remainder one.

Each friend will get 12 marbles and there'll be one left over.

And for three B, each bracelet can have a total length of 16 centimetres.

And by filling in the short division, your quotient should have been 16 remainder four.

For question four, these were the answers.

If you got them correct, give yourself a tick.

If you need a bit of time marking this, please pause the video here.

Well done.

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

You divided examples of a two-digit by a one-digit number using short division, with regrouping and remainders.

You can now use short division to solve problems, including regrouping and remainders.

You understand that if the number of ones, including any regrouped tens, is a multiple of the divisor, there will be no remainder.

Thank you so much for joining me in this lesson.

I hope you enjoyed it and I look forward to seeing you in the next one.