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.

Today, you will learn how to divide a 3-digit by a 1-digit number using partitioning and representations, including regrouping and remainders.

The keywords are on your screen now, and I would like you to repeat them after me.

Remainder, partitioning, regroup/regrouping.

Good job, let's carry on.

Now, a remainder is an amount left over after division.

It happens when the first number does not divide exactly by the other.

Partition means splitting a number into parts, and there's an example on your screen there.

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

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

100 can be regrouped for 10 tens, and I'm sure you know more.

So, for our first lesson cycle, you are going to be understanding division when multiple regrouping needs to happen or is happening.

And in this lesson, you'll meet Andeep and Izzy.

Now, you may have seen something that looks like this.

So, in this example, you only needed to regroup once from the hundreds to the tens.

Today, you will explore what happens when there are multiple instances of regrouping, and how to record that, and what to do when that happens.

Let's begin.

972 cakes are ready to be delivered in boxes of 4.

How many cakes will each box have? Will there be any leftover? So, our division equation is 972 divided by 4.

The dividend is 972 and the divisor is 4.

So, we've got our four boxes there, and we've represented 972 in hundreds, tens, and ones.

We're going to begin by dividing the hundreds first, and we're going to do this by skip counting in our divisor, which is 4.

So, 4 hundreds is 1 hundred each, that's 400.

8 hundreds is 2 hundreds each, that's 800.

Now, there is 100 left over.

9 hundreds divided between 4 is equal to 2 hundreds each with a remainder of 100.

So, that means you will have to regroup.

So, what we need to do is regroup the 1 hundred for 10 tens, so let's do that now.

There we go.

7 tens and 10 tens is equal to 17 tens.

So, now we can continue to divide 17 tens by our divisor of 4.

And let's do this by skip counting, and we want to skip count because if we were there sharing out ten one at a time, it would just take forever, so we need to be more efficient in how we do things and skip counting is definitely more efficient.

So, 4 tens is 1 each, that's 40.

8 tens is 2 each, that's 80.

12 tens is 3 each, that's 120.

And 16 tens is 4 each, that's 160.

So, 17 tens divided between 4 is equal to 4 tens each with a remainder of 1 ten.

That doesn't mean we stop dividing there, we have to carry on.

So, what do you think we do? That's correct, you now need to regroup 1 ten for 10 ones.

So, let's do that now.

So, 2 ones and 10 ones is equal to 12 ones.

So, we're going to continue dividing our 12 ones by our divisors of 4, and we're going to do this by skip counting.

So, 4 ones is 1 each, that's 4.

8 ones is 2 each, that's 8.

And 12 ones is 3 each, that's 12.

12 ones divided between 4 is equal to 3 ones each.

That's two regroups that we've had to do there.

So, lastly, we're going to add our partial quotients, and we can represent that like this.

We've got 2 hundred, 4 tens, and 3 ones.

We need to add those together to find our quotient, and that is 243.

Each box will have 243 cakes.

Over to you.

Your divisor is 6.

Which numbers will result in regrouping? Top tip, have a look at your hundreds digit.

You can pause the video here.

So, how did you do? B and C will require regrouping, and that is because 7 hundreds divided by 6 result in 1 remainder 1 hundred.

C will also require regrouping because 7 hundreds divided by 6 is 1 remainder 1 hundred.

And then, 19 tens, once we've regrouped 100 into 10 tens, we end up with 19 tens.

So, 19 tens divided by 6 is 3 remainder 1 ten, so again, we'd have to regroup.

974 cakes are ready to be delivered in boxes of 4.

How many cakes will each box have? And will there be any leftover? So, I want you to think about what your division equation might be.

Well, our dividend is 974 and our divisor is 4.

And we can again represent this using our place value counters.

We're going to going to begin by dividing the hundreds.

So, 4 hundreds is 1 hundred each, that's 400.

8 hundreds is 2 hundreds each, that's 800.

There is 100 left over, so what do you think we have to do? We will have to regroup the 1 hundred for 10 tens, but we can do that in a bit.

So, 9 hundreds divided by 4 is equal to 2 remainder 1 hundred.

9 hundreds divided between 4 is equal to 2 hundreds each with a remainder of 1 hundred, meaning we'll have to regroup.

So, we're going to regroup 1 hundred for 10 tens.

So, 7 tens and 10 tens is equal to 17 tens.

Now, we're going to divide 17 tens by a divisor of 4, we're going to skip count in 4.

4 tens is 1 each, that's 40.

8 tens is 2 each, that's 80.

12 tens is 3 each, that's 120.

And 16 tens is 4 each, that's 160.

So, 17 tens divided between 4 is equal to 4 tens each with a remainder of 1 ten.

So, now you need to regroup 1 ten for 10 ones.

So, 4 ones and 10 ones is equal to 14 ones.

Then, you're going to divide your ones by our divisor of 4 and we are going to skip count in 4.

So, 4 ones is 1 each, that's 4.

8 ones is 2 each, that's 8.

12 ones is 3 each, that's 12.

So, 14 ones divided between 4 is equal to 3 ones each and a remainder of 2.

So, that's two regroups.

Now, we need to add our partial quotients, and this can be written like this.

So, 14 ones divided by 4 resulted in 3 ones remainder 2.

Now, when we are adding our partial quotients, this is what we get.

243 remainder 2.

Now, it's super important that we add in our remainder, we don't just forget about it.

So, each box will have 243 cakes with 2 cakes left over.

Now, Andeep reckons there was an easier way.

He says that, "He knew there was a remainder of 2 straight away." Izzy says, "How?" "Well, if I know that 972 divided by 4 is 243, then I know the next multiple of 4 would be 976, which is divisible by 4." So, he can use the inverse of multiplication to help articulate his thinking.

4 multiplied by 243 is 972, and the next multiple would be 976.

Now, 974 is 2 more than 972, so the remainder is 2.

Do you agree with Andeep's thinking? Justify your thinking to your partner.

So, using what you already know can help you.

For example, 972 divided by 4 equals 243.

Now, 243 is a multiple of 4, there will be no remainders.

973 is 1 greater than 972, so there will be a remainder of 1.

973 divided by 4 is equal to 243 remainder 1.

974 is 2 greater than 972, so there will be a remainder of 2.

So, 974 divided by 4 is equal to 243 remainder 2.

Your turn.

Use the information to fill in the gaps.

You can pause the video here.

How did you do? So, 972 divided by 4 is equal to 243, which is a multiple of 4, there will be no remainders.

975 is 3 greater than 972, so there will be a remainder of 3.

So, 975 divided by 4 is equal to 243 remainder 3 Onto your main task.

Andeep and Izzy are using mental strategies to find the remainders.

I'd like you to fill in the gaps.

For task 2, you're going to complete the table by ticking if the equation will require regrouping and calculating how many of each unit will need to be regrouped? One has been done for you.

You can pause the video here.

Off you go, good luck.

So, how did you do? You can pause the video here to mark your answers.

If you got all of those correct, really good job.

Let's keep going.

Now, let's have a look at this question more closely.

You've got five division equations there, and you're going to be indicating whether regrouping will be required.

You've got 777 divided by 7, in the hundreds, tens, and ones are multiples of 7, we know that there will be no regrouping required there.

Looking at 840 divided by 7.

Now, I know that 84 is a multiple of 7, so 840 must be a multiple of 7.

However, when I look at my a hundreds digit, it is 8.

Now, 8 is not a multiple of 7, so we will need to regroup from the hundreds to the tens.

And the amount that needs to be regrouped is 100 because 700 is a multiple of 7.

Let's have a look at 875 divided by 7.

Now, similarly again because the 8 in the 800 is not a multiple of 7, we will have to regroup 1 hundred.

And then, that 1 hundred needs to be regrouped as 10 tens added to the 7 tens, which is 17.

Now, 17 is not a multiple of 7, however 14 is, and the difference between 17 and 14 is 3, so we're going to have to regroup 3 tens after that.

For 640 divided by 8, the amount regrouped is 6 hundreds.

And for the last question, so 973 divided by 6, you will have to regroup, and the amount that you're going to be regrouping is 3 hundreds.

And then after that, you will also have to regroup from your tens to your ones, and the amount for that would would've been 1 ten.

If you've got all of those correct, really well done, good job.

It shows that you are identifying when you have to regroup and how much.

Right, onto our last part of our cycle.

So, this time you're going to be dividing using partitioning including multiple regroups.

So, there are many ways to record and solve division equations.

You may have seen some of the strategies below.

So, these are known as informal methods.

A local bakery is having a grand opening.

It has a total of 523 slices of cake which are packed in boxes of 3.

How many boxes will be ready for the bakery's grand opening? What division equation is needed to solve this problem? Well, our division equation is 523 divided by 3.

The dividend is 523, this is the amount we are dividing up.

The divisor is 3, this is the amount we are dividing by.

And the quotient is unknown, this is what we are calculating.

Over to you, I'd like you to fill in the blanks.

You can pause the video here.

So, how did you do? The dividend is 956 because this is the amount we are dividing up.

The divisor is 6 'cause this is the amount we are dividing by.

And the quotient is unknown, this is what we're calculating.

And an example question could have been 956 cakes are packed into boxes of 6.

How many boxes will there be in total? So, this here is Andeep's method, and he's used the part whole model and the partitioning strategy to help him with his division.

And this is Izzy's method, she's used the informal written method.

So, which method do you prefer? Sometimes the part whole model is more efficient because it makes the process of regrouping easier as we can choose multiples that are divisible by the divisor.

And here, we can see that Andeep has picked 600 as a part, 300 and 56 as parts as well.

Now, 600 and 300 are multiples of the divisor, and we know that 56 is not, but we can find a multiple that is close when dividing 56 by 6, but ultimately it's made the division easier.

Right, so Andeep has collected 446 guinea cards.

He wants to divide them equally amongst 3 of his friends.

How many cards does each child get? And are there any leftover? So, what division equation is needed to solve this problem? So, 446 is the dividend because this is the amount we are dividing up.

The divisors is 3 because that is the amount we are dividing by.

And the quotient is unknown because that is what we are calculating.

Now, there are many ways we can partition 446.

We're going to begin by partitioning 446 into its highest multiples of 3.

So, I'm going to start off with 300, then 120, and then 26.

Now, we're going to divide each part by the divisor.

So, 300 divided by 3 is 100, 12 tens divided by 3 is 4 tens, and 26 ones divided by 3 is 8 ones remainder 2.

Lastly, we're going to add up our three partial quotients, which gives us a quotient of 148 remainder 2.

So, each friend will get 148 guinea cards and there will be 2 left over.

Over to you.

You're going to fill in the missing numbers.

You can pause the video here and once you're done, click Play so we can move on.

So, if you've got this, well done, you can give yourself a tick.

Let's move on.

Onto our task.

So, question 1, you're going to solve the following questions.

Record your calculations using the partitioning strategy.

1a, 947 divided by 8, 1b is 538 divided by 3, and 1c is 789 divided by 2.

For question 2, you're going to solve the worded problems using an informal method.

So, 2a, 436 cards are divided equally between 3 friends, how many cards does each child get? And are there any leftover? 2b, Izzy has 579 beads, she needs to make 4 friendship necklaces.

How many beads can each necklace have? Are there any leftover? You can pause the video here.

Off you go, good luck.

So, how did you do? So, for question 1, you should have got this.

So, your quotient should have been 118 remainder 3.

For question 1b, you should have got 179 remainder 1.

And for 1c, you should have got 394 remainder 1.

Now, for these questions, it was really important that you had identified the division equations that you were solving.

So, for this question, your dividend was 436 and your divisor was 3.

And for 2b, your dividend was 579 and your divisor was 4.

Now, let's have a look at 2a.

If you were using the partitioning strategy, the best way forward was to have found the highest multiple of 3 in 436, and then divide those parts by 3.

Similarly for question 2b as well.

So, if you got your quotient as 145 remainder 1 or 145 cards and 1 card being left over, you are correct.

Well done, you can give yourself a tick.

And for question 2b, each necklace can be made of 144 beads with 3 beads left over.

Or if you've got 144 remainder 3, you are also correct.

Well done, you can give yourself a tick.

Good job.

Fantastic, you have made it to the end of this lesson.

So, let's summarise our learning.

So, today you divided a 3-digit by a 1-digit number using partitioning and representations, which involved regrouping and remainders.

You now understand that if the hundreds number is not a multiple of the divisor, then the remainder is regrouped for tens.

You also understand if the tens number is not a multiple of the divisor, then the remainder is regrouped for ones.

Lastly, you understand if the ones number is not a multiple of the divisor, then there will be a remainder in the answer.

Well done, I really hope you enjoyed this lesson and I look forward to teaching you in the next one.