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 will be able to divide a 2-digit by a 1-digit number using partitioning and representations with regrouping.

Your keywords for today are remainder, partitioning, regroup, regrouping.

And I'd like you to repeat this after me.

Remainder, partitioning, regroup or regrouping.

Good job.

A remainder is an amount left over after division.

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

And in this lesson there may be quite a few of those.

I want you to think back to a time where you've had to share something but there wasn't either enough or far too many to be able to have shared it equally.

Partition means splitting a number into parts.

8 could be partitioned into 4 and 4, or 6 and 2, or many other various ways.

The process of unitizing and exchanging between case value is known as regrouping.

For example, 10 ones can be regrouped for 1 ten.

1 ten can be regrouped for 10 ones.

So for our lesson today, you're going to be dividing a 2-digit by a 1-digit number using partitioning with regrouping, and our first lesson cycle consists of understanding division with regrouping.

In this lesson, you will meet Andeep and Izzy.

9 glow sticks are shared equally between 4 children.

How many glow sticks does each child get? So we've got nine singular glow sticks here and we've got four children.

I'm going to be using skip counting in our divisor to help me solve this.

So 1 four is 1 each, so that's 4.

2 fours is 2 each, that's 8.

There is one glow stick left over, this is known as a remainder.

The remainder is expressed as r, and I'll show you how to write this answer down using that r.

So 9 divided by 4 is equal to 2 remainder 1, which means each child will get two glow sticks and there's one leftover.

So 9 divided between 4 is equal to 2 each, there is one glow stick left over.

Each child gets two glow sticks.

Now let's move on to dividing a 2-digit number by a 1-digit number.

52 glow sticks are shared equally between 4 children.

How many glow sticks does each child get? In each bundle there's 10 glow sticks, so I just want you to keep that in mind.

And I'm going to use skip counting again by the divisor to help me.

So 4 tens are 1 ten each, that's 40.

Hang on, what do I do now? I can't really divide this yet because it's in a bundle of 10, but what I can do is unbundle it.

But for now, let's leave that to the side.

What we can write down as to what's happened is this, 5 tens divided by 4 is equal to 1 ten remainder 1 ten.

5 tens divided between 4 is equal to 1 ten each with a remainder of 1 ten.

What do you notice? 5 tens cannot be divided equally by 4, therefore you must regroup.

We can unbundle the remaining 10.

So this is the same as regrouping 1 ten as 10 ones.

Let's go ahead and unbundle the 10 glow sticks.

Now we've got 10 ones alongside our two other glow sticks.

So 1 ten is equal to 10 ones, so 1 ten and 2 ones are equal to 12 ones.

In other words, 12 glow sticks.

Now we share the ones by skip counting.

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.

So now we have to add our partial quotient.

4 tens divided by 4 is equal to 1 ten.

12 ones divided by 4 is equal to 3 ones.

Let's add our partial quotient.

So our partial quotient here are 1 ten and 3 ones, which means 52 divided by 4 is 13.

Each child gets 13 glow sticks.

Even though you have to regroup, notice how there was no remainder, which means that 52 is a multiple of 4.

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

You can pause the video here.

So how did you do? You should have got 1 ten is equal to 10 ones, so 1 ten and 2 ones are equal to 12 ones.

Let's move on.

72 marbles are shared equally between 3 children.

How many marbles does each child get? Now you can use your place value counters to help you.

So 3 tens is 1 ten each, that's 30.

6 tens is 2 tens each, that's 60.

Now there's 1 ten left over, which means 7 tens divided by 3 is 2 tens remainder 1 ten.

7 tens divided between 3 is equal to 2 tens each with a remainder of 1 ten.

Now what do we do with this 1 ten? We can't get rid of it, we actually have to regroup it.

Okay, so we're going to regroup the 1 ten for 10 ones.

And you can see that that's on the screen now.

And let's not forget to add the 2 ones that we've also got.

So that's equal to 12 ones.

Next, you're going to skip count in threes because that's our divisor to share the 12 ones.

Now some of you may have already thought ahead and you already know what that is, but let's just still do this together.

So 3 ones is 1 each, that's 3.

6 ones is 2 each, that's 6.

9 ones is 3 each, that's 9.

And 12 ones is 4 each, that's 12.

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

Lastly, we're going to be adding our partial quotients.

So 6 tens divided by 3 is equal to 2 tens.

12 ones divided by 3 is equal to 4 ones.

We need to add our partial quotients, which is 2 tens and 4 ones.

So 72 divided by 3 is equal to 24.

Our quotient is 24, which means each child gets 24 marbles each.

Back to you.

I'd like you to fill in the blanks.

You can pause the video here, and when you're ready to join us, click play.

So how did you do? 3 tens are equal to 30 ones, so 30 ones divided by 6 is 5.

Andeep says, "I can tell straight away "if we have to regroup." Izzy asks, "How?" "Well, if the number of tens in the dividend "is not a multiple of the divisor," "we must regroup." Do you agree? Explain your thinking to your partner.

For example, 30 divided by 3, 3 tens is a multiple of 3, so we don't have to regroup.

There you go.

4 tens is not a multiple of 3, we do need to regroup.

So let's have a look.

60 divided by 3.

Now we know that 6 tens is a multiple of 3, so we don't need to regroup because we've got two groups of 3 tens which make 6 tens.

Over to you, for the first task, you are going to be ticking the equations that will require from the tens to the ones.

And I also want you to write down what you notice.

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

So how did you do? These are the equations that you should have ticked.

And what you should have noticed was that if the number of tens in the dividend is not a multiple of the divisor, we must regroup.

Let's move on.

So for this lesson cycle, you're going to be applying what we've just learned and it will involve regrouping.

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

You may have seen some of the informal strategies below.

So you may have seen this from a previous lesson that we've done.

You may have also completed a jotting that looks like this.

And lastly, you may have used the partitioning method to divide as well.

So these are all informal written methods.

And remember our toolkit, a skillful mathematician is able to reach into his or her toolkit and pick the most efficient method to use.

So let's have a look at this question.

75 marbles are shared between 5 children.

How many marbles does each child get? The first thing we need to do is figure out what division equation is needed to solve this problem.

I know that 75 must be our dividend because that is the number that we are dividing.

There are five children, so that must be our divisor.

We're calculating the quotient.

So the division equation that we are solving is 75 divided by 5.

Here's Andeep's method.

So he's partitioned 75 into 60 and 15.

He's then written 6 tens divided by 5 is equal to 12 ones.

15 ones divided by 5 is equal to 3 ones.

12 ones add 3 ones is 15 ones.

And here's Izzy's method.

I want you to have a look.

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 the multiples that are divisible by the divisors.

So this goes back to finding that highest multiple of the divisors that you know, and then finding the remaining parts, and then dividing both by the divisor.

Over to you, identify the incorrect informal method for the partitioning strategy shown.

Your division equation is 91 divided by 7.

And I'd like you to explain your thinking to your partner.

You can pause the video here.

So how did you do? You should have got a, and this is because the value of tens and ones are incorrect.

Okay, so this time what I'm going to do is work through this division question and then it's going to be your turn.

I want you to pay attention how I use my strategy to do this.

So my question is 68 divided by 4, 68 is my dividend, and 4 is my divisor.

Perfect.

Good job.

68 divided by 4 is equal to 6 tens and 8 ones.

6 tens divided by 4 is equal to 1 ten remainder 2 tens.

So 2 tens add 8 ones now gives me 28 ones.

So I move on to dividing 28 ones by my divisor now.

So 28 ones divided by 4 is 7 ones.

So 68 divided by 4 is 17, and I arrived at that quotient because I added my partial quotient, which were 1 ten and 7 ones.

Your turn.

I'd like you to calculate what 96 divided by 6 is.

Off you go.

How did you do? So if I were you, I would've found the highest multiple of six that I know or a simpler, and when I say simpler, I mean a multiple of 10 of 6.

So 60 and 36 is a good way forward, you may have also had 66 as one of your parts with 30 as your remaining part, or you may have also had 72 and 24 as your parts.

So 96 divided by 6, well that's equal to 9 tens and 6 ones.

9 tens divided by 6 gives us 1 ten with a remainder of 3 tens.

3 tens add 6 ones gives us 36 ones.

36 ones divided by 6 is 6 ones.

We then add our partial quotients, which is 1 ten and 6 ones, and that's 16.

Alternatively, if you use the partitioning strategy, you would've divided 60 and 36 by your divisor of 6, and you would've also come to the same quotient of 16.

Looking at this, I definitely prefer the part whole model because sometimes it could become a bit confusing recording it using informal jottings like this shown on the screen, but it's down to personal preference.

Right, over to you.

I'd like you to fill in the gaps.

You can pause the video here and when you're ready to join us, click play.

This is what you should have gotten.

7 tens divided by 3 is equal to 2 tens remainder 1 ten.

Because 7 tens is not divisible by 3, that is why we end up with a remainder of 10.

And then if we carry on, 12 ones divided by 3 is equal to 4 ones, so our quotient is 24.

Right, onto our last task for this lesson cycle.

For task one, you're going to use both strategies to solve the division problem: 98 divided by 7.

Have a look at the information on both sides and please fill in the gaps.

For the next task, you're going to be solving the following questions.

You're going to record your calculations using an informal written method.

So that could be a written method, that could be an informal jotting.

You can use your partitioning strategy as well.

Your questions here are 85 divided by 5, 84 divided by 6, and 64 divided by 4.

For question three, you're going to be solving the worded problems. So 3a, 57 cupcakes are shared equally between 3 boxes.

How many cupcakes in each box? 3b is 90 marbles are shared equally between 6 children.

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

Off you go.

This is what you should have got for question one.

You can pause the video here to check your work.

If you got all of that correct, good job.

You were solving the following questions and you were to record your calculations using an informal written method.

Here we can see informal jottings.

The quotient that you should have got were 17, 14, and 16.

If you use the partitioning strategy and still got the same quotients, well done.

Right, let's really focus in on these questions.

So for 3a, we need to figure out what the division equation is first.

So we've got 57 cupcakes altogether.

That means that is our dividend, the number that we are dividing up.

And our divisor must be three.

Because there are only three boxes, we need to figure out how many cupcakes can fit in each box, so three is our divisor.

So you may have used the partitioning method, and personally I would've as well, or you may have used informal jottings here.

We'll start off with 57 divided by 3.

If I was using the partitioning method, I would've partitioned 57 into 30 and 27 and then divided each part by 3 to get my answer of 19.

Alternatively, you could have also used the method shown on the screen.

If you've got 19 as your quotient, give yourself a tick, well done.

Now again, we need to figure out what our division equation here is.

So 90 marbles, that is our dividend because that's how many marbles there are altogether.

Six is the divisor because there's only six children that the 90 marbles are being shared between.

So if I was to use the part whole model, I would've partitioned 90 into the highest multiple of 6, that would make the division equation easier.

So instead of choosing 72, I probably would've chosen 60 and 30.

Both parts are divisible by six, they are multiples of six.

So 60 divided by 6 is 10, and 30 divided by 6 is 5.

10 add 5 is 15, so 15 would've been your quotient.

Again, alternatively, if you have an informal jotting that has also led you to the partial quotient of 15, you are correct, well done.

So that is the end of the lesson.

In today's lesson, you learn how to divide a 2-digit by a 1-digit number using partitioning with regrouping.

You now understand that if the dividend is not a multiple of the divisor, there will be a remainder and you have to regroup.

You can also divide a 2-digit by a 1-digit number using partitioning and representation, including regrouping.

I hope you found that lesson super helpful, and I look forward to seeing you in the next one.