Lesson video

Hello, and welcome to this lesson.

My name is Mrs. Behan.

And today I'm going to be teaching you all about division.

We might even throw a little bit of multiplication in there.

So when you're ready, let's get started.

Let's start by having a look at our lesson agenda.

We're going to begin by dividing by 100, using our understanding of place value.

We're going to move on to dividing by 100, using a grouping strategy.

Following that there is a practise activity and then an independent task.

And I know you'll be keen to find out how you got on, so I'll make sure I go through the answers with you.

For this lesson you will just need two things, something to write with a pen or a pencil and something to write on.

If you haven't got those things handy, pause the video whilst you go and get them.

Try to work in a quiet place where you won't be disturbed.

So to get ourselves warmed up and ready, we are going to practise dividing by 100, because you've got to this lesson I know that you know the secrets of dividing by 100.

When we look at a value, so here we've got two 100s in our place value chart.

I can move those to two places to the right.

So one place to the right, two places to the right.

So we've divided a multiple of 100 by 100, the value changes.

Okay.

So we've now got two ones instead of two 100s.

So the secret is that we can remove two zeros from the end of the number.

So we can take away the zero from the tens column and we can set of tens place and we can take away the zero from the ones place.

So we know our next activity calculation is going to flash up on the screen.

And all you have to do is just tell me what the quotient will be.

That's the number that we will have left at the end.

Let's make a start.

100 divided by 100 is equal to one, 200 divided by 100 is equal to two, 300 divided by 100 is equal to three, 400 divided by 100 is equal to four.

Joining with me as I say the calculations as well, they are going in a pattern.

500 divided by 100 is equal to five, 600 divided by 100 is equal to six, 700 divided by 100 is equal to seven, 800 divided by 100 is equal to eight, 900 divided by 100 is equal to nine.

1000 divided by 100 is equal to 10.

Now those questions, follow the pattern.

Let's see if you can answer some questions in and out of order.

And I may even throw in a multiplication question.

So what is 500 divided by 100.

Well, remove your zero from the tens place and the zero from the one's place the quotient is five.

50 divided by 10 tell me the answer? The quotient is also five.

What is 40 multiplied by 10? Let's make this number 10 times greater where we can place a zero after the 40.

So we now have a product of 400.

What's 14 multiplied by ten? 140.

800 divided by 100 is equal to eight, 250 divided by 10 is equal to 25, 720 divided by 10 is equal to 72.

Remember we just remove one zero from the ones place when dividing by 10.

And 900 divided by 100 is equal to nine.

Well done.

Great job.

So we have recapped that to divide by 100, we can move the digits to places to the right.

We use our understanding of place value to work it out.

We are now going to explore division by grouping to see if we get the same quotient.

So we're going to take a step back to remind ourselves what division by grouping actually looks like.

Just pause the video here, because I want you to come up with at least four equations that can be seen in this array over here.

Okay? So then when you've done it, I'll show you just some of the possibilities that you could have come up with.

So how did you get done? I'm sure you did just fine.

I came up with five multiplied by three is equal to 15, three multiplied by five equals 15, 15 divided by five is equal to three and 15 divided by three is equal to five.

Did you get any of those? We're going to describe the equations now using parts and wholes languages.

So let's take the first equation.

So five multiplied by three is equal to 15.

So you could have seen this as five groups of three.

So that would be three plus three plus three plus three plus three.

Or you might have seen it the other way where we had three groups of five.

So we've got five plus five plus five.

I've drawn some rings around them so we can see clearly.

Okay.

So take a look.

So we can see that this is five plus five plus five, which would be three groups of five, or it could be five three times.

Either of these multiplications work when there are rings around the arrays in this way.

Okay.

So I've changed the place of the rings now.

So we've got three plus three plus three plus three plus three, both calculations work with this array, depending on how you want to talk about the groups.

Okay.

The factors are commutative.

So as you can have both of those ways, so whether the rings were going horizontally or whether the rings were going vertically, those two calculations that you can see on the screen, both represent that array.

And that's because the fact is our commutative, whichever order we have our factors.

When we multiply, we have the same product at the end.

Okay? Say this sentence on screen with me.

If you change the order of the factors, the product remains the same.

Something very important to remember.

Let's see it's again.

If you change the order of the factors, the product remains the same.

Okay.

Doing well so far.

Let's take our division calculation.

So there's two ways we can divide.

We can divide by sharing, which means we would have a part of something and one for you, one for you, one for you, or we can group so we already have a set group say, so you can have three, you can have three, you can have three and so on.

So let's take our division calculations.

Oh, I'll just go back onto that.

So here our 15 has been shared into three equal groups and each equal group has five in it.

Okay.

Or we could say that the set size, the group size is five.

So then we've got three equal groups of five.

So our division calculations to represent this array would look like this.

15 divided by five is equal to three or 15 divided by three is equal to five.

Let me draw your attention back to the groups.

Okay.

So if here, if we are divided by grouping, our devisor here is showing us that the group size is five.

We would have three sets of them.

That's the strategy we're going to look at a little bit more detail.

We want to know if the grouping strategy will have the same outcome as shifting the digits to the right and removing zeros from the tens and ones places like all the practise we did when we explored place value charts.

So that we understand what each number in the equation is doing.

I'm going to go through some key words with you.

So here is the equation that we've been looking at.

The dividend is the whole.

Okay? So in this equation, it is number 15.

It is what we have to begin with and you will notice, or you should notice it's the largest number in our equation.

The divisor has the job of actually dividing the whole.

So this is either the number of groups you will share the whole between, or it is the number of objects you will group together to make the group size.

The quotient tells us the value of each set, if we shared it or the number of equal groups we made, if we divided by grouping.

So we have the dividend, the divisor and the quotient.

So I find that calculation up in the corner.

Again, say it with me, 15 divided by three is equal to five.

So when I had a look at this array, I have decided that my group size is going to be three.

I want to know how many groups of three are in 15.

So I've taken my array and I have drawn rings around the group size which is three.

Okay.

This number here is now telling me the group size is three.

So we can see that we've got five equal groups of three.

So we're going to say the sentences together that come upon your screen.

When you say something out loud, it helps you to remember and understand.

So please join him.

My whole is 15.

I made equal parts by grouping in threes.

There are 5 equal groups of 3.

So each group has got three in it.

So we can say 15 divided by 3 is 5.

Can you think of a calculation that might help us to check that that is correct? You might've come up with five multiplied by three is equal to 15.

We use the same array earlier to think of multiplication calculations, as well as division calculations and five multiply by three also gave us a product of 15.

So if you use the same numbers, but change the operation.

So we now understand that when we've used our division by grouping strategy, that the devices role tells us how many are in each group and how many the row in each set.

So now we're going to explore divided by 10 and 100.

And that's going to tell us the group size.

So we're going to be divided in where the group size is 10 or 100.

Let's have a look at place value chart.

I'm going to show you how to use a place value chart to show grouping.

So you can see I've got three 100s in my set.

I want to divide it by 100.

So I calculation is 300 divided by 100, but our divisor means we are going to group in 100s.

So let's move those counters.

So I'm going to move them down now.

I'm going to use the rest of my place value chart, spread out my counters.

So I now have one group of 100, two groups of a 100, three groups of a 100.

So 300 divided by 100 is equal to three.

The quotient is three.

We're going to use the inverse, which is the opposite operation.

So when dividing our inverse operation is multiplication.

Can you think of a multiplication that would help check this answer? I'm sure I could hear you saying three multiplied by 100 is equal to 300.

So if you use the same numbers, but the symbols are different and the operations are different, but we understand the relationship between the two.

And now I'd like you to have a go at drawing a place value chart, just like the one that you can see on the screen.

You might need to add a few more rows so that you can divide by grouping.

Like I showed you in the last example.

Here is some calculations on the right hand side of your page.

So you're going to use groups of 100 or groups of 10.

Okay.

So your first example, if you were doing 600 divided by 100, you would start by drawing six circles labelled with 100s in your 100s column.

You would then share a group at a time.

So you could draw each one down on another row.

All right.

If you would dividing by in groups of 10, you would make sure that you make 160, but in tens.

Okay.

So think careful about how many you would need for those.

Pause the video here whilst you have a call.

And if you find it a little bit tricky don't worry because I'm going to go through the answers with you in just a moment.

Welcome back.

How did you get on? Well, there's some easy questions.

Did you find any harder than the others? Let's start with 600 divided by 100.

So if you were to share them out in groups of 100, you would have six groups of 100 in 600.

How many groups of 10 can you make from 160, or you'd be able to make 16 groups of 10.

I'm sure that one took you a long time to draw out on your place value chart.

800 divided by 100 is equal to eight.

I'm sure you built to use your knowledge of place value to work out as well.

Something is equaled 70 divided by 10, that would be seven.

You would have drawn seven groups of 10.

To make the value of 70.

You would have drawn four groups of 100 to make the value of 400 for this last calculation.

How many did you get right? Did you get all five? So which strategy did you prefer? Do you prefer using our place value strategy, where we moved the digits to places to the right? And then we can remove zeroes from the tens and ones places, or did you enjoy drawing out the groups on our place value chart in different rows? Do you think it depends on the calculation as to which one is more efficient.

Efficient is that word there on the screen.

And that means doing the job well in the quickest and best way.

You might've found that six 160 divided by 10 by grouping and drawing out all of those place value counters took you a long time.

Perhaps on that occasion, it might have been easier to use our place value understanding because we know that if we divide by 10, we're able to remove the last zero.

We're able to remove the zero from the ones place on 160.

You're now ready to take a bash at your independent task.

With these calculations you have to work out the missing numbers.

Some have been divided by 10.

Some have been divided by 100.

So I think use your understanding of place value.

So to remove the zeros, or you can use your grouping strategy.

So you could find out how many tens they are, how many groups of tens there are in 60.

It's entirely up to you and it depends which one is more efficient at the time.

I'm going to read this to you.

Grayson and Katie are dividing numbers by 10 and 100.

They both start with the same three digit number.

Can you work out what number they each started with? Grayson said, "My answer has six 10s and zero ones." Katie said, "My answer has 6 ones." They both started with blank, Grayson divided by blank and Katie divided by a blank.

So please, can you fill in what number they both started with whether Grayson divided by 10 or 100 and whether Katie divided by 10 Or 100.

Pause the video whilst to complete your task.

When you finished come back to me.

Welcome back.

Let's go through the answers.

There are six groups of 10 in 60, so 60 divided by 10 is equal to six.

Eight is the missing number here because 800 divided by 100 is equal to eight and 700 divided by 100 is equal to seven.

There are seven groups of 100 in 700.

70 divided by 10 is equal to seven.

One is equal to 100 divided by 100.

25 is equal to 250 divided by ten, 600 divided by 100 is equal to six.

16 is the missing number in the next calculation.

160 divided by 10.

30 is equal to 300 divided by 10.

Imagine drawing 30 groups of 10.

In this question it probably would have been more efficient to use our place value understanding and remove the zero from the ones place.

610 divided by 10 is equal to 61.

92 is equal to 920 divided by 10.

I'm sure with that calculation, you use the inverse.

So you would have multiplied 92 by 10 to find out that the missing number was 920.

Five is equal to 500 divided by 100.

And then now a problem with Grayson and Katie.

Well, they both started with 600 and Grayson divided by 10, because 600 divided by 10 gives him the answer of six tens and zero ones.

Or in other words 60.

Katie divided by 100 because she only had six ones left and 600 divided by 100 is equal to six.

If you'd like to please ask your parents or care to share your work on Instagram, Facebook, or Twitter, tagging @OakNational, @LauraBehan21 and #LearnwithOak.

Thanks for joining me in this lesson.

So we have found out that actually, if you divide by grouping, or if you divide using our place value understanding where we can remove the zeros, actually the quotient is the same.

It's all about choosing the right method for the right calculation.

I hope to see you again soon.

Don't forget to take the quiz to test out your new learning.

Thank you.

Bye.