# Lesson video

In progress...

Hi, everyone.

I'm just looking through an old photo album.

It's something I like to do, if I ever want to relax a little bit or unwind or prepare myself for something that's coming up like this maths lesson.

Anyway, as I was looking through, I came across a photo that I thought I would share.

So this is me.

This is my brother.

I think I was in year five or year six when this photo was taken.

What do you think? Have I changed very much? It's been quite awhile since this photo was taken.

So looking very different now, I think.

Well, as I said, I wanted to get myself prepared for the lesson.

This lesson needs your full attention as always, so if you've got any distractions around you, press pause, take a moment to find yourself somewhere else, where you can settle down for the next 20 minutes of maths learning.

Press pause now, and I'll see you again when you are ready to start.

In this lesson, we will be solving division calculations that include remainders.

We're going to start off with a negative numbers activity, before I give you the chance to practise both short division and long division with remainders, you'll, then be set for your independent task to end the lesson.

Things that you're going to need.

Pen or pencil, some paper and a ruler.

Press pause if you need to, while you're going collect those items, otherwise let's get started.

So negative numbers.

Here is a number line.

I've marked the start and end points.

There are some arrows indicating the position of particular numbers.

I'd like you to tell me the numbers that the arrows are pointing to.

Press pause, complete the activity, then come back and we'll review the solutions.

Are you ready to take a look? Can you hold up your paper? 'Cause I'm curious to see how you have represented your solutions.

Have you drawn a copy of the number line? Have you got the correct number of equal parts, equally spaced even? Looking good.

Okay.

Let's reveal then you can mark these off on your paper.

So working from left to right, we're at negative eight, negative five, negative four.

We've crossed zero.

We're at one, five and eight.

How did you get on with that? I could see lots of smiley faces.

Excellent.

Okay.

Before we start looking at our division, it's important to remember that when faced with a division equation, expression, we're going to be completing the equation or addition or subtraction, any calculation, we need to look at it first and apply some number sense.

Although we'll be looking at short and long division in this session, there'll be times where they're not the appropriate strategy.

And instead, one of many mental strategies would be more appropriate and more efficient.

So just take a moment to look at these expressions.

Which of them would you solve mentally? And which would you solve using a written method? Press pause, come back when you're ready to share.

You ready? So, which do you think, mental or written? How many of them would be mental? Show me with your fingers.

Okay.

And so therefore.

Show me for the written.

Let me show you the ones that I think, with colours to match the word mental or the word written.

So mentally, I was thinking these three.

There's some nice connections to known facts or to equivalent division that I could use to solve those.

Whereas the others, I thought a written method, long division for dividing by 89 and 48, whereas a short division for dividing by 11 and four.

Another skill that we need for our work on division or any calculation is the ability to estimate.

Can you estimate the size of the quotients? Let me show you what I mean for the first one.

So with this, I would be rounding to some numbers that I could easily work with mentally, perhaps, where there's a connection between them, seven and 84.

A nice connection there of 12.

Seven twelves, 84, 70, 840.

Seven multiplied by 10, 84 multiplied by 10.

That relationship.

84 divided by seven is 12.

840 divided by 70, also 12 because I've increased seven and 84, both by 10.

The quotient size has been preserved, whereas from 70, I'm sorry, 8,400 divided by 70.

That's going to be 120, because I've increased 840, 10 times, the divisor has remained the same.

I'm going to increase my quotient 10 times as well.

Press pause and have a go at finding an estimated size of the quotient for the other two, then come back and share.

Let me see what you've recorded.

Noticing relationships? Good.

Some equivalent divisions, related facts certainly.

Let's check and compare them.

So I chose to round to 2000 and keep one as 50.

Then I was thinking about the relationship between five and 20, four.

And the divisors remained the same, but the dividends increased 10 times.

So my quotient increases 10 times to 40.

And here I'm increasing my divisor 10 times, my dividend 10 times, so my quotient remains the same, and my estimate is 40.

The last one, 900 for sure and 30.

Lovely connection between those two, 90 and three.

There's a relationship there.

Nine and three, three.

Three and 90, 30, because my dividend increased 10 times.

My divisor stayed the same.

My quotient increases 10 times.

Then my quotient stays the same, because my dividend of 90 and divisor of three have both increased 10 times.

An estimated quotient of 30.

Have a quick go at these three as well.

But for the first and the third, where we're dividing by one digit number, divisor of one digit, you might need to estimate by finding two sized.

Two estimated quotients that the actual quotient will fall between.

Have a go.

We'll go through it together afterwards anyway.

Press pause.

Here we need to think more about right.

So 8,000.

8,000 is four lots of 2000.

8,400 is four lots of 2,100.

So my estimate, the estimated size of my quotient.

Well it's going to be between 2000 and 2,100, because 8,277 is between 8,000 and 8,400.

So a little bit tricky to spot that as an estimation, compared to what you've probably done for the middle one, 2000 and 40, and then looking at the relationships between four and 200, four and 20, five, then 50 and preserving the size of the quotient here, because the dividend of 200 has increased 10 times to 2000, and the divisor of four has increased 10 times to 40.

The last one is going to be a similar approach as to the first one.

So if you struggled with that the first time, pause again now before I show you the solution.

Find an estimated size of the quotient using that sentence.

So the quotient will be between something and something.

Otherwise, let me show you the solution or possible solution for an estimate.

I was thinking eight.

Eight lots of 110 is 880.

Eight lots of 120 is 960.

918 falls between 880 and 960, so my quotient will be between 110 and 120.

Let's have a think now then about some division.

We're going to look at just a short division calculation.

And for this division, there's going to be a remainder.

And that's what I want you to focus your attention on.

So estimating first of all, 2000 divided by five.

20 divided by five is four, 2000 divided by five, 400.

An estimated quotient of 400.

Let's make the number 2,312.

We're dividing that by five, using our grids with our short division recorded at the same time.

If you want to pause and work through this independently, then come back and check, press pause now, or work with me as we go.

How many groups of five can we make from two thousands? Can't make any.

So let's exchange the two thousands.

Did you see that? Exchange the two thousands for how many hundreds? 20 hundreds.

So we've now got 23 hundreds.

How many groups of five can we make from 23 hundreds? We can make four, leaving three hundreds.

We need to exchange those three hundreds for tens.

Watch them go.

And notice the small three appear next to the one.

We've got 31 tens now.

How many groups of five can we make from 31 tens? Six.

Using 30 of them, we've made six groups of five and we have one 10 remaining.

We're going to exchange that one 10, for 10 ones and ask ourselves, how many fives, how many groups of five can we make from 12 ones? How many? Two.

Now we've got two left, two ones left, which is our remainder that we can record like this.

Remainder one, remainder two, sorry.

So we've solved there a short division with a remainder.

Here's one for you to try it.

So even if the last one you worked through with me, do press pause on this one.

Have a go at solving it and find the remainder.

Ready? Let's take a look then.

So I'm not using the counters this time.

We're just going to use the short division method.

Oh, for an estimate first of all, how would you estimate this? If you didn't already, how would you estimate it now? Yes.

Look at that.

64, 640, nice connection to eight.

How many eights are in 64 is going to help us.

We got to increase that 10 times because the divisor has increased 10 times from 64 to 640.

So an estimate of eight.

So how many groups of eight can we make from six hundreds? How about 65 tens? Eight, eight, 64.

We've made eight groups of eight from 64 tens, leaving one 10 to exchange for 10 ones.

How many eights can we make from 14 ones? One group of eight.

Leaving ow many as a remainder? Remainder six.

And that's a simple short division with remainders.

How about long division and remainders? It's going to work in the same way.

We're thinking first of course about an estimate.

So 6,359 divided by 13, an estimate first of all, and then using long division to solve it.

Press pause, have a go and see how you get on, then come back when you're ready.

Hi guys, I'm Ms. Jones.

And I'm going to be taking you through this solution before handing you back over to Mr. Whitehead.

So we had 6,359 divided by 13.

And the first thing he asked you to do was to create an estimate.

So this is how I made my estimate.

I rounded 6,359 to 6,000 as that's a number I can use my mental strategies with.

And instead of using the 13 multiplication table, I know my 12 times table.

So that might be easier for me to make an estimate with.

To work that out, I thought about what 60 divided by 12 is, which I know is five, which means 6,000 divided by 12 is 500.

Now that means that my answer to the above equation needs to be something similar to 500.

So a little bit more, a little bit less would be okay.

But if it's far away from 500, I know that actually, I might need to double check what I'm doing.

Okay.

So we're going to use that later when we check our answer.

Let's set up our long division now.

Okay.

So we've got 13.

And I want to see if it.

Let's look at our thousands digit.

Six.

We can't really use that, so we're going to need to use our hundreds digit.

So I've got 63 hundreds.

I going to think about how many thirteens will go into 63.

Now to help me with this, I'm thinking about my 13 times table.

So I'm going to make some jottings along the side, of multiples for 13.

And one times 13 is 13, two times 13 will be 26.

Something I can work out easily is 10 times 13, 130.

Okay.

Let's go back to my number 63.

Let's try five times 13.

That gets me 65.

Okay a little bit too high.

So let's do four times 13, 52.

Okay.

So now I know that four thirteens will go into 63, and I've got 52 remaining.

I can put my four on the top there and I can take away or subtract 52 from 63 to get my remainder.

And that leaves me with 11 hundreds.

So altogether I've got 1,159 leftover.

Okay so now let's look at this number.

Again it's going to be too difficult mentally for me to think about how many thirteens go into this whole number, so I'm going to focus now on the tens.

I've got 115 tens.

How many thirteens go into 115? Well I know how many thirteens.

I know that 10 thirteens go to 130.

So let's think about nine would get me 117.

That's a little bit too high.

So let's think about eight thirteens.

That will get me 104.

Okay.

So I know that there are eight thirteens in that tens column there.

And I'm going to take away 104 to think about what my remainder is now.

And my remainder is 11.

So altogether, if I bring that nine ones down, I've got 119 remaining.

So now I need to think about how many thirteens would make 119.

Let's look at what we've already got here.

I know that nine thirteens made 117 and eight thirteens made 104.

So I know that nine thirteens would go into 119.

If I take away that 117, we can do that mentally pretty much.

We've got two remaining.

So my final answer will be 489 remainder two, okay? So I've done a long division.

And I've put my answer there with a remainder: 489 remainder two.

Now, it's time for you to pause so that you can have a go at working through some short division and long division calculations that include remainders.

If you need to rewatch any parts of the video, please do.

Otherwise, I look forward to seeing you with your solutions when we can review them together.

Let's take a look.

So I'm just going to show you each of the pages.

Feel free to pause so you can look more closely and compare the estimates.

The helpful table of on this, in this case, multiples of 15 or some of the multiples of 15, and in the middle, the long division with the remainder.

So have a little look compared to your own.

Here's number two.

Short division, an estimated quotient between 70 and 80: 78 remainder seven.

Another short division between 200 and 300 was the estimate, 262 remainder four.

A long division, estimated quotient of 300.

We needed quite a few multiples of 23 in that table.

268 remainder nine.

And five, another long division.

Didn't need quite so many multiples of 34: 106 remainder 10, a quotient that was estimated to be 120.

Number six, a short division.

Estimated to be between 300 and 400: 319 remainder 11.

Oops.

Remainder one.

If you would like to share any of your fantastic short division, long division with remainders, with Oak National, please ask your parents or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

Thank you for joining me for that lesson.

I hope you enjoyed it just as much as I enjoyed teaching it.