Lesson video

Hello, everybody.

Great to see you again.

Thank you for joining me, Mr. Ward, here on Oak National Academy as we continue our unit on multiplication and division, and today we're going to be looking at formal short multiplication.

As always, it's good to be in a quiet space for your maths learning.

Make sure you've got everything that you need and that you're free of distraction so you can give 100% for the lesson.

Now, I'm excited about making a start, so if you've got everything, let's get started, shall we? See you in a few moments.

For those of you at home who are familiar with Mr. Ward lessons, you know that we cannot do anything or go anywhere or move on without sharing today's mathematical joke.

It just wouldn't be right.

So here is today's absolute cracker.

Why did 7 eat 9? It was advised to eat three squared meals a day.

It's all to do with three squared, three times nine, get it? I'm sure you do.

If it's gone over your head, please go and see your teacher.

If you don't like that joke, well, let's see if you can do better.

I'll be sharing details at the end of today's lesson, how your parent or carer can share some of your work and your mathematical jokes with us here at Oak National Academy, so please keep watching to the end, if only to help me out with my comic material.

Today's lesson looks a little bit like this.

We're going to look at short multiplication in terms of concrete and pictorial modelling.

Then you're going to have a go at using formal short multiplication.

Then we're going to develop it slightly by looking at how we can multiply in multiple of 10.

And then you're going to have a go at short multiplication in the independent tasks.

And then we finish our lesson, as always, with a quiz to see how much of that learning has been embedded, and hopefully you walk away confident in the learning that we have taught today.

Equipment, as always, you're going to need pencil, ruler, paper.

Grid paper's ideal, but if you haven't got that, square paper, lined paper, blank paper, or anything to jot ideas down is fine.

A rubber is optional.

Please pause the video now.

Go and get anything you need.

If you need a quick drink or you need the toilet, anything at all, go and do that now so that you're not going to be interrupted during the lesson.

Then come back, and when you are settled and ready to begin, resume the video and we can make a start on our learning.

So before we start our learning today, it's good to get our brains firing on all cylinders.

In front of you is a missing calculation slide.

I want you to use representations to identify the correct calculation which is being presented here.

Pause the video.

Spend a couple of minutes just trying to identify what the calculation is, and I'll share back in a couple of minutes.

Right, and let's see how you got on.

Hopefully you identified it as being 14 lots of six.

And for me, you can see the deans here.

Each row represented 14, 10 and four, and there was six of them.

But you may have used the area model where you had 60 given to you.

Well, I know what goes into 60 and 24.

Six is one of the factors that goes into both of them.

So I was confident I could do that.

So 10 and four, 14 lots of six.

And then that's how it's shown on a short multiplication.

So now to introduce today's learning content.

We're going to be looking at formal written method for short multiplication.

First question I might ask, and I've posed it in previous questions, previous lessons is when might you decide to use a formal method as opposed to using a mental strategy? When might you use the formal method of writing columns? You may identify that when there's multiple regroupings happening, so there'll be a lot of information for us to keep track of, and that can be quite complicated, and we want to be everything nice and clear strategy being used so we don't make any silly mistakes when we're adding or regrouping.

Where might the regrouping be happening in this calculation? I'm not going to answer that straight away.

I want you to see if we can find that out.

But just have a look at.

So where do you think the regrouping's going to happen? And before we do any calculation, we should really estimate, and we can do this mentally.

So first of all, let's estimate something that's appropriate.

Now, I'm going to round 248 to 250, to the nearest multiple of 10, but also I know 25 times three equals five.

Not only do I know 25 times three equals 75.

I know that if one of the parts, 25.

Sorry, if one of the parts is 10 times greater, it becomes 250, which means the product has to become 10 times greater.

So I know 250 times three is 750.

So that's an appropriate estimation to have for our sum.

Now I'm going to demonstrate short written multiplication by setting out the correct formal method alongside the pictorial representation to show you stage by stage.

The first thing we're going to do is we're going to multiply three lots of eights, which you should know is 24.

Now, I can't write 24 in the columns, can I? I can only write one digit at a time.

So I'm going to write four in the ones column, and I'm going to move two tens over to the next column.

And as you see in my formal method, I'm just going to write it small down there that I've got that to use for the next calculation.

Next stage I'll do is take three lots of 40.

Now, the mistake a lot of people make is to say that's three times four.

Now, that might look like the correct calculation, but in actual fact, it is 40 that is represented, 'cause it's in the tens column.

Three lots of 40.

Well, I know three lots of four is 12, So therefore three lots of 40 is 120.

I'm going to add my two additional tens here.

So I'm going to have 140.

Again, I'm going to show those four tens that were there, but 10 tens make 100.

I had 100 left over, 'cause I had 14 lots of 10.

There's four tens there.

There's 10 tens left.

I'm going to swap those 10 tens for 100 and place it over here.

And then I'm going to do three lots of 200.

Three lots of 200.

Well, three lots of two is six, so therefore three lots of 200 is 600, plus the 100, I've got 744.

And that is my answer.

Okay, let's have another go.

Again.

feel free to have a go as you through the video slides or watch my demonstrations.

You're going to have your own go soon in your independent task anyway.

So let's estimate this answer first.

462 times four.

Well, it worked last time, so I'm going to round it to a multiple, I'm going to run it to 450.

Multiple of five there, 50.

Closer to 50.

So 462 I'll round to 450.

I do that because I know my derived fact that 45 times two, well, that is 90.

So if I know that, I can actually by four or double 90, because if you double and double again, it's the same as multiplying by four.

So I know that 45 times four is 180.

Now, because I'm going to make one of the parts 10 times greater, my product is also going to be 10 times greater, therefore I know that 450 times four is 1,800.

That's going to be my estimated answer.

So again, let's go through the method.

in columns.

So start with four lots of two.

Well, I know two lots of four is eight, and I can fit that in one column.

I don't need to, no regroup, no carryover taken over.

There's eight in that column.

There's no regrouping taking place.

Then four lots of 60.

Well, four lots of six is 24.

Therefore if it's 10 times greater, four lots of 60 is 240.

I'm going to write my four tens there, but I had 24 lots of tens, so four tens moved down.

I've got two, I've got, well, 200 spare, haven't I? I've got 20 tens left.

20 tens is the same as 200, so I'm going to replace that with two hundred columns, counters, and put them in that column, and write it on my short multiplication with a little two clear there that I can add to at the end.

And we're finally going to finish with four lots of 400.

Four lots of 400.

Well, I know four lots of four is 16.

Therefore is a hundred times greater, four lots of 400 would be 1,600.

But I've also got two spare hundreds that we had that we've regrouped.

So I've got my 16 hundreds plus my two hundreds, and that will give me 18 hundreds.

So I put my eight hundreds here, and 10 tens make, or 10 hundreds make a thousand.

So therefore I can replace that with a counter there and I can put it in my thousand column.

And that is my answer, 1,848.

Let's have another go.

Think about how you would estimate this.

Pause the video now and try and estimate this answer for a minute and then resume the video.

Now, I'm rounding it to 600.

Why do I run it to 600? Because I know six lots of six makes 36.

Therefore if one of those parts is 100 times greater, my product is going to be 100 times greater.

So 600 times six is 3,600.

Right, okay, well, I'm just going to quickly do, write, show short multiplication formally just to make sure we're all on the right lines.

So we're going to say 575 and we'll multiply it by six.

I'm just going to put my lines in there to help.

So we're going to say six lots of five makes 30.

So obviously I'm going to put zero in there for place value holder, but I've got 30, which is three tens, and we'll have three spare.

I'm going to make it little here.

I'm going to, nice and clear so I can not forget to add that.

Now it's seven lots of six is 42, but it's not seven, as I said.

It's 420, isn't it? 70.

But I do know that six lots of seven is 42.

That's going to help.

Therefore that 70 is 10 times greater.

So that's 420, or 42 tens.

I've got three tens here.

So now I've got 45 tens.

I'm going to put five in there.

I'm going to carry my 40 over there because 450, I've got 50, and then I've got my four additional hundreds here.

And then I've got five, lots of six, which is 30, but of course it's not five, it's 500.

So 30, 10 times greater, 100 times greater, So 500 times six is 3,000, which is what, 30 hundreds.

And I've got four hundreds here, so I'm going to add the four hundreds there that I have, and three there to show 3,450.

I might just put a cross every time.

I should do that every time to show I've used that.

So my final answer is 3,450, which hopefully you can see is 150 away from the estimated answer.

Not bad for an estimate.

Right, so after all of that modelling and demonstration, you're going to have a go now independently.

Now, talk task often requires a partner or group to discuss the work, but if you are working on your own, not to worry, you can complete the task.

Just make little notes or jot down your ideas for future reference.

You're going to have a go at formal written multiplication.

Here's your steps.

I would like you to estimate the calculation using a mental strategy, then generate a maths story so you can write a word problem appropriate to the calculation.

Step three, to solve the calculation using formal short multiplication.

And step four, if possible, have a partner or group and explain each stage of the formal multiplication as you go.

And if you happen to be working on your own, you can still, in a sense, talk to yourself.

You can explain each stage as you're going through to help consolidate your understanding of short multiplication.

Pause the video now, spend as long as you need on this task, and then when you're ready to resume and check your answers, come back and press play.

See you all very soon.

Everybody, nice to see you back.

I hope you enjoyed that task.

Then the answers are on the side, and you'll see the estimations at the top and the derived facts that help you work that out.

And then you will also see the correct answer.

So if you have made a mistake somewhere, maybe at the end of the lesson, go back in and see where your misconception may be if they're not obvious right now where you may have gone wrong.

Okay, we're going to develop our learning a bit further now.

We're going to be continuing to show formal written method for multiplication.

Now, I bring this one up on the screen because it's the first time we introduced the concept of 10,000s.

But I think if you got down to the right, you're probably very familiar with and comfortable with the five-digit notion.

Essentially when you had 10 lots of a thousand, you could replace it with a 10,000.

So we would have done so here.

And so that's actually 12 thousands here.

That represents 12 lots of a thousand.

So we have the two thousands here and the 10 thousands gets replaced with a 10,000 counter.

Look at the calculation on your screen.

Why might it be different when using a formal method to calculate this? What might be different about calculating this number? Well, hopefully you've identified that we've done 425 times three, but now we're more multiplying it by a multiple of 10, so a double-digit number.

Let's estimate, first of all.

I know that 425 rounds to 438, a multiple of 10.

I know that 43 times three is 129.

Therefore I know that if one of the parts is 10 times greater, my product will be 10 times greater.

So I know that 430 times three would be 1,290.

And if one of my parts is 100 times greater, then so will my product.

If one of my parts is 10 times greater and my other part is 10 times greater, both being 10 times greater, that means it equates to 100 times greater, and there you see why my answer has become 100 times greater.

That's using derived facts that we know.

There's going to be three different strategies that you can use for multiplying by a multiple of 10.

I'm going to show you now, model different ways, and you're going to have flexibility in your independent test to choose which one you think you're comfortable using.

So there's three strategies.

The first one is to multiply each column by 30.

So you might have been used to, you may have seen long multiplication, which is in the next lesson, lesson 10 of the unit.

But this is quite different because we're multiplying by a multiple of 10.

And we know that when we multiply by a 10, our product becomes 10 times greater.

So here what we're going to do is we're going to multiply each column by 30.

So we're going to do 30 lots of five.

Well, five lots of three is 15, therefore five lots of 30 must be 150.

Well, I'm going to put my zero in as a placeholder and I'm going to put my five tens there, 'cause now I've got 15 tens.

I've got five lots of 30 is 150, 15 tens.

I'm going to put my five tens in the tens column and I'm going to regroup my 10 tens, my spare 10 tens into 100, and I'm going to move that hundred in here underneath the hundred columns, 'cause I haven't yet calculated in the hundreds column yet.

So we have a spare 100 there.

The next stage is to multiply my tens by 30.

Again, I know that two threes are six, but it's not three and it's not two.

It's 20 and 30.

So I'm multiplying 20 by 30, which gives me 600.

So I'm going to move my 600 over here and add it to the 100 that was already there and add them together, and that gives me 750.

Finally, I'm going to multiply 400 by 30.

Now, I know three times four is 12, and I know that three lots of 400 would be 1,200, but 400 times 30 would give me 10,000 and, or 12,000, sorry, 12,000.

So I can show you on my place value that that 12,000 becomes the two thousands plus the 10,000 counter.

And my total answer is 12,750 using strategy one, multiplying by 30.

Now we can do the same calculation and use strategy two, and this time we're going to multiply by three and then by 10.

And we're going to going to multiply by three by doing it short formal multiplication.

So we did this earlier on.

So three lots of five is 15.

Three lots of 20 is 60 plus a spare 10, which is 70.

And three lots of 400 is 1,200.

So there's my answer.

So now I've got multiplied 425 by three.

I'm then going to multiply it by 10.

Because as we've learned earlier in the unit, when you multiply a number by 10, the product becomes 10 times greater.

And therefore I can just move it across the column to the left by one, 'cause it's greater, 'cause each column's now 10 times greater than it was before.

And my answer is 12,750.

Strategy three is to do the reverse.

We're going to multiply by 10 because I know that my product is going to be, or my part's going to be 10 times greater if I multiply by 10, and then by three.

So I'm just going to multiply 425 by 10.

Well, each column is going to be 10 times greater, so they're all going to move one place to the left, become 4,250.

And now I'm going to multiply 4,250 by three.

So I'm going to do my short multiplication.

The three lots of zero is obviously zero and your placeholder.

Three lots of five, or three lots of 50 is 150.

I've got my five tens down here and my regrouping of the hundred in the hundred columns.

Three lots of 200 is 600 plus the 100, so that makes 700.

And three lots of 4,000 gives me 12,000, which we can represent with one 10,000.

We're going to have another go now.

I'm going to model this by visualising it onto my paper.

So you can see that I'm doing it as you will be doing it writing.

First of all, we need to estimate that question.

634 times 40.

Now I'm going to round it to the nearest multiple of 100, 600.

And I know six times four is 24.

Now, if I increase one of the parts by 100, therefore the product will be 100 times greater, to 600 times four will be 2,400.

Then if I increase one of the other parts by 10, the answer has to be 10 times greater still.

So 600 times 40 will be 24,000.

So that's going to be my rough estimate is my answer's going to be around that.

There's three strategies we're going to use, and I'm going to show you each one.

The first one is multiplying by 40.

So I'm going to do it nice and big so you can see.

So 40 lots of four.

Now, I know 40 lots of four.

Four lots of four is six, but 40 lots of four would be 160.

So that means I'm going to have 16 lots of 10.

So I'm going to put my place value holder zero, my six tens, and I've got 10 tens, which I can place as 100.

I'm going to put it in the hundreds column.

Now I'm going to take 40 lots of three.

Well, I know three lots of four is 12, but it's not three and it's not four.

It's 40 lots of 30, which gives me 1,200 plus, or 1200 plus the one extra a hundred is going to give me 1300.

I'm going to carry that thousand over.

And now I've got 600 lots of 40.

I know four lots of six is 24.

I know 40 lots of six would be 240.

But it's not six, it's 600.

So therefore I'm going to have 24 plus the five, I've got 25,360.

So my answer is 25,360.

That's strategy number one.

Strategy number two is to take six, three, four and multiply it by four and then by 10.

So four lots of four is 16.

Carry the 10 over.

30 lots of four is 120 plus the extra 10, so I've got 130.

Carry that hundred over.

Four lots of 600 2,400 plus the one extra hundred.

So I've got 2,536.

Now I'm going to multiply it by 10.

I'm not going to do it in the short multiplication because I know actually that when I multiply a product by 10 it's going to be 10 times greater.

So I know that it becomes 25,360 'cause I've multiplied by 10 'cause it's become 10 times greater.

And the last one is the other way round.

And again, I'm not going to, I know 634.

I know that when I multiply by 10, it becomes 10 times greater.

So by multiplying by 10 mentally to 6,340, now I'm going to take that 6,340 and I'm going to multiply by four.

I'm going to go the other way.

Four lots of zero is zero, place value holder needed.

Four lots of 40 is 160.

So put the hundred under there, six tens, 16 tens.

Four lots of 300 is 1,200.

We've got 1200 plus 100 is 1300.

And then four lots of 6,000 is 24,000 plus the 1,000.

We've got 25,360.

So three different ways there, and I've got to the same answer by multiplying by 40, multiplying by four and then by 10, and finally by multiplying by 10 mentally and then doing short multiplication to get to the final answer.

Having done lots of modelling demonstrations and visual representations, it's now over to you to see if you can do those strategies confidently.

I'll ask you to use short multiplication to complete the calculations on your screen.

You need to estimate first, then try each of the three strategies that we showed and we discussed together.

I am interested in which one you prefer, as having flexibility and having different strategies that you feel confident in using is a really good mathematical skill to have.

Pause the video now and complete your task.

Take as long as you need, and when you're ready to resume and check your answers, please come back.

See you all very, very soon.

Okay, let's just quickly check our answers.

And you will see on your screen the four short multiplication answers up there.

If you've made a mistake, have a look at the regroupings or the multiplications for each individual column and you may spot the mistake that you've made.

Sometimes it's just a recording error.

Sometimes it's a mistake in our times table.

Just check carefully if you have got any misconceptions.

Well done for doing that task and staying focused.

Those that are not quite ready to put away their pencil case just yet, I've got a challenge slide for you called multiplication master.

You need to create a maths story for each of the calculations you can see and write a set of instructions for someone to follow one of the strategies shown during the lesson today.

Best of luck with the challenge slide.

Take as long as you need.

It's almost time to relax and put our feet up, but not quite yet because it is quiz time, which is a custom here at Oak National Academy at the end of every lesson.

So please have a go with the quiz now, and I'm confident you are going to be familiar with the terms being used in the questions and you are going to do yourself proud.

If at any stage you struggle or you forget a concept, you can always come back to the video slides and double-check and rewatch certain parts of the video.

See you all very soon.

And just a reminder, we love to see the work being shared with us here at Oak National Academy, so if you've got a mathematical joke or you've done some fantastic work you're proud of and you want to show us, please ask your parent or carer to share your work on Twitter, tagging @OakNational and hashtag LearnwithOak.

And that brings us to the end of our lesson.

Doesn't time fly when we having fun? I knew you wouldn't let me down today.

You did a super job, as well.

Why don't you give yourself a pat on the back? Thank you for joining me today and I hope you got a lot out of that lesson.

If there's any content or vocabulary that you're unfamiliar with, please feel free to go back to earlier lessons within the unit.

Now, I look forward to seeing you all again soon here on Oak National Academy as we continue our journey into multiplication and division, but for now have a great rest of the day.

And from me, Mr. Ward, I look forward to seeing you soon.

Bye for now.