Lesson video

Hi, everybody.

Great to see you once again here on Oak National Academy.

My name is Mr. Ward, and we are continuing once again with our unit on multiplication and divisions.

Today, we're going to be looking at formal long multiplication by using a strategy of area models to help represent the calculations.

Now, unfortunately, it's raining outside.

It's a pretty miserable day.

So, I'm going to console myself by doing some fantastic mathematical learning.

And I hope you come with me on this lesson.

Make sure you've got everything you need.

Free of distractions and ready to focus on our learning for the next half an hour.

All set, fantastic.

So am I, let's get started.

For those familiar with lessons taught by myself, Mr. Ward here on Oak National Academy, you will know that I like to start every lesson with a mathematic joke to put a smile on your face, hopefully.

So, here is today's absolute belter of a joke, fingers crossed.

Why did the two number fours not feel like eating dinner? Because they already ate.

Best not to say anything, I know.

Smile, and let's move on.

Here's the today's lesson.

We're going to introduce the idea of area models again.

Then we're going to do some sketching with area models, and then we're going to take our area models and use them when demonstrating the formal method of long multiplication.

And then you are going to have a go, an independent task at long multiplication before rounding the lesson off by having a go at the end of lesson quiz, which is a custom here at Oak National Academy.

And as always, we cannot get the most out of our lesson if we don't have the right sort of equipment.

So if possible, please make sure you have a pencil or something to record your work on.

A ruler is always useful for a presentation or to set up some more jottings, some paper, grid, line, blank, back of cereal packet.

Anything will do, or a book your school may have provided for you.

A rubber in Mr. Ward lessons are optional, it's perfectly acceptable to put a line, a neat line through your work to demonstrate that you made a mistake and you understand why you made a mistake.

You're showing your misconceptions and you are showing your learning.

So, if you haven't got any of that equipment now, and you need to go and get it, pause the video, go and get what you need.

Go to the loo, get yourself ready and everything you need, to get the most out of this mathematical lesson.

And when you're ready to resume, press play, and let's make a start.

It's normally a good idea to start a session with a very quick activity to get you thinking mathematically.

Today's warm up is a doubling and halving activity.

Use the adaptive bar model to help solve the following calculation.

Do you see this example on the board, how we could use 25, doubled make 50, and 50 doubled makes 100 and I've got a little adapted bar model there to demonstrate that 25 times four equals 100.

Now we can use that to solve some of the equations.

I'd like you to pause the videos, spend a few minutes trying to complete the calculations using the adaptive bar model to help with your knowledge of doubling and halving.

See you in a few minutes.

Okay, let's just quickly share the answers.

25 times 16, well, if I know 25 times four equals 100, four lots of four makes 16.

That's how I would solve that.

25 times 24, well, half of 16 is eight, half of 400 then is 200.

So, you would add 200 to 400 to make 600.

And if you know that 25 lots of four is 100, you would done it 25 lots of 40, makes 1000, and then you would double 40 to make 80 and therefore double 1000 make 2000, and using our division, well, we know that we know that 25 times 40 is 1000 therefore 1000 divided by 25 gives us 40.

We would know that 25 lots of 25 make 625.

And hopefully we would know that 14 lots of 25 makes, oh, 350 divided by 25 makes 14, or we know 10 lots of 25 makes 250 and four lots of 25 makes 100.

So, if you added those together using the inverse, you would've got to 350.

So, therefore we would have known that 350 divided by 25 would make 14.

Well, hopefully that's got you ready for the math lesson and warmed up and ready to fire.

So, let's make a start on our new learning.

And we're going to look at the area models to start with.

And if you are familiar with dienes, you might find this quite a straightforward question, but how many dienes are there on your screen and how are you working it out? Just take a few moments, how many dienes are there, and how did you work it out? Hmm.

Hopefully you're thinking and adding what you see.

There are in total 782.

I hope you got that answer.

If you feel like I'm going too fast, please pause video at any stage to spend longer discussing the information or to have it go to the questions that emerge.

So, if you're familiar with dienes, you may be familiar to know that the blue square is worth 100 and the green squares, our grid green.

So, the green blocks are worth 10.

The long ones are worth 10 and the small ones are worth one.

So, the yellow ones are worth one.

And for the benefit today's lesson, because you will be doing some sketching later in the lesson, where we have to draw these or sketch these on your paper or your books.

So, a nice blue square or nice squares are worth 100, nice long green block is worth 10.

And a single diene is worth one.

So, without any gaps, imagine the gaps weren't there altogether, how long would each side be? Hmm, I'm going to think.

Well, how long do you think each side would be? Well, hopefully you would have identified that if on the side, if they're worth 100, if that block's 100 that means it must be 10 rows to 10.

So, one side would be 10, there's two of those, so there must be 20.

And then we can say that although that block's worth 10 it's 10 blocks of one.

So, therefore we have three ones because there's three rows.

So, three first 20 makes 23.

And along the top, we would have had three lots of 10, 30.

And again, four ones, basically or four 10, but one at the top.

So, four ones and three 10's, 34.

So in total, we've got 23 multiplied by 34.

We can use this to create an area model to demonstrate multiplication.

And this is the template for an area model.

This one you can see replicates, I've got this different, kind of in sections that suit the big rectangle here, to suit my six 100s.

And then the long, for the long 10s, another one, rectangle for long 10s.

And in the bottom a little square for the ones.

We can solve using an area model, and pause the calculation in our model, in our long multiplication.

So, first of all, we had two lots of three, didn't we, or 20 lots of 30, because each row are 20 up and across was 30, now you can see I've got six lots of 100 there.

So, six times 100 is 600, two times three is also six and 20 times 30 is also 600.

So, my first area is 600.

The second area down here you can see I've got three, three rows of 30, haven't I, three rows of 30.

So, three times 30 makes 90.

So, this area here is worth 90.

And the corner I've got yellow, it is worth one.

Well, again, I've got three rows of four columns, three rows of four or three times four is 12 because those four represent one unit at a time.

So, I've got three lots of four units, that makes 12 units.

My last area here, I've got four columns, and four columns, on each row.

So, I've got 20 lots of four.

Or four lots of 20, which makes 80.

Now four across there, 20 down the side 'cause there's two lots of 10, four lots of 20 makes 80, 'cause I know four lots of two makes eight.

So, altogether I've got my four areas, which together collectively can give me the final answer of 782, which can be represented by 23 times 34 in an abstract way, and represented by using dienes, and by using an area model.

Now have another go, again, pause the video if you need a few moments, but how many dienes can you see on your screen here? How many dienes can you see? Again, how are you working it out? Hopefully you got to the answer of 611.

Again, it's a way of representing long multiplication.

So, a way of representing 13 lots of 47.

And we're going to use an area model again to help with the different areas to break down the multiplication.

Where are the gaps? How long would each site be? Well we know there's one lot of 10 there, so that's worth 10, and three ones so that's 13.

And we know that it's four 10s there, which is worth 40 plus the seven units, seven ones there to make 47.

And my area model template is there, so let's go through the individual sections.

Again, I've got three lots of seven, three rows of seven columns, 21.

Here, I've got 70 in total.

We know that each one's worth 10 anyway.

And therefore I've got 10 lots of seven, which makes 70.

100 block we can probably count in 100s when using the dienes, but essentially I've got four 100s there but how do I know I've got 100's there? Well, because I've got each block is worth 10 across.

I got four of those.

So, I've got 40 across and then I'm multiplying by the 10 up, because 10 lots of 10 makes 100 for the square.

So, 40 lots of 10 make 400.

And I'm left with the final section, which is three lots of 30, three lots of 40.

Three lots of 40, because it's four lots of 10, so three lots of 40, 40, 80, 120.

Now what we're going to do is add those together.

So, I'm going to add my two sections here, 120 and four 100s is 520.

And then I'm going to add 21 and 70 to make 91.

And finally, I'm going to add 120 plus 91, to give me the answer of 611.

Okay, now it's your turn.

You might need to pause the video, but I'd like you to have a go.

I would like you to work out the calculation by completing the area model that you see on your screen.

So, sketch it if you want to, but complete the area model using the dienes that you can see to work out the individual areas of our calculation.

Then we can add them together to give us our final answer.

So pause the video, spend a couple of minutes doing this and then resume the video when you're ready to share your answer.

Best of luck.

Okay, you hopefully would have worked out that it, the calculation was 24 lots of 28 because there's two lots of 10 here.

That's 20 plus the four there, so 24 multiplied by two lots of 10, 20 and eight ones, 28.

So, we could have worked out that this was four lots of 20 in the first section there to make 80.

And then there was four lots of eight to make 32, there was 20 lots of eight to make 160.

And there was 20 lots of 20 to make 400, that give us 672.

Okay, I hope you did okay with that.

I hope it makes sense, using area models are a fantastic way of representing multiplication.

So, now we're going to have at the talk task.

Our talk task is this, you're going to sketch some area models.

I said earlier in the lesson, you're going to have to do some sketching today, and now is the time.

So, with a pencil or pen, you can sketch it by doing a square, nice big square for the 100 squares.

You can do a nice long thin one block for strips of 10, and can do a small yellow block for the one.

Now, you don't have to do it in colour.

It can just be black and white, so don't worry about colour, but if you haven't got colours, but please represent the shape to demonstrate the different value for each of the blocks.

So, sketch the dienes to make an area model, complete the area model and work out the product for the calculation.

This will take it a little bit of time and you might need to explain as you go through.

So, if you are working on your own, not to worry, just have a go at the work, try and talk to yourself as you go through talking through the stages that you're doing.

If you happen to be working in a group or with a partner, that's fantastic to hear the talk, so please talk about your method at each stage.

You see I've done an example on your board, I've done 13 times 24, and you can see how I've represented the 13 and the 24.

So, can you do the same for the three calculations you see on your board? If you get a bit confused, by all means, go back on the previous slides to have a look at other examples and have a look at our screen here.

Pause the video for as long as you need on this task, and when you're ready to resume the lesson, please press play and we'll share some of your sketches.

Okay? These are just a quick sketch that I would have done on my laptop.

And you can see, I have sketched 25 lots of 40, you can see I've done the squares and I've done my green and my yellow, they're not very neat obviously but they are only jottings.

It's not an art lesson now, I just want the jottings to be there, you can clearly see what represents what.

25 lots of 14 or 25 by 14 creates 350, 32 lots of 17 makes 544, 26 by 23 is 598.

So, hopefully your answers look a little bit like that.

Though not worry if they don't, not to worry if you're still, are you struggling a bit with the jottings, it's the first time you might have used area models and sketch them before, so not to worry.

But you can use the example on your board to see how, where you should have gone.

And hopefully even if your sketches were a bit off, you've got the calculations correct.

We're now going to introduce the formal method of recording long multiplication side by side with dienes and area models.

So, we've got the concrete, pictorial and abstract representations of the formal long multiplication.

On your screen you'll see a short multiplication, 34 lots of three and how I might record that in my book or on my paper.

Now the dienes here represent one row of 34 and I need to have three lots of 34, therefore three of those rows, which you can see makes 102.

How did I get there? Well, three lots of four is 12 units.

So, I put my two in my unit column, I regroup the 10s into the 10 column, and then I've got three lots of 30, which is 90.

So nine 10s, plus my one 10 I regrouped to make 10 10s, which is the same as 100, so 102.

And then when we look at a multiplying by the multiple 10.

34 lots of one was 34, obviously we double that.

And that become 68.

Well, I know that 34 lots of 10 is 240 because it's 10 times greater.

Therefore if I double that 34, so 20 becomes 680, I can see here.

So that's 340, and that would make 608.

My area model can record this.

I don't need to go view it in 10s because know that when I multiply by 10 it's 10 times greater.

So 20 lots of four is eight units, 80 units, and 20 lots of 30 is 600 or another two lots of three is six.

And I know 20 lots of three is 60.

Therefore 20 lots of 30 is 600.

Add those two together, 680.

Now, there was no regrouping in that.

There may be in this equation, 34 times 23.

So, let's put those two elements together and do a formal long multiplication with the representations alongside.

First area we're going to look at is the units, so three lots of four units makes 12 units.

So, I put my two units in the units column and I regroup 10 units at the 10 in the 10s column.

In my area model I just show it as 12.

And then I'm going to do three lots of 30, which is 90 or nine 10s, plus the regroup 10 to make 10 10s, in total that's 102.

Then I'm going to go into my multiplying my ends, so I'm going to do my second row, 20 lots of four is 80.

Now we show we can write just a zero as a placeholder to represent the fact that we multiply by 10 and then people sometimes go to lots of 40, lots of three, but I want us to be formalised on the math.

We are multiplying by 20.

Therefore we got 20 lots of four units to make 80 units.

I've got eight 20s now.

And 20 lots of 30 makes 600.

Now I know, I know that two lots of three makes six, so therefore it's 100 times greater, the 20 lots of 30 makes 600.

And now I've got my first row, which I created by multiplying by the units and my second row which I created by multiplying by the 10s.

I can now add those together.

And give me 782, and I've written it in the abstract number sentence at the top there, 34 times 23 equals 782.

It's also represented by our dienes, it's shown in our area model, and it's shown in our formal written long multiplication.

Have a go at another one.

Again, it's a short multiplication.

So, multiplying by units, two 10s, lots of four, where one of my rows is worth 28, two 10s and eight units, for them I get 112.

How do I know that? Well, four lots of eight units makes 32 units.

I put two in the units column and I've got 30 units which is the same as three 10s which I regroup into the 10s column, four lots of 20 makes 80, which is the same as eight 10s, eight 10s plus three 10s makes 11 10s, which is the same as 110, altogether I've got 112.

And again, when we're multiplying by the multiple 10, well I know 28 times one is 28, therefore 28 times 10, which is 10 times greater must be 280.

Well, if I got 280 here, two of those will add up to 560.

So, let's go through it.

I've got 20 lots of eight units, which gives me 160 units or that's 16 10s.

When I put my six in my 10s column, I carry that 10 10s over into the 100s column.

And then I've got 20 lots of 20, or two lots of two is four, and let's time this a 100 times greater.

So 20 lots of 20 make 400, I've regrouped and I've added my 100 into my formal methods to make 560.

And I add those two areas together, and my answer is 560.

Let's put those two aspects together.

We're going to do two rows first multiplying by units, and then my second row multiply by 10s.

So, two lots of eight that we took that was 32, so put my two units in the column and I regroup three 10s or 30 units into the 10s column.

And then I'm going to take four lots of 20, which is 80 or eight 10s, plus the three 10s I regrouped to make 11 10s, which is 110, and I've got my two units already.

So, that's my first multiplying by my units, and now I'm going to multiply my 10s.

And then I could put my zero in as a placeholder, but I actually, I prefer to, I think it's better to do 20 lots of eight.

So, 20 lots of eight makes 160, or 160 is made up of 16 10s.

So, I put my six 10s there and my 10 10s I can carry over and regroup.

I can regroup as 100.

And 20 lots of 20 is 400.

Well, I know two lots of two is four, it's a hundred times greater.

So 20 lots of 20 is 400, plus I'm going to add my 100, which I had regrouped to make 500, and I've got my two rows, now I've got my units row, and I've got my row created by multiplying the 10s.

I add those together.

I get the answer of 672.

Right everybody, we're almost at the end of the lesson but not quite because it is quiz time as always at the end of an Oak National Academy lesson.

So, I'm going to ask you to spend a couple of minutes, find the quiz, read the questions carefully.

Hopefully you're going to be confident and happy with your answers.

And so you'll whiz through that quiz.

If you're unsure about anything, please come back to early slides in the video and go to the sections that you are unfamiliar with.

Once you finished the quiz, come back and I've got a few closing messages for the end of today's lesson.

A final key message from me about today is to remind you that you now have different methods, both formal and mental strategies in your own personal toolbox to help solve a range of different calculations.

Especially if you've been following all the lessons in the unit, you're going to have different strategies that you can use at different points, which are going to allow you to be more flexible in your mathematical work.

Anyway, I'm digressing.

Please go and have a go at the quiz.

I'll see you in a couple of minutes to finish the lesson off together.

I've mentioned that after the lesson, if you have a mathematical joke or you have some work that you are very proud of, and I'm sure you are because you've been working very, very hard on these lessons.

You can share your work with us here at Oak National Academy.

Please ask your parent or carer to share your work and jokes on Twitter, tag it@OakNational and #LearnwithOak.

It's great to share work everybody.

So, please speak to your parents and carers about doing so.

Right everybody, that does bring us to the end of today's lesson.

Pat on the back for another splendid job.

Well done, I'm very proud of all of you.

I hope you found the use of area models a really good way of representing and explaining the method of long multiplication and give you a greater understanding of what's happening stage by stage when we use that method in our mathematics.

Now, if you have missed any of the previous lessons in the unit, and you're a bit unfamiliar with certain terms I've covered, please go back and watch any of the videos from the unit of multiplication and division.

I am going to go and have a nice warm cup of tea now because it's still raining outside.

It's still quite cold, pretty miserable, but I am cheered up because we did such a fabulous job with our mathematics today.

Have a great rest of the day wherever you are.

And I look forward to seeing you again very soon here on Oak National Academy.

So for me, Mr. Ward, have a splendid rest of the day.

Bye for now guys, bye bye.