# Lesson video

In progress...

I'm feeling really relaxed right now.

How are you feeling? I took a walk earlier.

The sky was blue, the sun was shining and it was just perfect for a walk along the river, taking in the sights and breathing in the fresh air.

It's left me as I said, feeling really calm and relaxed and ready for this maths lesson.

If you're not yet feeling ready, if perhaps you're in a space where there are some distractions around you, can I ask you to pause, take yourself somewhere else, where you are able to focus.

Give me your undivided attention, as we move on with our maths learning.

Press pause now, get yourself sorted then come back, and we'll get going.

In this lesson, we will be using formal written methods for both short and long multiplication.

Things that we'll be working through.

Starting off with an activity, looking at finding the highest common factor across two pairs of numbers, before we then spend some time looking at short multiplication, long multiplication, and that will leave you ready for your independent task, where you can practise both of those skills.

The items that you will need, a pen or pencil, a rubber, ruler and a pad or book or piece of paper to write onto.

Pause while you collect those things, then come back and we'll get started.

So, highest common factors.

Here are some pairs of numbers.

I'd like you to find the highest common factor across each of those pairs.

Press pause, have a go at solving the problems, then come back and we will compare.

Okay first of all, can you hold up your paper? I'd like to see.

Okay, first of all, hold up your paper.

Show me how you got on.

Looking good, oh, I'm really paying attention here.

Really paying attention here to whether or not you've been systematic in your approach to finding those common factors to start off with.

Looking good everyone.

Let me show you how I approached it.

So I started off by working through each of those numbers and recording the factors of each within the pair.

all of the factors of 49, wow, all of the factors of 84, 12 and 44, 25 and 40.

Once I'd found the factors, I was then able to look closely at the common factors and I've just coloured those in, a reddy pinky colour there.

Once I'd found the common factors, then I was able to spot the highest common factor.

So the highest common factor of 16 and 32 is 16.

Repeating that process, what is the highest common factor of 20 and 60? Can you say it back to me in a whole sentence? on three, one, two, three.

Good, uh, I'll say the sentence for this one.

The highest common factor of 49 and 84 is 7.

One, two, three? Good, and let's both say it for this last one.

You ready on three, one, two, three.

The highest common factor of 25 and 40 is 5.

Good start, well done everyone.

Let's have a look at this problem to get us started with our focus on written multiplication.

"Oak Travel is opening a new hotel.

There will be seven floors.

Each floor can sleep a maximum of 132 people.

How many people can the hotel sleep if completely booked out?" Press pause and have a go at answering these questions for me.

What do you know? What do you not know? And possibly, what knowledge or skills could you bring, to help you solve this problem? Now that last question you might not have any ideas just yet, but certainly you should be able to spot what you know and what you don't know.

Press pause, come back when you've got some answers.

Okay, should we take a look? Tell me something that you know.

Say that again a bit louder.

Yeah, good and tell me something that you don't know.

Okay, well done.

So highlighting that now in the text.

We know there'll be 7 floors, and we know that each floor can sleep 132 people, but we don't know is, how many people the hotel can sleep if it's fully booked.

And that is where our next step of using a bar model comes in.

That can really help us to make connections to the skills we've got already, and the knowledge that we hold that will help us solve the problem.

If you'd like to press pause, do that now, draw yourself a bar model to represent this problem, then come back and compare with mine.

Let's have a look.

What do we know? What do we not know? What can we use? So we know that there will be 7 floors in this hotel.

And we know that each floor can sleep 132 people, but we don't know how many people the hotel can sleep in total.

Looking at the bar model, compare it to yours if you have drawn one.

In fact, if you have drawn one, hold it up, let me have a quick look so we can compare.

Good, looking really similar, both representing the known and the unknown.

Looking at the bar model, what connections are you making to skills that you've got that can help you solve the problem? Say it? Some multiplication, good.

We've got 132, how many times? 7 times.

132 multiplied by 7, 7 lots of 132.

Now in this session, I'd like us to focus on using short multiplication to solve that problem.

There are other strategies that we can use, but I want us to focus on this skill for this session.

Let's start off by estimating.

Always useful to have an estimated product, or sum or difference or equations.

Whatever calculation you're doing, always useful to estimate so that when you solve the problem, if your estimate and your solution are really far apart, it can indicate that there might be some checking to do within your calculation.

perhaps something's gone wrong.

So an estimate, 257 multiplied by 7, how would you estimate that? I can see you quickly writing something down, that's good.

Okay, let's compare it.

Um, I'm thinking, about rounding 257 to the near, not the nearest multiple of 10 in fact, but to 250.

So I've not rounded, I've just changed it, so it's 250 because 250 multiplied by 7, that's something I can work with.

I can think about 7 lots of 25, so I can think about 7 lots of 250, 1750.

So I've got my estimate, how did that compare to yours? Maybe some of you rounded 260 and 10, 2,600? That's quite far away from my estimates where I've made a smaller change.

So often if we make big changes to our numbers with multiplication, the estimate that we end up with may not be as helpful.

Let's work on calculating it.

So, calculating by multiplying each part of 257 by 7, 7 sevens, 49, 7 fives.

Good, 7 fives 35, so 7 lots of five 10, 350 plus the 4 tens, 390.

7 twos, 14.

So 7 lots of 200, 14 100s.

1,400, plus the three 100s that we regrouped.

So the product is? Say it again? Good, 1,799.

But comparing that back to the problem of course, how many people can the hotel sleep if completely booked out? How many people? 1,799, that's a lot of people.

Compare it to the estimate as well.

An estimate of 1,750 and a product that's really close by.

So suggesting that things have gone well in the calculation.

Is there another strategy that we could have used? I said at the beginning that we're just going to focus on short multiplication here, but how else could we have solved it? Tell me? Good, we could have used an area model, We could have used a place value grid and drawings of counters, but the skill we focused on here, is short multiplication.

Another problem.

"Oak Travel's new hotel will cost 89 pounds per room, per night.

The hotel is fully booked for July with all 257 rooms booked out.

How much money will the hotel make in July?" Press pause and work through those three questions.

Come back when you've got something to share.

Ready? So what do you know, from reading this problem? Good, anything else? Excellent, and what do you not know? Let's see that highlighted.

So we know the cost per night, we know all the rooms are booked out, we don't know how much money they will make in July.

Here's a moment where you can pause, and have a go at representing the problem, using a bar model.

Press pause, and give it to go, then come back and we can compare.

Hold up your bar models for me let me take a look.

Good effort everyone well done.

So, we know that the cost per room is 89 pounds.

We know that if that's one room, there are another 256, we don't know how much will be made if all of those rooms are booked out, if each of them is 89 pounds.

So we've got 89 pounds, 257 times.

So what skills can we use here? Good, some multiplication.

Multiplying 257 by 89, 89, 257 times.

I'd like us to practise the skill here of long multiplication, even if there are other strategies we could use.

If you'd like to pause, work out an estimate and work through long multiplication, do that now.

Otherwise, let's work through it together.

So in terms of an estimate, how could we change those numbers? 260 multiplied by 90? 300 multiplied by 90? 250 multiplied by 90? Pause and note down how you would estimate it, then come back and share it with me.

Okay, I've gone for this option.

250 multiplied by 100, because 250 multiplied by 90 or 260 multiplied by 90, the estimate should be easy enough for me to calculate mentally.

250 multiplied by 100 is easier for me to work with mentally so I chose those numbers.

So we're looking for a product of around 25,000.

Let's work through the calculation then.

So multiplying 257 by 9 and by 80.

Each part by 9 each part by 80.

So we've got 9 sevens first of all, what is that? Good, 63.

9 fives, 9 lots of 5 1s helps us with 9 lots of 5 tens.

What is it? Good, don't forget the 6 tens that we already had, 51 tens, 510 and 9 twos is 18.

So 9 lots of 2 hundreds, 18 hundreds plus the 5 hundreds, 23 hundreds, 2,300.

So there's our first part.

That's 257 multiplied by 9.

We now need to multiply by 80, starting with the 7.

7 lots of 8 will help us with, 80 lots of 7.

What is that? It's 56, so in this case, 56 tens, 560.

Next, 80 lots of 50.

So 8 fives are 40, 80 lots of 50, 40 hundreds, 4,000 plus the 5 hundreds that were already there.

45 hundreds now 4,500, and then 8 multiplied by 2, 80 by 200, 8 two hundreds, 1,600.

80, 2 100s, 16 1000s, plus the 4,000 already there, 20,000.

That's it, that's quite intense, isn't it? When you're multiplying or when you're connecting the 8 times 7, the 8 times 5, the 8 times 2, when you're connecting that to 80 sevens, 80 fifties, 80 two 100s.

There's a lot to get your head around, but it's really important if you're truly understanding , the math that's happening in long multiplication.

Let me just take you back through that so that you can see.

560, 56 tens 45 100s, 4,520 and 20 1000s, 20,000.

We then of course need to total those two products.

So some addition to finish off, as we find our overall product.

257 multiplied by 89, 22,873.

Compared to the estimate, it's looking good.

Is there another strategy that we could have used? Place value, grid and counters, area model.

I'm glad you didn't say mental calculation or to mentally calculate.

That would be really challenging.

And the opportunities for errors, there would be so many of them.

This way, with long multiplication, we can be confident that the approach has been correct.

Taking that back now to the original problem.

So 22,873.

So we're saying that that the total made is 22,873.

You happy with that? Who's not happy? Why are you not happy with that as the answer to the problem? Oh, how much money will the hotel make in July? So we've worked out 89 pounds per room per night, we've worked out one night in July, could make 22,873 if all rooms are booked out, but we're looking for the whole of July.

How many days in July? How many nights In July? 31.

So one night in July, hopefully booked out, 22,873, but we're thinking about all of July.

31 days in July in total, what multiplies, 31 lots of 22,873.

A long multiplication is needed.

I'd like you to pause and have a go at using long multiplication to complete the problem, estimate as well please.

Come back when you're ready to share.

Let's take a look, shall we? How did you, first of all, what was your estimate? Okay, and they'll hold up your long publication let me see? Good work, let's compare.

I noticed 22,000 being close to 25,000.

And I can work with 3 lots of 25 quite easily mentally, to relate to 25,000 multiplied by 30.

So we're looking for a product 750,000 close by as we solve the main problem.

Okay, so multiplying each part of 22,873 by 30 and by 1, love it.

I love it when there's a 1 in the 1s place and we're solving a long multiplication, easy.

1 lot of each of those parts, it doesn't change, um when we multiply it by 1, fantastic.

Now we multiplying 3, by 30, by 30, and we can use multiplying by 3 to help us.

So we should have 90, then we should have 21, 21 hundreds.

We should then have 24 thousands, Plus the 2 thousands that we've regrouped.

Then we should hash it with 3 by 2, 30 by 2000.

So we've got 60 thousands.

plus the 2 10 thousands that we regrouped, 80,000, then another 3 by 2, 3 lots of 20,0000, 600,0000 because it's multiplied by 30, not by 3.

So again, that second row, it's complicated.

The language, the place value that's happening.

If you're able to talk it through and narrate it, and connect it, then you're showing really deep understanding of how this, written long multiplication works, not finished of course, so just compare please now your final product with mine, as I add those two products together.

Wow, 709,063.

Compared to the estimate, they're close enough for me not to be too worried.

It's not flagging to me that there's a potential error in my long multiplication.

Is there another strategy we could have used here? So again yes, we could use area models or good place value counters and grids.

No way would we be using mental calculation here.

The most efficient strategy, long multiplication, if we want accuracy.

Taking it back to the original problem, so we worked out the cost or that the money that could be made on one night in July, we multiplied it 31 times.

So in all of July, if fully booked, the hotel would make 709,063.

709,063 pounds.

That is a lot of money for one month.

I've got a couple of problems for you to work on.

I'd like you to approach them in the same way we have.

What do we know? What do we not know? Draw a bar model, reveal the maths, make an estimate and solve using short or long multiplication.

If you manage the two problems that have left and you're ready for a challenge, well here are two partially completed, short and long multiplications, What are there missing digits? Are you able to find them using your understanding? Press pause, go and complete your tasks and to come back when you're ready to share.

How did you get on? Can I have a look? Hold up your paper.

Fantastic, so I've got my first solution here for you to compare with yours already.

I've highlighted the parts that I know, the parts that I don't know.

I revealed my multiplication estimated and solved using long multiplication.

So just compare that with yours.

Next, again what do I know? What do I not know? The multiplication and the estimate, and then the short multiplication to solve it.

If you need to go back to the previous one, because you missed any of the parts when checking yours, please do.

Or if you need to pause now on this one to compare the two, then do that as well.

In terms of the gaps, I'm going to reveal these missing digits for you to mark off.

So we're multiplying by 7 there to reach 42, 6 lots of 7, 42.

And then once we've got that in place, we're able to move through the calculations, 6 lots of 20, adding on those 4 10s and needing 24 100s, 6 lots of 4, 24 100s plus the 100.

Coming down a row, we've got all of our digits there so we're just running the multiplication and we should be able to fill in the missing digits.

And when we're adding as well, with the short multiplication, 8 lots of something is something 6, something 6, could be six 16, it could be 56.

So then I'm looking what 8 lots of 3 has to be something 9.

If it was 16 or 1, something 8, if it were 56, something 4, it is 56, so that then it's 24, plus the 5 to make the 9, leaving 8 lots of 4, 8, 16, 24, 32, 32 hundreds plus the 2 100s, 4 was missing.

Wow, you deserve a break after all of that.