# Lesson video

In progress...

Hello, my name is Miss.

Sew, and I'm going to be your maths teacher for today's lesson.

Today's lesson is all about problem solving with multiplication.

And we're going to use different multiplication strategies and see which one is most efficient for each of our problems. I hope you're doing really well, and I hope you're ready for today's lesson.

Find a quiet space, and let's get started.

Welcome to today's lesson where we are problem solving with multiplication.

In today's lesson, we're going to be reviewing different multiplication strategies that you may be familiar with from other lessons.

If they are new to you, that's fine.

I'm going to be showing you how to do each of the strategies I show you today.

If they are familiar, then get ready because you're going to be going and working alongside with me and trying to solve them at the same time.

For today's lesson, we're going to warm up with our formal written method.

Then we're going to be using our known facts and look at them alongside our formal written method.

At the end, we'll think, which was more efficient? And at the very end of the lesson, it will be time for our independent task and quiz.

For today's lesson, you will need a pencil and paper.

And that's really important because you're going to be doing lots of writing today.

If you don't have them, pause the video and go get them now.

Now that you have all the equipment you need, make sure you're in a calm, quiet space, to help you with your learning.

If you have any notifications running on this device, make sure you've turned off notifications, so that you don't get disturbed during this lesson.

Let's get started with our warmup.

Here I have three equations for you.

And I'd like you to use a formal written method to solve each of these equations.

Pause the video and get started.

Let's take a look at the answers.

Here are the answers for our warm up.

Take a look at the answers at the very bottom of these equations.

And if you have a slightly different answer, pause and look at my working out to see where you might have made a mistake.

You might have forgotten to regroup, or you might have made an additional mistake.

So look carefully.

To start off this lesson, we're going to be looking at our known facts and our written method.

If you can see this equation and you think, "Oh, I can do this already," I want you to pause the video and have a go now.

If you want me to show you, then what I want you to do is to play and pause the video, and do it alongside me.

Let's start off with our known facts.

My known facts could help me solve this equation.

I am doing 53 multiplied by seven.

I can partition this and do 50 multiplied by seven, and three multiplied by seven.

I know that three multiplied by seven is 21, and if I know five multiplied by seven is equal to 35, then I know 50 multiplied by seven is 350.

Because 50 is 10 times greater than five.

Now, I just need to add all the different parts.

21 add 350 is equal to 371.

Let's have a look at our written method and see how it's similar.

Seven multiplied by three is equal to 21.

I have to regroup my two into my tens column.

Seven multiplied by five is equal to 35.

But I need to add the two, so it's 37.

I need to put this in my hundreds and tens column, which is equal to 371.

Now, we're going to have a go another equation using our known facts and our written method.

If you paused and joined in with me last time, this time, I want you to have a go on your own.

Pause the video and try this equation.

Let's have a look at the answers.

I'm multiplying 238 multiplied by seven.

I need to partition 200, 30 and eight, and multiply them separately.

I know that eight multiplied by seven is equal to 56.

Now let's look at the tens.

If I know that three multiplied by seven is equal to 21, then I know 30 multiplied by seven is equal to 210.

And if I know two multiplied by seven is equal to 14, then I know 200 multiplied by seven is equal to 1400.

Now I just have to add up my equal parts.

This is equal to 1666.

Let's check out our written method.

I'm going to multiply.

And I have to regroup and put the tens underneath if I have a number greater than 10.

So seven multiplied by eight is 56.

The six goes in the ones, the five goes in the tens column; 50.

Seven multiplied by three is equal to 21.

Add the five is going to be 26.

Six goes in the tens, and our two goes in our hundreds.

Seven multiplied by two is equal to 14; add the two is equal to 16.

And I have the same answer yet again.

Now that you've had a go on your own, I want you to think which method was more efficient? Which method had less steps for you? Which method was easier to do without mistakes? And which method was quicker? Keep this in mind as we go through the next couple of questions.

Now I'm going to be doing a three digit multiplication by a two digit multiplication.

I'm doing 357 multiplied by 17.

I can use my known facts, as I have done for my previous questions.

I can also do my written method.

I want to give you a clue.

When we're multiplying by two digits, it's really important you remember your placeholder.

We're not multiplying by one, we're multiplying by 10.

And so we need to put a placeholder here so that we remember to put our numbers in the correct place value columns.

Pause the video and have a go at this equation.

Let's have a look at the answers.

I'm going to show you my known facts first and then my written method.

Seven multiplied by seven is equal to 49.

Now let's do seven multiplied by 50.

If I know five multiplied by seven is equal to 35, then I know 50 multiplied by seven is equal to 350.

If I know three multiplied by seven is equal to 21, then I know 300 multiplied by seven is equal to 2100.

I multiplied seven by seven, 50, and 300.

And now it's time to multiply seven, 50 and 300; 357 by the ten.

357 multiplied by 10 is equal to 3570.

Now I have to add up all my parts.

This is equal to 6069.

Let's have a look at our written method.

Same as before, I need to write and regroup.

Seven multiplied by seven is 49.

My nine goes in my ones column, my four goes in my tens column.

Seven multiplied by five is equal to 35; add the four which is 39.

Nine goes in my tens, and three goes in my hundreds.

Seven multiplied by three is equal to 21; add the three, which is equal to 24.

And now I'm going to be multiplying by 10.

I know 10 multiplied by 357 is going to be 3570.

If I estimate my answer in advance, it can help me check to see if I've made mistakes.

I know I need to put my placeholder in first, because I'm not multiplying by one, I'm multiplying by 10.

And I will multiply each of these by one here.

But they will be in the correct place by houses because I've put in my placeholder.

Seven, five, and three.

And that's correct.

3570.

That's the answer I was expecting.

I'm going to regroup my one into my hundreds column.

Four add five is equal to nine; add the one is equal to 10.

Two add three is equal to five; plus the one I regrouped earlier, which is six.

The answer is 6069, just what I expected from doing my known facts.

By doing both these methods, I was able to check to see if my answer was correct.

Which method was more efficient for you? Which method was faster? Which method had fewer steps? And which method did you make less mistakes on? For me, my more efficient method is my written method.

When I do my known facts, I find that there's more steps for me.

And I tend to always make mistakes, because I have to think about the sentence structures.

And especially when I'm multiplying larger numbers, like a three digit by a two digit number.

I think my written method is more efficient.

How about for you? Because I have decided that for me, doing three digit by two digits is more efficient with a written method, I'm going to try another method by the side to this time.

I'm going to try my area method.

If you know how to do your area method, pause the video and join in yourself.

Otherwise, listen, and join in with me.

For the area method, I partition my number.

816 is partitioned into 800, ten and six; and 32 is partitioned into 30 and two.

I multiply each of these parts and I add them up at the end.

Let's have a look at the answers.

I went to do the written method alongside the area method.

Two multiplied by six is equal to 12.

My two goes in my ones, my one goes in my tens.

I can do two multiplied by six in my area method over here.

Two multiplied by 10.

Or I might just think of this as two multiplied by one is equal to two, add the one to the group is 30.

I can do the same here.

Two multiplied by 10 is equal to 20.

Two multiplied by eight is equal to 16.

And I'm going to be putting it over here; which means it's actually 1600.

I've put that in my area here.

Two multiplied by 800.

And now I need put my placeholder in because I'm multiplying by 30, not by three.

Three multiplied by six is 18.

And I can put this into my area method.

30 multiplied by six is 180.

Three multiplied by one is three; add the one is four.

30 multiplied by 10 is 300.

Three multiplied by eight is 24.

And in my Area method, 30 multiplied by 800 is 24,000.

Now I need to add up all my digits here.

And for my area method, I have to add all of these digits up too.

Two, 11, 10; add the one.

Five add the one; and two.

And if I add up all these numbers here, I would get the same answer.

Which method did you find more efficient? For our area method, we don't have to regroup because we are multiplying using our known facts.

But we do have to add up at the end.

In this lesson, we've looked at using our known facts.

We have used our short multiplication.

We have done our long multiplication with our placeholder.

And we've also had a look at our area method.

So we have looked at four different methods of multiplication.

Which methods have been most efficient for you? Have a think.

I want you to tell me the reasons why you find one method more efficient than others.

Is it due to the speed? Is it due to mistakes? Or is it due to the number of steps you have to remember? I've got two more equations for you here.

This one is a little bit easier than this one; which is really quite tricky.

And I want you to try out both of these equations using your formal written method and your area method that I just showed you.

Pause the video and have a go.

Let's have a look at the answers.

Here's the formal written method for both of the equations I showed you.

You can see from the pictures here that the regrouping has been done in a different place to the way I've shown you in my earlier video.

Now, this is also completely correct.

Different people, different schools, different teachers, regroup in different places.

They are still regrouping even if it is a different place on the equation.

I wanted to show you this so you understood that there is more than one way of regrouping.

Make sure you check with the adult who teach you which way of regrouping is best for you.

Thank you so much for joining me in our lesson today.

I know that we've done lots of work already; doing our equations alongside me.

But now it's time for your independent task where you can solve some different problems and show what you know.

Option one and option two.

Option one is the independent task that I would expect everyone to do.

Option two is a little bit trickier.

We have got three digit by two digits; whereas in option one we only have two digit by two digits.

And our last question in both of these is a little bit tricky.

Choose whichever option you would prefer and complete your work.

If you want to challenge yourself, I'd love it if you did both options.

Let's go have a look at the answers.