Lesson video

Hello, I'm Miss Miah and I'm so excited to be a part of your learning journey today.

I hope you enjoy this lesson as much as I do.

Today you'll be able to multiply a three digit by a one digit number using partitioning.

Our keywords for this lesson are partition and partial products.

So I'd like you to repeat this after me.

Partition.

Partial products.

So partition means splitting a number into parts.

Eight could be partitioned into four and four or six and two as shown in this example.

Can you think of any other ways eight can be partitioned into? Any of the multiplication results we get leading up to an overall multiplication result is a partial product.

So here we've got two examples.

We've got the grid model outlining some of the partial products there through that method.

And then we've also got an informal written method on the right hand side.

And you can see that the partial products have been outlined.

I don't want you to worry, we will be exploring this in depth during this lesson.

To begin with, we are going to be finding partial products and in this lesson you'll meet Andeep and Izzy.

So in the past you may have seen the informal written method that is shown on the screen.

In this lesson, we will explore how to find the partial products when multiplying a three digit by a one digit number.

Let's begin.

So two laptops cost 422 pounds each.

What is the total cost? Now Andeep saying that he can use an informal strategy because he thinks he doesn't need to regroup and Izzy is saying that she's going to use the base 10 blocks to help her.

I would like you to think about the multiplication equation needed for this question.

What do you think? So if you got 422 multiplied by two or two multiplied by 422, you are correct 'cause multiplication is commutative.

You could have written both those factors in any order.

The answer will still be the same.

So Andeep saying that he can use an informal method to calculate the answer.

He's going to partition 422 into 400, 20 and two.

And you can see that this has been represented by the base 10 blocks on the left hand side.

So we've got our two tens, which is 20 and two ones and it needs two groups of 422.

So he's going to now arrange that using his base 10 blocks and then we start to multiply by two.

So two multiplied by 400 gives us eight and you can see that we've started multiplying in our hundreds first.

Then we're going to move on to our tens.

So we've got two multiplied by 20.

Now if you don't know what that is, just think about it like this.

If you know that two multiplied by two is four, then you also know that two multiplied by two tens is four tens and four tens is equivalent to 40.

And lastly we're going to move on to our ones.

So two multiplied by two ones gives us four ones.

So partitioning our factor into hundreds, tens and ones has resulted in three partial products.

And you can see that it's been highlighted here in purple, but we don't stop here.

There is a further step.

What do you think that step is? Yes, we add our partial products.

So 800 plus 40 plus four.

There's no regrouping involved, which makes it a very easy calculation for us.

It's 844.

The product is 844.

So altogether two laptops will cost 844 pounds.

Over to you.

There's an equation here.

433 multiplied by two gives you 866.

I'd like you to partition 433 into hundreds, tens and ones.

Off you go.

How did you do? If you got 400, 30 and three you are correct.

Good job.

Now the reason to why we partition into hundreds, tens and ones is because it makes it easier to calculate.

Back to you.

This time I'd like you to multiply your hundreds, tens and ones by two.

You can pause the video here.

How did you do? If you got 800, 60 and six? You are correct.

Good job.

Let's move on.

So this time we've got another word problem that we're going to solve together.

Three bikes cost 122 pounds each.

What is the total cost? Now we can set out the calculation using different methods.

So here's one example, which is our partitioning strategy.

We're going to partition 122 into hundreds, tens and ones.

Now whilst I go through this calculation, I want you to have a look at what's happening on the right hand side of the screen.

Okay, so here we've got three multiplied by a hundred, which is 300.

Now I can represent that like this.

So 123 multiplied by three is equal to three multiplied by a hundred.

Let's carry on.

Then we're going to move on to tens and multiply 20 by three.

So three multiply by 20 is 60, but now have a look at the right hand side.

So if I read out our multiplication equation so far we've now got 122 multiplied by three is equal to three multiplied by a hundred, add three multiply by 20.

And lastly we're going to be multiplying our ones.

So we know that three multiply by two is six and then if we have a look at the right hand side, we can add that in as well.

So both are exactly the same, but it's just that the layout is different.

And then as you know, we add all the partial products.

So 300 add 60, add six.

So what you do after that is you add the partial products and that is 366.

The cost of three bikes is 366 pounds.

I dunno about you, but I really, really like the strategy on the right 'cause I just find that that type of layout is easy for me to use to calculate because I just find this method far more efficient than the partitioning method.

At this point I can partition quite efficiently.

So I definitely choose the method that is on the right.

Which method do you prefer? Over to you.

So this time you are going to be filling in the gaps.

Your equation is 221 multiplied by four.

Now it's following the method that I showed you before, the informal written method, something's missing.

Use the equation to help you.

You can pause the video here.

So how did you do? If you got this as your answer, you are correct.

I'm just going to quickly explain how you should have got that.

So by looking at your factors, you are multiplying 221 by four.

Now we are going to partition 221 into hundreds tens and ones.

And as we can see in our strategy below, we've already got the factor four filled in.

Seemingly there are three gaps.

We would've had to partition our three digit number into hundreds tens and ones in order to continue multiplying using this strategy.

Back to you.

This time we are continuing on with this method.

Think about what that next step was.

You can pause the video here.

How did you do having a look at this equation? We can see that at this stage multiply each by our factor of four.

So ideally you should have written all the partial products that you would've got from multiplying by the factor.

So you should have got 800, 80 and four.

The cost of three bikes is 884 pounds.

Let's move on.

Four bikes cost 143 pounds each.

What is the total cost? What multiplication equation do you think is needed for this question? If you got four multiplied by 143 or 143 multiplied by four, you are correct.

Good job.

Now in this example is easy, use the grid method to calculate this equation.

I love the grid method.

Let's see how she's used it.

Izzy's written four on the site.

This is because four is the factor that we're multiplying by.

Then she's partitioned 143 into a hundreds, tens and ones.

So 100 four tens and three ones.

What do you think she's going to do next? If you thought that she would multiply four by each number.

You are correct.

Now Izzy started with her ones this time.

Four multiply by three ones is? If you've got that, you're correct.

It is 12 ones.

Now let's move on to our tens.

Four multiplied by 40 is? If you got 16 tens or 160, you are correct.

And lastly, four multiplied by 100 is? If you got 400, you are correct.

Now what do you think the next step is? If you thought something along the lines of adding the partial products, you are correct.

So that's exactly what we have to do.

Now we say that we recombine the partial products.

So here what we're going to do is add 400, 160 and 12 together.

Over to you.

Which equation is the grid model representing? And I'd like you to explain how you know.

So have a look at the grid.

You've got two equations.

A is 347 multiplied by four and B is four multiplied by 374.

You can pause the video here.

Now if I was to tackle this question, I'd definitely look at what my factors are first and I'd start off with the easiest factor to spot, which is my single digit factor and we can see that that is four.

Now we need to look at our other factor and we can see that this has been partitioned into hundreds, tens and ones.

So what we need to do is regroup all of that together again and find out what that factor is.

So we've got three hundreds, four tens, and seven ones.

That's equivalent to 347 if you've got a, you are correct because the grid model is representing 347 multiplied by four.

Let's move on back to you again.

So which of these calculations match the grid model? Think very carefully as to what information you know and what information needs to be found out.

And I also want you to explain your reasoning.

You can pause the video here.

So how did you do? Let's have a look.

So seeming we are adding that means we've got our partial products.

If I have a look at the grid model here, I've definitely got the partial products there.

I can see that they've been written in.

So I've got 400, 80 and four.

We need to recombine these partial products to get our product.

So that means I need to add all three.

Now if I look to the left, if you got a as your answer, you are correct.

Let's move on.

Your task for this learning cycle, task one.

You are going to draw a line to match each multiplication equation with the correct partial product expression.

So let's have a look at what we've got.

We've got 121 multiplied by three, four multiplied by 212 and then two multiplied by 134.

Now in order to calculate the partial products, you will have to partition the three digit numbers and multiplied by the factor.

And then for your second task, you are going to use an informal method to answer these multiplication equations.

So that means you can use the partitioning strategy, the grid model, the written informal method.

It's whatever you find more efficient.

You're then going to underline your partial products in different colours.

You can pause the video here.

Off you go.

How did you do? So for question one, this is what you should have got.

If you got that, give yourself a tick.

So for question two, you were using an informal method to calculate the multiplication equations that were on your task sheet.

If you got something similar to this.

So for the first question, if you got 844 as your product and your partial products were 840 and four, you are correct, you can give yourself a tick.

And then for B, if your partial products were 900, 60 and nine, you can give yourself a tick.

And lastly, have a look at what the partial products here are on the screen and if you got them correct, you can give yourself a tick.

Okay, let's move on.

This time you are going to be using partitioning to multiply a three digit by a one digit number.

So three apples weigh 123 grammes each.

What is the total mass? Straight away when I look at this question, I think to myself, right, which strategy am I going to use? Should I use the written informal method or should I use the grid model? I personally love the grid model, so I'd probably use that method.

But before we go into that, what multiplication equation do you think is needed to answer this question? If you've got 123 multiplied by three or three multiplied by 123, you are correct.

So in this case we are going to be partitioning our three digit number and using the partitioning strategy.

So here we can see we've partitioned 123 into 100, 20 and three.

And then we're going to multiply each number by three.

So three multiplied by a hundred is 300.

What do you think we're going to multiply next? Well if you've got three, multiply by 20, you are correct, it's 60.

And then lastly, we need to multiply our ones.

What do you think the equation is there? If you've got three multiplied by three, it's nine.

You are correct.

What do you think we do next? That's correct.

We add our partial products and in this case, again, it's very simple because we don't need to regroup.

We are adding together 300, 60 and nine, which gives us a product of 369, which means that the total mass of three apples is 369 grammes.

Now Izzy tried to solve this question here.

What do you think went wrong with Izzy's calculation? Have a think.

She's partitioned 221 into 200, two and one.

And then you can see that she's written down her calculation underneath whereby she's multiplied each number by a factor of three.

So in this case, Izzy has mistaken two tens for two ones.

She should be multiplying three by two hundreds, two tens and one one.

And because she got that part wrong, it means that her overall calculation was also incorrect.

So that's why super important when we are partitioning that we make sure our place value of the digits are correct when we are writing down our partition numbers.

So after that, Izzy used the grid model to represent the problem.

So you can see here that she's got the informal written method on one side and now she's about to start using the grid model.

So she'll begin by partitioning her three digit number.

And you can see here she's partitioned 123 into 100, 20 and three.

And because she's multiplying by three, she's popped that to the side.

Now she's going to be multiplying each number by three.

So she's starting off with a hundreds.

When it comes to a grid model, it doesn't really matter which way you are going to be multiplying by your factors.

So three multiply by 20 is 60 and then three multiply by three is? If you've got nine, you are correct.

Now that she's got her partial products, what she has to do is she needs to recombine all three partial products and that will give her a total of 369.

Now I'd like you to think about what is the same and what is different between both methods.

Well, the partial products are recorded for both and the partial products combined result in the final product.

What's different is the layout.

Over to you, I'd like you to fill in the gaps.

You can pause the video here.

How did you do? So we can see that we're multiplying by a factor of three and by the looks of things we don't have to regroup.

So this should have been relatively easy for us.

So if you got 600,30 and nine, you are correct.

And for those of you thinking ahead, if you then recombined to your partial products and got 639, give yourself an extra tick.

Now let's have a look at this question.

Andeep has 207 marbles.

Izzy has four times as many marbles.

How many marbles does Izzy have altogether? So the first thing I'd like you to think about is what multiplication equation is needed and what strategy will you use? If you've got 207 multiplied by four or four multiplied by 207, you are correct.

And here we can see that we're going to be using our informal written method.

We're first going to partition our three digit number into hundreds, tens and one.

So this is how we're going to set it out.

Now what I want you to take into consideration here is that our tens digit is a zero.

We then go to calculating what each partial product is by multiplying by factor of four.

What do you think those partial products will be? Let's have a look.

So we've got 800 add zero, add 28.

And then once we've recombined those partial products, we get 828.

Now when using the grid model, this is what it would look like.

We're going to start off by partitioning into hundreds, tens and ones.

So we've got hundreds, tens, which is zero tens and then seven ones.

Now sometimes it's easy to get confused and forget the zero, but we must make sure we add it in as our placeholder in the tens column.

We're multiplying by a factor of, if we've got four, you're correct, we put that on the side.

Now is the fun part.

Let's start with our ones.

It doesn't matter which order, but we'll start with our ones this time.

So four multiply by seven is? If you've got 28, you are correct.

What's four multiplied by zero? If you've got zero, you are correct because anything multiplied by zero is zero.

And lastly, what is four multiplied by 200? If you've got 800, you are correct.

If you didn't know how to work that out, just remember the facts that you do know.

So you know that four multiplied by two is eight.

So then you also know for multiply by 200 would be 800.

What do you think we do next? Yes, that's correct.

We recombine our three partial products, which gives us 800 add zero, add 28, which is 828.

Which strategy do you prefer and why? My personal preference for this equation would've definitely been the grid model, and that's because when it comes to laying it out, I really like to see what the partial products are.

It's very visual to me.

I love it.

So I know that you might prefer the informal written method, which is also fine.

It's whatever is most efficient for you.

Remember it's like having a toolkit with all the strategies in there.

You just pick out the one that's most efficient for you.

This time I'd like you to calculate the partial products.

So you've got an informal written method here.

You can pause the video.

Off you go.

How did you do? So we can see that our three digit number has been partitioned into hundreds, tens, and ones.

We must now multiply by a factor of four.

So if you got 800, 80 and 28, you are correct, good job.

Onto your final tasks.

So for the first task, you are going to be using the information from the layouts to fill in the gaps.

For question two, you're going to be using an informal method to answer these word problems, you're going to underline your partial products in different colours.

So for question A, Izzy has 232 marbles.

Andeep has twice as many.

How many marbles does Andeep have? For 2B, the question is, so a box of cupcakes weigh 313 grammes, Izzy's mom buys three boxes.

What is the total mass? And just a helpful hint, think about what equation is needed first in order for you to solve each problem.

You can pause the video here.

So how did you do? Let's get ready to mark our work.

So for question one, this is what you should have got.

If you've got all the correct parts of the answers to the equation and the correct partial products, give yourself a tick.

And for question 2A, if you've got that, you can give yourself a tick.

2B, the total mass of three cupcake boxes is 939 grammes.

If you've got that, you can give yourself a tick.

Well done, we've made it to the end of the lesson.

I hope you enjoyed this lesson as much as I did.

So to summarise our learning, today you multiplied a three digit by a one digit number using partitioning.

So hopefully now what you can do is partition a three digit number into hundreds, tens of ones, and use this to calculate your partial products.

You can also now calculate the overall product by adding together the partial products.

And you can also use partitioning to support you when multiplying a three digit by a one digit number.

I really enjoyed that listen, and I hope you did too.