Lesson video

Hello, my name is Mr. Tajiman, today I'm gonna be teaching you a lesson from the unit that is all about multiplying and dividing by two digit numbers.

There might be a few procedures to follow today, but it's also important that you understand why we do each step of the procedure as well.

Okay, I hope you're sitting comfortably 'cause we're ready to start learning.

Here's the outcome for today's lesson then.

By the end, we want you to be able to say, I can explain how to multiply a three digit number by a two digit number.

The key phrase today is partial product.

I'd like you to say it back to me please.

Partial product, your turn.

Okay, but what is a partial product? Well, let's have a look.

Here's how we would define it.

Any of the multiplication results we get leading up to an overall multiplication result is a partial product.

You can see below that there is a model and some jottings and those are being used to complete the overall multiplication of 16 multiplied by four, which is equal to 64.

You might already know that answer, but what we are looking at is what are the partial products? Have a look at those jottings on the right, you can see that 16 has been partitioned into 10 and six.

Each of those have then been multiplied by four, so four multiplied by 10 equals 40 and four multiplied by six equals 24.

Now the 40 and 24 are both partial products because they are not the overall product that we're looking for, but they are multiplication results that we've got along the way.

You can see that they're then added together to give that overall product.

Now, if you're not sure about that just yet, don't worry, you're gonna get plenty of practise with that idea as we go through the lesson.

Let's look at the lesson outline now.

We're gonna start by thinking about multiplying two digit numbers by two digit numbers and then in the second part, we're gonna look at multiplying three digit numbers by two digit numbers.

Sam and Andeep are gonna help us today.

They're gonna be chatting through some of the maths that we look at and they might even give us some hints and tips, so make sure that you listen carefully 'cause we are ready to start.

Sam and Andeep go to watch a tennis match.

They think about how many people are in their section of the stands.

I can see seats in rows of 31, says, Sam, Andeep says "If there are 29 rows, how many seats would that be altogether?" 31 rows of 29 can be calculated by multiplying 31 by 29, so they've realised that this is a multiplication question.

31 multiplied by 29 is equal to something, an unknown.

We don't know yet, that's what we've got to calculate.

They show the calculation using a grid or area model.

You might have seen this in maths that you've done previously.

This is a grid or area model.

They've got the multiplication in the middle there, 31 multiplied by 29.

Then they've written 29 rows and 31 in each row.

Andeep says, this model shows that each row has 31 seats and there are 29 rows.

To make multiplying easier, we can partition the smaller number.

What do we mean by that? Well, there's two factors in that multiplication that we've written inside the grid model, 31 and 29.

29 is the smaller number, so we've partitioned that.

Andeep says there are still 31 seats in each row, but now we have partition 29 rows into 20 rows and nine rows and you can see that the grid model, the area model has also been partitioned by drawing a horizontal line across it.

We split it into two boxes now.

We've got 31 multiplied by 20 and 31 multiplied by nine.

Both of those multiplications might be a little bit easier to calculate.

We're trying to make it easier for ourselves to be more efficient.

The next weekend they go to watch a basketball game.

Sam says, I can see seats in rows of 43.

Andeep says, if there are 32 rows, how many seats would that be altogether? We've got ourselves another multiplication featuring two two digit numbers, 43 multiplied by 32, which is equal to an unknown.

We don't know yet, we've got to calculate that.

They use the grid model to show thinking again, you can see that they've drawn out that box and they've got 43 multiplied by 32 inside it, 32 rows and 43 in each row.

The grid model shows that each row has 43 seats and there are 32 rows, says Andeep, really good and Andeep.

It's always good to talk through your thinking.

Again, they go to make it easier by partitioning the smaller number.

Which of those is the smaller number? Well, there we go.

It was 32 and Andeep says, there are still 43 seats in each row, but now we have partition 32 into 30 and two and again, you can see that on the model.

Okay, it's time to check your understanding of what you've learned about so far, which representation below represents the equation 55 multiplied by 15? How do you know? Explain your thinking to a partner.

Remember that's the crucial part.

You've got to make sure that you can explain something because that will help you to make sure that you consolidate your learning.

Now we've got two different representations here, two different grid or area models.

One of them is 15 multiplied by 55 and you've got 15 rows and 55 in each row.

That's A and then for B, we've got two boxes that are joined together.

One is 55 multiplied by 10 and the other is 55 multiplied by five.

You've got 10 rows and five rows on one side and then 55 in each row on the other side.

So which of these represents 55 multiplied by 15? Pause the video and have a go.

Welcome back, which did you think, A or B? Well, we're about to find out, so the answer was actually A and B, both represent the equation 55 times 15.

I wonder if that tricked anybody and I wonder if you were able to explain why.

If you're still not sure, pause the video and have a go at explaining.

Let's move on then, a part, part whole model can represent the strategy for calculation.

You can see the grid model there on the left and it's been broken up into 31 multiplied by 20 and 31 multiplied by nine.

That's because the factor 29 has been partitioned into 20 and nine.

Look on the right you can see a part part whole model which has the overall multiplication written at the top as a total.

We've got 31 multiplied by 29.

Now watch, we've taken 31 multiplied by 20 and we've written that into one of the parts of the part part whole model.

Then we've taken the other multiplication that was in the grid model and we've written that into the other part of the part part whole model.

To find the product, we can calculate 20 groups of 31 and nine groups of 31.

These are partial products, remember that phrase, so each of those parts in a part part whole model is a partial product.

It's a multiplication that we can work out before working out the overall product.

First, multiply 31 by 20, 31 times two equals 62, and this is 10 times the size.

This gives the partial product 620, then multiply 31 by nine.

This gives the partial product 279.

Lastly, sum the partial products to find the product.

That's 899.

Now I know in there there were some columns and written methods being used and we went through that relatively quickly, but that's because we're looking at the process rather than thinking completely about using columns, there are the partial products written out and the overall product at the top, 31 multiplied by 29 equals 899.

There were 899 seats in the section of the tennis court.

Let's return to the basketball court.

We've got 43 multiplied by 22.

You can see from the grid model that 22 has been partitioned into 20 and two.

Makes sense, 43 multiplied by 20 is the first part in the part, part whole model and 43 times two is the second part in the part, part whole model.

First, multiply 43 by 20.

This gives the partial product 860, then multiply 43 by two.

This gives the partial product 86.

Lastly, sum the partial products to get the product.

That's 946.

Here are the models with the totals in each of the parts.

You've got the part part whole model there with 860 and 86 which have been added together to give you the overall product of 946, 22 times 43 equals 946.

There were 946 seats in the section of the basketball court.

Now it's your turn to check that you've understood what we've been learning about so far.

Use partitioning to fill in the missing expressions.

So you can see we've got a part, part whole model there and at the top we've got our overall multiplication, which is 45 multiplied by 18.

What multiplications would you put into the parts in this part part whole model? Pause the video, think about it and I'll be back in a little while to reveal the answer.

Welcome back, did yours look like this? In one part we had 45 multiplied by 10, and in the other part we had 45 multiplied by eight.

That's because we partitioned the smaller factor 18 into 10 and eight.

It's time for your first practise task then, for number one, I want you to represent the expressions using a grid model, you do not need to calculate the product, so for one A, B, C and D, it's not about calculating the product, it's about how you are representing them.

Remember, partition the smaller factor.

For number two, look at the grid and part whole models.

Use information from each to fill in the blanks and calculate the products.

Pause the video here, have a good go at those, think carefully, explain to a partner if you need to and I'll be back in a little while with some feedback.

Good luck, enjoy.

Welcome back, here are the answers for one, for 1A, 15 was partitioned into 10 and five, so you had 26 multiplied by 10 and 26 multiplied by five, for B, it was 17 that was partitioned into 10 and seven, giving you the two multiplication you can see there, for C, 24 was partitioned into 20 and four and for D, 27 was partitioned into 20 and seven.

Pause the video here if you need extra time to mark those.

Welcome back.

Here's the missing information revealed for two.

So on A you had 35 multiplied by 10 and 35 multiplied by two in the boxes in your grid model.

We also had 10 and two and 35 as our labels.

That meant that our overall multiplication was 35 multiplied by 12 and the missing numbers in the parts of the part part whole model were 10 and two.

For B, we had 43 multiplied by 10 and 43 multiplied by seven.

That gave us labels of 10 and seven and then 43.

So the overall modification was 43 multiplied by 17 and that went into the whole part of the part part whole model as well.

In the actual parts you had 43, which was written down twice as the two missing numbers.

Okay, let's move on to looking at the calculations now.

So for A, you needed to start by doing 35 multiplied by 10, which was 350, then 35 multiplied by two, which was 70.

If you summed those, you ended up with 420.

For B, we had 43 multiplied by 10, which was 430 and then 43 multiplied by seven, which was 301.

If you'd summed those, you ended up with 731.

Okay, pause the video if you need extra time to mark those calculations or to see where any mistakes may have been made.

Welcome back, let's move on to looking at multiplying three digit numbers by two digit numbers.

At a tennis event, a stall stocks 232 bottles of water on one set of shelves.

If it has 17 full shelves, how many bottles of water does it have to sell? Sam says we can represent this using a grid model.

We've got the multiplication 232 multiplied by 17 is equal to something that we're gonna find out.

Yes, says Andeep, partitioning the smaller number will be more efficient.

So here's the grid model.

We've got 232 multiplied by 17 with our labels on.

Andeep says this grid model shows that each shelf has 232 bottles and there are 17 shelves.

To make multiplying easier, we can partition the smaller number.

So which is the smaller number? Well, it's 17, so now we've got two boxes making up our grid model, 232 multiplied by 10 and 232 multiplied by seven.

Andeep says, there are still 232 bottles on each shelf, but now we have partition 17 shells into 10 and seven.

You can also use the part part whole model to show your thinking.

So there's the whole, 232 times 17 at the top.

We've got 232 times 10 as one part and 232 times seven as the other part.

First, multiply 232 by 10.

This gives the partial product 2,320.

Now some of you may have been able to calculate that without using the column method at all because we know how to multiply by 10 mentally.

Then you multiply 232 by seven.

This gives the partial product 1,624.

Lastly, sum the partial product to get the product.

That's 3,944, so that means that there's 3,944 bottles altogether.

Let's check your understanding Andeep has represented 245 multiplied by 33.

Is he correct? Justify your thinking to your partner, pause the video and give it a go.

Welcome back, what did you think? Was he correct? Well, he wasn't.

Andeep has partition 33 incorrectly.

The grid should show 30 and three, so if you look at the labels, there's 33 and three and it should be 30 and three.

Now, Andeep and Sam are a local football match.

Sam says, I can see seats in rows of 23.

Andeep says if there are 341 rows, how many seats would that be altogether? You can see that this context has been written as an equation below, 23 multiplied by 341 is equal to something we don't know yet.

You can use the part part whole model to show your thinking here or you could use the grid model.

You can see them both on screen there.

Let's start with one of the parts then, 341 multiplied by 20, that's gonna give us our first partial product.

Then we've got 341 multiplied by three.

That's going to give us our second partial product.

23 has been partitioned into 20 and three.

First, multiply 341 by 20.

This gives the partial product 6,820.

Then multiply 341 by three.

This gives the partial product 1023.

Lastly, sum the partial products to get the product.

That's 7,843.

Let's check your understanding then.

Which of these pothole models represents 312 multiplied by 22? Pause the video here and have a go.

Welcome back.

The answer was B, 22 has been correctly partitioned into 20 and two.

Have a look at this, Andeep has used an informal method to calculate 433 multiplied by 22.

Is he correct? Let's have a look.

Well, he's got his jottings there and he's done his part part whole method, but you can see that Andeep has partition 22 incorrectly.

It should be 20 and two.

He's got himself confused and he's used three, presumably because 433 features three in the ones digit.

Let's check your understanding again then, Sam has completed half of a calculation.

Use your knowledge of partitioning to help you to complete the rest.

So you can see that we've got a part part whole model that's been completed there.

Two partial products to calculate, your turn, you need to complete those jottings to help Sam, pause the video and have a go.

Welcome back, did you manage to complete that calculation? Well, here's what it might have looked like.

The first partial product was 2,480, the second partial product was 372 and if you added those two partial products together to give you the overall product, you would've got 2,852.

I hope you got it.

If you didn't, pause the video here and go back and look and see where you might have made a mistake.

All right, it's time for your second practise task.

For number one, you need to answer the following questions below.

Draw a grid model each time to show how you would partition the calculation.

For number two, Andeep has used an informal method to calculate 402 multiplied by 22.

Is he correct, why or why not? Okay, pause the video and have a go at those.

I'll be back in a little while with some feedback.

Good luck.

Welcome back, and here are the answers.

You can see that it should have been 7,429 is the overall product, but part of the question was also asking you to make sure that you drew a grid model.

Your grid model should have looked something like the one below, two boxes with two calculations that can be used to find the partial product.

23 was partitioned into 20 and three, so you had 323 multiplied by 20 and 323 multiplied by three.

That gave you the partial product 6,460 and 969, which added together gave you that overall product of 7,429.

Let's look at B then, 22 could have been partitioned into 20 and two, giving you two calculations as follows.

431 multiplied by 20 and 431 multiplied by two.

They gave you partial products of 8,620 and 862, which added together equaled 9,482.

Okay, pause the video if you need to catch up with any marking there.

Here's C, you should have got an overall product of 6,936 and the grid method, the grid model would've been labelled as 204 multiplied by 30 and 204 multiplied by four.

For D, the overall product was 5,040 and you had 420 multiplied by 10 and 420 multiplied by two.

Again, pause the video if you need to catch up with any marking there.

Here's E, the overall product was 4,668 and the grid has been split up into two calculations of 389 multiplied by 10 and 389 multiplied by two.

Pause the video if you need extra time.

Here's number two, then.

Well, Andeep is incorrect.

He has added the wrong partial product.

The partial products he should have added together are 8,040 and 804.

Nevermind Andeep, let's summarise the lesson then.

We can use informal methods of multiplication to calculate the product.

We can do this by partitioning one of the factors, calculating the partial product and then adding the partial products to recombine.

My name's Mr. Tajiman, I've enjoyed today's lesson.

I hope you did as well.

Maybe I'll see you again soon.

Bye for now.