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.

By the end of this lesson you will be able to represent partitioning in a column method for expanded multiplication.

Your keywords for today are expanded multiplication and partial product.

Now you may have seen some of these keywords before, if you haven't, please do not worry, we will cover them throughout the lesson.

Now, expanded multiplication is way of recording the steps of a calculation focusing on partitioning one or more factors and showing partial products.

So that's very key, we need to make sure we record our partial products when using expanded multiplication and you will see how we do this as the lesson progresses.

Any of the multiplication results that lead up to an overall multiplication result is a partial product.

So as you can see here, 40 and 24 are our partial products.

In this lesson we will be multiplying a two-digit number by a one-digit number using expanded multiplication and in this case, there will be no regrouping.

For our first lesson cycle, we will be focusing on and understanding expanded multiplication.

In this lesson you will also meet Jacob and Lucas.

Let's begin.

Two bikes cost £43 each.

What is the total cost? Now before we begin, I want you to think about what multiplication equation is needed, and what strategies can you use to solve this problem? Have a think.

So if you got 43 multiplied by two, or two multiplied by 43, that is correct.

You can have the multiplication equation in any order because multiplication is commutative.

So as we can see here, we've got our base 10 blocks and we are going to be recording our multiplication equation using expanded multiplication.

So we're going to start off the same as usual, we are going to be partitioning 43 into four 10s and three ones.

So we place 43 at the top.

I thought the order of multiplication did not matter.

For this, the larger factor goes at the top because it makes it easier to see the steps of the calculation.

We then place the smaller factor, in this case that is two, in the ones column.

We then begin by multiplying our ones.

Now in our informal strategies, we began by multiplying our 10s first, but in this case, we must start by multiplying our ones.

So two multiplied by three ones is equal to six ones.

So we write six in our ones column and that's very important.

Make sure you write the ones, six ones, underneath in the ones column.

We then move onto our 10s.

We multiply the 10s, so, two multiplied by four 10s is equal to eight 10s.

We place the eight underneath the 10s column.

Something's missing.

Hm.

Don't forget to put zero as your placeholder.

Now add the partial products.

So here our partial products are 80 and six.

So this part is quite similar to column addition.

So six add zero is six.

Eight add zero is eight.

So 80 add six is 86.

Two bikes will cost £86.

That is how we use expanded multiplication.

Over to you.

I want you to choose the correct expanded multiplication record for this representation.

So have a look at the base 10 blocks and then I want you to select whether it represents A or B.

You can pause the video here.

How did you do? If you selected B, you are correct.

We must look at the base 10 blocks.

So we can see that in one group we have 23.

Now there are two groups of 23, which means our equation must be two multiplied by 23 or 23 multiplied by two.

In this case, because we've placed the larger factor at the top, 23 must be at the top.

And then two must be placed underneath in the ones column and B represents this accurately.

Let's move on.

Now, Eric buys a pair of earphones for each of his four children.

Each pair costs £21.

How much does he spend altogether? So again, I'd like you to think about, what multiplication equation is needed? And what strategies can we use to solve this problem? Have a think.

The multiplication equation is four multiplied by 21 or 21 multiplied by four.

We're going to focus on solving this equation using expanded multiplication.

What do we do first? We place the largest factor at the top.

We partition 21 into 20 and one and we must remember to place the largest factor at the top.

And we will make sure the digit two goes into the right column as it represents two 10s and then we can place one one in the ones column.

Because we're multiplying by four, we place the smaller factor in the ones column as well.

We start by multiplying the ones first and write the digit in the ones column.

So four multiplied by one one is four ones.

Next, we multiply the 10s.

Two multiplied by four 10s is equal to eight 10s.

Record this in the correct column.

So eight in the 10s column and then we put zero as our placeholder in ones column.

So our partial products are 80 and four.

We then have to recombine both.

So by adding our partial products, we get four in our ones column, eight in our 10s column.

Four headphones would cost £84.

Over to you.

So as we can see here, we've got an expanded multiplication example and I'd like you to fill in the gaps.

What are those parts in our expanded multiplication called? Have a go, pause the video now.

How did you do? So let's have a look.

If for this section here you labelled four and 80 as partial products, you are correct, good job.

84 is our product because that is what we get when we recombine our partial product and is the answer to the equation 21 multiplied by four.

Okay, so Jacob and Lucas have used two different ways to record.

What I want you to think about as I go through the different methods is what's the same? And what's different? So in both we multiply the single-digit number separately, by the one and by the 10s of the two-digit number.

In both, we then add the partial products.

This results in the same partial product.

The layout, however, is different.

When the factors are recorded, the digits are aligned correctly.

Similar to laying out column addition and subtraction.

When partial products are recorded, they are also aligned correctly.

Back to you.

Jacob has used the informal method for a calculation.

So using Jacob's method, I'd like you to fill in Lucas's method for his expanded multiplication.

I also want you to think about which method you prefer and why.

You can pause the video here.

So how did you do? If you go 40 and six as your partial products in the expanded method, good job, that is correct.

Back to you again.

Which is the correct arrangement for this multiplication equation? So your multiplication is 26 multiplied by four.

I've arranged my numbers like this.

So there's two options here, A and B.

Which one's correct? I want you to explain your answer.

You can pause the video here.

B is correct.

We usually write the larger factor at the top.

We are multiplying by four ones, the digit four should be in the ones column.

Okay, onto the main task.

You will be labelling the expanded multiplication examples below for task one.

For task two, you're going to record the calculation of these multiplication equations using expanded multiplication.

Do remember to also record your partial products.

You can pause the video here.

Good luck.

How did you do? So for the first example, the first label was factors because factors are what you multiply to give rise to your product, which is labelled at the end.

And then you should have also got partial product.

So for this first example, we were multiplying 22 by four.

So you should have placed 22, which is your larger factor, at the top and four at the bottom.

You would've then multiplied four by two ones, which would've given you eight ones.

And then you would've multiplied four by two 10s which is eight 10s, that would've given you 80 as your second partial product.

You then recombine your partial products to get 88 as your answer.

For the second example, you would've placed 13 at the top and three at the bottom because it's your smaller factor.

Then multiply your ones first, which would've given nine as your first partial product.

You then would've moved onto your 10s, three multiplied by one 10 is 30.

Recombine 30 and nine to get 39 as your product.

And then for your last example, three multiplied by 32.

As 32 is your larger factor, you would've placed it at the top and three at the bottom.

You then would've multiplied your ones, so three multiplied by two ones is six ones.

Three multiplied by three 10s is nine 10s.

Don't forget to place the zero as your placeholder.

You then would've recombined 90 and six to get 96 as your product.

Okay, so onto lesson cycle two, using expanded multiplication.

One bike costs £41.

What do two bikes cost? So I want you to think about, what is known? And what is unknown? We know that two bikes cost £41, but we don't know what the total is.

One bike costs £41 and here we can see that the expanded multiplication is being used.

We can see that Lucas has got £10 as his answer.

Hm.

So we begin by multiplying in our ones column.

Two multiplied by one is two.

We then move onto our 10s column.

So two multiplied by four 10s is equal to eight 10s and we must remember to place it underneath.

Hm, okay.

What mistake could Lucas have made? So we'll start off with our ones.

Two multiplied by one one is two ones.

And then we'll move onto our 10s.

So two multiplied by four 10s is eight 10s.

We put the eight in the 10s column and we put the zero in the ones column as our placeholder.

So then we recombine our partial products, so in this case that's 80 add two and we get 82.

So the cost of two bikes is £82.

Back to you.

So, you're now going to match the multiplication to the correct arrangement of expanded multiplication.

The equation that you will be matching to is three multiplied by 23.

You can pause the video now.

How did you do? So, you should've got C.

This is because 23, being the larger factor, needs to go at the top and because we're multiplying by three, that needs to go at the bottom.

Three bikes cost £23 each.

What is the total cost? Think about the multiplication equation required to solve this problem.

If you got three multiplied by 23, good job.

So this time there seems to be a number missing, so we can use our multiplication facts to help us.

Where should we start? It's always best to start with our ones column.

I know that that three groups of three is nine.

So that means we will have nine ones in our ones column.

Now we can move onto our 10s.

Something multiplied by three is six 10s.

I know that three groups of two is six.

I know that three groups of two 10s is six 10s, which means two needs to go into the 10s column.

I will put zero as my placeholder in the ones column.

So now this is the part where we will recombine our partial products, so in this case that's 60 add nine which means that's also six 10s add nine ones which equals 69.

Three bikes cost £69 altogether.

The product is 69.

Okay, over to you.

Some digits are missing.

Which column should Jacob begin calculating from first? Pause the video to have a think.

So what do you think? If you got the ones column, that is correct and that is because Jacob should begin calculating from the ones column first because it will make the calculation steps a lot easier.

Okay, so we're onto our last two tasks.

For this first task, you're going to be completing the word problem below using expanded multiplication.

Lucas, Jacob, and Sofia buy caps costing different prices.

Who spent more than £90? So we've got Jacob who's bought four and he's spent £22 each.

Then we've got Lucas who's bought two caps at £43 and then we've got Sofia who's bought three caps at £31 each.

For this task you're going to be finding the missing numbers for each expanded multiplication that you can see on the screen.

Pause the video here to get started.

Okay so how did you do? For Jacob, he bought four caps at £22 each.

Jacob spent £88 in total.

If you got that, good job.

Lucas bought two caps at £43 each.

He spent £86 in total.

If you got that, good job.

And lastly, Sofia spent £93 in total.

So she was the one that actually spent more than £90.

If you got all three answers correct, amazing, well done.

So these are the answers for the missing numbers.

If you got all three correct, really well done.

So, we're now at the end of our lesson.

To summarise, what we did today was we multiplied a two-digit number by a one-digit number using expanded multiplication, there were no regroups involved.

So, you can now record multiplication calculations in different ways, the informal written and expanded multiplication recordings look different, but both show partial products.

We can use expanded multiplication to record the multiplication of a two-digit by a one-digit number where there is no regrouping.

Thank you and I look forward to seeing you in the next lesson.

Well done for getting to the end of this lesson, I hope you enjoyed it.