Lesson video

Hello, I'm Ms. 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 will use expanded multiplication to record regrouping from the tens to the one hundreds.

Your keywords for today are expanded multiplication and regroup or regrouping.

You may have come across these words before.

If you have, try and remember what these words mean.

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

The process of unitizing and exchanging between case value is known as regrouping.

For example, 10 ones can be regrouped for one 10.

One 10 can be regrouped for 10 ones.

So today, we'll be looking at multiplying a two digit number by a one digit number, using expanded multiplication.

In this case, there will be regrouping happening from our tens to one hundreds.

And our first lesson cycle is about understanding expanded multiplication.

In this lesson, you will meet Aisha and Jun.

So let's begin.

You may have seen something like this.

This is an example of expanded multiplication, and we can see that we're multiplying 41 by 2.

In this example, the partial product in the ones is a one digit number.

You may have also seen this.

In this case, we're multiplying 16 by 4.

In this example, the partial product in the ones digit is a two digit number.

However, partial products may not always be a one digit or two digit number.

Have a look at this example.

We are multiplying 33 by 4.

We've already multiplied our ones.

Now when moving on to our tens, we end up with 12 tens.

You'll be exploring what to do when this happens.

There are 4 rows, each with 33 chairs.

How many chairs are there altogether? Now we can see that the array has displayed this calculation.

What I want you to think about is what multiplication equation is needed.

If you got 33 multiplied by 4, or 4 multiplied by 33, you are correct.

You can have them in any order because multiplication is commutative.

So we're going to start by partitioning 33 into 3 tens and 3 ones.

We are going to be using expanded multiplication.

Aisha's going to use the base 10 blocks to help her.

Now the larger factor goes at the top, because this makes it easier to calculate our equation.

Now, when it comes to the base 10 blocks, we need 4 groups of 33, and we're also multiplying by 4, so the smaller factor goes at the bottom.

So we'll do that, and we will have our 4 groups of 33 there, represented by our base 10 blocks.

We're going to multiply the ones first.

3 multiplied by 4 ones is equal to 12 ones.

There is 1 ten in 12, so we regroup and place the 1 in the tens column.

There are 2 ones in 12, so we put the 2 in the ones column.

Make sure you align these digits correctly.

This will make it so much easier when we regroup our partial products, and it will lead to better accuracy.

Next, we're going to focus on our tens.

4 multiplied by 3 tens is 12 tens.

There are more than 10 tens in 12 tens.

We must regroup.

We'll now place the 100 in the hundreds column, place the 2 tens underneath, aligned correctly under the tens column, and place 0 as your placeholder.

Now, Aisha's wondering why do we have a 3 digit partial product? Jun's answer to that is because 12 tens is 120.

This time we are adding a 3 digit partial product to a two digit partial product.

We're going to be recombining our partial products.

This part is similar to column addition, so we're going to be starting off by looking at our ones first.

2 ones add 0 ones is 2 ones.

You're going to place the 2 in the ones column.

1 ten add 2 tens is 3 tens.

Place the 3 in the tens column.

And lastly, 100 add 0 hundreds is 100.

Place the 1 in the hundreds column, and you can see that all these digits have been aligned correctly.

So the product is 132.

There will be 132 chairs.

Aisha is calculating 32 multiplied by 4.

You can see her calculation over here.

She's got 20 as her answer.

Is Aisha's calculation correct? I want you to explain your thinking to your partner.

So how did you do? Oh, Aisha did not regroup.

Aisha did not regroup her tens correctly.

Moving on, there are 4 rows each with 26 chairs.

How many chairs altogether? Aisha believes that she will not need to regroup in the tens column, and she believes that her product will be a two digit number.

Do you agree? And what is the multiplication needed? I'm going to give you a moment to think.

So let's calculate this together.

The equation required is either 26 multiplied by 4 or 4 multiplied by 26.

Now, the larger factor goes at the top, because this makes it easier to calculate our equation, which means the smaller factor goes into our ones column and it needs to be aligned correctly.

You're going to multiply the ones first.

4 multiplied by 6 ones is 24 ones.

20 ones can be regrouped for 2 tens.

A 2 is written in the tens column.

There are 4 ones in 24, so we put the 4 in the ones column.

Next we move on to multiplying in our tens.

So 4 multiplied by 2 tens is 8 tens.

We place the 8 in the tens column.

There are 0 ones in 8 tens, so we place 0 as our placeholder in the ones column.

4 add 0 ones is 4 ones.

We then move on to our tens column.

8 tens add 2 tens is 10 tens.

10 tens equals 100.

We must regroup.

So 100 has 0 tens, so you put 0 as your placeholder in the tens column, and you place the 1 in the hundreds column.

What do you notice? I'll give you a moment to think.

Sometimes it does not look like we need to regroup our tens to hundreds, but when we sum partial products, we do.

Over to you.

12 tens can be regrouped as hundreds and tens.

You can pause the video here.

Off you go.

How did you do? If you got 100 and 2 tens, you are correct.

Back to you.

The 100 is placed in the column.

You can pause the video here.

Off you go.

How did you do? So you should have got hundreds column.

This is because 12 tens is regrouped as 100, 2 tens and 0 ones.

So the 100 needs to go in the hundreds column.

Okay, onto the first task of this lesson cycle.

For this question, you will fill in the gaps by calculating the partial products.

You can pause the video here.

How did you do? So for question one, we were multiplying 53 by 4.

Our first partial product was already filled out for us, but our second partial product was not.

So instead of looking at the ones column first, we needed to look at the tens column.

4 multiplied by 5 tens is 20 tens.

20 tens is regrouped as 200.

So you placed the 2 in the hundreds column, 0 as a placeholder in the tens column and the ones column.

Now, let's move on to part two.

Here we were calculating both partial products and the product.

So we will start off by looking at our ones column.

6 multiplied by one is 6 ones.

We finished that.

We can now move on to multiplying in our tens column.

6 multiply by 6 tens is 36 tens.

36 tens can be regrouped as 360.

So the 3 in 300 is placed in the hundreds column, and the 6 in 6 tens is placed in the tens column.

We write 0 as our placeholder in the ones column.

We then recombine both partial products to get 366 as our product.

If you've got both of those correct, good job.

Now we're going to be moving on to using expanded multiplication to solve problems when there are instances of regrouping from our tens to hundreds.

Let's go.

Tickets at a football stadium cost 41 pounds each.

How much did Jacob and Aisha spend individually? So Jacob's bought 3 tickets and Aisha's bought 5.

So what multiplication equations are needed to solve this problem? Have a think.

Right, so if you've got 3 multiplied by 41, or 41 multiplied by 3, and for the second equation, if you've got 5 multiplied by 41, or 41 multiplied by 5, you are correct.

Here we've got 3 tickets bought at 41 pounds, and in the second equation, we've got 5 tickets bought at 41 pounds.

So I will talk you through my expanded calculation.

I placed my larger factor at the top, which is 41, and I placed my smallest factor 3 at the bottom.

I started by multiplying my ones.

3 multiplied by 1 is 3.

If you've got that, good job.

Then I started multiplying in my tens.

What is 3 multiplied by 4 tens? If you've got 12 tens, well done.

Now, 12 tens can be regrouped as 102 tens.

Here we can see that it's been aligned correctly.

Now, when you recombine both partial products, you end up with a product of 123.

Your turn.

I would like you to use expanded multiplication to calculate 5 multiplied by 41.

You can pause the video here.

How did you do? So I will talk you through this calculation.

You would've placed your larger factor at the top, which is 41, and you would've placed 5 at the bottom in the ones column.

You then would've started multiplying in your ones.

So 5 multiplied by 1 one gives you 5 ones.

You place that underneath in your ones column.

You then would've multiplied 5 by 4 tens, and that would've given you 20 tens.

Now 20 tens can be regrouped as 200.

You place the 2 in the hundreds column, and you put 0 as your placeholder in the tens column and the ones column.

You then recombine those partial products, quite similar to column addition, and you should have got your product as 205.

So all together, Lucas spent 123 pounds and Aisha spent 205 pounds.

If you got that, good job.

Back to you.

So the missing partial product for 4 multiplied by 41 is either 16, 160 or 106.

And I'd like you to explain how you know to your partner.

You can pause the video here.

How did you do? So let's have a look at the ones column.

4 multiplied by 1 one is 4 ones, and that's already been filled out for us.

So we would've had to look at our tens column.

4 multiplied by 4 tens is 16 tens.

But our partial product is a 3 digit number, so 16 tens must be regrouped.

16 tens regrouped is 100, 6 tens and 0 ones, which is 160.

So if you got 160, you are correct.

Well done.

Let's move on.

Find the missing digits.

Now, I used to really struggle with this type of question, but what I realised was that if you break down the question and start by looking at separate columns first, it should make it easier.

So what I want you to begin by thinking about is what is known and what is unknown.

I'm going to give you a moment to think.

Let's start with what is known.

Our product is known, our partial products are known.

What's missing or what is unknown is our smallest factor, the factor that we are multiplying by, and part of our larger factor.

Begin by looking at our ones column.

The missing factor must be a one digit number that multiplies by 2 to make 8.

So let's use our 2 times tables that help us.

So something multiplied by 2 ones will give us 8 ones.

I know that 4 multiplied by 2 ones will give us 8 ones.

So the missing factor is 4.

Now we can look at our tens column.

In order to support us, so our partial product here is 280, or otherwise equivalent to 28 tens.

4 multiplied by something gives us 28 tens.

I know that 280 is 4 multiplied by something tens.

I can use my times tables to help me.

4 multiplied by 7 tens is 28 tens.

That's because if you know that 4 multiplied by 7 is 28, 4 multiplied by 7 tens must be 28 tens.

So that means the missing digit is 7.

Okay, back to you.

The missing partial product for 38 multiplied by 5 is, and your options are 530, 105 or 150.

You can pause the video here.

Okay, how did you do? Let's have a look at our ones first.

5 multiplied by 8 ones gives us 40 ones, and that's been recorded.

Our first partial product is known, but we don't know our second partial product, so we must look at multiplying our tens.

So if I know that 5 multiplied by 3 is 15, I also know that 5 multiplied by 3 tens is 15 tens.

If we regroup 15 tens, that is 100, 5 tens and 0 ones, which is equivalent to 150, which means 150 is our answer.

Back to you.

So Aisha believes the product of the single digit and tens number will always need regrouping.

Is this always true, sometimes true or never true? You could pause the video here.

Okay, what did you think? So let's start off with some examples.

21 multiplied by 2 does not require regrouping when multiplying in the tens column.

51 multiplied by 2 does require regrouping when multiplying in the tens column, and we know that because 2 multiplied by 5 tens will give us 10 tens, and we do need to regroup that.

So that means her statement is sometimes true.

Back to you.

Draw a line to match each multiplication with the correct regrouping.

So you've got the equations 31 multiplied by 4, 33 multiplied by 2, and 14 multiplied by 3.

Now, the instances of regrouping you are matching to are 0 regroup, regrouping in ones to tens, regrouping in tens to a hundreds.

You can pause the video here to have a go.

So how did you do? If you got 31 multiplied by 4 as having regrouping in the tens to a hundreds, you are correct.

33 multiplied by 2 results in no regrouping.

And 14 multiplied by 3, we can see that there will be regrouping in the ones to tens because 3 multiplied by 4 will give us 12 ones, and 12 ones is greater than 10 ones, so we must regroup.

Okay, onto our final 3 tasks.

So, the first task, you'll be completing these multiplication equations using expanded multiplication.

Your equations are 51 multiplied by 5, 84 multiplied by 2, and 73 multiplied by 3.

For the second question, I would like you to find the missing numbers.

And for the third question, using expanded multiplication, how close can you get to the target of 364? Now, Aisha's already used 364 multiplied by 1, so you can't use that.

Can you think of any more? You can pause the video here to have a go.

How did you do? Let's look at the second question.

So the larger factor at the top should have been 84, and we're multiplying by 2.

The partial products you should have got were 8 ones and 160 as your second partial product.

After recombining the partial products, you should have got 168 as your product.

If you got that, give yourself a tick.

And for the final equation, you should have got 9 as your first partial product, and then 210 as your second partial product.

Summed together, these partial products give us 219 as our product.

If you got that, give yourself a tick.

Let's move on.

So for both questions, please check that you've got the correct digit in the missing gaps.

If you managed to find all the missing numbers, well done.

And for question 3, now, I love these types of questions because they really do make you think methodically.

After multiplying 1 by 364 to get my product, another example answer that you could have had was 182 multiplied by 2.

182 is the larger factor, and then we multiply that by 2, and then you would've had 3 partial products here.

So you would've multiplied in your ones first to get 4 ones, then you would've multiplied in your tens, followed by your hundreds.

All 3 partial products summed would've given you 364.

Now, it's important to note that we have 3 partial products here.

We are multiplying by 3 a digit number.

Some of the alternative answers that you could have had were 4 multiplied by 91, and 7 multiplied by 52.

If you managed to get all of those variations, good job.

Well done, you made it to the end of the lesson.

To summarise our learning today, we multiplied a two digit number by a one digit number using expanded multiplication with regrouping happening in our tens to our hundreds.

You now understand how to use expanded multiplication, especially when regrouping tens to hundreds.

You can use expanded multiplication to regroup tens to one hundreds, and you can use this to solve problems. I hope you enjoyed this lesson as much as I did.