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.

In today's lesson, you will be using expanded multiplication to record regrouping from the ones to the tens.

Our keywords for today's lesson are: regroup, or regrouping, and expanded multiplication.

Now, you may have heard of these keywords before.

If you have, try and remember what they mean.

To begin with, the process of unitizing and exchanging between place value is known as regrouping.

For example, 10 ones can be regrouped for 1 ten.

1 ten can be regrouped for 10 ones.

Similarly, 10 tens can be regrouped for 100, and 100 can be regrouped for 10 tens.

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

We will be using expanded multiplication today in our lesson.

Our lesson outline: multiply a two-digit number by a one-digit number using expanded multiplication.

And in this lesson, we will be regrouping ones to tens.

We will be understanding expanded multiplication.

In this lesson, you will meet Jacob and Lucas.

Now you may have seen this, we've got 41 multiplied by 2 and you can see that the partial products have been recorded and our product is 82.

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

So in this case we've got 2 ones.

However, the partial products may not always be a one-digit number.

So here we've got an example.

We've got 16 multiplied by 4.

Now when we look at our ones column and we multiply in our ones column, we've got 6 multiplied by 4, which gives us 24 ones.

Where will we put the 24 ones? So what we are going to be doing is exploring what to do when this happens.

Let's begin.

Four packets of felt tip pens each have 16 pens.

How many pens are there altogether? What multiplication equation is needed? Have a think.

Jacob is going to use base ten blocks to help him.

You got 16 multiplied by 4, or 4 multiplied by 16, you are correct, good job.

It could be in any way because multiplication is commutative.

We can use expanded multiplication to record this calculation.

So what we're going to do first is partition 16 into 1 ten and 6 ones.

First, we need to place the larger factor at the top.

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

Then place the smaller factor 4 in the ones column, and this goes underneath.

We're going to multiply the ones first.

So 4 multiplied by 6 ones is 24 ones.

Now this is where we would usually have a one-digit number, but because we've got a two-digit partial product, I want you to focus in on how we are going to place this partial product.

So 20 ones can be regrouped as 2 tens.

A 2 is written in the tens column.

There are 4 ones.

So a 4 is written in the ones column.

And you can see that both digits have been aligned correctly directly underneath where they should be.

So what do you notice about this partial product? The product of the ones digit is greater than 10, so our partial product is a two-digit number.

Next, we're going to multiply the tens.

So 4 multiplied by 1 ten is equal to 4 tens.

So we place the 4 underneath aligned correctly under the tens column, and then we put 0 as your placeholder into the ones column.

Now we add our partial products.

This time we are adding two two-digit partial products.

This part is actually similar to column addition and subtraction.

So 4 ones add 0 ones is 4 ones.

Place the 4 in the ones column.

2 tens add 4 tens is 6 tens.

Place the 6 in the tens column.

64 is our product.

There will be 64 felt tip pens altogether.

Over to you.

You always have a one-digit partial product when multiplying a two-digit by a one-digit number.

What do you think? Is this always true, sometimes true, or never true? I want you to prove it.

You can pause the video now.

Off you go.

How did you do? So the answer is sometimes true.

For example, 24 multiplied by 3.

3 multiplied by 4 ones is equal to 12 ones, which is a two-digit partial product.

Then in our next example, 22 multiplied by 3, is 3 multiplied by 2 ones, which is equal to 6 ones, and 6 is a one-digit partial product.

So your partial products really do depend on the numbers that you are multiplying by.

Back to you.

Have a look, this is expanded multiplication and I would like you to fill in the gaps.

You can pause the video here.

Off you go.

How did you do? So let's look at the first section.

We've got 16 multiplied by 4.

These are our factors, and when we multiply our factors, especially when using expanded multiplication, we must record our partial products.

And then when we recombined or added the partial products, this gives us our product.

Well done if you got all three correct.

Let's move on.

Okay, so there are 14 felt tips in a packet.

If there are six packets, how many felt tips are there altogether? So without calculating, will you need to regroup in the ones column? How do you know? Have a think.

Let's think together.

There are 14 felt tips in a packet, and there are six packets altogether.

So in order to figure out whether we are regrouping in our ones column, we must partition 14 into 10 and 4.

So we'll take 14, which is our larger factor, and we will partition 14 into 10 and 4.

So we are looking at our ones, which means we will multiply 6 by 4 first.

This gives us 24.

Jacob says, "I know that 6 multiplied by 4 ones is 24 ones, so I will need to regroup.

This means I will have a two-digit partial product." And for those of you that are thinking ahead, yes, 24 can be regrouped as 2 tens and 4 ones.

So let's complete the calculation now.

So we partition 14 into 1 ten and 4 ones and we place the larger factor at the top.

Then we place a smaller factor 6 in the ones column.

We begin by multiplying our ones first.

So we know that 6 multiplied by 4 is 24.

20 ones can be regrouped for 2 tens, and 2 is written in the tens column.

Now remember, this part is very important.

We must place the 2 in the tens column and we must make sure that we align that correctly.

Otherwise when it comes to adding our partial products, this may lead to errors.

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

So what do you notice about the partial product? Have a think.

It's a two-digit number because the product of the ones digit is greater than 10.

If you have more than 10 ones, 10 tens, or 10 one hundreds, we must always regroup.

So now we can multiply our tens.

So 6 multiplied by 1 ten is equal to 6 tens.

Place the 6 tens underneath, aligned correctly, under the tens column.

Is that it? Do we finish here? We definitely don't.

We must remember to put zero as our placeholder in the ones column.

So we've got 60 there now as our second partial product.

Now we recombine the partial product, so we add 24 and 60.

This part is similar to column addition.

So 4 ones add 0 ones is 4 ones.

So we place the 4 in the ones column.

And then we move on to adding our tens.

2 tens add 6 tens is 8 tens.

We place the 8 in the tens column.

So the product is 84.

There will be 84 felt tip pens altogether.

Over to you.

Which multiplication will need regrouping in the ones column only? So you've got three equations there: 18 multiplied by 3, 6 multiplied by 11, or 21 multiplied by 6.

And I'd like you to explain your thinking to your partner or to the person sitting next to you.

You can pause the video here.

Off you go.

How did you do? If you got 18 multiplied by 3, you are correct.

Well done.

This is because if we partition our larger factor 18 into 10 and 8 and if we then multiply our 8 ones by 3, we end up with 24.

24 is greater than 10 ones, so that means we will need to regroup in our ones column.

Okay, moving on.

So there are different types of layouts to represent multiplying a two-digit by a one-digit number, and you can see that on the screen now.

So you may have seen the grid model, an informal written method, or an expanded multiplication method, which is what we're focusing on right now.

Jacob has used all three layouts to show 4 multiplied by 16.

So I want you to think about what's the same between all three and what is different? Well, the first thing that's different is the layout.

We're still multiplying, but you can see quite visually that all three are different when it comes to the layout.

The partial products are the same.

And lastly, regrouping is still needed.

Your turn.

Lucas used a grid model.

Using his model, I would like you to fill in the gaps for the expanded multiplication.

You can pause the video here.

So how did you do? Now I can see in the grid model that if we recombine 10 and 9, we end up with our larger factor, which is 19, and we are multiplying this by 4.

Now this information is already present in our expanded multiplication.

We've got 19 multiplied by 4.

What's missing is the partial products.

So I know my factors, I don't know my partial products.

I also know the product that I get at the end of the equation.

So the grid model, if we have a look, we can see that the partial products are recorded.

We can start off with our ones column.

So if we multiply 4 by 9, we end up with 36 ones, and we can see that that's been recorded in the grid model.

We actually didn't need to use any calculation because we can transfer that information from the grid model to our expanded method.

But the order of the recording of partial products matters because when it comes to our expanded multiplication, we always start by multiplying in our ones column.

So in this case, we would place the 36 first as our partial product.

And then if we move on to multiplying in our tens, we know that 4 multiplied by 1 ten is 4 tens, this is equivalent to 40.

We would then place that partial product underneath our first partial product.

So if you got that as your answer, good job.

Let's move on.

Back to you.

What mistake did Lucas make? I want you to explain your thinking to your partner.

How did you do? So there's something that doesn't look quite right there in our expanded multiplication.

Lucas did not align his partial products correctly.

It's interesting because when we are working in class, sometimes in a rush, we may align our partial products incorrectly.

So I really, really want you to make sure that you align your ones and your tens correctly when recording your partial products.

So you have two tasks for this first lesson cycle.

Task one, you are going to use the grid model and expanded multiplication to fill in the gaps.

And question two, you are going to fill in the gaps using expanded multiplication.

You can pause the video here.

Off you go.

So how did you do? In this question, our smaller factor was five.

This would give rise to a partial product of 45 and our second partial product was 50.

Both partial products recombined give us 95.

And for question two, have a look at the answers below.

Give yourself a tick if you got them correct.

Onto our second lesson cycle.

This time, you'll be using expanded multiplication.

Tickets at a football stadium cost 17 pounds each.

How much did Jacob and Lucas spend individually? So as you can see here, Jacob's bought three tickets at 17 pounds.

Lucas has bought five tickets at 17 pounds.

I want you to think about what multiplication equations are required to solve this problem.

What is known and what is unknown? So I'm going to have a go first.

So Jacob bought three tickets at 17 pounds, which means I know what the factors of my equation are, I just don't know what the product is, and this is what I will be calculating using expanded multiplication.

Lucas, on the other hand, has bought five at 17 pounds each.

And similarly, you'll be working out the product.

So I would place my larger factor at the top and my smaller factor at the bottom.

So I've got 17 multiplied by 3.

I'll start off by multiplying in my ones column.

3 multiplied by 7 ones is 21 ones.

I would regroup my 20 as 2 tens and place that in the tens column and then I would place the 1 one in the ones column.

I would then multiply in my tens column.

So 3 multiplied by 1 ten is 3 tens.

I would place the 3 tens in the tens column and the 0 as a placeholder in the ones column.

I will then recombine those partial products to give me my product.

So this part is similar to column addition.

So 1 add 0 is 1, 2 tens add 3 tens is 5 tens, which gives me a product of 51.

Now over to you.

I would like you to calculate 5 multiplied by 17 using expanded multiplication.

How did you do? You should have placed 17 at the top.

You're multiplying by five, so that would go in your ones column underneath.

Make sure you've aligned this correctly.

And then you would start off by multiplying in your ones column.

So 5 multiplied by 7 ones is 35 ones.

You would regroup 35 as 3 tens and 5 ones.

So you would place the 3 tens in your tens column and your 5 ones in your ones column.

You'd then move over to your tens column.

5 multiplied by 1 ten is 5 tens, and that is equivalent to 50.

You would put the 5 in your tens column and 0 as your placeholder underneath.

You'd then recombine your partial products.

5 ones add 0 ones is 5 ones.

3 tens add 5 tens is 8 tens.

So your product is 85, which means Jacob spent 51 pounds altogether and Lucas spent 85 pounds altogether.

If you got 85 pounds, good job.

In this question, you are finding the missing digits.

Some of Jacob's digits have rubbed off.

Now I want you to look at the expanded multiplication and think about what is known and what is unknown.

Have a think.

So I know that 14 is my larger factor.

However, my smaller factor is missing, the factor that I am multiplying by.

Part of my partial product is also missing.

What I do know is my product.

We are going to start off by looking at our ones column.

Something multiplied by 4 ones gives us 12 ones.

We need to think about our four times tables.

We can use our table facts to help us.

What multiplied by 4 gives us 12? Well, I know that 4 multiplied by 3 ones is 12 ones.

So 3 ones must be our missing factor.

Now that we've figured out what our missing factor is, we can now proceed onto calculating what our missing partial product is.

So we've already multiplied in our ones column.

We now need to move on to our tens column.

3 multiplied by 1 ten is something tens.

So now we're going to move on to our tens.

3 multiplied by 1 ten is 3 tens.

We can place the three in our tens column.

You have now completed your expanded multiplication.

Over to you.

The missing partial product for 4 multiplied by 17 is, and you've got three options: 40, 11, or 28.

You can pause the video here.

How did you do? So let's look at this together.

We need to look at our ones column.

We've already partitioned 17 into 10 and 7.

We'll start by multiplying in our ones column.

I know that 4 multiplied by 7 ones gives me 28 ones.

So you should have got 28 as your answer.

Back to you.

So the missing partial product for 3 multiplied by 18 is, you've got three options here: 24, 30, or 4.

You can pause the video here to have a go.

How did you do? So this time I'm not multiplying in my ones column because I've already got my partial product from multiplying in the ones.

I now need to look up my tens.

So 3 multiplied by 1 ten gives me 3 tens.

If you've got 30 as your answer, well done.

Onto our final tasks.

For this question, you are going to be completing the word problem below using expanded multiplication.

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

Underline partial products in different colours.

Who spent the most? Was it Jacob, who bought three tickets at 19 pounds? Or was it Lucas, who bought five tickets at 15 pounds each? Or was it Sofia, who bought four tickets at 17 pounds each? Now for the next task, you are going to be finding the missing numbers for the expanded multiplication equations you see on the screen.

You can pause the video now to have a go.

So how did you do? Let's have a look at Jacob's equation first.

For his equation, we were calculating 3 multiplied by 90.

Now we've placed a larger factor at the top, which is 19, and we've multiplied 19 by 3.

His first partial product is 27 because 3 multiplied by 9 ones is 27 ones.

And the second partial product as 3 tens, which is 30, because 3 multiplied by 1 ten is 3 tens, which means that the product is 57.

So for Sofia, the equation that you were calculating was 4 multiplied by 17.

So the first partial product that you should have got was 28 because 4 multiplied by 7 ones is 28 ones.

And then the second partial product that you should have got was 40 because 4 multiplied by 1 ten is 4 tens.

4 tens regrouped is 40.

Combining these partial products, you should have got 68 as your product.

And lastly, Lucas.

So Lucas bought five tickets at 15 pounds, which means the equation that we were calculating is 5 multiplied by 15, or 15 multiplied by 5.

So when looking at our first partial product, we multiply our ones first.

So 5 multiplied by 5 ones is 25 ones, which can be regrouped as 2 tens and 5 ones.

So if you've got that as your partial product, good job.

Our second partial product here was 50 because 5 multiplied by 1 ten is 5 tens, and 5 tens regrouped is 50.

We placed the 5 tens in the tens column and we place 0 as our placeholder.

We then recombined 25 and 50 to get 75 as our product.

So that means Lucas spent the most.

If you got that as your answer and you got all three correct, good job.

Now for question two, have a look at the expanded multiplications.

If you got the missing numbers, you are correct.

If you got all three questions correct, amazing, fantastic job.

We've come to the end of the lesson.

So to summarise, today we were multiplying a two-digit by a one-digit number using expanded multiplication.

In this case, we were regrouping in our ones to our tens, which means any partial product that had more than 10 ones we would've had to regroup.

This would've given rise to a two-digit partial product.

We now understand how to use expanded multiplication for a two-digit by one-digit multiplication, regrouping ones to tens.

We have learned that partial products can also be a two-digit number.

We can use expanded multiplication, including regrouping in ones to tens to solve problems. Well done for getting through to the end of the lesson.

I really hope you enjoyed this lesson.