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 will be able to use short multiplication to record regrouping from the 10s to 100s.

Your keywords for this lesson are short multiplication, regroup or regrouping.

Now if you've come across these keywords before, I want you to think about what they might mean.

A method using columns to set out and calculate a multiplication is short multiplication.

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

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

One 10 can be regrouped for 10 ones.

Today what might be helpful is thinking about 10 10s can be regrouped as 100 and 100 can be regrouped as 10 10s.

So anything greater than 10 10s must be regrouped.

So in this lesson you'll be multiplying a two digit number by a one digit number using short multiplication.

In this instance regrouping from your 10s to 100s.

And in this lesson cycle we will be understanding short multiplication.

You will meet Sophia and Alex, four rows each with 31 chairs, how many chairs altogether? Now we can see that there is an array model here that has represented the equation.

Now we know that this isn't an efficient method.

Short multiplication however is and short multiplication is the method that we will be using to answer this question.

But before we get onto that, I want you to think about the multiplication equation needed for this question.

If you got four multiplied by 31 or 31 multiplied by four, well done.

It can be in any order because multiplication is commutative.

Now as I explained earlier, if he was to draw all of those chairs using an array, it would take him very long time.

And similarly, Sophia's actually ran out of counters.

You can use short multiplication to calculate this equation.

So we will begin by partitioning 31 into three 10s and one one.

We're going to first place the larger factor at the top, and we do this because this makes it easier to calculate our equation.

Then we are going to place the smaller factor in the ones column.

And you can see here that the four has been placed in the ones column and it is aligned correctly.

It's very important that you align correct otherwise you may find it difficult when it comes to multiplying.

And this could lead to inaccurate answers.

So first we're going to start with multiplying our ones, four multiplied by one one is four ones, we put the four in the ones column.

Then we're going to move one to our 10s column.

Four multiplied by three 10s is equal to 12 10s.

You must regroup 12 10s to 100 and two 10s.

And this is because 1210s is greater than 10 10s.

And we can see that in our base 10 blocks.

This has been done.

Now we're going to write the one in the 100s column and the two in the 10s column.

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

The additional 100 has been recorded one column to the left of the 10s digit.

So in other words, in the 100s, column over to you, which short multiplication is correct for 52 multiplied by four, which gives us a product of 208.

You've got three examples here.

Have a think you can pause the video now.

how did you do, so if you've got C as your answer, you are correct.

And that's because 52 is our largest factor.

So that goes at the top, four is our smallest factor.

So it goes at the bottom.

When multiplying our ones, four multiplied by two ones gives us eight ones.

We place that in the ones column.

We then move on to multiplying our 10s, four multiplied by five 10s gives us 20 10s.

This can be regrouped as 200 and it needs to be regrouped because 20 10s is greater than 10 10s.

So we place the two in the 100s column, which is next to the 10s digit, and then we place the zero as our placeholder.

Well done if you got that correct, let's move on.

Four rows each with 26 chairs, how many chairs altogether? Now Alex thinks he will not need to regroup in the 10s column and he also believes that his product will be a two digit number.

Do you agree? And what is the multiplication equation needed? Have a think, so our multiplication equation that we require is 26 multiplied by four.

And to figure out whether we need to regroup in our 10s column, we are going to calculate this together.

So we'll begin, the larger factor goes at the top because it makes it easier to calculate our equation.

So we'll first place the larger factor at the top, and that's 26.

Then we're going to place the smaller factor in the ones column.

Make sure you align this correctly.

So after that we're going to multiply the ones first, four multiplied by six ones is 24 ones.

20 ones can be regrouped for two 10s.

A two is written underneath the 10s column.

There are four ones in 24.

So we put the four in the ones column.

So next you're going to move on to multiplying our 10s, four multiplied by two 10s is eight 10s.

Eight 10s, add the regroup two 10s from the ones column will give us 10 10s altogether.

This can be regrouped as 100.

So we placed the one in the 100s column and we place the zero as our placeholder in the 10s column, over to you.

True or false, you'll need to regroup in the 10s column for this equation, 41 multiplied by two.

I want you to justify your answer.

Is it because two multiplied by four 10s is eight 10s or two multiplied by four 10s is 80 10s? You can pause the video here.

It's false, and this is because two multiplied by four 10s is eight 10s, which is less than 10 10s.

We will not need to regroup in the 10s column, back to you.

You will need to regroup in the 10s column.

And similarly to before, I'd like you to justify your answer.

Is it because five multiplied by four 10s is 20 10s or five multiplied by four 10s is two 10s? Make sure you have a look at the equation that you are calculating.

You can pause the video here.

How did you do, so this time, it's true.

You will be regrouping in your 10s, and that's because five multiplied by four 10s is 20 10s, which is greater than 10 10s.

You may have seen expanded multiplication before.

It is another method you can use to represent multiplication problems. So we've got an example of expanded multiplication on our left and we've got short multiplication on our right.

I want you to think about what is the same between both methods and what is different.

Well, let's talk about what's the same.

In both methods, you've got the same factors and you end up with the same product.

What's different? Well, for expanded multiplication, you must record your partial products.

For short multiplication, only one product ends up being recorded, back to you, using the expanded multiplication, fill in the gaps for the short multiplication that you can see on the right hand side of your screen.

You can pause the video here.

Okay, so how did you do? Well, you did not need to calculate for this because your expanded multiplication would've given you enough information for you to then fill in the gaps.

So let's begin with our larger factor.

Well, we can see in the expanded method that our larger factor is 51.

So the missing number here would be five.

Now we're multiplying by a smaller factor.

So if you look back over into our expanded method, our smallest factor is five, which means we're multiplying by five.

You could then put the five in your ones column underneath the one.

Now for your product, we can see that in our expanded multiplication it's 255.

So if you've got something like this, you are correct.

Well done, so for this task, you have two questions.

For this first part, you'll be using expanded multiplication and short multiplication to fill in the gaps for both methods.

For the second question, without completing the calculations, I'd like you to tick the ones that involve regrouping only in the 10s.

You can pause the video now, off you go.

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

Have a look at both methods.

If you managed to fill the gaps with the correct digits, give yourself a tick.

Good job, let's move on.

So for this question, you were ticking the calculations, which only involve regrouping in the 10s, you were not calculating.

So for this, you should have ticked off B because four multiplied by four 10s gives you 16 10s, which is greater than 10 10s.

You should have ticked D as well because two multiplied by six 10s gives you 12 10s.

You should have also ticked F because two multiplied by five 10s gives you 10 10s.

And if you have 10 10s, you must also regroup.

And then for G, three multiplied by four 10s gives you 12 10s, which is greater than 10 10s.

Onto the second part of our lesson.

This time you'll be using short multiplication to solve problems, especially problems which involve regrouping in your 10s to 100s.

So tickets at a football stadium cost 41 pounds.

How much did Sophia and Alex spend individually? Want you to think about the multiplication equation needed to solve the problem? So Sophia's bought three tickets at 41 pounds and Alex has bought five tickets at 41 pounds.

So I will be showing you how I would calculate the amount that Sophia has spent first.

So my equation for this calculation is three multiplied by 41.

I'm going to place the larger factor at the top, followed by the smaller factor underneath.

I'm going to start off by multiplying in my ones first, three multiplied by one one is three ones.

So I've put three in the ones column.

Then I'm going to move on to my 10s column.

Three multiplied by four 10s is 12 10s.

1210s is equal to 100 and two 10s.

So I'm going to write one in the 100s column and two in the 10s column.

Now it's your turn, I'd like you to calculate what five multiplied by 41 is.

Off you go.

How did you do, so you would've placed 41 as your larger factor at the top and then five as your smaller factor at the bottom.

Five multiplied by one one would've given you five ones.

So you'd place the five in the ones column.

Then you would multiply five by four 10s, which is 20 10s.

Now 20 10s is equal to 200 and zero 10s.

So you'd write two in the 100s column and zero in the 10s column.

So altogether, Sophia spent 123 pounds and Alex has spent 205 pounds.

Okay, using the multiplication equation, four multiplied by 32 equals 128, I'd like you to fill in the gaps, pause the video now, have a go.

How did you do? So, 32 being the larger factor would've been placed at the top and we're multiplying by four.

This is our smaller factor.

So we would've aligned this correctly in the ones column underneath.

You would've begun by multiplying it in your ones.

So four multiply by two is eight ones.

So you'd place the eight in the ones column.

Then you'd move over to your 10s, four multiplied by three 10s is 12 10s.

12 10s is equal to 120.

You'd place the one in the 100s column and the two 10s in the 10s column.

So the product is 128, let's move on.

Okay, this time we are finding the missing digit.

Some of my digits have rubbed off.

I want you to think about what is known and what is unknown.

So we know that our product is 213.

One of our factors is three.

Part of our factor is missing.

We will start off by looking at our 10s column, three multiplied by an unknown is equal to 21 10s.

So I know that three multiplied by something is 21 10s.

We can use our three times tables to help us.

Three multiplied by seven is 21.

So three multiplied by seven 10s is equal to 21 10s.

The missing digit is seven.

Over to you, which column will you look at first to solve this problem? Is it A, the 100s column, B, the 10s column or C, the ones column.

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

How did you do? If you got the ones column, you are correct.

And this is because there is part of our factor missing in our ones column.

So we must begin by looking there back to you.

Which column will you look at first to solve this problem? Is it A, the 100s column, B, the 10s column or C, the ones column.

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

You can pause the video here.

How did you do, if you got the 10s column, you are correct.

And that is because part of our factor in this case in our 10s column is missing.

Okay, onto our final tasks, there are two tasks.

For this task, Complete these multiplication equations using short multiplication.

So for question one, you'll be calculating 51 multiplied by five.

Question two, it's 84 multiplied by two.

For the last question, it's 73 multiplied by three.

I know that you may be thinking I could use a mental strategy, that's great.

We're practising using short multiplication, so maybe you could compare which strategy was more efficient for you.

And for question two, you are going to be finding the missing digits for the three short multiplication you see in front of you.

Off you go, you can pause the video now.

So how did you do? For the first question, 51 is your larger factor.

So that should have gone at the top, five is your smaller factor.

So you would've placed that at the bottom, five multiplied by one one is five ones, so you would've placed five in the ones column.

Five multiplied by five 10s is 25 10s.

This is regrouped as 250.

The two goes in the 100s column and the five 10s goes in the 10s column.

For question two, 84 multiplied by two, two multiplied by four ones is eight ones, two multiplied by eight 10s is 16 10s, which is regrouped as 160.

The one in 160 is placed in the 100s column and the six 10s is placed in the 10s column.

And lastly, 73 multiplied by three.

So we begin by multiplying in our ones column, three multiplied by three ones is nine ones.

We place that in the ones column underneath aligned correctly.

Three multiplied by seven 10s is 21 10s.

21 10s can be regrouped as 210.

You place the two in the 100s column and the one in the 10s column.

Have a look at the short multiplication.

If you found the missing digits and you got them correct, give yourself a tick.

Well done, you've done fantastically.

To summarise our learning, today we multiplied a two digit number by a one digit number using short multiplication.

And for this, we specifically looked at regrouping our 10s to a 100s.

You should now understand how to regroup from the 10s to a 100s when using short multiplication.

I really enjoyed this lesson, I hope you did too.

And I hope that you can use this learning to help you become more confident when solving worded problems, including short multiplication.