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 this lesson, you'll be able to use short multiplication to record regrouping from the ones to the tens.

So your keywords for this lesson are short multiplication, regroup, and/or regrouping.

Now I want you to think about whether you've used these keywords before.

If you have, try and remember what they mean.

A method using columns to set out and calculate a multiplication is short multiplication, and we will be using this method today.

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

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

One 10 can be regrouped for 10 ones.

And for those of you thinking ahead, yes, 10 tens can be regrouped for 100, and alternatively, 100 can also be regrouped for 10 tens, and this can go into our thousands, our 10,000s and whatnot.

Our first lesson cycle consists of understanding short multiplication.

In this lesson, you'll meet Sophia and Alex.

Four packets of felt tip pens each have 16 pens.

How many pens are there all together? And I want you to think about what multiplication equation is needed? What is known and what is unknown? This will help you to figure out what equation is needed for this question.

Have a think.

If you've got 16 multiplied by four or four multiplied by 16, well done, you're correct.

You can use short multiplication to record this equation.

When you use short multiplication, you record the partial products differently.

So we're going to begin by partitioning 16 into one 10 and six ones, and then we're going to place the larger factor at the top.

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

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

So we multiply our ones first.

We know that four multiplied by six ones gives us 24 ones.

24 ones can be regrouped for two tens.

The two is written in the tens column.

This time, however, we must record the two tens underneath the tens column because we still have to multiply in our tens column.

But what do we do with the four? Well, the four ones in 24, we place underneath the ones column.

We then move on to our tens.

We multiply our one 10 by four.

There are four tens all together, but because we already have two tens in our tens column from regrouping in the ones, we need to add the tens together.

So four tens add two tens gives us six tens all together.

We place the six in the tens column, So our product is 64.

There will be 64 felt tip pens all together.

Over to you.

I have regrouped how many tens? You can pause the video here.

So how did you do? In this short multiplication example, we can see that we are multiplying 16 by four.

The product is 64.

How will I know how much has been regrouped or what has been regrouped? Well, if we look at the two underneath the tens column, that tells us how many have been regrouped, and we can check this because we know that four multiplied by six ones is 24.

When it comes to recording the regrouped amount, we always place it underneath the appropriate column.

So in this case, 24 can be regrouped as two tens and four ones.

The two tens is placed underneath the tens column.

Moving on, there are 16 felt tip pens in a packet.

There are five packets.

How many felt tips all together? Now, without calculating, will we need to regroup in the ones column? How do you know? Have a think.

Right, let's figure this out together.

When you partition 16 into 10 and six, now because we're trying to figure out whether we will regroup in our ones column, we need to look at our ones column.

And in this case, 16 partitioned is 10 and six.

We must multiply five by six or six by five.

Six multiply by five is 30 ones.

So we will need to regroup three tens.

If you got that, good job.

So Sofia's tried to calculate what 16 multiplied by five is.

Have a look at her short multiplication method.

What mistake might have Sofia made? Explain your thinking to your partner.

So what did you think? Five multiplied by six ones are 30 ones and we can see that she's got 30 there.

However, 30 ones can be regrouped for three tens.

So the three is written in the tens column underneath.

That's super important you remember to place the regrouped amount underneath the appropriate column.

And as you can see here, Sofia's stating that she forgot that step.

You then place zero as your placeholder in the ones column.

You then move on to your tens column.

Now, you know that five multiplied by one 10 is five tens, but at this point, do not forget to add your regrouped amount, which is the three tens that are underneath.

So five tens, add three tens is eight tens.

You placed the eight tens in the tens column.

So 80 is your product.

Alex used an expanded method for this calculation.

I want you to think about what is the same and what is different between both methods? So what answers did you come up with? So you may have said that the partial products are not recorded in short multiplication, whereas in the expanded method, the partial products are recorded.

In both methods, the product is the same, and if you look at short multiplication, regrouping is recorded underneath.

Over to you.

I'd like you to label this method.

So you've got the short multiplication example here where you've got 14 multiplied by five.

You can pause the video here.

How did you do? So 14 and five are your factors because you are multiplying both numbers.

This then gives us our answer, which is also known as a product when it comes to multiplication.

Now, the two underneath is the amount that has been regrouped.

If you got that, well done.

How many tens have we regrouped? Is it four, 54 or two? I want you to explain how you know to your partner.

You can pause the video here.

How did you do? If you got two as your answer, you are correct and we can see that because we know that three multiplied by eight is 24.

We know that three multiplied by eight ones is 24 ones.

24 ones regrouped is two tens and four ones.

The two tens must be placed underneath the tens column, which means the two has been regrouped.

Onto your tasks for this lesson cycle.

For this task, you are going to be completing the sentences.

You've got the short multiplication, 25 multiplied by three.

75 is your answer, and you can see that we've regrouped once.

And for this second task in pairs, partner A will narrate the calculation below, using expanded method.

Partner B will complete the short multiplication.

And for the last question in this lesson cycle, in pairs, partner B will narrate the calculation below using the expanded method.

Partner A will complete the short multiplication and I'll outline an example of how you'll be doing this.

So for example, 15 is the larger factor.

Now I'm going to pretend I'm partner B.

Well, then that means I will place 15 at the top because it is the larger factor and you can see that that's been done there.

Now I'm going to go back to being partner A.

Three is the smaller factor.

I will place three below because it is the smaller factor.

Okay, you can pause the video here.

Off you go.

How did you do? So our first task was to complete the sentences.

Three multiplied by five ones is 15 ones.

15 is made up of one 10 and five ones.

I will regroup one 10 and place it underneath the tens column.

If you managed to fill that out correctly, good job.

Next question.

So for this task, partner A was meant to narrate the calculation below.

Partner B, if you managed to get this short multiplication, good job.

The main thing to remember here is that the partial products are not recorded in your short multiplication.

And for the last question, this is what you should have got.

So 16 multiplied by three with 48 as your product and one instance of regrouping in your tens column.

Well done if you managed to get that.

Okay, let's move on to our second lesson cycle, using short multiplication.

So everything that we've just learned in our first lesson cycle, we will now be using to solve problems. So tickets at a football stadium cost 17 pounds.

How much did Jacob and Lucas spend individually? So Jacob bought three tickets at 17 pounds.

Lucas has bought five tickets at 17 pounds.

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

Have a think.

So if Jacob bought three tickets, we know that the calculation will be 17 multiplied by three.

We don't know what the product is, so that is what we will be calculating.

What we do know in this equation are the factors, and that is because we know that Jacob bought three tickets at 17 pounds, which means we are calculating 17 multiplied by three.

We do not know what the product is.

So we're going to start off by writing the larger factor at the top.

17 is the largest.

You may have noticed a bit of a difference with the style of recording.

It's still short multiplication.

Now are not using the headings because we don't need them.

Then we're going to move on to writing our smaller factor below.

Three is the smallest.

We're to make sure we are lining up the digits correctly.

Now, we're going to start by multiplying in our ones column.

Three multiplied by seven is 21.

21 ones can be regrouped for two tens.

So a two is written in the tens column underneath.

And the one is written in the ones column.

After that, we'll move on to multiply in our tens column.

So three multiplied by one 10 is three tens.

We already have two tens in our tens column from regrouping in the ones.

We need to add the tens all together.

So three tens are two tens is five tens.

We write the five in the ones column.

So our product is 51.

Jacob's tickets will cost 51 pounds all together.

Over to you now.

How much would Lucas's tickets cost all together? You could pause the video here, have a go.

How did you do? So 17 being our larger factor, we must place that at the top and we know that five is the smallest factor.

So you would place five underneath, aligned correctly in the ones column.

We then begin by multiplying our ones, five multiplied by seven is 35 ones.

We must regroup.

So that means three tens would go underneath the tens column and the five ones would be placed in the ones column.

We then move on to multiplying our tens.

So five multiplied by one 10 is five tens.

We then must add our regrouped three tens from our ones.

So five tens add three tens is eight tens, and we place that in our tens column.

So that means our product is 85 and Lucas spent 85 pounds all together.

If you got that, good job.

Okay, now we're going to be finding the missing digits.

When I was younger, I remember really struggling with this type of question.

However, if we break it down, this will help us figure out what the missing numbers are.

So we start off by thinking about what is known and what is it unknown.

If we have a look at this short multiplication, we know that 14 is one of our factors.

We have a missing factor, the number that we are multiplying by, and then part of our product and the regrouped amount is missing.

So to further break this down, what we're going to do is we're going to be looking at our ones column only and I want you to ignore everything else.

I know that the product of something and four must be a two-digit number that ends with zero.

Something multiplied by four needs to give us a two-digit number that ends with zero.

Well, I know that five multiplied by four is 20 ones, so I need to then regroup the two tens in 20.

Jacob's done this though.

Is this correct? Explain your thinking to your partner.

Remember, when we regroup from our ones, we place the tens underneath the tens column.

So the two tens need to go underneath.

Now we can go onto multiplying in our tens column.

So I know that five multiplied by one 10 is five tens.

Don't forget to add on the regrouped two tens from the ones column.

So five tens add two tens gives us seven tens all together.

We place the seven in our tens column, our product is 70.

We've completed our short multiplication calculation.

Over to you.

What is the missing factor? We've got short multiplication here.

Think about what you know, think about what you don't know and then begin by looking at your ones column first.

I want you to explain how you know as well once you've got the answer to your partner.

You can pause the video here.

How did you do? So when calculating this equation, I'm only going to look at my ones column.

Something multiplied by seven gives me 28 as my number, as my two-digit number.

So I know that seven multiplied by four is 28.

So four is the correct answer.

If you got that, good job.

Back to you again.

What is the missing factor? Remember to start off by looking at your ones and seeing if there is any regrouped amount.

You could pause the video here.

How did you do? If you've got three as your missing factor, you are correct and this is because three multiplied by eight gives you 24 and you can double check your answer by then completing the rest of the calculation.

Okay, onto our final two tasks of this lesson cycle.

For question one, you are going to be completing the calculations.

You've got three short multiplication equations here, so 13 multiplied by five, 27 multiplied by three and 14 multiplied by four.

For question two, you've got three multiplication equations there.

Please do use short multiplication when calculating these answers.

And for task three, you're going to be completed the word problem below using short multiplication.

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

How much did they each spend? Jacob who's bought three tickets at 19 pounds.

Lucas who's bought five tickets at 15 pounds and Sofia who's bought four tickets at 17 pounds.

Do remember to use short multiplication for these questions.

You can pause the video here.

Off you go.

So here are the answers for question one and two.

Give yourself a tick if you got those correct.

Please make sure that you've noted down your regrouped amount in each instance.

These are the answers that you should have got for question three.

Let's look at how much Jacob spent first.

So for this question, you were calculating 19 multiplied by three.

You would've placed the larger factor at the top and the smaller factor underneath aligned correctly.

We know that three multiplied by nine ones is 27 ones.

Regroup 27 as two tens and seven ones, placing the two in the tens column and the seven ones in the ones column.

You would've then moved on to multiplying in your tens.

So three multiplied by one 10 is three tens.

However, don't forget to add the regrouped two tens from the ones column.

So three tens, add two tens is five tens.

Place the five in the tens column, you would've got 57.

Jacob spent 57 pounds all together.

Now, Lucas bought five tickets at 15 pounds.

So the equation here was 15 multiplied by five.

Five multiplied by five ones gives us 25 ones.

The two tens needs to be regrouped and placed underneath the tens column.

The five ones can go into the ones column.

We then multiply in our tens column.

So five multiplied by one 10 is five tens.

Add the two tens that we regrouped earlier.

Gives us seven tens all together.

Place the seven in the tens column.

So all together, the product was 75, which means Lucas spent 75 pounds all together.

Lastly, Sofia bought four tickets at 17 pounds, which means the equation that we were calculating here was 17 multiplied by four.

Four multiplied by seven ones gives us 28 ones.

We then regroup 28 as two tens and place the two tens in the tens column followed by the eight ones in the ones column.

We then move on to multiplying in our tens column.

So four multiplied by one is four tens, and then we must remember to add on the remaining two tens, which is six tens.

We place the six in the tens column.

The product is 68, which means that Sofia spent 68 pounds all together.

If you got the answers to all of those questions correct, good job, you did amazingly.

Well done, we've gotten to the end of this lesson.

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

This time there was regrouping happening from our ones to our tens.

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

You can now regroup the tens by remembering to place the digit underneath.

You can use short multiplication, including regrouping in ones to tens to solve problems. I hope you enjoyed this lesson.