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 partitioning and place value equipment to represent multiplication.

Your keywords that you'll be using today are product and regrouping.

You may have come across these words before if you have, try and remember what they mean.

The result of two or more values multiplied together is called a product.

We've got three multiplied by seven equals 21.

Our factors are three and seven and our product is 21.

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

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

One 10 can be regrouped for 10 ones.

We are going to be multiplying a two digit number by a one digit number using partitioning and representations.

In this instance, there will be two regrouping happening.

In our first learning cycle, we will be multiplying using partitioning.

Let's begin.

In this lesson, you will meet Aisha and Jun.

To begin with, we have four rows each with 33 chairs, how many chairs altogether? Our array here has presented four rows of 33 chairs.

So I want you to think about what multiplication equation is needed to answer this question.

I'll give you a few seconds to think.

So the equation that we need is four multiplied by 33 or 33 multiplied by four.

It could be in any order because multiplication is commutative.

Now Jun says that this will take him a very long time to draw as an array, and Aisha is saying that she has no more counters left and that is true because Jun is having to draw his array it will take him a very long time and with the amount of counters needed, Aisha will end up having none left.

A more efficient method is the grid method and we can multiply our equation using a grid method.

So we will start by partitioning 33 into three tens and three ones.

So here we've got 33, and we've got three tens here and three ones.

We need four groups of three tens and four groups of three ones.

So we multiply four by three tens, four groups of three tens is 12 tens.

We then multiply four by three ones.

So four groups of three ones is 12 ones.

This is also equal to 120 and 12.

Why do we have a three digit answer? Well, Jun states that it's because 12 tens is 120.

This is correct.

12 tens can be regrouped as 10 tens, which is 100 and two tens, which is 20.

This ultimately means that our answer will be a three digit number.

Sometimes when we are adding our regrouped amount, it can lead to a three digit answer.

So we continue, we add 120 and 12.

12 is one 10 and two ones.

We must regroup.

So again, this is our second instance of regrouping.

We've already regrouped before.

We are regrouping again.

12 tens add one 10 is 13 tens.

We add the remaining two ones, so 13 tens can be regrouped as 130.

And then once we've added the two ones, our total is 132.

Over to you.

Which arrangement shows 45 multiplied by three? Now do remember 45 needs to be partitioned? You can pause the video here.

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

45 by three, B is correct.

And we know that it's correct because when we partition 45 we end up with four tens and five ones.

And if we have a look at A, A is incorrect because 45 has not been partitioned.

Additionally in B, we are multiplying by three and we can see that the three has been placed on the side of the grid model.

Well done if you got that correct.

Back to you.

What is the multiplication shown with this grid model? What are the factors that you are multiplying by? There is a number that has been partitioned.

You may need to recombine that number.

Pause the video now and have a go.

How did you do? If you got seven multiplied by 53 you are correct.

If you got 53 multiplied by seven, you are also correct.

It can be in any order.

We know that this is correct because one of our factors must be seven and we can see that because seven is on the side of our grid model.

Now if we have a look at the top, we can see that there is a number 50 and three.

Those numbers form our parts and and when combined together they will form our whole, which is 53.

So here we have another example of a grid model.

Now Jun has got 128 as is product.

What do you think? Without calculating, do you agree with Jun? Well, we start off by partitioning 46 into four tens and six ones.

We need three groups of 46.

So here we've got 46 and it's been partitioned into 40 and six.

We need three groups.

We then multiply four tens and six ones by three.

Three multiply by four tens is equal to 12 tens.

Three multiplied by six ones is equal to 18 ones.

This is equivalent to 12 tens and 18 ones.

Now we need to regroup our ones.

And how do we know this? Well, we have 18 ones which is greater than 10 ones.

Anything greater than 10 ones in this case we must regroup.

So 18 is one 10 and eight ones 12 tens add one 10 is 13 tens.

Now 13 tens is greater than 10 tens.

We can regroup, but we will just wait till the end to do that.

13 tens add eight tens is equal to 138.

So we've actually regrouped into our hundreds at this point and we've ended up with a three digit answer.

So what error did Jun make? Jun forgot to regroup one 10 from 18.

Over to you, which multiplication we'll need two instances of regrouping, so regrouping in the ones and the tens.

Pause the video now to have a think.

How did you do? So C was the correct answer.

If we have a look at A, if we were to multiply two by four ones, we end up with eight.

And then if we were to multiply the tens, so two multiplied by three tens, that's six tens.

Again, we did not need to regroup.

For B, if we look at multiplying our ones first, that's two multiplied by three ones, that's six ones, so we didn't need to regroup.

If we were to multiply two by four tens, again, that's eight tens and we don't need to regroup.

Looking at C, I know I'll have to regroup because I know that four multiplied by four ones is 16 ones.

16 ones is greater than 10 ones, so I'll have to regroup.

Then when multiplying my tens, so in this case it's four multiplied by three tens.

That's 12 tens.

12 tens is greater than 10 tens.

So at some point I will have to also regroup after I've added on my 16 months.

I'm now going to introduce you to the first task of our learning cycle.

In pairs, use the grid model to answer the multiplication equations below.

You've got 43 multiplied by six and 37 multiplied by four.

You're going to take turns to explain to your partner where the regrouping happens.

You can pause the video now and start the task.

Off you go.

How did you do? I'm going to focus on the first example and I'm going to talk through something you may have said.

When looking at 43 multiplied by six, I regrouped when I was multiplying my six by my three ones.

I ended up with 18 ones.

I can regroup 18 ones as one 10 and eight ones.

I then looked at my tens.

Now six multiplied by four tens is 24 tens.

I can add the one 10 that I regrouped from the 18 to my 24 tens.

That gives me 25 tens and then I must add the remaining eight ones.

So that altogether gives me 25 tens and eight ones 25 tens and eight ones is 258.

So I regroup twice in that equation.

Now, we are going to be looking at multiplying using a grid model.

Here's our first question.

Four rows each with 26 chairs, how many chairs altogether? Now we can see that an array has been used.

So Jun believes that you only need to regroup once.

Do you agree? Have a think.

What multiplication equation is needed for this question? If you got four multiplied by 26 or 26 multiplied by four, you are correct.

Well done.

So we start off by partitioning our 26 into two tens and six ones.

We can show this using a grid model and here you can see that the 26 has been partitioned into 20 and six and we've got the four on the side because we've got four groups of 26.

So we are multiplying by four.

We multiply four by two tens, so four multiplied by two tens is eight tens.

Next we multiply four by six ones.

Four multiplied by six is 24 ones.

So eight tens is equivalent to 80, 24 ones is equivalent to 24.

Now we need to add eight tens and 24 ones.

So 24 is two tens and four ones.

We must regroup.

At this point, what we need to do is add the eight tens and the two tens together and you can see that we've got the four ones left over in our ones column.

This becomes 10 tens and four ones.

Again, we must regroup.

We have another three digit answer and yes, that's happened again because within our regrouping we've had to add eight tens to two tens, 10 tens is a hundred, which is a three digit number.

So now we need to add 100 and four.

100 add four ones is 104.

The total amount of chairs that we have is 104 chairs altogether.

Over to you.

Aisha believe that whenever you multiply, you will always regroup.

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

Pause the video now and have a go.

The answer is sometimes true.

I'll give you some examples to prove that.

If I was to multiply a two digit number such as 33 by two, I can use a mental strategy to prove this.

I know that 33 doubled is 66.

I did not need to regroup.

Now if I was to multiply say 37 by two, I would have to regroup and in this case I'd have to regroup in my ones column because seven multiply by two is 14.

So I could regroup that 14 as one 10 and four ones.

For this part, I would like you to draw a line to match each multiplication with the correct amount of regrouping.

These are your three equations that you'll be matching.

16 times 4.

33 multiplied by three and 54 multiplied by six.

So how did you do? This is what you should have got.

We've got 33 times three and this involves no regrouping and that's because when you multiply three ones by three we get nine ones.

And then when we multiply three tens by three, we actually get nine tens.

So we did not need to regroup.

Now when it comes to 16 times four, yes, we do need to regroup once, and that's because when we look at our ones in our two digit number, which is 16, it is six, and we know that six times four is 24, which means we'll have to regroup in our ones to our 10th column.

Lastly, 54 times six, we need to regroup twice, and that's because when I look at the digits individually in 54, I can see that four times six would give me 24, which means I'll have to regroup from my ones to my tens.

And then my tens column five tens times six gives me 30 tens.

So I would have to regroup 30 tens into my hundreds, which is the same as saying 300.

Well done if you've got that correct.

Let's move on.

This is your main task for the last cycle.

Well done for keeping up and getting through this lesson.

You are going to be playing this game with a partner.

You will have a sheet, you'll have to cut the cards out, and then the aim is for your calculation to involve more regrouping than your partner.

So you'll start this off by picking three digit cards and then you'll arrange them in this expression.

So have a look.

You'll have a two digit multiplied by a one digit.

Now you are going to use the grid model to find the product, the person with the most regrouping scores one point.

If you both have two regroups score one point each, the first person to five points wins that game.

I'll give you an example.

So I'm versing Aisha.

Aisha gets one, six and three.

She is going to arrange her digits like this.

Now I want you to keep in mind that arrangement really matters.

Now the product that she got was 36.

She didn't regroup, so she scored zero points.

However, if she had arranged her digit cards differently, she may have scored more.

How else do you think Aisha could have arranged her cards to score points? Well, let's have a look.

This time, Aisha's larger factor is 16 and the factor that she's multiplying by is three.

And you can see that this has been displayed in the grid model below.

Now we know that three multiplied by six ones is 18 ones.

And three multiplied by one 10 is three tens, 18 ones is one 10 and eight ones.

So she'll have to regroup.

So the product is 48.

She regrouped once, so she scored one point this time and that's all because she arranged her cards differently.

Now it's her partner's turn.

So whilst playing this game, do think about the arrangement of your digit cards and see if you can get two instances of regrouping to really get ahead and beat your partner.

These are the cards that you will be cutting as you'll be using scissors.

Please ensure that you do use them safely.

How did you do? Who won? So here is an example answer.

I got 34 multiplied by three.

I had to regroup twice, so I scored two points.

So let's talk through that.

Three groups of three tens is nine tens, three groups of four ones is 12 ones, and I already know that I'll have to regroup because 12 ones is greater than 10 ones.

I will regroup 12 ones as one 10 and two ones.

One 10 add nine tens is 10 tens.

I will regroup 10 tens, which is a hundred.

So that's my second instance of regrouping.

A hundred add two ones is 102.

So the trick here was to really think about the way you arrange your digit cards.

We are now at the end of the lesson.

Well done for getting through.

I hope you really enjoyed this lesson.

To summarise our learning, we are now able to multiply a two digit number by a one digit number using partitioning.

We can multiply a two digit number by a one digit number using the grid model.

In this lesson, we focused on regrouping in two instances, whether that was from our ones into our tens or even our tens going into our hundreds.

I hope you do feel confident now after this lesson and I hope to see you in the next lesson.