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'll be able to use partitioning to organise multiplication.

Your keyword today is partial product.

Now, you may not have come across this keyword before, so don't worry if you don't know what it is because I'm just about to explain.

Any of the multiplication results we get leading up to an overall multiplication result is known as a partial product.

Now here we've got two representations.

We've got the grid model and we've got an informal written method.

Let's have a look at the grid model.

We can see that 4 multiplied by 1 ten gives us 4 tens.

4 tens is the partial product.

4 multiplied by 6 ones is 24 ones.

So in this case, 24 ones is also a partial product.

Now let's move on to the other side.

We can see that 16 has been partitioned into 10 and 6.

4 multiplied by 10 equals 40.

4 multiplied by 6 is 24.

40 and 24 are our partial products.

Our lesson outline is to multiply a two-digit number by a one-digit number using partitioning.

Our first lesson cycle is to understand partial products and regrouping.

In this lesson, you will meet Alex and Sofia.

Right, four headphones cost 16 pounds each.

What is the total cost? I want you to think about the multiplication equation required to calculate this equation first.

Okay, so we've got four headphones at 16 pounds each.

So our equation would be 4 multiplied by 16.

I can use an informal method to calculate the answer.

For example, 16 multiplied by 4.

I can partition 16 into 10 and 6.

First, I'll multiply 4 and 10, which gives us 40.

Then, I'll multiply 4 and 6, which gives us 24.

These are our partial products, so any multiplication leading up to the product will give us our partial products.

40 add 24 equals 64.

By adding the partial products, we get our answer, otherwise known as the product.

So the product is 64.

Okay, this time, three caps cost 18 pounds each.

What is the total cost? Now, before we tackle this question, I want you to think about what is the multiplication equation required to calculate this problem.

If you got 18 multiplied by 3, or 3 multiplied by 18, you are correct.

Let's move on.

So again, we can use an informal method to calculate the answer.

So we begin with our equation, 18 multiplied by 3.

You can partition the largest factor 18 into 10 and 8.

So first, you can multiply 3 and 10, which gives you 30.

You then can multiply 3 by 8, which gives you 24.

These are our partial products.

30 add 24 equals 54.

So as you can see here, by adding the partial products again, we get our answer.

The product is 54.

So three caps altogether would cost 54 pounds.

Okay, over to you now.

You will be filling in the gaps for this informal written method.

So 15 multiplied by 4 equals 10 multiplied by 4 add 5 multiplied by 4.

You will be writing the partial products that are formed.

Off you go.

Pause the video here.

How did you do? You should have got 40 add 20, which gives you a product of 60.

So more importantly here, the partial products for this equation was 40 and 20.

So let's have a look at the first question.

Three bikes cost 42 pounds each.

What is the total cost? Now, when using an informal written method, we need to make sure that the equal signs are aligned.

So I'm going to start off by writing 42 multiplied by 3 is 3 multiplied by 40 and 3 multiplied by 2.

I've partitioned 42 into 40 and 2, and I've multiplied both those numbers by three.

This means our partial products are now 120 and 6.

This is because 3 multiplied by 40 is 120, and if you didn't know what that was, do remember to use your table facts to help you.

For example, if I know that 3 multiplied by 4 is 12, then I also know that 3 multiplied by 4 tens is 12 tens.

12 tens is equal to 120.

At this point, you need to add your partial products, or in other words, recombine your partial products to get the answer.

126 is the answer, nice and easy because you did not need to regroup.

Now it's over to you.

Your question is, seven bikes cost 42 pounds each.

What is the total cost? You can pause the video here.

How did you do? So we know that 42 can be partitioned into 40 and 2.

We then multiply both numbers by seven.

7 multiplied by 40 is 280.

And like I said, if you don't know what 7 multiplied by 40 is, use your multiplication tables facts to help you.

4 multiplied by 7 is 28.

So 4 multiplied by 7 tens is 28 tens, which is regrouped as 280.

We can then move on to 7 multiplied by 2 ones.

This is 14 ones.

We then add 280 and 14 to get 294.

So by adding our partial products, we get our product, which is 294.

This means that the cost of seven bikes is 294 pounds.

If you got that, really good job, well done.

Back to you again.

This time I'd like you to fill in the gaps for this question here.

So 6 multiplied by 28 is equal to 6 multiplied by something add 6 multiplied by 8.

Using that information, I want you to figure out what the partial products are and then what the product is.

Off you go.

You can pause the video here.

Okay, how did you do? So you should have got 6 multiplied by 20 add 6 multiplied by 8.

So at this point, the 28, because it's our larger factor, we are able to partition this into 20 and 8.

We then multiply 20 by 6, which is 120, and then we multiply 6 by 8, which is 48.

We can then add the partial products, which gives us a product of 168.

If you got that, well done.

Back to you.

Which of these calculations did Sam use to find the product? So the multiplication equation that he's calculating is 26 multiplied by 7.

Was it A, 140 add 42; B, 100 add 40 add 42; C, 150 add 32; or D, 100 add 82? You can pause the video here and select your answer.

How did you do? If you selected A, you are correct.

And the reason to why it's A is because if we partition 26 into 20 and 6, we can then multiply 20 by 7, which gives us 140, which is our first partial product, and then we multiply 7 by 6, which is 42, which is our second partial product.

So altogether, our partial product pair would be 140 add 42.

Let's move on.

Your first task for this cycle is to draw a line to match each multiplication equation with the correct partial product pair.

So you've got three equations here.

You've got 26 multiplied by 6, 6 multiplied by 23, and 54 multiplied by 6.

You will be matching these equations to the correct partial product pair.

The second task is for you to use the informal method to answer these multiplication equations that you can see on the screen.

You're going to underline your partial products in different colours.

Okay, so your first equation is 42 multiplied by 7, 8 multiplied by 72, 5 multiplied by 57, and the last equation is 36 multiplied by 8.

You can pause the video here and get started on your task.

So how did you find that? For the first task, these are the answers that you should have gotten.

So you should have matched across like this.

So 26 multiplied by 6.

The correct partial product pair for that was 120 add 36.

For B, it was 120 add 18.

And then for C, it was 300 add 24.

If you got that, really good job, well done.

Now for the second task, this is what you should have got.

So for A, 42 multiplied by 7, we need to partition 42 into 40 and 2 and then multiply both by 7.

So your partial products that you should have underlined were 280 and 14, and altogether that gives us a product of 294.

For B, 8 multiplied by 72, again, you would've partitioned 72 into 70 and 2.

You would've multiplied both by 8, resulting in a partial product pair of 560 and 16.

You then combine the partial product pair to get 576 as your total.

For C, you would've partitioned 57 into 50 and 7 and then multiplied both by 5.

250 and 35 would've been your partial product pair.

You then would've recombined 250 and 35 to get 285 as your product.

And lastly, for 36 multiplied by 8, you would've partitioned 36 into 30 and 6.

You would've multiplied both by 8, and this would've given your partial product pair, which would've been 240 and 48.

240 and 48 recombined would've given you a product of 288.

If you got all of those correct, really good job, well done.

For lesson cycle two, you'll be multiplying using partitioning.

So biscuits cost 26 p each.

What is the total cost of four biscuits? 4 multiplied by 26 is equal to 4 multiplied by 20 and 4 multiplied by 6, which gives us our partial product pair of 80 add 24.

Our product is 104.

What did you notice? Have a think.

When adding the partial products, we had to actually regroup the 10 tens into 100, which gave us a three-digit answer.

Now, this may not always be apparent when multiplying a two-digit by a one-digit number, but sometimes when adding our partial products, we do end up with a three-digit answer.

Over to you.

You will be filling in the gaps.

The equation is 25 multiplied by 4 is equal to 4 multiplied by something add 5 multiplied by 4.

You can pause the video now.

So how did you do? If you got 4 multiplied by 20 add 5 multiplied by 4, with the partial product pair of 80 and 20, then recombining both to get 100, you are correct, well done.

You would've had to regroup 10 tens for 100.

Now sweets cost 3 p each.

What is the total cost of 34 sweets? So we can see here that the equation has been completed using an informal written method.

And we've remembered to regroup.

Is Alex correct? I'm going to give you 10 seconds to think, and then once you've got an answer, I'd like you to explain your answer to your partner.

Let's have a look at this.

We begin by partitioning 34 into 30 and 4.

This time we're going to use a grid model to help us.

So we're multiplying by three, so that gets put on the side.

I know that 3 multiplied by 30 is 90, 3 multiplied by 4 is 12.

Our total is actually 102, not 112.

So Alex has actually made an error when adding 90 and 12.

The correct answer is 102.

If you got that, good job.

So the total cost is 102 pence.

Over to you.

Which of these calculations match the multiplication equation, 36 multiplied by 3? You've got three options here.

You can pause the video now.

How did you do? If you selected option A, you are correct, and that is because 36 can be partitioned into 30 and 6.

These numbers are then multiplied by three.

So the partial products that you should have got were 90 add 18 in that order.

You then add 90 and 18, and your product is 108.

So you would've regrouped.

Okay, onto the main task.

For this task, you are going to be picking three cards and you're going to generate a two-digit by one-digit multiplication equation.

You are going to choose any informal method of working.

So that could be your grid model, that could be your written informal method.

It's up to you.

So the fastest partner with the correct partial products and answers wins.

I will also show you an example of what this might look like when you're having a go.

Okay, so in this example, Aisha's got three digit cards and she's arranged them like this.

She's used an informal written method and you can see that her calculation is there.

She's remembered to partition her 16 into 10 and 6.

She's also recorded her partial products, and that's really important because if you don't record your partial products, you'll lose out on the points and you won't win.

Make sure you also combine those partial products to get your product.

And if the answer's correct and your partial products are correct, that is a point.

You can also use the grid method and you can see that's been displayed below.

Again, 16 has been partitioned correctly into 10 and 6, and this has been multiplied by 3.

The partial products have been recorded in the grid model as well.

Do remember to recombine your partial products to get the answer.

So here are the cards.

Use scissors to cut them.

Please use your scissors safely.

You can pause the video now.

Good luck.

So how did you do? Who won? Here is an example that you can see on the screen.

So this time we had the cards 31 multiplied by 6 and they were arranged like this.

Aisha used the grid model and then we can see over here that the informal written method was also used.

In both instances, the partial product has been recorded as well as the answer.

So to summarise our learning.

In this lesson, we were multiplying a two-digit number by a one-digit number using partitioning.

You can hopefully now identify partial products and use this to calculate the overall product.

You can multiply a two-digit by a one-digit number using informal methods, including regrouping.

I hope you enjoyed this lesson and I look forward to seeing you in the next lesson.