Lesson video

Hello, I'm Miss Miah and I am so excited to be learning with you today.

Okay, in this lesson you will be able to use an array to represent multiplication and use place value in an array to represent multiplication of a two digit number.

So your keywords for today are, array, product and regrouping.

Now you may have come across some of these words before.

Can you remember what they mean? An array is the layout of the items such as objects, numbers, or anything else arranged in rows and all columns.

So you can see in this image here that you've got the counters arranged in rows and columns.

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

And you can see in this example here, 3 multiplied by 7 is 21, 21 is the product.

And the definition of our last keyword, regrouping.

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

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

One ten can be regrouped for 10 ones.

Our lesson outline for today is to multiply a two digit number by a one digit number using partitioning and representations.

And within this, there will be one instance of regrouping.

Our first lesson cycle is to multiply using partitioning, focusing on regrouping in our ones column.

And in this lesson you'll meet Laura and Izzy.

4 packets of felted pens each have 16 pens.

How many pens are there altogether? And I want you to think about what multiplication equation is needed here to help you solve this problem.

So the multiplication equation needed here is 4 multiplied by 16 or 4 groups of 16.

Now Laura says she wants to calculate 4 multiplied by 16, but she only knows her multiplication up to 12.

You can use an array to help you.

16 can be partitioned into 10 and 6.

So here we've got 16 partitioned into 10 and 6, and we've got our first row of our counters.

So you can see that we've got 10 counters and then our additional 6 counters which make 16.

Now we need 4 groups of 16.

So that is what our array looks like when we've got 4 groups of 16.

First we can find 4 groups of 10, which is 40, and then we can find 4 groups of 6, which is 24.

So far, this can be written as 4 multiplied by 16 is equal to 4 multiplied by 10, add 4 multiplied by 6.

So now we need to add the 4 tens and 24 ones.

Now because there are more than 10 ones, we must regroup the ones into the tens.

So 24 ones is two tens and 4 ones, 4 tens, add two tens is equal to 6 tens.

Now we need to add our 6 tens and 4 ones.

So 6 tens, add 4 ones is equal to 64.

Because there are fewer than 10 tens, we do not have to regroup the tens into the hundreds, we only had to regroup the ones into the tens in this example.

So we only ended up regrouping once and there are 64 felted pens altogether, the product is 64.

Right, over to you.

I want to calculate 3 multiplied by 18.

I can partition 18 into? Have a go.

How did you do? So you should have got 10, add 8, sum to 18.

Back to you.

I want you to draw the array for 3 multiplied by 18.

How did you do? So I would've started off by partitioning 18 into 10 and 8 and I would've drawn my 10 counters first, followed by my 8 counters after that.

And because I need 3 groups altogether, I would've then drawn two more rows of 10 and 8 underneath.

Now you could have drawn this horizontally, you could have also drawn this vertically as well.

Okay, there are 14 felt tips in a packet.

If there are 6 packets, how many felt tips are there altogether? What is the multiplication equation needed for this calculation? Have a think.

Good job, If you got 6 multiplied by 14, you are correct.

Now sometimes when we are drawing that array, it can take a very long time, and if you're doing this practically with counters, you may even run out of counters.

I want to introduce you to the grid model.

Now this is a representation of the calculation that is quicker to draw and use and you'll see how we can use the grid model to do this.

And whilst we're doing this, I want you to think about which method is more efficient.

So like before, we will partition 14 into 10 and 4.

Now, 6 groups of one 10 is equal to 6 tens, and then we have to move on to our ones.

So 6 groups of 4 ones is equal to 24 ones.

What you do at this point is that you recombine 60 and 24, which is 84.

So there are 84 felt tip pens altogether.

Over to you.

Which grid represents the multiplication fact, 26 multiplied by 4? You've got 3 options here, pick one.

(no audio) How did you do? If you selected B, you are correct.

We can see that 26 needs to be partitioned into tens and ones, and B shows this because we've got 26 partitioned into 20 and 6 and then we need 4 groups of that, and the 4 is represented there on this side.

It can't be A, 26 has not been partitioned correctly, we've got two ones and 6 ones at the top.

And for C, we can see that the numbers have been flipped, the grid model is not accurate.

Your main task for this cycle is to represent each multiplication using a grid model.

You're going to write your calculation to show the steps for each strategy.

So your 3 multiplication calculations are as follows, 3 multiplied by 14, 28 multiplied by 3, and 7 multiplied by 13.

Question two is, what could the factors of this grid be if the product is 78? I want you to think about how many variations you can have within that, there is definitely more than one.

Take some time to complete this task now.

You can pause the video.

(no audio) How did you do? So let's focus on our first calculation, which is 3 multiplied by 14.

If you got something like this, good job.

We can see that 3 is being multiplied by 14, the 14 has been partitioned into 10 and 4, 3 multiplied by one ten is 3 tens, which is equivalent to 30, 3 multiplied by 4 ones is 12 ones which is equivalent to 12.

We then recombine 30 and 12, which gives us 42.

For this question, we needed to partition 28 into twenty and 8.

We then multiply this by 3.

So I know that 3 multiplied by two tens is 6 tens.

This is equivalent to 60.

Then we move on to our ones.

3 multiplied by 8 ones is 24 ones which is equivalent to 24.

We then add 60 and 24 and we get 84 as our product.

And our last example, we needed to partition 13 into 10 and 3.

We then multiply 7 by one 10, which gives us 7 tens.

This is equivalent to 70.

We then multiply 7 by 3 ones.

This gives us 21 ones, which is equivalent to 21.

We then add 70 and 21 together, which gives us 91 as our product.

Okay, how did you do for this question? We've got many variations that we could have had.

So for 78, our first example shows 78 being partitioned into 70 and 8, and then we could multiply that by 1 to get 78.

Here are some more variations that you could have had as your answer.

So 39 multiplied by 2.

26 multiplied by 3.

13 multiplied by 6.

Did you manage to get all of them? If you did, good job.

Okay, so for lesson cycle you'll be multiplying using partitioning and this time with a focus on regrouping in your tens.

There are 4 rows each with 32 chairs.

How many chairs are there altogether? And we can see that this has been represented using an array.

There are 32 chairs and there are 4 rows.

What multiplication equation is needed to calculate how many chairs there are altogether? Have a think.

If you've got 4 multiplied by 32, good job.

So our largest factor 32 can be partitioned into 30 and two.

We need to find 4 groups of 32.

And we can do this using a grid model.

Next we can find 4 groups of 3 tens, which is 12 tens.

Then we move on to our ones.

We need to find 4 groups of 2 ones, which is 8 ones.

So 12 tens is 102 tens.

We're going to have to regroup.

Now because there are more than 10 tens, we must regroup, the tens into hundreds and tens.

So this then becomes 102 tens.

We then add the 102 tens to the 8 ones, which is equal to 128.

So this time we have regrouped once in the tens column.

We did not need to regroup in the ones column.

Over to you, Laura is calculating the product of this multiplication, 42 multiplied by 3.

She thinks she will not need to regroup.

Is she correct? I want you to explain your thinking to someone sitting next to you or your partner.

(no audio) How did you do? Laura is incorrect.

Multiplying 3 groups of 40 gives us 120.

We must regroup the tens into the hundreds and tens.

Okay, tickets at a football stadium cost 31 pounds each.

Izzy needs to buy 7 tickets and has 200 pounds.

Can she buy all 7 tickets? Now I want you to think about what multiplication equation is needed to solve this problem.

If you got 31 multiplied by 7, you are correct.

Good job, this is because there are 7 tickets and each of the tickets cost 31 pounds.

So our multiplication equation is 31 multiplied by 7.

If you got 7 multiplied by 31, that is also correct because multiplication is commutative.

So I will partition my largest factor, 31, into 30 and one.

I will then multiply this by 7.

So I'll put 7 on the side of my grid model.

Now 7 groups of 3 tens is 21 tens, 7 groups of 1 ones gives us 7 ones.

So 210 add 7 is 217.

Izzy, in this case she can only buy 6 tickets.

31 multiplied by 7 is the equation that we are calculating.

Now, Izzy got 28 as her product.

What mistake do you think Izzy's made? Now, have a look at the grid model and have a look at the number that she had to partition.

It's 31.

Izzy multiplied 7 by 3 ones instead of 3 tens.

So she actually should have written 30 instead of 3.

Back to you again.

So this time I would like you to tell your partner the steps for calculation by filling in the blanks.

Laura wants to calculate 3 multiplied by 18.

Off you go.

(no audio) Okay, so how did you do? Your feedback would've sounded something like this.

My factors are 3 and 80.

I can partition 18 into 10 and 8.

3 groups of 1 ten is 3 tens.

3 groups of 8 ones is 24 ones.

3 tens add 2 tens is 5 tens.

5 tens add 4 ones is equal to 54.

The product is 54.

If you've managed to get all of that correct, good job.

Okay, so onto the main task of the final cycle.

Well done for keeping up.

So, Lucas needs a box which has more than 130 pens, but less than 160.

Which box should he choose? So you've got 3 options here.

Box A has 8 packets of 32 pens.

Box B has 3 packets of 42 pens.

And box C has 7 packets of 21 pens.

So the first thing that you're going to have to do is represent each multiplication fact using the grid model.

And then the second step is that you'll be writing your calculation to show the steps for each strategy.

And then for task two, which of the following would cost more than a hundred pounds? Buying 3 bikes at 31 pounds each, buying 4 at 23 pounds each, or buying 4 at 42 pounds each? Over to you.

(no audio) So how did you do? Let's look at task one.

For question A, 8 multiplied by 32, you should have got 3 multiplied by 32 is equal to 8, multiplied by 30, add 8, multiplied by 2.

This is 240, add 16, which is 256.

B is 42 multiplied by 3.

So you should have got 42 multiplied by 3 is equal to 3 multiplied by 40, add 3 multiplied by 2, which is 120 add 6.

And the product for that is 126.

For C, you should have got 7 multiplied by 21.

7 multiplied by 21 is equal to 7 multiplied by 20, add 7, multiplied by one.

This gives you 140 add 7, which sum together is 147.

In order to help Lucas pick his box, he should pick box C.

In order to calculate 3 bikes at 31 pounds, you are going to be writing the equation, 3 multiplied by 31, which is equal to 3 multiplied by 30, add 3 multiplied by one.

This is 90, add 3, which is 93.

Buying 4 bikes at 23 pounds results in 4 multiplied by 23, which is equal to 4 multiplied by 20, add 4 multiplied by 3.

So that's 80, add 12, which is 92.

So altogether 4 bikes at 23 pounds is 92 pounds.

And lastly, buying 4 bikes at 42 pounds, You should have got 4 multiplied by 42, which is equal to 4 multiplied by 40, add 4 multiplied by two.

This is then 160, add 8, which is 168.

So buying 4 bikes at 42 pounds would cost more than a hundred pounds.

Well done for getting to the end of this lesson.

To summarise your learning, you can now multiply a two digit and a one digit number using partitioning, particularly regrouping in our ones column.

We can multiply a 2 digit by a 1 digit number using partitioning, regrouping in our tens column.

We can use an array and a grid to partition when multiplying 2 digit by 1 digit numbers.

So thank you for joining me in this lesson and I can't wait to see you in the next.

(no audio).