Lesson video

Hello.

My name is Mrs.Behan And for this lesson, I'm going to be your teacher.

So by the end of the lesson, you will be able to use arrays to show multiplication of a two digit number by a one digit number.

So let's make a start and we'll check out the lesson agenda.

We are going to begin by reviewing partitioning.

To see what that means and what it looks like.

We're then going to look at using arrays to multiply.

There will be a practise activity, that we will go through together, and then you will have a go at an independent task.

I know you be keen to find out how you get on, so we'll make sure, that I'll go through the answers with you.

There's just two things that you'll need for this lesson.

Something to write with.

So a pencil or a pen and something to write on.

If you haven't got any of those things handy, just pause the video now so as to go and get them.

Try to work somewhere where you aren't going to be disturbed for the lesson.

For the first part of the lesson we are going to look at partitioning two digit numbers.

You can see the word partition on your screen.

My turn, your turn.

Do the action with me.

Partition.

You can see the word part hiding in there at the beginning of the word.

Another word we will use is, recombine.

Can you do that action with me? Off we go.

Recombine.

When we take two parts and we put them back together this is what we call recombining.

Let's take a look at number 32.

If we had to partition this number or pull it apart, how could we do it in terms of tens and ones? 32 is the whole, so what two parts could we make? Well, we could partition it into tens and ones.

So we have three tens or 30 and two ones.

Can you think of another way we could partition 32? Well, we could always exchange one of the tens and break it down into 10 ones.

So this way we would have two tens or 20 and 12 ones.

What's another way that we could have partition number 32? Well, we could do the same again.

Well done.

We could take another one of the tens break it down into 10 ones.

This way, we would have one 10 and 22 ones.

If we recombined 10 and 22, we would have 32 all together.

I know that you are fantastic at partitioning whole numbers into tens and ones.

We're going to use this strategy to multiply.

Let's look at five multiplied by 12.

You may think this is quite an easy multiplication fact, which it is by now, but let's have a look at it in terms of partitioning.

The first step is to partition 12 into two nice easy numbers to work with.

We know that 12 is made up of one 10 and two ones.

So I've partitioned 12 into 10 and two.

Let's look at the array.

We can see here that we have got five rows of 12.

You can also see that we've used different colours to show the different parts.

So now I have five rows of 10, and five rows of two.

So I know that five multiplied by 12 is equal to five multiplied by 10 plus five multiplied by two.

So I have partitioned 12, and I'm getting ready to recombine it.

So I know that five multiplied by 10 is equal to 50.

And two multiplied by five is equal to 10.

Let's recombine those parts.

So 50 plus 10 is equal to 60.

Let's have a look at another example.

Three multiplied by 13.

Why might partitioning be a good strategy, when multiplying these numbers? Have a think.

Here are my thoughts.

Well, I know that counting in thirteens is definitely tricky and I can't count three 13 times well.

But I do know that counting in tens is easy.

So I'm going to partition 13 into 10 and three ones.

So here is the array.

You can see I have three rows of 10 and three rows of three.

Three multiplied by 13, is equal to three multiplied by 10 which is this blue section of counters, plus three multiplied by three, which is this section of counters.

Three multiplied by 10 is equal to 30.

And three multiplied by three is equal to nine.

Let's recombine those numbers.

So 30 plus nine is equal to 39.

In this example, we have more difficult numbers.

We haven't learned to count in sevens yet.

And we have already talked about the difficulty of multiplying by 13.

I think you could give it a go, if I show you the array.

Let's take a look.

Our first step is to partition 13 into 10 and three.

We have seven rows.

What do you think would go in the boxes? Pause the video whilst you have a think about which numbers would go in each grey box.

When you're finished, come back to me and we'll have a look together.

How did you find it? Was it tricky? Was it easy? Did partitioning help? Let's go from the top, we'll work through it together.

So seven multiplied by 13.

Let's partition 13 into 10 and three, to lovely easy numbers to work with.

Here is the array to show our example.

We have seven rows of 10 and plus seven rows of three.

So our calculation would look something like this.

Seven multiplied by 13 is equal to seven multiplied by 10 plus seven multiplied by three.

So the partial products are 70.

Seven multiplied by ten equals 70 plus 21.

Because seven multiplied by three is equal to 21.

Let's recombine those to get our product.

70 plus 21 is equal to 91.

To make sure that you are super secure, I have one more example for you.

See if you can figure out what the missing numbers are.

Pause the video here whilst you have a think, and then come back to me when you are ready.

Ready? Let's have a look at this together.

So eight multiplied by 12 is equal to eight multiplied by 10 plus eight multiplied by two.

Our arrays show it clearly that.

Eight multiplied by 10 plus eight multiplied by two.

So we have 80 as a partial product and 16 as a partial product.

And what do we need to do now? That's right, we need to recombine.

So 80 plus 16 is equal to 96.

Much easier than trying to count in twelves or eights.

So this shows us how we can multiply a teens number by a one digit number.

What would happen if we had one more 10 in our two digit number? Well, our array would be huge.

So drawing out the array, just would not be efficient with all of our small counters.

So this is good to help us understand that partitioning is an effective strategy.

And we could go straight to drawing the grid like you see on the screen.

Let me show you.

So in our example, Marcus gives 15 sweets to six people.

So how many sweets did he give out all together? We're going to take our multiplication.

Does it matter that our two digit number, is the first factor? No, because multiplication is commutative.

We can change the order of the factors, and the product remains the same.

15 multiplied by six.

What's step one? That's right.

We're going to partition 15 into 10 and five.

So we have two lovely numbers to work with.

Now, this is what I mean when I say going straight to the grid.

We're not going to draw all of the little spots.

We're just going to draw out two boxes.

Where I can write 10 and five above the two sections.

We know that if we're drawing the counters, we would have six rows.

So, here we've put six on the left-hand side.

Our most sentence is, 15 multiplied by six is equal to 10 times six plus five times six.

Let's work out the partial products.

60 and 30.

We now need to recombine sixty plus 30 is equal to 90.

Let's put our answer into a full sentence.

Say it with me.

Marcus gave out 90 sweets all together.

Do you think you've sussed it now? Do you think you could solve any multiplication question that I give to you? Well, you see, I gave this question to somebody before and they made a little mistake.

See if you can spot it.

Layla sells t-shirts.

She sold 12 t-shirts to seven people.

How many t-shirts did she sell all together? I'm going to show you the working out and then the answer or the product that she came up with.

Remember, you're trying to spot the mistake.

Pause the video here whilst you have a little look.

When you're ready, come back to me.

Okay, then let's take a look.

So firstly, we could use our estimation skills to recognise that actually 12 times seven is larger than 10 times seven.

And 10 times seven is equal to 70.

So, we know that this person is way off with 34 as the answer.

Did you spot where the mistake was? Yes.

Here is the mistake.

So this person has partition 20, sorry has partitioned 12 into 10 and two.

But they've written this number two in the wrong place.

This number two has come from the 12.

So she should have written 10 here and two over here.

The 12 is the amount sold to each person.

So this would be a long the top.

This is how long our row would be.

And she sold to seven people.

So this should be seven rows.

That early mistake, has meant that everything she did following was incorrect.

So let's see it done the right way.

Oh! the correct product is 84.

But let's go through the working out, just to make sure that we've worked it out correctly.

So here's one box and here's another box.

Now, why have we got these two boxes on the screen? Are these two grids? Yes, that's right, because we are partitioning 12 into 10 and two.

That's how many t-shirts people were given? So nice easy numbers 10 and two rather than working with number 12.

She gave out those t-shirts to seven people.

So we would need seven down the side, because we would have seven rows.

Say the calculation on the screen with me.

12 multiplied by seven is equal to, 10 multiplied by seven plus two multiplied by seven.

Our partial products would be 70 and 14.

What do we do now? That's right.

We will recombine to get our full product.

So 70 plus 14 is equal to 84.

We must remember to put our total or our product into a full sentence answer.

So our answer is, Layla sold 84 t-shirts all together.

I think you've got the skills and knowledge now to tackle your independent task.

And you're going to fill in the missing numbers.

So starting with 13 multiplied by four.

You can't fill in that product straightaway, because you need to do the working out.

So look at the boxes underneath, figure those out before you can write in the product.

Once you've done that, I'd like you to multiply 14 by seven, and once you finish that, multiply 17 by three.

Pause the video here to complete your task.

Once you've finished, come back to me and we'll have a look at the answers together.

How did you get on? I'm sure you've smashed it.

So we need to fill in the missing boxes.

13 multiplied by four is equal to 52.

And we know this because we've partitioned 13, into 10 and three.

We're going to write 10 and three across the top of our grids and four down the side because we're multiplying 13 by four.

Our calculation would be written like this.

13 multiplied by four is equal to 10 times four, plus three times four.

Our partial products were 40, because of four times 10 and 12 because of four times three.

When we recombine our products, we have 52.

So 13 multiplied by four is equal to 52.

In our next example, you were asked to multiply 14 by seven, which gives a total of 98.

14 partitioned into tens and ones is 10 and four.

So we're going to write 10 and four across the top of our row here.

There are seven rows all together.

Because we are multiplying by seven.

So we've written seven down the left-hand side.

Our calculation reads 14 multiplied by seven is equal to 10 times seven, plus four times seven.

Our partial products, seven multiplied by 10 is 70, seven multiplied by four is 28.

So let's recombine.

70 plus 28 is equal to 98.

Did you get 51 as a product in our final example? 17 multiply by three is equal to 51.

Because 17 partitioned is 10 and seven.

Let's put them across the top of our row here.

There would be three rows of 17.

So we're going to write three down the left.

Our calculation reads, 17 multiply by three is equal to 10 times three plus seven times three.

Our partial products are 30 and 21.

And then? That's right, you guessed it.

We recombine 30 plus 21 to make 51.

So, 17 multiplied by three is equal to 51.

Excellent job.

If you'd like to, please ask your parents or carer to share your work on Instagram, Facebook or Twitter tagging @oakNational, @LauraBehan21 and #learnwithOak.

You have been absolutely amazing today.

There's been so much information to take in, but I know you've done a fantastic job.

Well done.

Don't forget to take the quiz to test out your new learning.

I'll see you again soon.

Bye-bye.