Lesson video

Hello, and welcome to the maths lesson today.

My name's Miss Thomas, and I'll be going through the lesson with you.

But before we start, I thought we'd kick off with a bit of a joke.

So if you know the answer or if you want to have a guess, you can call it out to your screen.

So what did the pupil say to the teacher after they ate their own homework? What do you think? They said, "You told me to, "you told me it was a piece of cake." Get it? Piece of cake.

All right, let's not waste any more time telling rubbish jokes.

Let's get started with the lesson.

I'm really looking forward to going through it with you.

Off we go.

In today's lesson agenda, first, we'll be partitioning arrays to solve multiplication equations.

After that, we'll go to the Let's Explore task where you can have.

Then we'll be partitioning area models this time to solve multiplication equations.

Finally, we'll finish with the end of lesson quiz, where you can test yourself on the learning.

The equipment you will need for the lesson is a pencil, paper, and a ruler.

Pause the video now if you need to get the equipment.

Let's begin our lesson.

Our star word is, my turn, partitioning.

Your turn.

Partitioning means to separate parts of a whole.

In maths, we can partition numbers.

We can use part/whole models to do this.

If the whole is 17, I can separate it into parts.

I could have 10 ones and 7 ones.

How else could you split the number 17? You might like to use a part/whole model to show this.

Pause the video now and find other ways you can partition the number 17.

Great work.

Here are some of the answers you could have for partitioning the number 17.

It's important to know in maths that different parts can equal the same whole.

We've got Nina here, and she has a problem.

She says, "I need to multiply 7 by 14, "but I only know my 7 times table up to 7 times 12." I think many of us are in the same position as Nina, and we know our times tables only up to 12.

So what could need Nina do to solve her problem? Pause the video now and decide what Nina could do.

You might have decided that Nina could partition this problem and use her known multiplication facts to find the answer.

To help Nina, we could partition the problem using the distributive law.

Let's learn on new star phrase, my turn, distributive law.

Your turn.

Distributive law means to get the same answer when the parts are solved separately.

We are going to look at the array and see how the distributed law could help Nina with her problem.

Here is an array to represent 7 times 14.

The array could be split into smaller arrays, which will represent different multiplication facts.

These can then be added together to find the answer to the original equation.

I can split the array to represent 7 times 12.

I know my 12 times tables, so I can do 7 times 12 is equal to 84.

I could then split my array again into two groups of 7.

Let's go through our equations.

So I would do 7 times 12 is equal to 84.

Then I would take my product 84 and add my group, one of the groups of 7, which is equal to 91.

Finally, I would take the answer 91 and add the final group of 7, which is equal to 98.

I was able to do this without using my 14 times table, but I still found the answer to 7 times 14, which is equal to 98.

Decide how else 7 times 14 could be calculated using the distributive law.

Split the array and write down the equations.

You might find more than one way.

Pause the video now and have a go.

Great distributing.

Let's take a look at what you could have found.

You could have found the array in half and calculated 7 times 7 is equal to 49 twice.

Let's look at the next one.

You could have also done 7 times 10, which is equal to 70, and then 7 times 4 which is equal to 28, because we know that 10 plus 4 is equal to 14.

Finally, you could have done 7 times 12, which is equal to 94, and then calculated 7 times 2, which is equal to 14, because we know that 12 add 2 is equal to 14.

Well done if you found a different way to find 7 times 14.

Next, how, next it's your turn for the Let's Explore task.

How could you calculate 7 times 16 using known facts? Use the array to help you use the distributive law to calculate the answer.

Pause the video now and complete your Let's Explore task.

Let's look at some of the ways you could have used the distributive law to solve this calculation.

We were looking at 7 times 16.

Now we could look at 7 times 16 like this 7 lots of 16 or 16 lots of 7.

And we'd get the answer 7 times 16 is equal to 112.

But I wanted you to explore other ways we could have looked at that using the distributive law.

If we look at this one on the right here, we could have split 16 into two factors of 8.

7 times 8 added to 7 times 8 is the same as 7 times 16.

Here that would have made it easier to work out potentially.

I know that 7 times 8 is 56.

If I double 56, I get 112.

You could have done it in a different way.

You could have done 7 times 10 added to 7 times 6.

I know that 7 times 10 is 70.

I know that 7 times 6 is 42.

And if I combine those together, I get 112.

What about this way? 7 times 12 is equal to 84, 7 times 4 is equal to 28.

If I combine them together, I get 112.

All of these will get me the same answer, but it's about us working the answer out efficiently.

Which way do you prefer? Here is an array model for 14 times 6.

This can also be represented in an area model.

I don't know my 14 times table, so I want to use the distributive law to partition the numbers.

Area models can also be used to help us use the distributed law to partition multiplication problems. We're going to explore how to do this.

I'm going to show you some examples of how 6 times 14 can be calculated using the distributive law.

In the first area model, it's distributed to 10 times 6 and 4 times 6.

And the answers are added to get the product 84.

Pause the video now and decide how else the area model could be partitioned.

Great work.

In my second area model, the model is halved, 7 times 6 is solved twice, and then the answers are added.

In my final model, 12 times 6 and 2 times 6 are calculated, and then the products are added to reach 84.

There are other ways to which you may have found, such as continuous addition.

So why do you think distributive law can be useful when solving multiplication equations? Call out your answer.

Great job.

Using distributive law can be helpful because often many multiplication facts are only know mentally to 12.

This helps us go beyond 12 quickly.

We're now onto the Spot the Odd One Out.

You might need a little thinking time here.

Look at each of the arrays and the maths that has been done to calculate 8 times 17, which array is the odd one out? Pause the video now and explain out loud.

Excellent explaining.

The first array is the odd one out because the factor 8 has also been partitioned into two lots of 4.

If you weren't sure on your 8 times table, this would be a useful way of solving 8 times 17.

This is the odd one out, as the others do not partition the factor 8.

They only partitioned the factor 17.

So the blue one at the top is the odd one out.

Super maths learning.

You're now ready for your independent task.

Here you have three area models with different equations.

You must use the distributed law to partition and solve the equations.

Pause the video now to complete your independent task.

Fantastic work.

There are many different ways you could have partitioned the area models.

All of them could be partitioned into tens and ones, or you could use continuous addition or other known multiplication facts that produce the same answer.

Here are the correct answers for the equations.

Fantastic work this lesson.

You can now use the distributed law to partition two digit multiplication equations.

Head over now to your quiz to test yourself on the learning.

Well done for all your hard work.

This lesson in maths you've done really well.

Give yourself a hip hip hooray.

See you next time.