Lesson video

Hello, and welcome to today's lesson about models of multiplication.

For today's lesson, all you'll need is a pen and paper or something to write on and with.

Please take a moment to clear away any distractions, including turning off any notifications.

Finally, if you can find a quiet space to work where you won't be disturbed, please do so.

Okay, when you're ready, let's begin.

Okay, so time for the try this task, what different multiplication and division facts does each bar model show? I'd like to pause the video and have a go.

Pause in three, two, one.

Okay, welcome back.

Hopefully you've got some of these.

Now, can we see these in our diagram? Can you see a group of nine, four times? Can you see four groups of nine? Can you see how many groups of nine are in 36? Can you see if we share 36 into four equal groups, how many are in each group? And it's the same over here.

In each group is 12, and there are seven groups, how many people are there? If we've got seven groups of 12, how many do we have in total? If we've got 84 and there's 12 in each group, how many groups are there? If we have 84, shared into seven groups, how many people are in each group? Now those last two there that I talked about, and indeed, most of these, there's a subtle difference between them.

But that difference is really important, and it's all to do with the idea of sharing a grouping.

And we'll explore that in future lessons.

So don't worry if you don't quite understand the difference now.

Okay.

So I'd like you to just pause the video.

Can you see, how this model represents each calculation? Pause in three, two, one.

Okay.

So you might've been able to see a few of them.

You might have been able to see, there's four counters in each group and there's three groups.

You might have been able to see that there are three groups of four counters, so there are 12 counters.

And then this is the grouping and the sharing thing again.

Okay.

So we share 12 into three equal groups.

How many counters are in each group? This one, we have 12 shared into groups of four.

So that means the must be four in each group.

How many groups would there be? Three.

Okay, next model.

And this is one of my favourite models.

Can you see, four times three? Four lots of three columns.

Can you see three lots of four rows? Now this is my favourite because it shows that these two are equal really nicely.

It shows that four times three equals three times four.

And that's an important property.

It's called the commutative property, okay? Multiplication is commutative.

You might want to practise saying that word because it's a really important word that we'll look at in future lessons, okay? Commutative.

Alright.

So what have we got here? Well, we've got 12.

If we have 12 squares and if there's three rows, how many are there in each row? Or if we have columns of three, how many columns do we have? If we have 12 and there's four in each row, how many rows do we have? If we have 12 shared into four columns, how many are in each column? And again, that's the difference between grouping and sharing going on there.

Okay, what about this one? This number line representation.

Maybe you want to pause and see if you can find these calculations.

Okay, so what have we got? We've got one group is four, three groups is 12.

We have three groups of four, one group, two groups is eight, three groups is 12.

Okay, if 12 is three groups, how many is there in one group? This last one's a bit tricky to see.

Maybe you can see it.

We've got 12 divided by four equals three, how many fours are in 12? Three, like that.

It's a bit tricky this one.

What about this one? Well, what I like about this one is it shows how many times bigger something is.

12 is three times bigger than four.

Four, three times is 12.

Three times that length of four is 12.

Four is three times smaller than 12.

Four goes into 12, three times.

Okay, and this is more of a, some of the others, we could see repeated addition there, but this one is about how many times bigger, what I like to call a stretch.

Okay, so that's another way we can think about multiplication and division.

Okay, so now it's time to have a go at the independent task.

I would like you to pause the video to complete your task and resume once you're finished.

Okay, welcome back and here are my answers.

You might need to pause it to mark your work.

Okay, so now it's time for the explore task.

Generate as many different problems for the calculation, 27 divided by nine.

Draw a model for each of your problems. Okay, so we have Yasmin there.

Yasmin thinks she's going to draw an array, and I'll just, I didn't actually mention the names of our models before, hand's going crazy, I am, so.

This is an array.

Alright, so there we're asked where's arrays, arranged into rows and columns.

So she thinks she's going to draw an array.

What else could you draw? Could you draw a bar model? Could you draw the number line? And then Zacky, he's going to make his problems about sweets.

I'm going to share 27 sweets between nine people.

Okay, so you might choose to make it about sweets, you might choose to make it about something else.

Be creative, make more than one problem.

Try and draw a few different models.

Okay, so I'd like you to pause the video, to complete the task and resume once you're finished.

And here on my axis.

It's probably a good idea if you pause and mark and compare.

Do your models look like mine? Did you use different models? Did you use the same context of sweets? Did you have a sharing ward? Did you have a grouping ward? Did you have how many times bigger? And that is it for today.

So I hope you've enjoyed the lesson.

And if you'd like to, please ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

Thank you very much for taking part, and I look forward to seeing you next time.