Lesson video

Hello, and welcome to this lesson about multiplication and division.

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

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

And if you can, try and find a quiet space to work where you won't be disturbed.

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

Okay, time for the try this task.

I'd like you to pause the video and have a go.

Pause in three, two, one.

Okay, welcome back.

Now, let's have a look at these statements here.

This is Beanie's statement, she can see seven groups of three, one, two, three, four, five, six, seven.

And each group has three in it.

Okay, what about Zacky's statement? He sees a group of seven three times, one, two three.

Three groups of seven, okay? And it doesn't matter which way you see it and which way you see it has different uses for different situations.

And this is particularly obvious when it gets to division, okay? So, which calculation goes with which diagram? 21 divided by three.

21 children are put into three equal groups.

So they are those 21 children are shared into three equal groups, one two, three.

So that means there is going to be three groups, so this and this they go together.

And this one, 21 children are put into groups of three.

So, in each group, there is going to be three.

This first one here, this is called sharing, where you share something into equal groups.

So that is how many groups and your answer tells you how many there is going to be in each group.

So in this case it's seven, seven in each group.

Whereas over here, we're putting children into groups of three.

So in each group there is going to be three.

So this is how many in each group, and the answer, the answer of seven is the number of groups that there is going to be, okay? So, 21 divided into groups of three will mean that there seven groups.

21 divided into three equal groups means that there are seven in each group.

And these differences between grouping and sharing are very subtle, but they're very important.

Okay, so we're going to try and come up with different word problems associated with these images.

So we'll start with the multiplication first.

Now, we've got one, two, three, three groups of seven.

But I want the calculation seven times three.

So I'm going to say this, each person has seven pounds.

There are three people, how much money do they have altogether? Okay, can you see that? Seven pounds, seven pounds, seven pounds, three people.

Okay, what about this one? Well, this time I want to change my wording slightly, change my order slightly, 'cause there are seven powers of three.

So this time I'm going to say there are seven people, each person has three pounds.

How much money do they have altogether? Okay, now I've just changed my order here.

I've just changed my order to match the picture.

One, two, three, three people each have seven pounds, how much money do they have in total? So this is very similar.

And with multiplication, the difference between these two it's not really that obvious, whereas with division, I feel it's bigger.

And you'll see that in a minute.

Okay, so this one, well, we've got to change.

We want our three to come first to make the number sentence match this calculation.

So I'm going to say, each person has three pounds, there are seven people, how much do they have in total? Okay, now division, this is where the differences is a little bit bigger.

Okay, so it's 21 pounds in total there.

Now, I'm putting these to 21 pounds into groups of seven, I am grouping.

So I'm going to use a context of buying a ticket for this question.

And I'm going to say a ticket cost seven pounds.

So if I have 21 pounds and a ticket costs seven pounds, how many tickets can I buy? I have done this because I want groups of seven.

So I've assigned a cost of something, a cost of seven pounds, so that means I can get groups of seven.

Whereas this might be slightly easier.

So there's one, two, three, four, five six, seven, seven piles.

So I'm going to share 21 pounds between seven people.

How much does each person get? Okay, next one.

Well, it's shared, the 21 is shared equally into three piles.

So it's sharing this one.

So, 21 pounds is shared equally into three amounts, how much is in each amount? And now, now when less than one, well, I'm putting them into groups of three.

So we want a grouping and word problem.

So let's use our tickets again.

I have 21 pounds, I want to buy tickets that cost seven pounds.

How many tickets can I buy? Okay, and I've just use a slightly different context of playing a game, how many goals can I do? But it's the same idea, okay? These two, they are grouping.

These two, they are sharing.

Okay, sharing into equal groups, sharing into seven groups, sharing into three groups.

These are groups of seven, groups of three.

Okay, so hopefully you starting to get an idea or get a sense of that difference there.

Because it is now time for the independent task.

So I would like you to pause the video and have a go.

Resume once you're finished.

Okay, welcome back.

And here are my answers.

You may need to pause to mark your work.

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

We have two word problems here and I want you to try and work out why they have the same answer.

And then maybe use a diagram, maybe use a diagram to show why their answer's the same.

Okay, so a representation, one of the ones we've looked at in a previous lesson.

And then make up two problems yourself.

Maybe make multiplication problems, or maybe make some division problems. So pause the video to complete your task, resume once you're finished.

Okay, and here are my answers.

I've drawn this, I've drawn a bar model.

Here is six lots of 12 and here is 12 lots of six and they have got the same answer.

They have the same answer because multiplication is commutative.

12 times six equals six times seven.

And here is just a possible word problem that I've made up.

So hopefully you've made up some yourself and hopefully they're really interesting.

Okay, and that is it for today.

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 all your hard work in this lesson.

I look forward to seeing you next time.

Thank you.