Lesson video

Hello there, I'm Miss Brinkworth.

I'm going to be going through this math lesson with you today.

Shall we look at the learning objectives together? So what we're going to be learning about today is the understanding that multiplication and division are inverse operations.

Now that seems like a lot of big words, but it's actually a really handy skill to have.

It will help you, enable you to answer questions as you want to, and to choose the answer that, the question that you feel more comfortable with.

So it's actually a really, really handy trick once you've got it.

So let's get started.

Our agenda for today's lesson is that we are going to be recapping on the bar model that we've been using for multiplication.

Hopefully that's something you're quite confident with using at the moment.

We are then going to relate bar models to division.

So probably, up to this point, you've been using bar models to show multiplication, what we're going to be doing with this lesson, through bar models, is showing that multiplication and division are very closely related operations.

And if you are feeling confident with some division questions, they can help.

I'm sorry, multiplication questions, they can help you with division questions, which sometimes people feel less confident with.

We're then going to really come and really dig into multiplication and division as related operations and why that is.

And then, towards the end of the lesson, you'll have time for your independent work, which will give you a chance to embed that learning and take as long as you need to do some work on your own.

And then finally, there's that exit quiz, which is just a way of you seeing how much, how much of today's new knowledge has gone in.

Okay, all you'll need is pen or pencil and some paper, a smile will go a long way as well.

So pause the video here and take as long as you need to get what you need.

Okay.

Let's get started together.

So here's a nice warm-up for you.

You've got the numbers going down the middle, and all I'm asking you to do is half them and double them in the columns at the side.

So for an example, I've given you four.

Half of four is two and double four is eight.

So pause the video here and have a go at those other questions.

How did you get on? I wonder whether you found some easier than others? Did it get a bit trickier as you got to the two digit number of 12 at the end? Let's go through these.

So eight.

Half of eight is four and double eight is 16.

Maybe you're using your two times table to help you with that.

Or maybe you're using your eight times table.

You know that two times eight is 16.

It's obviously related to the two that came before it as well.

So double two.

Sorry, half of four is two and half of eight is four.

So there's lots of related facts there.

And that's going to help us, that kind of knowledge about using related facts is going to help us with today's learning objectives as well.

Moving on to six then.

Half of six is three.

Two times three is six.

And six times two, so double six, is 12.

Well done if you knew that.

Maybe that means you're really confident with your six times tables, and that's fantastic.

Finally, we have 12.

And you can see that we've already got one of these answers because if we know that 12 is double six, then six must be half of 12.

And to double 12, I would partition it.

So double the 10 gives me 20 and double the two, gives me four.

24 is double 12.

And you can see that those numbers in the middle I picked are all even numbers.

That means that they're in the two times table, and they can be evenly split in two.

I had to pick even numbers, why do you think that is? It's because if I picked odd numbers, we wouldn't have been able to halve them.

We'd have been able to double them, but we wouldn't be able to halve them and get a whole number answer.

So I had to pick even numbers for that question.

Like I mentioned a moment ago, these questions, if you use known knowledge to help you, known facts to help you, you're not always learning new things, often it's about taking what you already know and applying it in new situations.

And I'm hoping that's what today's lesson is going to be all about.

So, what do we think is being shown here? We have a part-whole model, so you can see we've got some parts and the whole is missing.

We've got some parts and the whole is missing.

How many parts have we got? How many parts? Well, we've got 1, 2, 3 parts, three boxes, three groups.

How many is in each group? 1, 2, 3, 4.

Have they all got four in? Yes.

We've got three groups of four.

So what do you think is being shown here? Maybe three times four? And well done if you know that the answer is 12.

So this is a part-whole model where we've been given the parts and the whole is missing.

This makes it a multiplication question.

In multiplication questions, we have the parts and the number of parts, and we need to work out what the whole is.

Here are our parts, and then we use them to work out our whole.

Moving from part-whole models to bar models, which are very closely related.

We still have the parts and the wholes.

Which one of these do you think shows a division questions? Have a go, pause the video, I'll give you a clue.

Two of them show division questions.

Okay.

Let's see how you got on.

Now, if we go back to the assignment we've just done, just to show you that when we have the parts, when our question gives us the parts, it's a multiplication question.

Normally.

Might be an addition question, but when we have more than one, like this, it's a multiplication questions.

When we have a division question, we are given the whole.

We know what the whole is.

It's the amount in each part or the number of parts that we're looking for to answer the division question.

So that's your little clue to help you with these bar models.

Which ones show division? Well, the ones that show division are the ones that have already given us the whole.

We know the whole that we're looking at, that the question is all about.

So that's this one and this one.

These are both showing division questions.

The other two, that haven't been circled, are showing multiplication questions because you are given the parts, rather than being given the whole.

Let's look at that in little bit more detail.

Here's one of those bar models.

We've got the whole.

The whole is 12.

We've got that line at the bottom, which is saying "all together we've got 12." So what's the question? Well, how many is 12 being split up into? How many equal parts has that 12 bar been split up into? 1, 2, 3, 4.

12 has been split into four.

And how many will be in each part when we've split it into four? How many fours are there in 12? So if we count our fours until we get to 12, we'll get the right answer.

4, 8, 12.

There are three fours in 12.

So that's what that bar model is showing us.

So we've looked at bar models, or you've looked at bar models before, where we're looking at multiplication.

Today, we're looking at division, but actually the bar models will still look very, very similar.

Now here's the same bar, but instead of the parts being missing, the parts are there, and the whole is missing.

So that's the same numbers used in a multiplication question.

So twelve divided by four is three.

And we can use a very similar looking bar model to give us three times four is twelve.

This is because multiplication and division are inverse operations.

When we are given the parts and we're looking for the whole, it's a multiplication question.

So there you can see each part represents three.

There are four parts in total, three times four is 12.

That's our multiplication question, but the same bar with different information, we've got the whole of 12, 12 split up into four is three, gives us the division question.

I'll just put that slide up big, just for a moment, for you to have a look at what I'm talking about.

Okay.

Let's move on.

Here it is again, we have another division question, showing with a bar model we've been given the whole, so we know we're being shown the division question.

The whole is 12, but this time, how many groups is it being split into? We've got three equal groups, 12 divided by three.

How many threes can I get out of 12? 3, 6, 9, 12? I can get four.

But as a multiplication question, what would that look like? Can you have a go at pausing the video here and writing me a multiplication question with that bar model? Well hopefully, you can see, we don't start with the whole this time, we start with the parts.

There were four parts and we know from our division question, that that means there's three in each part.

So if there are three parts, there are four in each part, so three times by four is 12.

So it's the same bar, split up the same way.

But the question being asked differs between are we being asked to find the whole or are we being asked to find the parts? Okay, so here's it just written out for you.

Multiplication, we have the parts and we're looking for the whole.

So the number gets bigger.

We've got the small parts, the small equal parts that it's been split up into, what's the whole? Our answer will get bigger and that looks like this.

For division, we start with a larger number.

We start with the whole, and we split it up, and we're being asked "how many equal parts are there?" or "how much is there in each equal part?" So that looks like this.

So for division we would, sorry, with multiplication we would expect the answer to be bigger than the numbers we were using in the question because we're looking for the whole.

And in the division, we start with the larger number.

We start with the whole and split it up.

So the answer we would expect to be smaller, okay.

Have a go at finding the inverse calculations.

So where it's a multiplication, I'd like you to write a division, and where it's a division, I'd like you to write a multiplication.

Let's see how you got on.

Now, some of these could be done in different orders.

So your numbers might appear slightly differently to mine.

Let me show you what I mean.

Six divided by two is three is a division question using those three numbers, using the same fact family, using the same times table knowledge, but moving it to a division question.

You could also have 6 divided three is two.

For this division, 16 divided by four is four, you could only really have four times by four 16, and that's a because we've got two fours so there's only the one order that it can go in.

Five times by ten is 50.

As a division question 50, the whole, has got to come to the start of the calculation.

So your calculation has got to start with 50, but you might do 50 divided by five is ten.

You might do 50 divided by 10 is five.

Here we've got a division question again.

Eight divided by two is four.

For multiplication, the whole then goes to the end.

The whole is the answer, so eight is at the end, but you might have four times by two or you might have two times by four, either order is fine.

Well done if you got those right.

Okay.

What about this one then? Let's have a go at this together.

The whole is 20.

There are four equal parts, and the value of each part is five.

What we need to do is write this out, as a mathematical calculation.

The whole is 20.

So, if the whole is 20, and there are four equal parts with five in each part, we can make these two, our multiplication and our division, from the same information.

So four times by five, there were four equal parts and there are five in each part, so I've got 20 in total, my whole is 20.

For my division question, my whole goes to the start of the calculation, 20 is the whole, divided that into four, I've got four equal parts, and in each equal part, there are five.

Now there is some wiggle there.

So I could have had, for my multiplication, I could have had five times four, instead of four times five.

And for my division, I could have had 20 divided by five is four, but 20 for the division, has to be at the start of the calculation.

And, for the multiplication, the 20 has to be at the end.

Okay.

Are you ready to have a go at another one? So here's your run.

The whole is 14.

There were two equal parts and the value of each part is seven.

Can you please write me a multiplication and a division calculation using that information? How did you get on? Hopefully, you've got something like this, but you can have two times by seven is 14, and you can have 14 divided by two is seven.

As long as you've got a question, at least, as long as each question uses all three numbers.

And as long as for your division, the whole is at the start of the calculation.

And for the multiplication, the whole is the answer, after the equal sign.

Then you're doing really well.

Well done.

Okay.

Time here is for your independent work.

So pause the video and take as long as you need, but do come back, and we'll go through the answers together.

Hello everyone and welcome back.

My name is Miss Jones, and I'm going to be talking you through the answers to your independent task.

So let's look at number one, okay.

For each of these questions, I need to make sure I understand what's the whole and which are the parts.

So for my multiplication equation, I know that I need to use my parts, which in this instance are eight and three, as the two factors in my equation, and put the whole at the end.

And then for my division equation, I need to start with the whole.

So our multiplication equation here was eight times three is equal to 24, or you could have had three times eight is equal to 24.

The division equation was 24 divided by eight is equal to three.

And again, you can change around those parts.

So you could have had 24 divided by three is equal to eight.

Let's look at number two, the whole is 15.

There are three equal parts.

Each equal part represents five.

So our parts of three and five.

So for our multiplication, we can start with our parts and our whole goes at the end.

So we've got five times three is equal to 15, but I could have had three times five is equal to 15 as well.

Then our division, we start with the whole.

15 divided by three is equal to five, or you could have had 15 divided by five is equal to three.

Number three, the whole is 25.

There are five equal parts.

At this time, we don't know the value of our parts, but we know there are five of them.

So we need to work that out.

Now, if I know that 25 divided by five is equal to five, I know that five would be my other number in the equation.

So I've got here, I could have five times five is equal to 25, or 25 divided by five is equal to five.

Okay? Because we've used five twice here.

Of course, that's the only solution for each of those you could have had.

And then finally there are four equal parts.

Each equal part represents three.

Again, you've got a little bit of working out to do.

This time we don't know the whole.

We know, in our multiplication, the whole needs to come at the end.

So we've got three times four, which I know is equal to 12.

For our division equation, we start with our whole, 12 divided by three is equal to four, or could have had 12 divided by four is equal to three.

Let's move on to part B.

Write a multiplication and division calculation for this pens image.

So I need to think about what my whole is, how many parts I have, and what the value of each of those parts is.

My equation might be, here, six times four is equal to 24, or four times six is equal to 24, or 24 divided by six is equal to four, or 24 divided by four is equal to six.

We have here six groups of four, and we have 24 pens in total.

For number two, it's a little bit of a sneaky one because actually they both are correct here.

And you might notice that, actually, each person has the same amounts of circles there, but arranged differently.

And we know that three times four is the same as four times three, or three lots of four is the same as four lots of three.

Okay.

I'll pass you over to Miss Brinkworth to end the lesson.

Okay.

I would love to see your work, I'd love to see your working out with how well you got on with today's lesson.

So if you'd like to, please ask a parent or carer to share your work on Instagram, Facebook, or Twitter, it's tagging @OakNational and #LearnwithOak, but before you go, please have a go at that exit knowledge quiz, to just see how well today's learning's got in.

I've been really, really impressed by all your hard work today, everybody.

Well done! Enjoy the rest of your learning today.

Bye bye.