Lesson video

Hello, and welcome to another video.

In this lesson, we'll be focusing on writing calculations.

Again, I am Mr. Maseko.

Make sure you have a pen or a pencil and something to write on before you start this lesson.

Okay, now that you have those things, let's get on.

Okay, now complete the trios of worded descriptions, which are these, function machines, and calculations.

Pause the video here and give this a go.

Okay, now that you've tried this, let's see what you come up with.

Well, if we look at this, this says, "I start with 12 then add 6.

I then multiply my answer by 2 and then divide by 4 to get a final answer of." Well, what is 12 and 6? That is 18.

Multiplied by 2, that gives you 36.

Divided by four, that gives you a final answer of nine.

So what's the calculated based on those gaps? We just get nine.

We have the calculation written for us already.

Why did we have to put the 12 add 6 in brackets? Good, so you remember from the last lesson, we had to give priority to the addition over the multiplication and the division.

Okay, now this next one.

It says, "I start with 12 then." Well, let's see what's happened.

Started with 12, and then if we look here, we're told then we multiplied, I'm going to use a multiply sign, by, multiply by three.

And then we divided by two.

And then we finally subtracted four.

So 12 multiplied by 3, well, that is 36.

Divided by 2, that is 18.

If we take away 4, that gives us 14.

So that's 14.

Well, what calculation do we write? So we've got 12 times 3 divided by 2 take away 4, which gives us 14.

Do we need to use brackets in this one? Well, no, because we are going to do the multiplication and the division first and then the subtraction at the end, so we don't have to use brackets because we're already doing things in the order the priority gives.

Now, if we look at this, now we're told we start with 12.

We know we have to do things in the brackets first, so what happened to 12? Well, the first thing we did to 12 is we divided 12 by 3, and then we took away 2, and lastly we multiplied by 5.

Well, 12 divided by 3, that is 4, take away 2, that is 2 times 5, that gives you 10.

So that's what you should've written here.

I start with 12, and then I divide by 3 and then take away 2, and finally I multiply that by 5 to get a final answer of 10.

Okay, now, let's explore this idea of writing calculations and the way we use brackets further.

Now, in this section, we're looking at a game.

So I'm going to read this paragraph out to you.

It says, "To play in a prize draw, you are given 12 cookies and four tickets." So these are the four tickets.

So what happens? So you have to choose the order in which you use your tickets in order to maximise the number of cookies you have left at the end.

So what order should the tickets be used in order to get the maximum number of cookies at the end? And write a calculation to match the order that you use.

Pause the video here and give this a go.

Okay, now that you've tried this, let's see what you have come up with.

Well, if we look at this, what could we have done? Well, we could have, let's say, doubled our cookies first.

So we could have doubled, so multiplied by two.

And then we could've then added 10 cookies and then lost half, so divided by two, and then lost 10 cookies, so we took away 10.

So what would that be? 12 multiplied by 2, well, that is 24.

And 24 and 10, that's 34.

34 divided by 2, well, that gives us 17.

And then 17 take away 10, that gives us 7 cookies.

For that method, all it's done is taken us to less cookies than we started with.

Did you come up with a way to get more cookies than we started with? Well, let's see which order you should've played your cards to get the maximum number of cookies.

Oh, this is what you should've done.

The first thing you should've done is divided by 2 and then added 10, then multiplied by 2, and then took away 10 in the end, and that would've given you 22 cookies.

So if you look, 12 divided by 2, that is 6.

Add 10, that is 16.

Multiply by 2, that is 32.

If you take away 10, you're left with 22.

So if we write this calculation out, let's see what's happened.

So we start with 12, then we divide by 2, and then add 10.

We then multiply all of that by two.

And then finally, we take away 10, which gave us 22.

Why did we have to put brackets around all of this? Why could we not have written it as 12 divided by 2 add 10 times 2 take away 10? Why? Exactly, because if we wrote it like this, we would have to do 12 divided by 2, which is 6, and then 10 times 2, which is 20, and then add these things together.

So 6 add 20 is 26.

Take away 10, that would give us 16.

But that's not what we're trying to do because we know that we have to do the addition before the multiplication.

Because we have to do the addition before the multiplication, we have to put that inside the brackets to show that that gets given priority.

Now, inside the brackets, we know we have to do division first because we divided by two first.

So we don't have to use brackets inside the brackets because we know that division always comes before addition.

Using brackets is really important.

It's a skill that we have to get used to because they show they give priority to operations that would otherwise not have it.

Okay, so this is the calculation you could've used in order to get the maximum number of cookies.

In this independent task, these three students start with 12 cookies, and these are the cards they've been given.

So Xavier, these are his cards.

Zaki, these are his cards.

And Yasmin, these are her cards.

Now, who is going to end up with the highest number of cookies? So you've got to pick the right order to play the cards in.

So if played in the right order, who is going to end up with the highest number of cookies? Pause the video here and give this a go.

Hi, guys, it's Ms. Jones, and I'm going to just take you through the answers to your independent task, and then I'll hand you back over to your teacher.

Okay, so I'm going to display the solutions and then talk through them.

You were asked to start with 12 cookies, and we were looking for the highest possible answer, thinking about what order we could do the cards in and whether that would affect the total answer that we have.

So in this first one, the highest possible was 72.

Now, because we're only adding and subtracting with these cards, if we think about adding and subtracting, they have equal priority.

So if we were to swap these around, it wouldn't affect our total.

So it doesn't matter the order that we do these in.

The answer is always going to be 72.

Similarly, with this second one, here we're using division and multiplication.

We're halving, doubling, tripling are all ideas around division and multiplication.

So again, our highest answer is 72, but if we were to change the order around, we'd still get 72.

However, on this third one, we had addition here, subtraction.

We had tripling and halving, so we had all four operations.

So here it does matter what order we do the operations in.

And this is the order that I've put them in to get the highest possible answer of 103.

I just want you to look at that for a moment and think, why have I put it in this order? How did I know to put it in that order to get the highest total? Okay, so think about the order we're doing this in.

We've put our division deliberately at the beginning because we don't want to divide our final answer and get a really small answer.

And we put the addition in before we multiplied.

The idea is before we triple, before we multiply by three, we want to get the highest number we can using these operations.

So we then will subtract at the end, okay? Now, if you didn't get this arrangement, have a think about why and why your arrangement might not have got such a high total.

But we can see if we do this, by far we're getting more cookies than these two, and that of course has to be a great thing.

Okay, I'm going to pass you over to your teacher again to finish off the lesson for you.

Now, for this explore task, here are four tickets.

Use these in any order you want.

How many different totals can you find? And write a matching calculation for each total that you find.

Pause the video here and give this a go.

Okay, now that you've done this, let's see what you've come up with.

Well, we want to find the maximum number, so what did we.

Let's just start with the maximum number first.

What did we do before? What did we say? Well, if we want to maximise what we're adding, so we don't want to multiply first, so what do we always do? We first divide it.

So if we do the same thing here, we first divide by two, so we lose half our cookies, and then we add 20 and then multiply by 3 and then take away 5 at the end.

Do you see? We've seen this calculation already, so look.

So 12 divided by 2.

So this is 12 divided by 2, add 20, multiply by 3, and then take away 5.

And that will give you a maximum of 73 cookies.

Now, this was just to find the maximum number, and it was the same calculation that we had for Yasmin's maximum.

Why does this find us the maximum? Remember, because we're adding 20 then multiplying by 3.

In effect, this is the same as adding 60 'cause three lots of 20 is 60.

We don't want to put the subtraction before the multiplication because it will compound how much we're losing.

Now, this is just one of the calculations you could've come up with.

Here are two more.

We've seen this one already.

Now, here is one to find us.

Here are some to find us what? Really low numbers.

Look.

Look what's happened.

When we put the subtraction before the multiplication, we end up with fewer cookies.

Why? Because we are compounding how much we're losing.

If we're taking away 5 and we're multiplying it by 3, in effect, we are losing 15 cookies.

So same thing here.

If we take away 5 and are multiplying it by 3, in effect, we're losing 15 cookies.

This is why you don't want to put your multiply sign inside your brackets, 'cause it just compounds how much you're losing.

Now, there's so many other calculations you could've come up with.

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

I will see you again next time.

Bye for now.