Lesson video

Hello, welcome to today's maths lesson with me, Ms. Jones.

I cannot wait for today's lesson because we're going to be using some new knowledge in order to solve some really interesting problems today.

Before we start though, I've got a little brain teaser for you, a riddle.

Riddle me this riddle me that.

Today's riddle is, what has a head, a tail, but no body? Let me say it one more time.

What has a head, a tail, but no body? Have a think.

Shall I tell you the answer? The answer is a coin, a coin has a head, it has a tail, but no body.

Did you like that one? Hopefully, you can share it with your friends afterwards.

Okay.

Let's get started with today's lesson.

In today's lesson, we're going to be looking at order of operations.

Thinking about whether it matters if we do certain operations in a different order.

And if it does, which one should have priority? So we're going to start by looking at just that, trying to figure out what happens if we change the order of operations, and which order we should be doing operations in.

Then we're going to apply what we've learned to do some problems. Then we've got our task, and lucky you, I've put in an extra challenge today as well.

And finally, we've got our multiple choice quiz.

For this lesson, all you'll need is a pencil and a piece of paper, or something else to write with and write on.

Make sure you're in a quiet place without any distractions, too.

If you haven't got what you need, pause the video now and go and get what you need.

If you're ready, let's get started.

We're going to start with this question.

Does it matter which order we complete operations in in any calculation? Have a think about that.

Maybe it will help if I show you an example.

So let's look at this one.

I'm starting with 4, then I'm going to add 3.

Afterwards, I'm going to multiply by 3, and let's see what that's equal to.

I start with 4, if I add 3, I get 7.

Then if I multiply my 7 by 3, I get 21.

What would happen if we change the order of the items here? See if you can make a prediction.

What would happen if we change around our two blue cards? Let's see if we can find out.

Here, I've changed around my two blue cards, so I'm going to start with 4.

This time, I'm going to multiply by 3.

What do I get? 4 times 3 is equal to 12.

Then I've got to add 3, 12 add 3 is equal to 15.

Interesting.

If I've changed around multiplication and addition, I don't end up with the same answer.

These operations, you can't just change around.

They have to be in a certain order.

Hmm.

So they don't have equal priority.

Wonder why this happens.

So, let's just look at keeping all calculation in the same order, to 4 add 3 times 3.

Now, even then, there's two different ways I could look at this.

I could look at this as 4 add 3 which is 7, then times by 3 is 21.

Or I can look at this as 4 added to, to 3 times 3 which is 9, which gets me 13.

So how do I know which is the correct way? And what's the correct answer to the calculation? Well, there's a certain rule that we need to apply here, and that's that multiplication and division take priority over addition and subtraction.

So it's not just about reading it left to right and doing it in that order, you need to make sure you do the multiplication and the division of a calculation first.

So let's look back at our calculation here.

Before I add on the 4, I need to multiply 3 times 3.

3 times 3 is 9.

So this equation means to be 4 added to 9, and that will get me 13.

Now, this is the only right answer to this equation because multiplication takes priority over addition.

Let's look at a couple more examples to make sense of this.

So here, we have 12 subtract 6 divided by 3.

Have a think about which order we need to do the operations in.

To help us, we've got this girl, who's going to share what she thinks.

I know that multiplication division takes priority over addition and subtraction.

So, before I can subtract, I need to calculate 6 divided by 3, which is equal to 2.

Now I know what to subtract from 12, 12 subtract 2 is equal to 10.

Okay.

That sounds right to me.

Let's just makes sense of that.

So she says that we need to make sure we do this part of our equation first because division takes priority over subtraction.

I know that 6 divided by 3 is equal to 2.

So what we're really doing here is 12 subtract 2, which is equal to 10.

Let's look at one more.

3 times 7 plus 2 is equal to 27.

Do you think that's correct? Let's see what this boy thinks.

I think a mistake has been made here because I calculated 3 multiplied by 7, and then added to 2 as multiplication takes priority over addition.

My answer was 23, which is different.

I think they have added 7 and 2 first, and then multiplied 3 by 9.

What do you think? Let's make sense of that again.

So if we were doing this calculation, let's forget this answer for now.

What would we do first? We do 3 multiplied by 7 because multiplication takes priority over addition, which gets us 21.

Then we'd add 2, so our answer shouldn't be 27, it should be 23.

I think he's right.

I think what they've done is added the 7 and 2 first, then multiplied by 3, which isn't going to get them the correct answer.

Multiplication and division always take priority over subtraction and addition.

Okay.

it's your turn to have a go at some of these.

For the first two, I'd like you to think about how you would correctly calculate these solutions.

For the next two, I want you to have a look closely and see if they are correct or incorrect.

Are there any errors in these calculations? If you think they are incorrect, you'll need to explain why on your piece of paper.

Okay.

Don't forget about our key concept.

Multiplication and division always take priority over addition and subtraction.

Pause the video now to have a go.

When you're done, press play again.

Okay.

Let's go over some of these together.

So, looking at the first one, we've got 4 multiplied by 5 take away 3, or subtract 3.

I know that multiplication and division are our priorities.

We need to do the 4 times 5 first, which gets us to 20, we take away the 3, and we should get 17.

In the second one, rather than from reading left to right here, I need to start with the division.

So 6 divided by 2, which is 3.

So we need to do 4 added to the 3, which gets us to 7.

Looking at these, we should've done 10 divided by 2, which is 5, then added 3.

So this one is incorrect.

We should've done the division first.

Looking at the bottom one, we need to start with the multiplication, 4 times 6 is 24, then add 2.

So it looks like this one is correct.

We start with the multiplication, and then we add on the 2.

Okay, let's take what we've learned, and this time we're going to apply it to some real life maths problems. And for this, we're going to be looking at some piggy bank problems. Thinking back to that calculation we looked at earlier, 4 plus 3 times 3.

Now, if you remember correctly, we know that multiplication has priority, so it's the same as 4 plus 9, which was 13.

Now, I'm going to show you two different word problems. What I want you to think about is which word problem can be represented by this equation correctly.

Pause the video now to have a think about that, and press play when you're done.

Okay.

Let's have a think about that together.

So looking at the first problem, Arlo had £4, and then he saved £3 for three weeks.

Okay, so we need 3 lots of 3 here, and the £4 he already had, so it's 4 added to 3 times 3, which is the same outcome as what we've get if we wrote the equation just like this.

So it works for this problem.

Brilliant.

Let's look at the second problem.

Each week, Naya earned £3 for doing chores, and received £3 pocket money.

She saved all of this money.

So 4 and the 3 together for three weeks.

So in this problem, we need to find the answer to add first ,and then multiply it by the 3.

But if we, we write it down, multiplication takes priority, how can we get this across in our equation or our calculation? Well, let's have a think about that.

Taking this first problem, we can express the problem as a calculation with brackets.

Now, brackets are not just something we use in English, we can use them in maths, and the way we use them in maths is to express which parts of a calculation take priority.

So looking at that second problem, what we can do is put the brackets around the addition, and this means that addition now has priority.

Key concept is whichever part of the equation or calculation is in brackets, needs to take priority.

So you do the part in brackets first before doing the rest of the equation.

Now in this one, you could argue that we don't really need the brackets here, but you can still put them in to, in to make it really, really clear about which bit you want to do first.

But if we took the brackets away, we'd still get the same answer of 13.

Now that we've got our brackets in our second one, we do the 4 plus 3 first, which is 7, then multiply it by 3, and we do get 21 this time.

Okay.

So let's investigate this a little bit further.

Let's develop our learning.

I've got a calculation here.

20 take away 3 times 3 plus 2.

First of all, I'd like you to find the correct solution as it is using what you know about which operations take priority.

Then, I want you to have a play with this with some brackets.

I want you to try putting brackets into different parts of this calculation, and see if you can get anything, which is a different answer once you've used brackets.

See how many different answers and how many different arrangements you can make.

Remember, when you're doing that, think about our key concepts.

Usually, multiplication and division take priority, that's when there's no brackets.

But when you are using brackets, brackets take the priority, so we do anything in brackets first.

If there aren't any thing in brackets, we do multiplication and division before we do addition and subtraction.

Okay? Okay, pause the video now and see how you get on.

Okay, shall we have a look at some of the possibilities together? Okay, so first of all, I've tried it without any brackets, whatsoever.

So, I've done 20 take away 3 times 3 to 20 take away 9, added to 2 is 13.

Multiplication has priority so we get 13.

Now, there are lots of other ways where you could've changed some of the answers by using brackets.

Let's have a look.

Okay, so in this first one, I've just tried putting my brackets around 3 times 3, and because multiplication takes priority anyway, my answer hasn't changed, it's still 20 take away 9 plus 2.

Now in this one, I've put my brackets around the 3 plus 2, and my answer has changed.

So now, the thing in the brackets takes priority, so I've got 20 take away 3 lots of 5, these have been added to 5 first.

20 take away 3 lots of 5, or 20 take away 15 is 5.

Up here, I've put my brackets around three different numbers here.

So 20 take away 3 times 3.

I do everything in the brackets first.

So 20 take away, now within my brackets, multiplication takes priority.

So 20 take away 9 is 11, then I add 2, I've got 13 again, same answer as before, that's interesting.

This time, I put my brackets around these three numbers.

So, I'm going to do everything in here first.

3 times 3 is 9 add 2 is 11, 20 take away 11 is equal to 9.

And this time, I've got 20 take away 3, which is 17.

Then I'm going to multiply it by 3, add 2 to 51, and then 53.

Okay.

That's a really different answer, isn't it? It's interesting how we can manipulate the, our calculation by just using the brackets and thinking about which bit takes priority.

Why are some answers the same? That's a really interesting question to think about too.

Okay.

I think it's time for your main task.

For each calculation in your main task, you'll have to first of all, solve it without any brackets, thinking about order of operations.

Remember, multiplication and division take priority.

Then, I'd like you to investigate how you could use brackets in the calculation.

Think about which of your calculations with brackets will be the same, and which will be different from the original answer, and try to explain why if you can, then solve your calculations with brackets.

Here are the calculations you're going to be working with.

Okay.

Pause the video now and go off and do your main task.

Okay.

Let's go over some of the answers together.

Here are some of the possibilities that you might've come up with.

So first of all, hopefully, you tried the calculation without any brackets.

And so 18, now we've got to use the division first, so 18 take away 2 is 16, add 3 is 19.

Now, I've put, tried put in the brackets in some different places.

So for example, I put it around 18 take away 6, which got me 12, then I've divided that by 3 to get 4, and added 3 to get 7.

And here are some of the other ways that I've tried it.

Now, looking at the next calculation, again, first of all, you should've tried it without any brackets, so remembering the multiplication and division take priority.

So we need to make sure we do this bit and this bit together.

So we've got 12 times 3 is 36, added to 8 divided by 4, which is 2.

So 36 added to 2 is 38.

Here are some other ways that I've tried it as well.

So, here I've put the brackets here.

Now, because division has priority anyway, I've got the same answer.

But when I've put the brackets here, around these three, and I've included the addition, I've got a slightly different answer.

So I've got here 12 times 3, which is 36, added to 8 is 44, and then I divided by 4, which got me 11.

So it's slightly different answer, which was really interesting.

Just to finish off, we've got a challenge question.

I want you to have a think about everything we've learned during this lesson, and apply it to this different situation.

Okay.

9 squared take away 36 divided by 9.

Now, I know we haven't covered squared during this lesson, but have a think about everything you know in here, if you can think about how to solve this.

Pause the video now to have a go, and then I'll go over how I might tackle it.

Okay.

So looking at this, what do I know about 9 squared? I know that 9 squared is the same as 9 times 9.

And then I've got to take away 36 divided by 9.

Now that I've written it like this, it looks like something that I can solve.

So, we do the 9 times 9 first, multiplication has got priority, and we make sure we do our division here.

I've written 3, but I mean 36.

Okay.

So we've got 9 times 9, I know it's 81, and we need to take away 36 divided by 9, 36 divided by 9 is 4, so 81 take away 4, I'm going to count back, it should leave me with 77.

Okay, but there's lots of different ways you could make mistakes in here if you didn't know what to do with order of operations.

For example, we could've divided by 9 after we take away 36.

So it's something to watch out for.

Always remember the key concepts, multiplication and division takes priority over addition and subtraction, and if you've got brackets, they take priority.

Hope you've enjoyed today's lesson.

If you want to, ask your parents or carer if you can share some of your work with Oak National.

Now you're ready to take our quiz to finish the lesson.

Thanks guys.