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Hello, and welcome to another video.

In this lesson, we'll be looking at Order of Operations and Arrays.

Again, I am Mr. Maseko.

Make sure you have a pen or a pencil and something to write on.

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

Okay, here are a couple of arrays.

What calculations can you write for these arrays? Here's an example of a calculation that you could write for this first one.

Pause the video here and give this a go.

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

Well, if you look at that first one, how else could we have written that? Instead of saying six times four add three times four, or you could have done six add three times four, that's one, six add three times four.

Is there another way you could've done this? Well, what else could you have done? Well you could have written three add six times four, but this, remember addition is commutative, so that means the exact same thing.

Now let's look at this bottom one here.

What could we have done for this one? Well, you could have written four times three and then add six times one or just four times three add six.

Do we need to use brackets for that second one? Well, no, because we know that multiplication has priority of addition, so we don't have to use brackets.

We had to use brackets here.

Why? Because we had to do the addition first and then the multiplication.

So here's examples of all of different calculations that you could have come up with.

Now, if we look at the two arrays that the students have, but they both attached this calculation to them.

Who do you agree with and why? And then write a correct calculation for the other array.

Pause the video here and give it a go.

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

Well, who do you agree with? Well, you should have agreed with Javier.

Why? Because if you look at this, there's the five and then there is the two times three.

So that's five add two times three.

calculation thus should have been, you could have either written five add two times three, or you could have done five times three add two times three.

Now, if you look at the two calculations, we don't have to use brackets for the second one because the multiplications would get done first and then the addition.

Now, if you plus five add two, well that's seven times three is 21, but five times three is 15, two times three plus six, 15 add six that also gives you 21.

So both calculations are equivalent that give you the same thing.

Now, how else can we show that difference? Because these two pictures are not the same.

So how can we show that difference? So if you look this total here, five add two times three, that's a total of, what? 11.

So how can we show that difference of 10 between those calculations? Well, if you look at this image, shaded in, that difference of 10 can be seen by comparing the arrays, and if you look this region that's shaded in the region there that is five by two.

So that's the bit that's missing from this arrays.

That's where the difference of 10 comes from.

For this independent task, how many equivalent calculations can you write for each array? 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, for this first one, what could you have written? Well, you could have written two add five times 12, or for this one, you could have written 30 times 15, don't need brackets, add 60 times 15.

Why do we not need brackets? Because 30 times 15 gets done first, and then 60 times 15 also gets done, and then the addition gets done after.

We didn't have to use brackets.

What about this? What calculation could we have used to represent that array? Well, we could have done five multiplied by 0.

8, takeaway five multiplied by 0.

2.

Now why did I takeaway? Well, because it looks like this region has been taken away from that big region there.

So that's some of the calculations you could have come up with.

Let's see others.

So these are all the different calculations you could have come up with for each of those arrays.

So 12 multiply by five add two, five times 12 add two times 12, or you could have done seven times 12.

So if you got any of these, really well done.

Now in this explore task, add brackets to one side of the following equality statements to make them all true.

At the moment without brackets, they're not true.

Add brackets to make them all true.

Pause the video here and give this a go.

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

Well, if we look at this first one, what's the difference between the right-hand side and the left-hand side? On the left-hand side, we're doing seven multiplied by five.

While on the right-hand side was five multiplied by five add two.

How can we make that seven multiply by five? Well, if we put brackets around the five add two, because five add two gives us seven and of the seven multiply by five.

Brackets give priority to the addition.

Remember we add brackets to give priority where it would otherwise not be given.

Let's look at the second one, what do we do here? So we've got A add B divided by C.

So first we've got to do A add B and then divide, because all of it is divided by C.

So on this side, we should put brackets around the A add B to show that all of that is divided by C.

And then here, you've got triangle times square takeaway triangle times diamond.

So where can we add our brackets here to make this statement true? Well, if you look at this, you can add your brackets around the square takeaway diamonds.

Why? Because you look at this on this side, the triangle is multiplying the square and the triangle is also multiplying the diamonds.

Now let's put some numbers to this to see whether this will be true.

Let's say the triangle is worth three and say the square is worth four and the diamond is worth two.

Would this work? Well if we do, that's three times four takeaway three times two.

Would that be the same as three times four takeaway two? Well, what's three times four? That would be 12.

Takeaway, what's three times two? That's 12 takeaway six.

Is that the same as three times plus four takeaway two, or four takeaway two is two, 12 takeaway six that is six, three times two is six.

If you look at it, this is another way of writing this because the triangle is multiplying both the square and the diamonds, see triangle is multiplying the square and triangle is multiplying the diamonds.

We have just expanded the calculation on that left-hand side.

Now, if we look at the right-hand side, where would we add our brackets? A times two add three times A is equal to 10 takeaway five A.

Well, you would add your brackets, where? Around 10 takeaway five, because A times two add three times A, that is the same thing as saying five times A, which on this side, we also have five times A.

Now really, really well done if you've got any of these.

If you need to watch this lesson further to see where you put your brackets and why we put them where we put them, just rewind the video and watch that again.

If you have work to share, ask your parents or care-er to share your work on Twitter, tagging @OakNational and #LearnwithOak.

Thank you again for participating in today's lesson.

I'll see you again next time.