Lesson video

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Hello, and welcome to this lesson on calculations with variables, again, I am Mr. Maseko.

Before you start this lesson, 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.

Now here's a try this task.

Yasmin is thinking of a number.

She divides the number by two, and then add six and finally multiplies them by four.

What number could Yasmin be thinking of if a final answer is between those numbers listed there.

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.

Alright, well, Yasmin is thinking of a number then she divides it by two and then add six and then multiplies by four.

Well, let's try a number.

Let's say she's thinking of the number 12, yeah, lets do 12.

What's the first thing she does, well she divides by two first, okay? And then, well, she divides by two and then what does she do after? And then she adds six, and then she multiplies by four.

Well, we know that and we'll put this in brackets because we want to do the addition before the multiplication.

Well 12 divided by two well, that is six and then six add six, well, that is 12.

And then 12 times four all that is 48.

Ah, almost got to 50, almost, well since we know this, let's try number bigger than 12.

Let's try the number 16.

Well with the number 16, let's say 16 divided by two, add six and then multiply that by four.

Well that's eight add six, what's eight add six? Eight add six is 14, multiply that by four, 14 multiplied by four that will give you, good that is 56.

Yeah, and there we go.

Yasmin could have been thinking of the number 16 because that gives us an answer between 50 and 100.

Or try 50, for example, 50 divided by two, add six, times four.

Well, this would be 25, add six that's 31, times four that would give you 124.

And that there is between 100 and 150.

So could have been thinking of 50.

The first one we said could have been thinking of 16.

What about that last one 240 to 260? Hello everyone, hello, Mr. Maseko.

My name's Ms. Jones, and I was hoping I could just come in here and tell you another strategy.

So I thought actually, instead of just trying random numbers, there's another way that I could work a little bit more systematically in order to solve this.

Did you think of any other ways I'm wondering? Well, I thought, well, what if we take our end point where we want to get to, so one of these numbers or a number in between one of these areas and then work backwards to think about where we would have started.

So for example, if I wanted to satisfy C here, I might take a number within C.

So I'm just going to take 240 and then work backwards and use the inverse operations what we've used here.

So I know that the last thing that we wanted to happen was multiply by four.

So I'm going to take 240 and I'm going to do the inverse, and I'm going to divide by four, which will get me 240 divided by four is 60.

And then before they asked us to add six, so what I'm going to do here is then do 60 subtract six, which will get me 54.

Before that it asked us to divide the number by two so I'm going to multiply it by two.

So 54 times by two, you can call it out 108, and that's it.

And that would be our starting number.

And you could work that forwards again in your head.

So we think of the number 108, we divide it by two 54, we then add six to get 60 and then multiply by four to get 240 so that would work.

And then we could go to 241 and see what the starting point would be there, 242, and we could find all the solutions here by working a little bit more systematically.

Okay so the next thing to think about is how else could we express Yasmin statement? Hmm, okay, I'm going to hand you back over to Mr. Maseko who's going to explore that with you.

Well, if we say the number that Yasmin was thinking of was X so we assign it a letter so this is a variable 'cause a variable, it can be any number that's why we call it a variable.

And then we just put all her statements onto a function machine.

Well, the first thing she did was she divided by two and then added six and then multiplied by four to get her final answer.

Well, so she did X divided by two, add six, and then all of that was multiplied by four.

So this, there that's the calculation you'd have to do.

So if you look, we have now expressed Yasmin statement in a different way using the variable X to represent that unknown number.

And this is what we're going to try and explore in this lesson.

How can expressed statements like this, in this way.

Now, here's another students who make another statement.

Can you express this on the function machine and write the matching calculation? Pause the video here and give that a go.

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

Well, what's the first thing that she does, well the first thing is she adds two.

Then after adding two, she squares, how's the thing she says, "Then I square the answers." So I'm going to put brackets to represent squaring, and then subtract one.

So she then takes away one and then finally divide by two.

And I'm going to put this here, finally divide by two.

And what calculation would that give us? Well, we have X and two.

Well, all of that is squared.

And then she took away one and then all of that, if you look was divided by two.

Now look what happened.

I had to use an extra set of brackets otherwise I would had to do my division before my subtraction.

Now here's an independent task for you to try.

Which of these calculations match Atoni's statement? For those that don't, write a correct matching statement.

Pause the video here and give that a go.

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

Well, Antoni thinks of a number and then subtracts five.

So looking for some by say X takeaway five first, well we have X takeaway five there, there, there and we have it there as well.

And we have it there, we have it in all of them so we can't really differentiate them.

And multiply the answer by six.

Well, that's good multiply by six.

Well, that doesn't have multiply by six so that can't be true.

Okay, this has multiply by six, okay? Well this, this has multiply by six, oh this has multiplied by six and also, so does this.

Then it says next I add five.

Well, this has add five, I've already.

This one has add five, but it wouldn't happen next 'cause the division will happen before the addition there so no.

This has add five.

This one is dividing by six then adding five so that can't be the case.

And the final thing is that I divide by six.

So what you're left with is this.

Those are your three correct statements and your three incorrect statements.

What you could have written for the incorrect statements is as follows.

So listen very carefully.

So we'll look at best one first.

I think of a number, I subtract five, I then multiply by 11 'cause six add five gives 11 and then I divide by six.

So that could be the statement for that income, that statement there.

What about this one? Well, it's same thing, I think of a number I take away five, I then multiply it by six and add five divided by six, now this was a more complicated one for you to have done.

So I will write this one on for you.

So this is one statement you could have written for that.

I think of a number, I subtract five, I and multiply by six, I then divide five by six and then add that to my answer.

And then for this last one, you could have said, I think of a number, I take away five and then multiply by six and then divide by six, and finally I add five.

Well, if you multiply by six and then divide by six, all that cancels out, 'cause multiplying by six and then dividing by six takes you back.

So it's just, I think of a number, I take away five and then I add five.

Well, if you take away a five and then add five, that just takes you back to your number.

So really that last statement could just be written as, I think of a number.

Okay, now for this explore task, write matching think of a number of statements for each of these calculations.

Pause the video here and give this a go.

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

Well, you could have come up with this.

The first one is think of a number, multiply by seven and then add two.

And the second one is thinking of a number, subtract two, 'cause if you look you subtract two first and then multiply by seven.

This is think of number, add seven and then multiply by two.

This one is, think of a number multiply by two, then subtract seven.

This is think for number, multiply by two and then add seven.

This is think of a number, add two and then multiply by seven.

Now really well done for getting through this lesson.

And if you've got any of those answers, you have made some great progress.

Now this here is the last lesson of this unit and I know that you've learned a lot.

And if you want to share any of your work, ask your parent or carer to share work on twitter tagging @OakNationl and #LearnwithOak Thank you again for participating.

I will definitely see you again next time.

Bye for now.