Lesson video

Hello, my name is Mrs. Buchmire and today we're going to be learning about subtracting positive numbers.

But first make sure you have a pen and paper, it's really important you take notes.

And when I pause, when I ask you to pause you do pause the video and write something down and have a go.

Remember you can pause whenever you like, this is all about your learning so go at your own pace.

If you need to rewind the video, feel free to do that, it's all about your learning.

Okay, let's begin.

So for the try this, I want you to select two of the integers and calculate their sum.

So the integers are there on the side, you can see them and I want you to input them into the sum and work out what would the total be? I want you to think, can you find a zero pair? What is the greatest or least sum you can find? And what other numbers can you make? Okay, so let me know, pause the video and do have a go, write down your answers.

Okay, so can you find a zero pair? So, there were lots there.

So we had eight plus negative eight equals zero, seven plus negative six, six plus negative six, five plus negative five, three plus negative three and two plus negative two.

So hopefully you've got a few of those, if not all of them.

Well done, if you did.

What was the greatest sum? Yeah, you get the greatest, the largest by adding the two largest numbers together.

So you get 15, eight plus seven.

And the least? Good by adding the two smallest numbers together.

You get negative 15.

So what other numbers can you make? Did you have a go? Correct, you can make all the integers from negative 15 to 15.

Okay, so the new learning.

What I really want you to know today is that subtraction is the equivalent to the addition of the additive inverse.

Now, if you've done a lesson before with me maybe you know what additive inverse is, if not, can you tell everyone else? What is additive inverse? Good, is when two numbers that add together to equal zero.

So those zero pairs, they were additive inverses of each other.

So negative eight and eight are additive inverses of each other.

So here Carla says, "I drew this diagram to calculate "nine takeaway five and it equals four." And Zacky says, "I drew this diagram to calculate "nine plus negative five equals four." Okay, let's have a little look.

So with Carla, nine takeaway five so, going back with five, translating five spaces to the left and we get to four.

Yeah, that's correct.

And for Zacky? Nine plus negative five, so nine.

And then the translation is going to be negative five so, you're plussing it but it's in the negative direction so, it's plus negative five, it still equals four, good.

So one, Carla has done a subtraction and Zacky has an addition but both make the same answer.

And you see so, the reason why the subtraction is equal to the addition of the additive inverse is because five is the additive inverse of negative five.

So nine takeaway five is the same as nine plus negative five.

Okay, feel free to pause the video and write that down.

We're going to have plenty of practise.

Okay, so write two calculating that could each of these number lines been used to work out? So two calculations that these number lines could be used to work them out, okay? Pause the video and have a go.

This is your time to practise.

Okay, so for the first one, so nine takeaway three equal, nine takeaway 23 equals negative 14, okay? So that missing number there, let's write in actually instead.

Here, was negative 14.

So what else they could've got? So the addition of this, if it was written as a sum would be nine plus negative 23 'cause 23 is the additive inverse of negative 23.

They're all score zero pairs so, I say additive inverse but also you can use zero pairs, we use them both.

Okay, so what about this one? What did you get as the missing number? Negative 32 take away 99, good is going to be negative 131.

So we can write it as negative 32, take away at 99 or tell me? Good, negative 32 plus negative 99.

So 99 and negative 99 are a zero pair.

Well done, if you got those.

Okay, so for your independent task, there's quite a few questions but the main thing is for question two, you do not have to actually work out the values, just try and identify equal pairs of calculations.

So you don't need to work them out.

But for three, I would like you to work it out.

And for four, I would like a sketch.

Pause the video and have a go.

Okay, so for each of the number line, write down two calculations, an addition and a subtraction.

So this is what we just practised for beforehand, so hopefully it was okay.

So this first one could be 15 takeaway three equals 12 or 15 plus negative three equals to 12.

And so what are the zero pairs? Yeah, three and negative three.

Here, we could have four plus negative four equals zero or four takeaway four equals zero.

The zero pairs? Tell me? Yes, negative four and four.

And then we have these answers for the last two, check them carefully.

Okay, this next one now, I'm not actually going to work it out instead I'm just going to try my best to identify equal pairs.

So for 12 plus negative five, so for a is going to pair up with, now, what's the additive inverse of negative five? Yes, five.

So it's going to be 12 takeaway five, which one's that? Good, h.

So a and a match up.

So next one, five takeaway 12, so what is the additive inverse of 12? Yes, negative 12.

So, it's going to be five plus negative 12.

So b and g.

Okay, what about c? Negative five takeaway 12.

So what is the additive inverse of 12? Good, negative 12.

So it's going to be negative five plus negative 12.

So c and f match up.

And finally five plus negative five, the additive inverse of negative five is five so, is equal to five takeaway five.

And we actually know that both of them equal to zero because they are a zero pair, but d and e match up as well.

Okay, so 20 takeaway 14, you going to be six, 14 takeaway 20 then? Good, it's negative six.

So when we take away 20 from 14 we go past the zero and into our negatives.

15 takeaway 30? Again we go and 30 left or past the zero and to negative 15.

And 30 takeaway 15? Excellent, it's 15.

Here are the answers for the next ones, check them very carefully, especially your signs.

Okay, pause if you need more time but I'm going to go on to the next question.

So drawing a sketch of a number line.

So first six plus 12.

so I'm starting at six, that's meant to be a straight line, and I'm increasing by 12 so, I'm going 12 spaces to the right to translate the point to here, which is 18.

Okay, and negative six takeaway 12.

So I start at negative six, I'm going 12 to the left.

So I end up at negative 18.

This is equivalent to doing negative six plus negative 12.

And this one is equivalent to doing six takeaway negative 12.

Well done, if I've got those right.

Okay, so for our explore, I want you to consider each of the following statements.

Decide for each one if it is always, sometimes or never true.

So it's for x is a positive number.

So you might like to just look carefully at them and reason about it.

You might like to substitute values in but do come up with some kind of reason as in to why you think whatever answer you think, okay? Have a go and if you need some more support, come back and listen for a bit longer.

Okay so, now if you want to try a substitution method, I would normally try numbers that are in and around kind of a given value.

So here I would try a number that's a bit more than two.

So I try three, and then I would try two, I'd maybe try one, zero and negative one.

Now always like to have some positive and some negatives when I like, I'm looking and trying to understand something better.

And also zero is such a key number so it's really helpful sometimes you use the number zero.

So you can substitute these and you might not have to substitute them all in.

You might have to just substitute one and proves that something's not possible as in, sometimes it isn't possible and then you substitute something else and it is possible and then that tells you oh, sometimes it's true.

And if you think it's always true, try and reason, think about why.

Maybe even some of the key words that you've learned today.

Pause the video and have another go.

Okay so, x takeaway two is greater than zero is sometimes true.

So if you were trying it out, then when x is less than two, so let's say you tried out one, well, one takeaway two equals to negative one which is not greater, this is great if that's the sign for like not and put a line through it.

So it's not greater than zero so therefore it's not true.

And here it's saying when x is less than two, so for all values when x is less than two then actually x takeaway two is less than zero.

So whenever x is less than two, x takeaway two is a negative number so therefore it's not true.

What about when x equals two? When x equals two, well actually equals to zero.

So again, is not greater than, is actually equal to zero so therefore it doesn't work again.

So, it doesn't work, does it ever work? Yeah, if you try, let's say three.

So when x equals to three which is greater than two, three takeaway two equals to one and one is greater than zero, so is true and actually it's always the case when x is greater than two.

x takeaway two is greater than zero, so is true.

So that's why it's sometimes.

Okay, x plus negative two equals to x takeaway two, this is always true.

Could you explain why? Okay, so it's because negative two is the additive inverse of two.

So we know that subtraction is the addition of the additive inverse.

So the subtraction x minus two is the addition of the additive inverse, which is x plus negative two.

So therefore it is always true.

Okay, for negative two take away x is greater than negative two plus x.

Now this is actually never true.

And the reason is because if we start with like negative two and then we take away x, well, this is the same as negative two takeaway x.

And then, it's for the right hand side, if we think about just two plus x verses more of a negative, so we're going plus two and then plus x, well the negative is going to be the opposite direction.

So it's going to be takeaway the negative of two plus x.

And we can actually see that this negative or brackets two plus x is the same as minus two takeaway x.

So actually the exact same thing so they're not greater than or less than, they actually equal to each other.

The next one I want you to talk about this word commutative.

So maybe you've heard it before, if you have what do you think it means? Okay so, basically for addition is commutative because the order does not matter.

So what that means is for negative x plus two, we could go negative x first so translating starting at this point and then go negative x.

And then we would plus two so from this point we're now going plus two.

So all together from our start to finish, we've gone negative x plus two.

Or we could actually do the plus two first.

So, at first we could go plus two, then we can takeaway x, and then the difference would be two plus negative x.

So two plus negative x is the same as negative x plus two because it's commutative.

And for my lesson today, we actually know that two plus negative x, I'll write it here.

So we just showed that negative x plus two equals two plus negative x.

And then we know that because the additive inverse of negative x is x, we can actually do that's equal to two takeaway x.

So yes, it is always true.

Right, really, really well done today everyone.

I hope you enjoyed the lesson.

Hopefully you now understand how you can use additive inverse with subtraction as well.

Do do the quiz, is super useful to check your understanding, for you to show off what you know and get some feedback as well.

Have a lovely day, bye.