Lesson video

Hello, my name is Mrs. Buckmire.

Today I'm going to be teaching you about subtracting negative numbers.

Make sure you have a pen and paper.

Remember to pause whenever I asked you and do have a go at the questions and pause whenever you need to and rewind as well.

So if you need to hear something again rewind it, sometimes that's super helpful in just helping you understand it.

Okay, let's begin.

So if I try this.

I want to know how many ways can you put the integers into the inequality to make it true? Now have a look at this.

If you're not sure, then I will show you hint.

But see if you can work it out first.

Okay.

So if you're not really sure what I would do is actually just have a go.

So just choose some random numbers that matters.

might choose negative three plus negative one.

What do I get? Negative three plus negative one, is going to be negative four.

And then the other number is negative five plus negative eight.

Negative five plus negative eight gets me to negative 30.

So which one's bigger? Negative four? negative 13? Good, negative four is actually bigger.

So that means my negative three and negative one go on this side and my negative five and negative eight go on this side.

So just choose two of a different pairs of numbers and have a go.

Okay.

So there's the first one I got.

Here's another one.

And this one, did you get the same? slightly different? Do you remember of all about commutativity? Good, it means that the order in addition doesn't matter.

So where've you got negative three plus negative one, or instead you swap them around and did negative one plus negative three.

It's the same answer.

It's the same here.

These can be swapped around and you're getting the same results.

So do you pause the video and check your answers carefully.

Okay.

I'm using GeoGabra here is a mathematics mastery App.

And I've got a number line and we can see two here, the arrow and the negative two.

What calculation do you think this is? Okay.

So did you give me a subtraction? So a subtraction, is going to be two take away four equals negative two.

Did anyone give it to me as an addition? What would it be as an addition? Good, it'll be two plus negative four equals negative two.

Because we know that actually, subtraction is the same as the addition of the additive inverse and additive inverse four is negative four.

Now this bar here, this is actually going to change my 'b' value and I can make it smaller.

So when I make it smaller, what do you thinks going to happen? Excellent.

So my actual number gets bigger because I'm taken away less.

So I'm taking my four.

If I'm taking away three, we get to negative one.

If I'm taking away two, Oh, we get to zero.

Why is that? Yes, because two and negative two are additive inverses.

And what are additive inverses? What's the definition? Good.

It means that they sum to zero.

So actually here, I end up back at zero.

Let's keep going.

Okay.

So when I do two take away zero equals two and two plus two equals two because the additive is zero, is zero.

Now, what do you think is going to happen when I make it even more negative.

So 'b' is about to become negative one.

What do you predict will happen? Hmm let's see if you're right? Way, so beforehand, my arrow was going negative and it was in red, but actually now when I get to negative one, it becomes a positive.

So two subtract a negative one actually equals three.

Cause we know that subtraction is the same as the addition of the additive inverse.

So we ended up adding the additive inverse in negative one, which is positive one, so we ended up with two plus one equals three.

So when I do 'b' as negative two, if I do two takeaway negative two, what's that going to equal? Yes.

Four add one more? Good.

Five There's five.

And we have six.

Okay.

Let's explore this a bit further.

Okay.

So I said it many times, subtraction is equivalent to the addition of the additive inverse.

Repeat that.

Subtraction is equivalent to the addiction of the additive inverse.

Good.

Okay.

So do say it out loud.

Subtraction is equivalent to the addition of the additive inverse, cause that's going to be really helpful to understand that.

So just the key words there, additive inverse, What was that again? Yes.

It's when two numbers sum to make zero.

So here, Jacky said, I use this calculation to calculate an addition.

This person, Jasmine, I used this diagram to calculate a subtraction.

Hmm could both the students be correct? What calculations could they have been working out? Pause the video and have a think.

Okay.

So maybe, Jacky, did negative 12 plus 14 equals to two.

That would work starting at negative 12, translated 14 spaces to the right.

We get to two.

What could Jasmine, what did you write the Jasmine? Yeah, it could be negative 12, take away negative 14 equals to two.

All right, so both of them could correspond to that diagram.

So through independent tasks, I want you to think and write down two calculations.

One of addition and one subtraction for each of the number lines.

For question two, you do not need to calculate the value.

You need to identify the equal pairs of calculations.

And finally for question three.

I do want you to calculate subtractions, but the numbers are quite similar, so hopefully we get used to working with them.

Okay.

Do pause the video now and have a go.

Okay.

So with this first one, we're starting at two and we're increasing by 10 to 12.

So we can write two plus 10 equals 12 or so we can do as a subtraction.

So two take away the additive inverse of 10, which is negative 10 equals to 12.

So these are equivalent calculation.

Both can be represented by this number line.

So for this next one you could have started at negative three, three plus three, to get to zero, or you could have negative three, What did you get? Good.

Takeaway, negative three equals to zero.

So three, is the additive inverse of negative three.

And you know that because negative three plus three equals to zero.

So for this next one you actually had to work out, did you notice that? See nothing was on the arrow? So hopefully you've figured out, that you had to work it out yourself.

So while we're figuring it out.

Let's write on negative four to get to four.

Well it's going to go past zero and four more.

So it's going to be plus eight.

So when we do, we're going to have negative four plus eight, or, yeah, negative four takeaway negative eight.

And finally, again, we need to write it on and it doesn't go past zero.

So how many steps do we need towards the right to get to negative three? Excellent! Did you get plus six? Good.

So it's negative nine plus six equals negative three or negative six takeaway negative six equals negative three.

Well done if you've got those.

Okay so for question two, I didn't want you to work it out, I want you to kind of use your reasoning instead.

It's fine if you did work it out.

I'm sure you've got the correct answers.

So seven subtract negative six is the same as seven plus the additive inverse in negative six, which is positive six.

So 'a' and 'H' match up.

Okay.

So negative six takeaway negative seven, do you see there are two takeaways there.

Often they're off brackets, but not always.

So that's the same as adding the additive inverse of negative seven, which is plus six.

So 'B' and 'F' match up.

Okay.

So see negative six takeaway negative six, so that's the same as adding the additive inverse in negative six, which is six.

So what was it? Good.

'C' and 'E' were definitely ones you might've got.

Did you notice something else? Good, 'E' and 'D'.

are commutative.

So actually, the negative six and the six have just been swapped around.

And so they are actually also equal.

So all three of them were equal.

So 'C', 'E' and 'D' were equal.

If you worked them out, you would have got, Oh, all of them equal to zero, but if you use reasoning skills really well done, that's good mathematical sense there.

So actually 'G' is an odd one out.

Aww.

Nothing much to it.

Sad times.

Okay.

So for these ones, the answer.

So 90 takeaway negative 100, you get to 90 plus 100, which equals 190.

90 takeaway 100 , where do you get? Excellent, negative 10.

The next one is equivalent to negative 90 plus 100, we get to the positive 10 and 'D' is negative 90 takeaway 100, So its 100, negative 190.

Check those negatives really carefully.

Here are the next set of answers.

Do check them carefully.

Maybe you notice what was the same and different between different questions that might have helped you.

Well done.

Okay.

So for your explore was the same and what's different about each of these calculations.

Okay.

So write some notes on that.

Then, I want you to tell me which of these number lines could be used to represent them.

If you want a fair of a challenge, you can maybe think about the ones that aren't represented.

Actually what subtractions or additions could you use to represent those number lines.

Okay.

I think with all the practise you've had, you can have a good go at this.

So do pause and spend some time thinking about these problems. Okay.

So what's the same and what's different.

Well, maybe you said they all have a seven in them and they all have a 12 in them.

True.

Do they all have a negative seven? Hmm.

I would call this negative seven, this negative seven, this negative seven.

I would actually to call this subtract to seven.

So I wouldn't call it negative seven.

Depends how you talk, how you say it.

And there's plus in this one and this one and there's subtraction in the other two.

Maybe you did some working out.

So which of these number lines were used to represent them? So for the first, one number line, I got, it could be negative seven plus 12.

Cause what we can see is they're actually working out negative seven, they're getting seven to zero and then number five, to make the whole thing plus 12.

So it's negative seven plus 12.

Or it could be negative seven subtract negative 12, because that's the additive inverse negative 12 and 12 or whichever.

And so these are equivalent.

And so you could think of it like that as well.

For this next one, I thought maybe you would have matched 12 plus negative seven.

So actually, adding the negative 7 so again opposite direction which translate into the left.

And we end up with five.

Or maybe 12 takeaway seven.

So these are equivalent because seven is the additive inverse of negative seven.

Okay.

Did you match any other ones? Maybe you created some examples for the last two number lines.

Excellent.

Wonderful if you did.

Okay.

Fantastic work today.

That's all our learning, but you would be fantastic if you did the exit quiz.

Okay.

Just quickly.

What is an additive inverse? Good.

It was when the two numbers sum two equals zero.

And so what did you learn today? What was important? Excellent, write that down? Because I really want you to remember that, whatever you just said about subtraction, checking your notes and write it down.

Maybe put a highlight around it.

Okay.

Off you go to the exit quiz.

Have a lovely day.

Bye.