Lesson video

Hello, my name is Mrs. Buckmire and today, I'll be teaching you about order and absolute value.

Now, first make sure you've got a pen and paper.

Pause if you need to go get them.

Okay remember, you can pause the video whenever you like.

So if you need more time to do something, then do pause.

I will tell you to pause at times when I want you to try and have a go at something and do have a go is all for your learning.

And if you ever need to rewind it as well, feel free to do that, sometimes it's helpful to hear something again.

Okay, let's begin.

So, for your try this there's a number lines here.

I want you to tell me which one could accurately plot to the following groups of numbers.

So here some groups.

I need to choose, for example number one, negative 20, 120, 180 which number line from A, B and C, can you use to accurately plot it? Okay, there might be more than one answer for some of them, they might not be answers for some of them.

Think carefully, pause the video and have a go now.

Okay, so let's see what we can get.

so which number line could be used to accurately plot it now it starts a negative 20, now they all have negative 20 that's fine but then it goes up to 120.

Now the only one that goes up to 120 is C so one matches to C.

Okay, what about two? So the two negative eight can be plotted here, negative four and 10 can be put accurately halfway between eight and 12.

Now here, it would be hard to put new to very accurately because we've got between negative 10 and five here but then we actually don't know exactly where it would be negative eight so it would be this read between negative 10, negative five and similar here it's really hard for the last one so that's why thought question two it would just be A.

Three negative 15, 10 and 20 it would be B.

But four, four is actually none of them in case it doesn't match to A, B and C or C sorry.

And finally for five, well, that's actually all of them so you can plot exactly negative 20, negative 10 is halfway between negative eight and negative 12, 10 up here and 20 and similar here.

So negative 10, negative 20, 10, 20 and here is negative 10 halfway between zero and negative 20, negative 20 is here, 10 and 20.

So this one was A, B and C.

Well done if you've got those right.

Okay, so for the connect.

The thing you'll learn about today is absolute value.

Now the absolute value of a number is it's distance from zero.

So here Yasmin says the absolute value of negative four is four.

As we can see the distance from zero to negative four is four, so that's why it's the absolute values.

So my questions to you, how many numbers can you find that have an absolute value of three? Find two numbers that have the same absolute value where the distance between them is 11 and is the absolute value of a number always positive? Pause the video and have a think of these questions now.

Okay, so for the first one how many numbers can you find with absolute value of three? So while I can definitely see that three is three away from zero.

So three is one of them and then also negative three.

So you're just like negative four and absolute value of four, negative three is one, two, three away from zero.

So, negative three also I can find two numbers that have an absolute value of three.

Now let us find two numbers that have the same absolute value where the distance between them is 11.

So if they have the same absolute value they're going to be the same distance from zero and at this, between the 11.

So zero must be halfway between them.

Hmm, half of 11 or half of 10 is five and half of one is 0.

5, ah, so it's 5.

5.

So it will come up to here like there so 5.

5 this being 5.

5 and negative 5.

5 around here.

Could then both of them have a distance of 5.

5 away from the origin and 5.

5 plus 5.

5 equals 11.

So well done if you've got that.

And find is the absolute value of a number always positive? Well, it is positive for negative four 'cause she hasn't told us it was four.

We saw for negative three it has an opposite value of three.

So same that will negative numbers have absolute values that are positive and or positive values.

Well, their absolute value will be positive cause their positive distance from zero.

So is it true? Wait, what about zero? What's the absolute value of zero? It would be zero 'cause zero is distance of zero away from zero.

So if zero is an absolute value, then actually no an absolute value of a number is not always positive 'cause zero isn't positive or negative.

So no, because of zero.

So the absolute value of zero is zero and zero is not positive or negative, so not all absolute values are positive.

Okay, so Yasmin says the absolute value of negative four is greater than the absolute value of three.

Anthony says three is greater than negative four because three is to the right of negative four on the number line.

Hmm, do you agree with either of their comments? Pause the video and maybe write down your thoughts? Yeah, make sure it did have a little think.

So with Yasmin, do we agree or not? The absolute value of negative four is greater than the obviously valuable three.

So there's a nice little diagram here.

So think that this is going to be zero here, so that means that makes this negative four and makes this three.

What's absolute value again? Tell me? Yes it's the distance from zero.

So the absolute value of negative four is kind of shown in this diagram, and the absolute value is four.

The absolute value of three is three.

So the absolute value of negative four is greater than the absolute value of three.

So yes we agree, we agreed with Yasmin.

Hmm, three is greater than negative four 'cause three is to the right of negative four on the number line.

What do you think? Yes, it is true.

So the further we go towards the right the bigger the numbers get, okay? So four is bigger than three, five is bigger than three.

Here negative one is bigger than negative four, negative two is bigger than negative four so actually yeah, the further to the right we get on the number line then the bigger the numbers get.

So because three is for right or negative four on the number line three is greater than negative one.

Remember this means greater design.

So some people like to think of it as a crocodile eating some people like to draw in and see actually you can draw in more bricks here then you can do here so that why this side is great than whatever works for you.

Well done if you agreed with both of them because it's true that they are both correct.

Okay, really quick check.

Say the absolute value out loud so I can hear it.

So I'll give you the number negative three.

What's the absolute value? Good, is three.

What about 4.

2 or decimal we haven't had those.

What's the absolute value? Good it's four point two from zero is two.

What about zero? you've had this, the absolute value? Zero.

What about negative half? What's the absolute value? Distance from zero? Well done it is one half.

[Mrs. Buckmire] Okay, you are then easily ready for the independent tasks, okay? So there are four questions, four confidence that you can do this.

I think one and two you'll do pretty quick.

Hopefully, question four is a little bit more thinking, okay? So do pause the video and have a go now? Okay then, so let's go through it.

So all the possible values and numbers even with an absolute value of seven? well we have seven and negative seven they both have a distance of seven from zero.

Here are the next answers.

Okay do you pause if you want to check those carefully if you weren't sure.

So for question two, for each of the following add the correct symbols: So greater than symbol or less than symbol.

So for seven and five, seven is greater than five, negative seven is less than five, negative seven is less than negative five seven is greater than negative five, negative two is less than zero and negative eight is greater than negative nine.

Well done if you got those correct.

Okay, for each of the pair of numbers in question two, certain number, the largest absolute value.

So this is no longer about which one's big or small it's by the absolute value being bigger or smaller.

So here seven has an absolute value greater than five here although negative seven is less than five, negative seven has a greater absolute value than five.

Negative seven also has a greater absolute value than negative five.

Seven has a greater absolute value than negative five.

Negative two has a greater absolute value than zero and negative nine has a greater absolute value than negative eight.

Well done if you got this right.

Four, find two numbers that have the same absolute value where the distance between them is four.

So that's similar to the question I went through about 11.

So we want zero to be halfway, so it's going to be negative two and two they're both have absolute value of two and the distance between them is four.

The next one is negative 2.

5 and 2.

5 so they both have an absolute value of 2.

5 and there's a distance of five between them.

Oh, this one was tricky, find two numbers where the absolute value of one is double the absolute value of the other and the distance between them is six.

You know what I did I just had a go I just had a guess like, oh if I had one and then negative two, then yes one absolute value is double the other one but then actually the distance between them wasn't six.

And then eventually I got two negative two and four.

So the absolute value of negative two is what? Good, is two.

And then the absolute value of four is four, so four is double two and then the distance between them is six.

Well done if you got that right.

You got another wrong answer? Yes you could also have negative four and two.

So double two gets us to four and the absolute value of negative four is four.

So yes, one does have the double of the other and the distance between the six, there were two answers.

Well done if you spotted that.

Okay, so for our explore task we're going to be using this grid.

I can see on this grid as we go down it the value decreases, as you go right the value increases again so what I want you to do is place four of the nine introduced in the two by two grid and see how many solutions can you find.

So like, don't have loads of different copies how many divisions can you find? And then see, can you find a solution for a three by three grid? So this is a two by two grid can do a three by three.

Okay, I think you should have a go at this if you need support, there'd be some coming up but do have a little go first.

Okay, I'm hoping you've already had a go okay but if not I'm going to give you a little start.

If you got into trouble and was not sure you could put negative six here and then you want a here an absolute value bigger than negative six here and a value smaller than negative six and in here and absolute value great than the one to the left.

And maybe here you could put like the number three and then think through the similar problems. Okay, so there's a start I think you can have a good got it.

Okay, so I started here on negative six, so value decreases so it could be like negative eight and then you want the absolute value to increase.

So the absolute value of negative six is six.

So an absolute value increase could be negative seven 'cause negative seven is further away from zero.

The negative six and absolute value increase on from negative eight could be negative nine and that works out.

So the value decreases going down and the absolute value increases going from left to right.

And what was this one? I start three so absolute value increases could be like four and then the value decreasing say three is a lot bigger than like minus two and the absolute value increasing could be like negative five, okay? You could have actually just shows in four numbers and thought about how to fit them in that's another method.

So three by three, I got looking like that so you could have lots of different answers these are not the only solutions, okay? Just check yours really carefully thinking carefully about the absolute values.

Well done today, everyone.

So if you had to go for try this, the independent tasks and understood the connect really, really good job it was all about having a go.

I hope in the explore tasks, you had fun finding lots of different arrangements from those boxes and I really would recommend doing the exit quiz because then you can see, oh how much do you really understand about absolute values? Wait, what is an absolute value? Good, is the distance from zero? I'll see you next lesson.

Remember that for next lesson? Bye.