﻿Hello! My name is Mrs. Buckmire and today I'm going to be teaching you about - numbers in context. Now, you need to have your brain ready, you need to have a pen, you need to have paper and just needs to be up for learning. So make sure you've got those things, pause if you don't and we will soon begin. Ah! But not before I tell you to remember to pause the video whenever you need to. Because it's just about helping yourself learn. So if you need that extra time you take it and also rewind if you need to hear something again. Let's go. So for "Try this." Now you can see it's kind of like a building here. It could be kind of a hotel maybe, and you need to go down one floor to go from the second floor to the first floor. Yeah, that's true. What other journeys can you describe? How might you number the red and orange floor? So here is, this is the red floor. And this is the orange floor. And I want to know how might you number those. How might you number the floors on a different building? So if you had to create your own big hotel, how would you number the floors? Pause the video and have a think about those questions. Okay, so what other journeys can you describe? Oh, there are so many, I'm going to tell you some out loud. So you can go down one floor to go from the first floor to the 0th floor. You could go up one floor to go from the first floor to the second floor. You could go up two floors to go from the 0th floor to the second floor. Lots of different ways. So how might you number the red and orange ones? Well, it seems like all the floors are numbered using integers. And these are all integers here. And the ones on the right are positive integers as shown and one on the left are negative integers. And so I think after 0, I might put, for example, this one being the -1 for this floor. Let's do it in black actually so you can see it. And maybe this one -2, as the floor since they're below the ground. okay? How might you number the floors on a different building? Maybe you're a fan of prime numbers. So actually you might have your, the floor you come in on reception, being maybe the second floor, number two, floor two, and maybe the next one is floor three and the next one is floor five, the next floor seven. Maybe you like, multiples of 10. And you go, oh, 10 20 30. You know, you can really number them by names maybe. Lots of different ways. Maybe you want to be creative. What's worth noticing is here, is the positive numbers go from 1 onwards and the negative numbers go from -1 onwards. So 0, is not negative or positive. Interesting. Okay, so here the sea level is being used as a point of reference and that's really important. So in our first question, we had kind of a reception level at 0 for the point of reference, and then you'll be going one up from the zeroth floor or two up from a zeroth floor or one down or two down. And that was our point of reference. And here, the sea level is point of reference. So, if I just show you here, that is the point of reference, the sea level here. And so, we're told the lake is +200 metres. So yes, because we can see, if this is the sea level, it's 200 metres higher where the lake is. And what about the sea bed? So sea bed is down here, so it's 150 metres below the sea level. So the sea is 150 metres deep here, and so is -150 metres is the elevation of it. So what would the elevation of A be? Using the sea level as a point of reference. Good! it would be +250 metres. What about B? Yeah. +400 metres above sea level? C? Can you find it? Yeah down here. Good! C is -50 metres. And D? Excellent! is -100 metres compared to the sea level. Okay, so I want you to apply this to our independent task. So looking at the thermometer, can you find the missing temperatures and then work out the other information. Using the thermometer will help you, so do pause and maybe look at the worksheet to help you out. Okay, so let's quickly go through this. So A, is between 30 and 40. So it's going to be 35 degrees. B, so it's halfway between 0 and -20, so it's going to be -10 degrees. C. Good, what did you get? Yes, Yes! So it's halfway between -30 and -40. So it should be -35 degrees. I'm going to write this actually ,

35 degrees. And D? 10 Lower than -40. Yes! -50 degrees. Okay, so what temperature is 35 degrees warmer than -15? So -15 is here, so 35 warmer? Well, there's five warmer and then 30 warmer , 10 20 30. So it's going to be 20 degrees. What temperatures 35 degrees colder than -15? So, let's start at -15 again, so that here. Let's actually rub everything else out so you can just see what I'm saying. So - 15 is here, 35 degrees cold, is that's five colder, and then 10 more colder, 10 more colder. 10 more colder it ends up here at D. So that's -50 degrees. Okay, describe a temperature change from C to A? so to get from C to A, so it would be from -35 to 35 or -35 and we could come up in fives, and if you did that you'd get to +70 degrees 'cause it's same degrees warmer. A to C? Oh, that's the opposite. So be -70 degrees or 70 degrees colder. D to C? So to D to C is up 10, 15 degrees. So + 15 degrees. C to B? Again it's getting higher then, so five, 10 25 degrees. +25 degrees. And D to B. final one, what did you get? D to B? 10, 20, 30. Was it +40 degrees? Well done if you got those. Okay, for our explore tasks, we're looking at a robot. Now this robot can be programmed to move east and west. I've shown you a little diagram there which way east is and which way west is. Now, he's starting here at 0. You can see him looking around. Wants instructions, we have to tell him where to go. So A, if you programme A it means, the robot moves east five spaces. So moves five spaces left, that actually is east. And if you programme B, the robot moves the west three spaces, so three spaces in that direction. For example, if they're moving A B B, they would move five east, then they would move three west, then they'd move another three west, then they'd move another five east. So if I show you that movement, it would be five east. So one, two, three, four, five then three west one, two, three, then number three west one, two, three, and then five east, one, two, three, four, five. So it ends up at four. Use a combination of A's and B's to send the robot from 0 to the following numbers. So you always start at 0, so always start each question at 0. And then I want you to get to +2,

6

1 +7 +6. Now if you feel already confident with this, for challenge, can you find an integer that the robot can't reach? Okay, so you can pause the video now and have it go. Otherwise, I'm going to give you a little bit more support in the next slide. Okay, suppose the point, I'm just going to show you for +2. Really, you just want to kind of just have a go with it. So I would say move five east. So one, two, three, four, five. I end up at five. So that's the first bit. It's A. And then move on west three. Okay, so west 3, one, two, three. Oh! I end up at two. So A B is +2. And really, if you just have a go at it, like try A B B, try B A A, try B B B. Like just try things out. And I'm pretty sure we could have a go. Maybe you'll start, maybe even form a strategy to get to those other numbers. Okay, is all about having a go. I believe in you. Okay. Pause the video and just try it out. Okay, so how was that? Yeah, let's see. So, I want to first say order does not matter. Okay? So here, there are multiple solutions. If I say A B and you say B A, they're both the same and the equivalent to the same thing here, and they're both correct. So that's fine in this case. So +2 is what I showed you A B, you might have got B A, fine.

6 is B B going to west, and three times and then another west three times.

1 is A B B. +7 gets A A B. And +6 gets A A A and B B B. Okay, check those carefully, check you've got the same even if it's in a different order. Did you even think about why is it the same? Why does the order not matter? That's for you to think about. The challenge: Can you find an integer that the robot can't reach? Did you find any? No? Okay, can you prove why you can't find any? Right, let's get into it. So you can reach every single integer. Okay, I am about to prove to you why? and I love proofs in maths. And this is called like an exhaustive proof. So I'm going to show you every single option and so, yes it's always possible. So firstly, for negative integers, now you have already been a star and worked out -1. Now, if you did A B B, and then A B B again, you'd get to -2. If you did it three times, you get to -3. And you could keep doing that to get all of the possible negatives that ever exist. Okay, if you don't believe me try it. But it takes too long, so just just believe me, or maybe try a few examples to convince yourself okay, but it is true, so you can always keep repeating that A B B to get to all the negative integers. So about the positives, can you think of a way to get to one and then maybe you can keep repeating it? Maybe pause and have a go. Okay, so for positive integers, you can do A A B. So A A will get to five and five again we'll get to 10. And then B B B. So back B will get to seven and then back three more. So wait, so we've go to 10, which will be somewhere over here, and I would recommend maybe drawing it out. And then we get one of B gets you to seven, another B gets you to four, and another B, this gets you to one. And then you just keep repeating it, so you get A A, B B B, A A B B B. And actually, computers are so cool, you can actually group kind of the instructions together and just repeat those, so we didn't have to keep typing in the same thing. Okay. That would be great. So have you got all of them? Ah! What about 0? 0 is an integer but we haven't found a way to get to 0. He is already at 0 but let's say we wanted him to move. How could we use A and B to get it to back to 0? You got it? Yeah? something about multiples? Yeah, So we could have three lots of A and five lots of B. 'Cause 3*5 is 15 and 5*3 is 15. So let me just show you, so you could go through lots of A to get to 15, and then want to go back the other way, So we need to use B, and do it five times and we get back to 0. Try it out if you're not sure. Like extend the number line as you draw it out to help yourself. I hope you're convinced. So we've shown for negative numbers we have some instructions we can use, for positive numbers we have some instruction we can use. And we got 0. So yes, the robot can reach every integer so you could not find an integer that robot can't reach. Ah! Mrs. Buckmire I was trying so hard. Just got to keep thinking. Really, really well done today guys. If you had a go at the try this, if you had a good guy the connects questions, the independent task and explore task, even if you didn't get anything right, maths all about having to go and then you actually learn really well from your mistakes. Okay, So as long as you listen to the feedback, you will keep improving. Now I would love you do the exit quiz 'cause this is where you can really test yourself and see, oh! did I understand everything? And there's some feedback in there as well to help you for anything you've gotten wrong in there as well. Have a lovely day. Bye!

Which answer best completed the missing gaps?          The	whole numbers on the number line are called ________. _____ is an	example of a positive integer,	______ is an example of a negative integer.

Tick ALL of the numbers below that are integers.

What is the missing temperature A?

What are the missing temperatures B, C and D?

What is the temperature 10 degrees warmer than -30 degrees?

Negative Numbers in Context Quiz

In this lesson, we will interpret negative numbers in a variety of contexts and explore movement on an 'extended' number line.

Maths

Y7 Maths

Key Stage 3

Year 7

Negative numbers in context

Positive and negative numbers

Number

THEME

UNIT

Order and absolute value

Modelling Addition

Further Addition

Subtracting positive numbers

Subtracting negative Numbers

Multiplication as scaling

Negative scale factors

Further multiplication

Division

Further division

Axioms and negative numbers

Calculate (-29) + 29

Which word best completes the gap: -14 and 14 are additive inverses as they sum to ____

Which calculation gives the smallest answer?

True or false: The absolute value of a number is always greater than the number itself.

Find the absolute value of the number 0.

Which word best fills in the gap in this sentence: We can think of addition as _____________ a point on the number line.

What is the additive inverse of -4.2?

Joanna thinks the following calculation pair are additive inverses: 10 + (-50)  + (-18) and (-10) + 50 + 18. Is she correct?

Calculate (-2) + (-5)

Fill in the gap: In the diagram below the top arrow can be visualised as stretching -10 by a scale factor of_____.

Calculate the following product: 0.5 x (-12)

Lesson overview:Negative numbers in context

Core Content

Positive and negative numbers: