 Cool testing one two eight eight eight. Okay, so we're gonna start with integers integers mean whole numbers Okay, again whole numbers not fractions not decimals whole numbers. All right, so we've got zero Zero is in the middle. Okay. That's the That's the middle in this case to the left is negative to the right is positive. Okay, that's all it means Negative means we're going to the left of zero or below zero. Okay, you know when we're reading temperature When we have degrees Celsius if we go below zero, they say negative four degrees Okay, it's below zero that way and then if we're talking about Let's say money. Okay, we normally go on a horizontal scale So if we go into negative money, we owe money. We are in debt We have less money negative money. We're going to the left. Okay, so I Want you to do this for me? Okay. I want you to have a look at this equation here. We're gonna go negative 46 plus 12 Now some of you brainiacs are about to put the answer in the comments fantastic, okay, and and I will show you yeah, so you pretty much already know the answer but Let's have a look at and label this properly now a lot of kids struggle with this So let's label the first number. Okay, we're going to label this The starting point the starting point. Okay starting point. We're going to label this plus in this example The direction and then we're going to label this how far or Duration, but let's go how far and then the answer is going to be the Destination Okay, so there's your first bit of notes if you want to copy this down Feel free to screenshot it if you like, but I'd rather you copy it down so you remember now here we go What we're going to do is we're going to start at negative 46 So negative 46 is going to be about maybe here. Let's pretend. It's here. So negative 46. Okay So that's our starting point, right? So we have our number line We've got our starting point now. We're going to plus the direction is Plus so which way is the direction going to go left or right left is minus Right is plus. So which way do you think we'll go? Right, that's it right. So we're going to go right. We're going to go right and how far do we go? To 12 that's right. We're going to go 12 Paces or numbers or counts to the right. Okay. Now. Here's the tricky bit a lot of students think that When we add to a negative, it's gonna this number is going to go up No, because it's a negative it actually goes up more to the negative. We're not adding a negative We're adding a positive. Okay, this actually says negative 46 plus Positive 12 when we do positive numbers, we don't have to put a positive in front of the 12 Okay, that there means add. Okay, or or we can do it like this. We can make it Okay, we've got a negative 46 and a plus 12 okay So What's the going to be the difference? All right, what's going to be the difference in total? and then Now we don't go here because remember it's the it's the how far we're going. It's not the other Starting point. It's how far we're going from negative 46. Anyway, let's get it going Okay, anyone that thinks this is so boring. Please leave the live. You're welcome to stay But if you're gonna comment, this is boring then you are a loser. Okay negative 46 We're gonna get a bit savage. I know but hey, it's my house. I can do what I want negative 46 we're gonna go this way Towards zero so that number is going to go down. So we're going to go 46 and Then 12 so that'll become 44 We're going to take two steps because that will get rid of the two and then we're going to go 10 more steps We're at 44 10 more steps becomes 34 okay, so that'll equal 34 But because we're still on this side of the zero We have to put the negative number in there. So negative 34. Okay, and that's your final answer who got negative 34 Who got negative 34 if you got negative 34 give yourself a big tick well done, okay Now now that you know this and labeled it if you haven't labeled yet feel free to take a screenshot three two one go Cool. All right Now we're gonna do another problem. Okay, firstly We're going to redo that problem again, but with different numbers and want to see if you can figure it out Okay, you're not allowed to use a calculator now if you didn't take notes if you didn't screenshot that and You're struggling with the next question I'm gonna blame you because you didn't take the notes. Okay now. Let's have a look at another question. Let's go with 18 plus negative seven Now the reason why I put the negative seven in brackets is so it's easier to read. It's not 18 plus subtract seven Okay, now Again, have a look at it. Where's the starting point? The starting point is 18 now. Is there anything at the front of the 18? No, so what does it mean? It's a positive. That's right. It's a positive so Which side of the zero are we going to start on the left or the right? The right that's it. So we're gonna go here. So 18 is about here The direction is plus. So which way are we gonna go? That way right to the right again, however, however When we add a negative it reverses the other way it goes negative So here's a note you can take whenever you see a positive and a negative add Like this It becomes a subtract Okay, so it's 18 Take away seven Okay, now we have the official direction. We're gonna go to the left. So 18 we're gonna take seven paces that way 18 17 16 15 14 13 12 11. Oh, there it is. The answer is 11 and it's positive 11, but you don't have to write a plus in front of it Who got it right? Cool, excellent. All right, I'm just gonna Block a few more people again that Being a little bit annoying guys, please don't flood the chat. I'm just gonna block you straight away Cool, excellent if you got it. Well done. Okay. All right 120 people online damn. That's awesome. Okay, so Here's a note that you can take as well All right, here's a note that you can take if you have a Negative and then you add a negative Which way are you going? Are you going left or right in total? If you have a negative and you add a negative which way are you gonna go? Negative, okay, so negative Right, so if you start here and you add a negative you actually end up going to the left. Okay, if You go positive and you add a positive you're gonna go positive Yeah, yeah, what about if you go Negative and you add a positive You're gonna go positive All right, if you have what's another one we haven't got we have a net positive and you're gonna take away a Positive which way are we gonna go? We're gonna go towards the negative, okay, but it doesn't mean the answer is positive or negative We're just going in that direction. All right, so yeah, it's a bit confusing But if you have these two like so it automatically becomes a negative Positive and a positive stays a positive a positive and a positive stay a positive and again, this is the same That that becomes a negative so we're going that way and then there's also a Let's go with a positive Take away a negative equals. Oh take away a negative. Oh, what do you think it's gonna be? What do you think it's gonna be guys if you're asking me what my YouTube channel says it is it's literally on the board right here Literally right here. Okay. It's gonna be a positive. It's actually gonna be a positive. Okay, that's right Aiden well done. So it's actually gonna be a positive Well done Okay That's it So there's some more notes for you and then if it's a negative take away a negative What do you think it'll be feel free to screenshot it if it's a negative take away a negative? What do you reckon it'll be? Let's have a look positive Positive so let's have a look if we have negative forty seven and we take away Negative eight equals What do you think the answer is? Here's another way I explain this in terms of money and debt. Okay, so let's say you owe $47 You owe $47. You're in the red. Okay, which means you owe someone $47 and then you pay them back $8 You pay them back $8. Okay, if you pay them back, you're getting rid of you're subtracting another negative Okay, that's a good thing if you're taking away debt, which is what the minus is you're going to be Taking away from forty seven, but it's in a negative. I know this is the confusing part, but this is what happens. So you So you're actually starting here forty seven and because that negative eight Becomes a positive We're going to the right so forty seven Plus eight to the right That forty seven goes down. I know that's super confusing and bear with me I'm still trying to figure out as many as possible analogies to make sense with it Okay, so forty seven all the way to zero. We're going to end up at negative 39 so negative 39 so we've just paid back eight dollars. We've got thirty nine dollars left to give. Okay Here's another example In terms of analogy Okay I'm gonna use some different colors. Okay. This is one of the things that my colleague at school shoutouts to Joe Has given me it's called the hot air balloon Analogy, so we're going to have a hot air balloon like so Okay Hot air balloon like this All right, and how does a hot air balloon rise? Flames like flame emojis, we're going to make them blue. Okay, and we're going to make them positive Okay, every plus represents one extra positive that the One meter from the ground that it raises. Okay, so One positive is one meter, but let's not get into that super hardcore where we convert converting Units and all that stuff. Anyway, so let's say we've got four positives. What do we what? What's our number? four or positive four right now we're going to use blue as our negative we're going to what makes the balloon go down and The answer is sandbags. Okay, so these ones here Are our sandbags. Okay, so we've got four negative sandbags. So negative four If the hot air balloon right now was on the ground Does it take off? Yes or no if it has four negative and four positive? Does it take off? The answer is no. Okay, because negative four and positive four cancel out negative four plus four equals zero if we're on zero We are on the ground. Okay, so let's go and use this equation This is my favorite, right? I'm going to use purple. Okay shout outs to all the queens out there Whose color whose favorite colors purple whose favorite colors purple? Yes, okay, so I'm going to write an equation here And I want you to read the symbols and have a think of what the negatives and the positives are doing Okay, let's do it. Okay, so negative 12 plus negative 32 okay Does first question does the hot air balloon get off the ground? No, it doesn't that's right. Okay, so negative 12 plus 32 the plus and the minus means we're adding more negatives Okay, so we have negative 12 we got we have 12 sandbags, right? And we're adding more sandbags So how many sandbags do we have in total 12 and 32? 12 plus 32 equals 44 now that's sandbags. What do we use to represent sandbags? Negative, that's right. So negative 44 And that's the answer There you go. How about that for a trickery maths thing? Okay? Does that make sense does that make a little bit easier to understand integers? Okay, I'm going to test you on this one. All right. Have it keep thinking about hot air balloons sandbags and flames Okay, I'm gonna erase all this Okay, hopefully you're taking the notes Okay, so let's do it. Let's go with Another problem, let's see if I can find one Let's go with 24 Take away negative six Take away negative six taking away negative Taking away negative. Okay, so let's have a look. How many pluses do we put in? That's a positive. Okay, so we've got plus 24 So we're about 24 meters off the ground. Okay, hypothetically And then we take away negative six. Okay, if we're taken away now This is the confusing bit for some of you if we're taking away a negative We're actually getting rid of sandbags Because we're taking them away by Felicia Taking away a negative. We're throwing the sandbags off the hot air balloon. No, we don't need you So if we're taking them away, that means we're adding to the flame emojis. Okay, we're gonna be even lighter So then we're going to be adding More because the hot air balloons lighter. Okay, plus six equals Plus 30 you don't have the right plus 30 you can just write 30. Okay We got 30 Yes, yes, well done Queens. Good job. All right, cool Hopefully that makes more sense with the hot air balloon sandbag and flame stuff analogy If that's really helped you, let me know. That's a really good one. Okay, so if you're ever thinking about any integers ever Think about like this. I'll give you one more for fun as a practice a really hard one. We're gonna go with negative eight take away negative 14, okay, we've got sandbags First question out of the blocks does the hot air balloon raise off the ground? Does the hot air balloon raise off the ground? Yes, it does. Well done Now, let's have a look at back at the original analogy. Our starting point is negative eight. So we've got eight sandbags We're very heavy right now with our hot air balloon. We're not getting off the ground. Okay, but We've also got 14 We've also got 14 Sandbags so Theoretically, we've got a lot of sandbags. However, we're gonna take 14 sandbags away. All right, so eight take away 14 Which gives us what? Because in theory we have I mean a lot more, but let's say eight and we're gonna take away 14 so eight We're going in the negative direction, which is that way But because it's negative 14. We're taking negatives away. So we have to go that way Right, and yes by all of your comments. We are at Positive six Okay, positive six. Do we get off the ground? Yes, we do by Felicia six meters. Whoop now here's another way to do this Some people struggle to get from eight to the positive six in one step Here's a way to do it. How many steps do you take or how many sandbags do you take from negative eight to get to zero? To get to zero Eight, that's right. Now. How many more sandbags do you need to get rid of still? The answer is the difference between eight and 14 Six so from zero We've got six more sandbags to get it rid of and now we're in the in the positive section. It's plus six That's why the answers plus six Okay Right that concludes integers. I hope that's helped Next time with integers. We're going to be dividing and multiplying integers Okay, but adding and subtraction that subtraction. I hope that helped Yaskwains