 Okay, we're live any questions from page 44 lesson 2 that you'd like me to go over from page 44 lesson 2 so number 2 3 4 and 5 6 a 8 those all went well Yeah, I would love to do 6 a 6 a this is gonna sound insulting so 6 a is actually so easy that it's tough And I'll show you what I mean okay if I read it first of all lovely chart By the way, what's the biggest province? Look at the chart which province is the biggest area is None of it technically a province or not they change the rules after I was in high school Do we call none of it a province or does it have a different name? Okay, so back to my question. Sorry none of it Which is the biggest province? Go back Okay, then Ontario then is BC 3rd We're the third largest province the fifth logic the fifth largest Thing province and or territory Emily question a says how many times larger is the total area of Quebec and the total area of New Brunswick The first thing I did and as I said well total area Quebec. There's the total area of Quebec and There's the total area of New Brunswick. I did that I underlined it or I highlighted you okay with that step The real question is what the heck do I do with those? Whenever they give me a question and I don't know the answer and it's big yucky numbers One of the great strategies that I can teach you is I fall back and use easier numbers. Are you ready? Joe has five bucks You have ten bucks How many times more do you have than Joe? How'd you get a two from a five and a ten what mathematical equation or operation could you do with a five and a ten? That would give you an answer of two You just answered the question here by the way. I'm going to go one thousand one million five hundred and forty two thousand fifty six divided by seventy two thousand nine hundred and eight Just I asked exactly the same question how many times larger, but I fell back and use easier numbers That's a great strategy. You knew the answer actually just didn't know if you knew what to do as soon as I made Easier, I saw you look at me like do it. That's boring the way thing like that. Okay, that's why I meant by this question is so easy Good strategy my math 12s. I'm trying to teach them that one all the time I have no idea what that works out to and I want to the nearest whole number So, okay, that's how many times bigger Any others from the homework? Can you all turn to I think it's page? 54 54 I think it's a blank page is page 54 a blank page Good, you're gonna do some notes there. I don't think the textbook does a great job of this In fact, I got to be honest right now in my mind. I'm giving unit one with this textbook barely a C I think you try and anyhow, you guys don't care. You're just doing the homework So page 54 it's a blank page and what I'd like you to do at the top as a little heading here is write down S. A and V S. A and V S. A stands for surface area V stands for volume and what we're going to do is we're gonna look at the simplest shape possible actually the real simplest shape is A sphere, but that's a bit yucky. We're gonna look at a box So I'd like you to draw Roughly a three-dimensional small box Over on the left-hand side of your page Mine's gonna I'm gonna cheat by the way mine's gonna look like this insert Where's my draw And I'm gonna go like that right-click copy Right-click paste and then I'm gonna go Draw three-dimensional box You guys here I had it right-click There's my 3d box and then what I'd like you to do next to it is try and draw Right-click copy over here Paste try and draw a box. That's the same Dimensions looking but larger in other words same angle make it similar same shape, but bigger if you can Try and be roughly accurate Here's where I get a little bit clever ink white ink Now comes the dotted line see that and that should be a dotted line too shouldn't it? And that should be a dotted line There now it really looks 3d And when you've done drawing that Doesn't have to be great. We're not going to use this as our notes This is where we're going to explain the concept and we'll go to the actual notes look up when you're done Still got a few of you. It's not a work of art Get the perspective angle right whatever We're good, okay Surface area and volume Of a box I'd like you to imagine that this is the box that you drew But please imagine that there are no bumps on this so right now there's a lid with the ridge right here Imagine it's perfectly smooth. I couldn't find a perfectly smooth cardboard box that was unopened Surface area asks how much wrapping paper you would take to cover this In fact, you know what the surface area of this box is It's this side Plus this side. Wait a minute. Are these two sides the same? You know what it's this side times two plus this side times two Plus this side times two Two ends top and bottom two sides As an equation Surface area as an equation is By the way, my abbreviation for surface area is s a it's Let's label this box. Shall we l actually let's call that width length Surface area is what shape is this that's facing you No, no this What shape is just this the ends of the letter r rhymes with rectangle Rectangle, right? What's the area of a rectangle? Come on. We've done this. How do I find the area of a rectangle? Okay, it's going to be length times width times two plus Length times height times two Because there's two sides right plus Width times height times two. It's this two l w plus two l h plus two Which two sides am I missing h w? As long as you get all of them. I don't care what order you write them in but you've got to get all of them volume For which I use the letter v Let me know the volume of a box is well first of all, what does it mean when I say what's the volume of this box? I'm asking you how much water can it balance it how much water can it hold? How much can you fit in there? What's the equation for the volume of the box anybody know? length times width times height l w h By the way for a candy by raising your hand. I've been calling this a box What's the fancy math word for this is anybody know? Yeah That's one of them that gets your candy. There's an even more stupid obscure one It's actually called a parallel pie head. It's a stupid name for a box If it's okay with you, I'm going to use the word box and when I use the word box What I mean, Jeremiah is something like this because there are cardboard boxes that aren't necessarily rectangular But let's pretend when I say the word box, that's it. Okay candy for you Let's add some numbers then Suppose I told you that the width Was two the length Was five and the height Was four And let's put a great big number one next to this box. We'll call it box number one What is the surface area of box number one? Well, it's going to be two times Five times two plus two times five times four plus two times four times two On your calculators or in your head, I don't care which but most of you on your calculators You can type that in a one straight great big line. Your calculators will do the bet mass for you What is the surface area a box number one? What do you get? Sorry 76 anybody else? Yes 76 what are the units? Well, let's go back to our diagram and let's call these uh meters meters and meters What are the units? I'll give you a surface area I gave you a stupid rhyme with area to remember units for area and this still works for surface area What are the units meters? What? Meters squared I said you want a dumb thing to remember square area Sam believe it or not I still use that okay so far so good What's the volume? A box number one Well, that's going to be length times width times height. It's going to be five times two times four Ten times four. I can do this in my head. I think what's ten times four? 40 what are the units for volume? Well Meters Meters what? Cubed you know how you can remember that it's meters to the third power How many different variables are there in this equation three? That's one way to remember or you can just remember a cube is a box and oh cube Nothing profound so far in fact sam. I would argue. I think that's math eight or nine The surface area and volume Okay now Have a linear scale factor of Three to one We're going to have a linear scale factor of three to one What that's going to do is that that's going to change my width my length and my height If I have a linear scale factor of three to one if this one is bigger And the ratio is three to one My original width is two What's my new width six? What's my new length? Emily when you're done yawning if my ratio is three to one if my scale factor is three to one. What's my length? 15 good recovery And what's my new height? Well, what I want to ask myself is If I triple if I add a scale factor of three to one's here if I triple everything Will my surface area be tripled? Will my volume be tripled? I'm going to find out I'm going to in my high-tech numbering call this box number two surface area box number two is going to be Twice What's the length 15 six and 12? 15 times six plus two 15 times 12 plus two Six times 12. There's my no not sick. Yeah There's my twice the length l w plus two L h plus two h w Now sierra said she thinks we're going to be three times as big three times as big as this would be 210 plus 18 would be 228 do you get an answer on your calculator since I know you're following along Do you get an answer of 228? Nobody say it out loud sierra's going to confirm or deny this for us What do you get? 684 is that right folks? No, people are nodding. Yeah, have some confidence. You're smarter than you look. I mean well make that a compliment. Okay And what would the units be uh meters squared? Okay Here's the question we want to ask ourselves then My linear scale factor was sierra three to one What's my surface area Scale factor. Well, what's my new area of my big shape divided by what was my original surface area? When you go 684 divided by 76 by what scale factor did the area increase? When we added a linear scale factor of three to one what you get? Nine or are you german's is benedict saying no nine Nine. No, that's pretty good. No. Yes. No. Eh little german in there for you. Nine is the german word for it. Anyways back to here now. Um nine times Nine to one Three to one became nine to one. Can you see where that nine came from looking at that three? Do you see how we might have been able to turn a three into a nine? What mathematical operation does that? More specific what type of multiplication it's got a fancy schmancy word Marcus Square and you know what? Last lesson. We said that area Ended up being linear squared square. Yeah Surface area also ends up being squared square So that whole area square is stupid thing that I gave actually really works if you know the linear scale factor The surface area scale factor is going to be nine to one Okay, what about The volume of shape number two now it's going to be length times width times height that's going to be 15 times six times 12 What's the new volume this I can't do in my well, maybe I can 15 times 6 60 and 5 90 times 12 1,080 someone don't check me I could be wrong Woo-hoo units centimeters cube Meters cube. Thank you, Jordan candy for you later. Let me forget What's my scale factor here? What's my volume scale factor Well, if I go new volume divided by what was the original volume? Jordan, what do I get? Do I get 27? Hmm, what would turn a three? Into a 27 9 is correct except that's not the mathematical operation. I'm looking for let me see if I can walk you to it as it turned out Area ends up being your linear squared Three squared is nine Volume ends up being your linear cubed cubed This is actually Three cubed Turns out volume if you for example Double the length double the width and double the height if you had a linear scale factor of two What's too cubed? What's two to the third power on your calculator in your head? What's two times two times two? The volume scale factor is going to be eight times bigger Or sam if you multiply the length width and height by four a linear scale factor of four Your area is going to go up by four square at 16 Your volume is going to go up by four cubed Four times four times four Which is what? I don't know is it four times four 16 times four 64 That's today's lesson. We want you to realize that surface area Is related to the linear scale factor Because it's the square But the new one emily is volume is related to the linear scale factor By being the cube Can you think of an easy way that I could remember that volume is the cube of the linear? Is there somewhere maybe in volume in the units? Perhaps where there might be a little reminder that as it turns out volume is the cube of the linear Can you find some easy way that I could maybe remember that volume is the cube of the linear? It would really be convenient if there was some easy way If you haven't figured it out yet Can't help you Now let's go to the lesson lesson seven, please page 47 And get your calculators out all of you And we may be finding a couple of new buttons for some of you Specifically cube root and square root and things like that So page 47 once again it wants us to fill in this chart We're not going to fill in all of it instead. We're going to look for some shortcuts. We're going to look for some patterns. We're going to look for some hints Ready ox yoik here we go They filled in the first example for us. They said here's your original rectangle box Surface area, let's write over here just so we don't forget surface area equals two l w plus two l h plus two h w and volume equals l w h You got your calculator seen What they've done here joe is they have made up three numbers They found the surface area for a box with those dimensions They told you the scale factor of two or two to one, which means the three is going to become a six the five is going to become a Ten And the two is going to become a that's where the one's going to become a two Then they found the new surface area by going here and they said if you go new surface area divided by old surface area You get an answer of four two squared b What's my scale factor? Can you read it to me boston? You know what my surface area scale factor is going to be Square it boston what's one squared? yes over What's six squared? I'm betting the answer is going to be that let's write down what we think the answer is and let's prove it How do I find a scale factor of one to sixth of one sixth? How do I reduce this by one sixth? Well on my calculator. It's very simple Get your calculators out If I want to find one sixth of nine and one sixth of six and one sixth of 12 I go nine times one divided by six That's how you multiply by a fraction Top number divided by the bottom number times whatever we're talking about what is nine times one divided by six sorry 1.5 So this rectangle is going to be 1.5 by What's one sixth of six? What's six times one divided by six? by What's one sixth of 12? What's 12 times one divided by six? That's my new rectangle With a scale factor reduction of one sixth What's my original surface area? Well my original surface area is going to be two times nine times six Plus two times nine times 12 plus Two times six times 12 twice Lw plus twice Lh plus twice hw Courtney, what's my original surface area? Do you get 468? Didn't do it or did Oh, you didn't do it Okay, folks you want to practice with your calculators I have a feeling there's a bunch of first of all your test is actually not very far away I only got one more lesson in this unit. I will not help you figure out your calculator on your test In fact, if you asked me mr. Duck, how do I use this calculator? How do I do this on a test? It means a couple of things either Marcus. You didn't do the homework Or you're dumb enough to bring a brand new calculator that you borrowed from a friend to a test Either way, not only will I not tell you the odds are very good I'll stand next to you while you write the test and do an evil laugh Did you get 468? Okay, what do you type? Your surface area, right? The quick way is it's going to be two times that times that plus two times that times that plus two times that times that Am I wrong? Is it 600? What did you guys get for an answer? Hey, what goes here? Okay Where's your calculator get it out Where's your calculator got it out? Thank you Where's your calculator got it out? Show me Thank you. Taylor you got one out. Okay Follow along boys and girls I don't want to hear crickets chirping the last block. I don't care suck it up a little bit Is the answer 468 right here? Yes, okay, if you didn't get that I'll come help you later. Let's try this next one It's going to be two times that times that plus two times that times that plus two times that times that What's my new surface area? Do you get 13? No, am I wrong? 13 Did you get 13? You're lying Okay Did you try it? No I really hope that you can get these I won't help you You're not trying right now. This is the chance for you to raise your hand. I'll come help you and I won't make funny you here Believe me. Okay Any luck No, okay, let me come watch what you're typing pause for a second No We need to figure this out We can too Fair enough I is the answer 13. I need some confirmation. Yes. I got needs more people nodding Now if I go new area Divided by old area 13 new surface area Joel the new surface area Divided by the original or old surface area of 468 Does that work out in lowest terms to 1 over 36? Which we predicted Which I thought we'd get to a lot quicker until I had to tell so many of you to start pulling the calculators out Let's try and pick the pace up a little bit follow along. Let's move along. Here is a 4 by 8 by 5 rectangle Box What's its surface area? Can you go 2l w plus 2l h plus 2h w? It's ready kiddo. Here's what I would type ready Two times the first two four times eight plus Two times four times five Plus Two times eight times five and do you get? Whoo-hoo 184 184 Now my linear scale factor this time is three to two. It's a fraction. How do I find three halves of four? We answer this last class. How do I find three halves of four? I take the four and what do I do with this times by Yes, thank you, Jordan You're impressing me despite the fact that you're wearing half of this hoodie. That's okay His arms are cold, but then his body is warm. That's strangely more clever than I thought I'm not used to that from you Times by three divide by two. You know what? I think the new one is going to be six by And the eight is going to become Times by three divide by two a 12 by And the five is going to become whoop didn't want to hit that mr. Duk Times by three divide by two A decimal. Is that a yucky decimal? Not too bad. I'll live with it 7.5 What's my new surface area? My new surface area is going to be Don't quit hitting that mr. Duk My new surface area is going to be Two times six times 12 plus Two times six times seven point five plus Two times 12 times seven point five What'd you get for your surface area? 414 414 is that right? Yeah, okay I can Can you press the go to button when it says syntax error option number two And the cursor Sorry, it's taking a little longer than I want it 414 They want us to go new surface area divided by original surface area. They want us to go 414 divided by 184 I'm going to make a prediction I'm going to make a prediction that this works out to nine over four How did I get a nine over four? Squared square square the top square the bottom. Let's see 9 over 4 as a decimal is that 414 divided by 184 as a decimal is 414 mr. Duk type it right divided by 184 as a decimal is 2.25. You know what they are the same So the whole point of this devin is to realize Area surface area square the linear And you have your area scale back Let's skip the last line. Let's go to the next one. Whoo, but here we're going to cheat Here's what I want you to realize Because we've already filled in the dimensions and stuff on the previous chart Taylor, what's my linear scale factor here? You know what my volume scale factor is going to be it's going to be One over six cubed Which is going to be What's one cubed on the top? What's one times one times one? What's six cubed now you need to find your exponent button is my exponent button This is a little hat right here. I go six to the power of three You need to find where your y to the x exponent button thingy is You need to somehow find how you can go six Press a button hit a three And get an answer of 216 If you can't find your exponent button now is your chance to ask me. I'll show you where it is I can find it in about two seconds. Everybody found it. Okay They can help you so What's my linear scale factor here Shay, just read it out to me My volume scale factor is going to be three over two cubed What's three to the third power three times three times three? 27 Over what's two to the third power two times two times two? eight Scroll up a tiny bit To this line here where it says complete surface area scale factor is equal to linear scale factor squared squared Volume scroll down to the bottom of the page look down the bottom of the page volume scale factor is equal to linear scale factor Cubed let's do a couple of examples and I can turn you loose Turn the page Page 48 alex is one of the pages I think that I would dog hear or post it note or bookmark or do something Because this is a summary of everything we've done so far this unit that involves measurement Says linear scale factor is a ratio Looks like a over b It can describe an enlargement or a reduction and you can find it by going The new length divided by the original length if they don't tell you the linear scale factor Perimeter scale factor is also a ratio It describes how many times to enlarge or reduce the perimeter of a figure And you can calculate it by going new perimeter divided by old perimeter. And here's the key The perimeter scale factor Equals the linear scale factor. This is so much fun. Mr. Doock. Let's do another one. Oh, I shall area scale factor What was the dumb rhyme I gave you for area Square yeah, it's actually going to be now you can calculate it by going new area divided by original area Or it's linear scale factor squared if you knew the old if you know the old one Multiply it by the linear scale factor squared surface area is how much wrapping paper Sierra it can be calculated by going new surface area divided by old surface area And you can find the scale factor by going linear scale factor squared. It's also area square. Yeah volume Not what you do on your stereo, but the mathematical concept volume The volume scale factor is also a ratio How can you calculate the volume scale factor? You can go new volume divided by old volume Or it's equal to the linear scale factor fumed to the third power And here as well is a lovely summary This is what you absolutely need to know on the test That if you know linear you can find perimeter it's the same You can find the area scale factor. It's the linear scale factor square You can find the surface area scale factor That's the linear scale factor squared and you find the volume scale factor Which is the linear scale factor cube turn the page our next page over So where can we use this access globes company? manufacturers globes Little bit bigger than this its globes have a diameter of 30 centimeters They want to enlarge one of these they want to make a great big globe And they want to make it have a diameter of 1.5 meters to put on the roof of their building Okay, by the way If the diameter is 30 centimeters, what's the radius? 15 If the diameter is 1.5 meters, what's the radius? 0.75 meters Turn back to page 54 the blank page, please This one s a and v of sphere Surface area and volume of a sphere There's my sphere What do we call that distance there? the radius I went to go see a pirate move the other day, but I couldn't get in because it was rated r It's two equations and these are on the inside cover of your book, but I always like to talk about them The surface area of a sphere And the volume of a sphere These are really hard to figure out. In fact, they weren't proven for quite some time to be accurate They suspected these were the equations because the answers were really close to this But it took a long time. You did calculus to prove this surface area of a sphere is 4 pi r squared Don't ask me The volume of a sphere Is still 4 still pi But it's r cubed which doesn't Surprised me because we said that volume was cubed uh All divided by 3 It's 4 pi r cubed over 3 Sometimes emily instead of all over 3 you'll see them write it as 4 3rds pi r cubed regardless you're going to go multiply multiply multiply divide by 3 However, you want to write it Back to our notes, please In example a it says okay The surface area and volume calculations of the globe with diameter 30 centimeters are shown below They went 4 pi r squared. They went 4 pi times 15 squared. They got a surface area Of 2,827.4 square centimeters There you go To get the volume they went 4 times pi times 15 cubed divided by 3 And they got 100 uh, sorry 14,137.2 centimeters What they would like us to do Is they would like us to calculate the surface area and the volume of this great big globe that have been a problem though What are the units for the radius of the small globe? What are the units for the radius of the small globe go the units for the rate say it louder Don't say the number the units only what are the units for centimeters? What are the units for the radius of the big globe? I don't want to do that 0.75 meters how many centimeters is that here's a hint Okay, they changed it to centimeters first Let's find the surface area. So the surface area Of the 1.5 globe is going to be 4 times pi times 0.75 squared now you need to find your pi button You need to find your squared button Give a graphing calculator. It's probably like this 4 pi is usually second function this thing right here times 0.75 squared I get 7.068 58 Blah blah blah blah Oh, I put a 0.75 in like a complete meathead Mr. Duk not 0.75 at 75 centimeters. Let's try that again. Mr. Duk. Good gosh Instead of a 0.75 Courtney. I said we want to use 75 centimeters. Let's do that You get the same number but the decimal's in a different place. You get 70,685.83571 Yes So anybody who can't get that there's your chance and I'll help you with your calculator Everybody got that okay? Okay I get so and they want to the nearest point one. So 7 0 6 8 5 0.8 7 0 6 8 5 0.8 Units Centimeters what area goes with what? Squared area square you Let's also find the volume of the 1.5 meter dome globe That's going to be 4 times pi times 75 cubed all over three Going to be 4 times pi times 75 to the third power divided by 3 And I get 1 7 6 7 1 4 5 point 8 6 5 anybody else No, yes 1 7 6 7 1 4 5 0.9 So everybody didn't get that answer I could happily help you Get that answer so your calculator's all worked. Okay, what are the units centimeters what? Cubed Because volume is cubed B says Use the above results to determine the scale factors The linear scale factor the area scale factor and the volume scale factor. Let's find the linear scale factor What's the new radius in centimeters? 75 What's the original radius in centimeters? anyone If to read the question, what's the original radius in centimeters? Where the 15 come from You're right. Where is it? Hey, yeah, how about even uh right there? Whoo-hoo screen froze I'll lose signal for a second again Come on. It's been doing so good the back Okay To the back. Oh, yeah, they sorry about that little technical difficulties Radius 15 So It's going to be 75 over 15. What was my linear scale factor? Someone type that in By the way folks, I generally look for some give and take and some participation I don't care that it's last block and that you guys are tired and that drill's coming out of you Suck it up and wake up your grade 11 kids. Let's go. Whoo Or I'll get violent with my little air zuka whatever I need to to help you stay awake Did I hear a five? I did hear a five. Thank you, Sam. My angel joy of my heart now What should the surface area scale factor be if the linear is five? What should the surface area scale factor be? Should be five squared What should the volume scale factor be if all goes well should be Five cubed should be let's see What's the new surface area right here? one four one three seven Point two divided by what's the original surface area two eight. Sorry, mr. Dewick Read this properly. Jeez. Now you guys got me doing it. That's my fault. What's the new surface area? How about I use this number here? What's the new surface area? Seven zero six eight five point eight. What's the original surface area? two eight two seven point four When you divide those shea on your calculator shea, what do you get shea? and everybody What is nine the calculator? Yeah Bring one What do you get you get 25? So this one works Oh now let's go volume over volume new volume, which is one seven six seven one four five point nine divided by old volume one four one three seven point two What'd you get shea? 124.6. What's five cubed? You got a calculator. What's five cubed? 125. So did we get an answer really really close to 125? Where'd the error come in? Well, we round it off, okay? So this works as well. Thank you for the thumbs up. I'll give you one right back. Absolutely What's the point Jordan? If it's cubed Then it's volume squared surface area or just plain old area linear C asks this Show how to use the volume scale factor determine the linear scale factor Let's suppose. I told you let's suppose. I told you that the volume scale factor was actually oh heck Suppose I told you that the volume scale factor was actually 343 and I said find the linear scale factor If the volume scale factor was 343 How can you find the linear scale factor? What's that right there? Cubed, what's the opposite of cubing? How do you go backwards? Cube root. How do you cube root on your calculator? Find the cube root of 343 right now Now on my graphing calculator, it's hit the math button Option four cube root of 343 You should get seven of an answer if you can't find your cube root button If you can't figure out how to type in a 343 and get a seven back Call me now. I'll show you where it is. Okay Courtney, here's what I would write the linear scale factor is equal to the cube root of 343 Which is seven? What if I wanted to use the volume to find the area scale factor? Here's the volume scale factor Did I just find the linear Danielle say yes? How can I use the linear to find the area? What's the relationship between linear scale factor? Ah So the short answer is you can't use the volume to get there directly take the cube root of the volume scale factor To get the linear scale factor and then square it to get the area scale factor What is your homework? Number one this lovely chart All of it. Yeah Number two this lovely chart all of it. Yeah number three a three b three c four a four b Turn the page I'll pause there Okay Next class I will have a take home quiz for you. Believe it or not. We're technically done the unit right now I'm looking at your test being towards the end of next week sometime Thursday or friday next I don't know if I have you guys friday next week. Uh Don't know we'll find out So you have the remainder of class that took a lot longer to get through because people weren't Hey, the faster you guys are on your calculator the less time I'm sitting there waiting for us to type and find an answer