 There we go. All right, I'll do this joke again. If she gets everything right, answer G. Desk. She figured it out. She hit her face. By the way, the next unit that we're doing is called logic and reasoning. So that was logic and reasoning. See, right there. Understanding jokes is part of it, believe it or not. Assuming that these two figures are similar, now what that means is they've multiplied this by some number to get all the missing sides and it's been the same number for each side. They're the same shape. Are they the same size, Zach? Say no. No, but they're the same shape. Similar objects are exactly the same shape. Find the missing measurements. Now the first thing you need to do is you need to find the one set of sides where we have a pair, where we know both of them. I said, you know what? I know this guy and this guy. That's going to be my conversion factor. Big over small equals big over small. And all I'm going to do for the rest of this is it's going to be cross-multiplying. I'm going to go like this. Big shape over small shape equals, now let's see, what does W go with in the big triangle? 12. Big shape over small shape equals big shape over small shape. How do I solve this equation when I have one fraction equals one fraction? I learned it in grade eight. Cross-multiply and divide as a matter of fact. It's going to be 10 W equals 72, six times 12, W times 10. W is going to be 7.2. 7.2 centimeters. One more. X. What does X go with in the big shape? 15. So, big shape over small shape. There's my conversion factor equals big shape over small shape. How am I going to solve this? Cross-multiply. I'm going to get 10 X equals 15 times six, which is 90, I believe. Oh, this one works out evenly. X equals nine, nine centimeters. Makes sense, Nikki? So far so good. Okay, one of these will be on your test. I don't think it's the first question, but it's on there somewhere. I made up a test last night. Why? Because I asked you to. Oh, oh, why goes with which in the small? Yeah, as long as you get the same answer, don't you? Yeah, the nice thing is you could have gone small over big, small over big. The only issue is what you cannot do is big over small, small over big. You can't mix and match in the same question. You have to have the stuff lining up on the same level. Great question. I'm going to go, I usually go big over small just because, actually, you know what I usually do? This one over that one, whichever one came first because I usually read right to left. 10 over six is going to be, why is the big one? Why over 2.5? Screen froze? Thank you for telling me. I need to learn how to troubleshoot this thing. Bear with me for one second. Cross-multiply, you're going to get y equals 25 over six. Now I skipped one step. I noticed that it's cross-multiply and then divide. I did the divide right away, too. That's going to be 25 divided by six. 25 divided by six. Well, 24 divided by six would be four and one, six. Is it 4.166, or 4.... I think 4.17, if you round out properly, isn't it? I would take 4.2. I would take 4.17. I would not take 4.16. I think I have to mark off and say round off properly, please. Go ahead. What have you got? Sorry, say that again. Lawyer with me later. Give yourself a wrong right now, but lawyer with me later. I need to see what you did, but it's easier to just look at it than trying to understand it from a distance. On your test, by the way, I think at the very, very beginning, I say give every empty to two decimal places unless I say different. So if you're not sure, go to two decimal places. Yes? It's not four. It's 4.16666. I'm going to take a half mark off, mister. Yes? So show me later. Mark it wrong right now and lawyer with me later. Zed, it's still going to be big triangle over small triangle. There's my conversion factor. What does Zed go with? Zed's in the big triangle and it goes with four. Zed over four. You're going to get Zed equals 40 and then I divide by six, which is 20 over three, which is 6.666, so 6.67. I would take, I would take 6.7. Seven is just rounding off way too much. I'll take a half mark off on this one because I'm not counting this quiz anyways and I'm telling you next time I'll take a half mark off. Any questions on those? Then lawyer with me later. All right, I stole this right from the notes, right from the homework. If we look at, hello, lesson here, scale factors and perimeter, we had a little chart, I think, show me in the homework. Oh yeah, and the notes right about here. This is fairly similar. I combined it with a couple of charts from the homework, which I think we're right about here. Let's take a look at it. Original dimensions, it's a rectangle. The original dimensions are 2.9. How do I find the perimeter of a rectangle? There's two ways to find the perimeter of a rectangle. It's twice the length plus the width or you could just go to L plus W. Those will both give you the same answer. If you add the length on the width together first and then just double your answer, that's the same as times in the first one by two plus times the second one by two. In other words, nine plus two is 11 times two, 22. Now, I'm gonna show you how to mark this in a second. What it's going to be is, there are one, two, three, four, five, six, seven lines. What's this question out of? 14, two marks per line, but a half mark off for each square that's wrong. In other words, if you get four of these wrong, you get zero. This is gonna be 36. This is gonna be 30. I can't do that one yet. Two plus three is five times two, 10, 24 plus six is 60. How do I find the area of a rectangle? So the area here is gonna be 18. The area here is gonna be 72. The area here is gonna be 50. The area, oh, don't write so big, Mr. Duke. It's gonna be 50. The area here is gonna be six. The area here is gonna be 144. What's the heading on this column here, Adrian? You looked like you were dying on me, so I thought I'd pick on you there. Yeah? So this is the linear scale factor. That means this is what we multiplied our original dimensions by. Two times three, six by nine times three, 27. What's my linear scale factor in this one, Natasha? So that's gonna be times by two divided by three. It's gonna be take this number, six to multiply by two thirds. It's times two divided by three. That's how you multiply by two thirds. Four by 12 times two divided by three, eight. This one here is a bit trickier. I've gotta figure out the linear scale factor. Well, a five became a 15, a 10 became a 30. What is my linear scale factor? Three to one or three. You could write three colon one or if you just wrote three, I'm good. Oh, this one's forcing us to go backwards. If I know my linear scale factor is four to one and I finished with a 20 by 44, what was the original dimensions? Five by 11 divided to go in the other direction. Oh, which tells me my original perimeter was add them together in times by two, 32 and my original area was 55. I'll come back to this line because this is dealing with area scale factor. I'll come back to this line. I'll come back to this line. Let's fill in the whole first line now. What's the new perimeter? Add those together in times by two, 66. What's the new area? Length times width, 27 times six, 27 times three is 81 times two, 162, yes? Woo-hoo, I got some math game. Perimeter scale factor, there's two ways to find it. The way to find any scale factor is new one divided by old one. In this case, new perimeter divided by old perimeter. If you go the new perimeter, 66 divided by the old perimeter, what do you get? Now, there's another way to get your perimeter scale factor. Perimeter is the same as the area scale factor. In other words, the perimeter scale factor here is gonna be three to one or three. Perimeter scale factor is gonna be here, two to three or two thirds. You know what perimeter scale factor is gonna be here? Three to one. Here it's gonna be four to one. Here I don't know yet, here I don't know yet, here I don't know yet, but your linear and your perimeter are the same. Worth having here, worth memorizing. And again, Nicole, the second way you can find it is to always, you can always go new perimeter divided by old perimeter. If you go new divided by old, you get the scale factor of three. My new B, four by eight, add them together, 12 times two, 24 and 32. Oh, if I know my linear scale factor, what's my area scale factor? What was the relationship between linear and area? Not the same. David, squared. What was the stupid way to remember? Square, whatever works for you, but you got to remember it for the test. So it's not going to be three to one. It's going to be nine to one or nine. How do I square this one? Square the top divided by square the bottom, four over nine or four, colon nine. Uh, next row, new perimeter, 15, let's 40 at 90 and 450. I'm keeping you awake too much on my ball. You're good. Shloste. Mude. Mr. Mude. I miss you. Ah, I can help with that. Sorry about that at home, folks. You have to keep kid awake. Um, let's fill in this. My area scale, my, sorry, my linear scale factor, which is my perimeter scale factor is three to one. What's my area scale factor? Nine to one and I can find it two ways. I can either square this or if I go 400 new area, 450 divided by old area, you know what I'll get nine and off the clue in that it's over one. Did you say nine, Mr. Do it? No, Paul. I'm not saying no. I'm saying nine. Yeah, yeah, German saying no is nine. Yeah. Okay. So nine or nine to one. Okay. So far, so good. Coming back a little bit. Now they get a little bit trickier. Let's see here. Um, well, no, I got my new dimensions 20 by 44. So 20 plus 44 is 64 times two is 128 is my new perimeter. Twice the length. By the way, I am noticing a bunch of people filling in this column. Really? You couldn't find the primitive rectangle. I think you quit. I would hope that you would, if you actually thought this quiz was for Marx and counted, you'd be going, well, I'll get every single blank that I can instead of just up and quitting when I get to a line that's tough. We'll do that here. Uh, new area length times width, uh, 20 times 44, 20 times 44, two times 44, 880. Yes. Woo-hoo. I'm doing that for my head. Now my perimeter scale factor is four to one. What's my area of scale factor then? What's the other way I could find that? Cause what if I didn't give you this new area divided by old area? I guarantee you 880 divided by 55 to 16. Okay. Now in G, I gave you the area factor. Okay. If I know the area of scale factor, how can I go backwards and find the linear scale factor? Okay. This is where you have to know how to square root, square root. So what's the square root of 36? And now I can say, oh, the new dimensions times by six times by six, two times six is 12, three times six is 18. And now I got two options. Now I could find the new perimeter. What was the original perimeter? 10. What's my scale factor? So I should also be able to go, don't make a mistake here. Two times six, two times five, okay. Five times two, that's good. Perimeter 10, oh, times by six. Yes. There we go. So 60 is this plus this times 260. Yes, it is. What's my new area? I can either go length times width or since I know my scale factor, it's going to be six times 36, which is the same as 12 times 18. Six times 36, 216. That one I know. Because it's six to the third power and I know my exponents. What's the perimeter scale factor? Same as linear scale factor. I'll probably take both. I'll take six or six to one. Certainly if it's a fraction, I'd look for either as a fraction or the cone. Yep. Okay. Area scale factor 49 to one. What's my linear scale factor then? Seven, which is also my perimeter scale factor. So that means these new dimensions came from this scale factor. What did I start out with over here then? If I ended up with a 14 by 28, how do we go backwards? Two by four. Divide, right? If you multiply by the scale factor to get that, divide by the scale factor to get back to your original, two by four, which has an original perimeter of two times four, sorry, two plus four is six times 12. Original area of eight and 14 plus 28 is 32. Is it 90, I don't know, 84, I think? And 14 times 28. Ooh, can I do this one in my head? It's going to be 49 times four. 50 times four is 200. So 49 times four, 196. 192. That's what I said. Listen closely. 392. Oh, good gosh, I'm way off. Okay, yeah, now the numbers are getting big enough that I can't do them in my head. All right, trickiest is when there's fractions. Here's my area scale factor. What's my linear scale factor? I'll give you a hint, something over something, two to three, which means take this times by two, divide by three. Six times two is 12, divide by three, four by 24 times two, divide by three, 16. The new perimeter is going to be 40, this plus this times two. And the new area is going to be 64. Perimeter scale factor, same as linear scale factor, two by three. So the way you'll mark this is each one of these is out of two, half mark off for each square that was wrong. That's how I would be counting it on Wednesday. That's how I'll be counting it on the test. Does that make sense? Clearing things up a little bit. It's so much fun, let's keep going. How can I not keep going? This is like a roller coaster ride where you know the ending is better than when you start. Oh boy, complete the following chart, it says, okay, I shall. Linear scale factor, six to one. Surface area scale factor, area squareia. What was the volume scale factor? And this you have to memorize. So I've given you the dumb rhyme for area squareia, whether it's just straight area or surface area. Volume, you just got to remember, although you can usually figure it out from the units too, what is it? Where the 216 come from? Six to the third power. Cubed, volume is cubed. Volume is linear, cubed. Yep, you're right, 216 to one, or you could just write 216. So linear seven to four, that means 49 to 16. That's your surface area. Cubed, it's going to be 343 to 64, I think. You're going to have a calculator on the quiz, so I'll expect you to actually give me the number. No, I won't give you one reference. I won't give you one, you won't end up with something like this. That doesn't fit. I've kept them all below 1,000, well, in other words, I think the biggest you'll get is probably nine cubed, which is 800, no, sorry, good gosh, nine cubed is 81 times nine is 729, probably the biggest thing that'll show up. Well, no, maybe 10 cubed to 1,000, that's a nice number, but nothing beyond that. You'll be able to evaluate them when you calculate it, but you have to have a calculator. Oh, now they gave me the square, the squareia, the surface area. How can I find the linear? Ashley, what's the linear if this is nine to four? How can I go backwards in the other direction? Yeah, square root, square root. Now that I have linear, how can I find volume? Nine to the third, so I'm going to write in our notes here, nine to the third over four to the, or sorry, over two to the, not nine to the third, two to the, it's this, three to the third over two to the third, which is 27 to eight. All right, hot shots. Volume, they gave me the volume scale factor, how do I go backwards? If I square root for area scale factor, what do I do for volume? Cube root, okay? So you need to know where your cube root button is. Now you have some of these memorized, I know some of you do, but just in case, my cube root button is there, cube root eight, the linear scale factor is two, area scale factor is four. Again, they gave me the volume, it's going to be cube root, in fact it's going to be this. The cube root of 125, 125 Mr. Dook, over eight. Now how do I do that? Cube root at the top divided by cube root at the bottom. The cube root of 125 is five, cube root of eight is two. Three, two, two, two, 10 in binary. Oh, square it, square it to get the square area, 25 over four. One over 343, cube root of one is one. Cube root of 343 is, okay, you need to know how to use your cube root button, seven, and then one to 49. How many marks is this one worth? Six, how many lines are there? Probably one mark for each line, how many squares in each line did you fill in to? You know what, it's a half mark for each square. Yeah, okay, and then I would normally say, give yourself a score out of 20. I'll be saying that on Wednesday, probably turn the page, okay. Now I'm asking you to take this here table from number three and apply it. Show you what I mean. What's my original surface area? In A, 120. What's my original volume in A? 200, here's the key. What's my linear scale factor? Okay, let's do the area first. What's the area scale factor if my linear is three to one? Nine, take your original area, that's your new area. Your new area, if you triple everything, your new area is gonna be nine times larger than the original. What was the original? 120. New area is gonna be 1,080. What about the new volume? What was my linear scale factor? Three to one, she needs some help, okay. You awake? You sure? Take your jacket off if you fall asleep. The volume scale factor is gonna be 27. Take your original volume times by 27. The new volume is gonna be 10,800 cubic centimeters. 400 times 27. Oh, I'm sorry, hang on. Original volume is 200 times 27. 5,000, what was it, 5,040? What was your question, Paul? It just is, cause I told you that's what it was. We did to get the area scale factor to get to there and we used it for the... Nine and 27. Okay, I don't mind re-explaining this, it's just tricky. We're good? Yep, yep. Here my linear is one to two. My area is gonna be, you know what? I'll just write it really small, one to four. My volume is gonna be one to eight. So take my original area, times by one, divide by four. 30. Take my original volume, times by one, divide by eight. Where the one over eight come from, cubed, cubed, cubed. Where the one over one to four come from, squared, squared. Square area, cubed. 400 divided by eight is 200 divided by four. 50, yes, yeah. Sorry, 5,400, not 5,040. Cause I can't read my own calculator. That makes way more sense to me cause 27 times two is 54. Bugging me for a second there. Okay, here I'll start here. What's my new surface area? 5,000. What's my original surface area? What's the area scale factor? How can I, I said there's two ways to find out the area scale factor. It's linear squared or it's always new divided by old. I can go like this, 5,000 divided by 50 and my area scale factor is that. I'm gonna write that down here. Area scale factor equals 100. How's that help? If my area scale factor is 100, what's my linear scale factor? Square rooting, right, going backwards. What's my volume scale factor then? This to the power of what? Three, so if I go 10 cubed, my volume scale factor is gonna be 1,000 which means I'm gonna take this original volume to 100 and multiply it by 1,000. I'll get a new volume of 10,000. What did they give me here in D? Ah, new volume. So I can find out the volume scale factor because scale factor is always new shape divided by old shape. The volume scale factor is going to be 125,000, sorry, 12,500 divided by the original volume of 100. The volume scale factor equals 125. How does that help me find the linear scale factor which is really what I need to do all the rest of them? How do I go backwards if I know the volume scale factor and I wanna find the linear? How do we do it on the previous chart? Cube root, what's the cube root of 125? Ah, linear scale factor is gonna be five to one. What's the area scale factor gonna be? 25 times 80. 25 times 80. 25 times 200, 2,000, that's what I said. No, please, that's what I said when you were listening. You're not very awake, you just move it. There you go. This is entertaining, I gotta have him here more often because he jumps, this is great. You say a bad word, you didn't say a bad word there. You would never say a bad word right in front of your teacher, would you? Especially ones in German that he probably knows. Nicole, is that okay so far, you have a question? We're good? Okay, now it gets a bit tougher, now we're dealing with fractions. Okay, there's my linear, what's my area scale factor? Okay, it's gonna be square, square, it's gonna be nine to four. So take my original area, times my nine, divide by four. What was the original area? 60 times my nine, divide by four. New area is gonna be 135. If my linear is three to two, what's my volume scale factor? 27 to eight, which means times my 27, divide by eight. 80 times my 27, divide by eight. 270 is my new volume, F. Area scale factor from a five to two linear is 25 to four. Volume scale factor is 125 to eight, Mr. Duit. So volume 80 times 25, divide by four. 500 for area, volume 120 times 125, divide by eight. 1875, same marking as before. Six lines, a half mark for each rectangle. Am I wrong? Yo, I don't know. Yes it is, C is wrong and he next to zero. Page, candy for you later. 100,000, thank you. Number five is the same as number the chart, except I just phrased it as the word problem. I gave you the original surface area, I gave you the original volume, I gave you the linear scale factor. What's the surface area scale factor? Nine over four or nine to four? What's the volume scale factor? Cube cube, 27 over eight or 27 to eight. What's the new surface area? Take this. Yawning now, times by nine, divide by four. New surface area, 27. Units, square centimeters, square yet. What's the new volume? It's gonna be 20 times 27 divided by eight. 20 times 27 divided by eight. And I get 67.5 cubic centimeters, centimeters cubed. I was gonna scare you while you're boiling your nose and see what happens, sorry. See that guy, there's my volume scale. What's the original volume? 20 times 27 divided by eight, did I do that wrong? Nope, I think I'm good, right? How's that? Nearly done. Number six, I'll bring that up later. I will later, but I wanna get this done and then people can lawyer with me. No, I'll put it up later. Don't fall back on this one, don't fall behind on this one. Let's get this question here. Number six, when you measure this with your ruler, how long was it? Sorry, four centimeters exactly? I tried to be. So, here's our original scale. One centimeter to 54 meters equals, on this particular model, it's four centimeters to X. How would I solve this? Four times 54 divided by one. Four to 216 meters high. And have you been on the Eiffel Tower? Yeah, fairly high, nice view. 3.9, okay, four times 3.9 is 54, yep. Now, give yourself a score at the top just cause even though I'm not collecting it. Come lawyer with me, now is the time. What's your question? And the first quiz that I gave you, about a week and a half, two weeks ago. Both of those. And, hey, can you all open to page this thing? Page 55, the practice test. I told you which questions I like. So, I'll start out by saying optimistically once again. Hey, I wonder if any of you have any questions from the homework from here that you were going, I have no idea how I'd like to get that. Sam, number eight, okay? Number eight, this is actually very, very similar to the quiz that we just did. They're giving me the linear scale factor. What's the linear scale factor? What do they want me to transfer it to? The, what was the second word you said? Square ya. I'm gonna, first thing I'm gonna try is this. Linear is surface, sorry, surface area is linear squared. When you go 1.15 square, what do you get? So, 1.5 squared, what do you get? Turns out, that's the same as a area scale factor of 2.25. Love to do number nine. We have one centimeter equals one meter as our scale. And they want us to find the scale drawing height. So, here's how I think to this. Scale drawing over real life equals, this is how I think of this. Scale drawing over real life, what are they asking me to find the scale drawing or the real life in the particular question here? Which height are they asking me to find? So, look up, scale drawing over real height, scale drawing is the X that's gonna go there because scale drawing went on top over on this side as well. Real height, now, 24.5, what? What do I have here? This question's gonna require me to change this into meters. I'm gonna go do that over here. 24.5 feet, on the inside cover of your book, is there a conversion factor for feet to meters? That would be convenient if there was. There is feet to meters though as well? Yeah, so I'm gonna multiply, I want feet to cancel, so it's on the bottom. I want meters on top, what was the conversion factor? One foot equals 3048. How many meters is 24.5 feet? I think 24.5 times 0.3048 divided by one, which I'm not gonna bother doing. Right, and that's what we were working on, that's the conversion factor trick. 7.46, what? 7.6, look at that. Now what, cross-multiplot? This'll give you an answer in meters, by the way. What are we being asked to find, the height of his scale drawing? I hope you were clever enough to say, there's no way his drawing is 74.7 kilometers high. Like that to me is a silly answer. In fact, you know what? I'm pretty sure his drawing is not 7.5 meters high, because that would be higher than the ceiling. Now, why would be, where do you think B came from? The 24.5, where did they take that number from, do you think? Yeah, sorry? See, I would look at this and say, oh, there's no way the feet is gonna be the same as the centimeters, unless it was an incredible fluke. You can actually almost do this question without doing the question by saying, for Pete's sake, that's the only answer that makes sense, but I would make up better multiple choice answers than that. Your test has four or five multiple choice at the very, very beginning. Pretty basic, and then the rest is written. Any others? Yeah, love to. Did you try it? Okay. You have to read the little paragraph like a picture up above there, right? It looks like we went from five to 7.5. So the first thing that I would do, Nicole, is I would think, here's my scale factor. Do I see that answer there anywhere? Not yet. Then I would say, hey, maybe I'll change this to a decimal, see what I spot. Maybe I'll spot something a bit easier. So I would actually go five divided by 7.5. And as a decimal, I get 0.6666. Oh, I see that answer now. Where? B, right? If that hadn't worked, I'd probably try going to a fraction. Yes, I should have gone, I went old over new. I should have gone new over old. My fault, Nicole. How do we find a scale factor? It's always new one divided by old one. I think I've said that like eight times today and I forgot it. So it's gonna be 7.5 divided by five, which I don't see, but now I would go like this. And I would say, oh, 1.5. I don't see that anywhere, or do I? Is that 1.5? Is that 1.5? Is that 1.5? What about that one? Ah, that's really the one there. Is that okay? Any others? Yeah, 14. What's the linear scale factor? What did you find for number 13? B, 50 to three? The tricky part here is it's meters and centimeters, so it's really 15 centimeters over 250 meters and then lowest terms, sorry, 250 centimeters over 15 centimeters, lowest terms 50 over 50 over three. That's your linear scale factor. What's your volume scale factor then, if you know linear scale factor? How do you find the volume scale factor? You gotta memorize. Really, did I say the word area anywhere? Okay, this you absolutely want memorized, okay? And if you are confused, by the way, on unit seven, sorry, lesson seven, on page 48, there they are. How can you find volume if you know linear? Take the linear scale factor and do what? Cubed. This is one of those pages I said was worth dog-earing, worth putting a bookmark on. It was a reason I had that in my mind. So if I do that, it's gonna be 50 over three cubed cubed times the original. This is just like we did in the chart where if you told me the volume scale factor and the original, I multiply it. Whatever the heck that is, I don't know. Oh, this is in centimeters cubed. This is gonna give me an answer in centimeters cubed. 14,000 times 50 cubed divided by three cubed. I get that there, that's cubic centimeters. First of all, I'm kinda leaning towards this answer here because it starts out with a six, four, eight. How do I go from cubic centimeters to meters? Well, six, four, eight, one, four, eight. I'll round off to there, it's a bit much ready. This is centimeters cubed. How many centimeters are in the meter? Okay, and this is where I'm gonna say you've all used a meter stick so far in science. How many centimeters are in a meter? Did you not notice? It was worth noticing if you haven't already. It is a hundred. How many centimeters in a cubic centimeter? Well, we want centimeters cubed to cancel, we want meters cubed on the top. How many centimeters in a meter? What's right here? Cubed, what's right here? So instead of saying one meter is 100 centimeters, one meter cubed is 100 centimeters cubed. It's gonna be that number divided by 100 cubed, which is where the six, four, point eight comes from. I heard one more question. Thought I did, or not? Okay.