 Let's erase the pause here, picking up from where we left off. So again, quick reminder, we noticed, we just played around with some numbers. We said if we had a 2 by 6 rectangle that had a perimeter of 16, and if you doubled, sorry, if you did a 3 to 1 scale factor, instead of 2, this became a 6, instead of 6, it became an 18, the new perimeter was 48. And we noticed that the perimeter scale factor, do I hear a phone beep over there? Someone might want to make darn sure that that phone is powered off, or at least on vibrate, because if I hear it again, I'm getting the hankering for those timbits. I'm telling you, I don't know where it came. I'm pretty sure I do, because about eight people all look at the same person. But I'll choose to keep my eyes front, and let them take care of their cell phone. What we noticed was, if you had a 3 to 1 scale factor, you had a 3 to 1 perimeter scale factor. And the way to calculate the perimeter scale factor was, new perimeter divided by old perimeter. So it says, complete the table using the linear scale factors in A. So the linear scale factors were 2 to 1, 3 to 1, 1 to 3, and 2 to 3. So I'm just going to write that down, 2 to 1, 3 to 1, 1 to 3, and 2 to 3. Now, remember Danielle, we said, although we're writing it as a ratio right now, as a colon, you could write it as a fraction, you could write 2 over 1, or just plain old 2, or you could write it as a percentage. If you're doubling something, that's a 200% scale factor. We said enlargement or reduction. If your scale factor is 2 to 1, is that an enlargement or a reduction? Do you remember how what the easy way was to tell? Stay on this page. Stay on this page. We said a scale factor bigger than 1 describes an enlargement. A scale factor between 0 and 1 is a reduction. So now that I've said that, enlargement or reduction? Enlargement. You know what? I'm going to abbreviate enlargement as nl, I'll figure that out. 2 to 1 scale factor. That's going to be an enlargement. What about 3 to 1? That's going to be an enlargement. What about 1 to 3? And if you're not sure, think of it as a fraction, 1 third. Is that fraction bigger than 1 or less than 1? Less than 1, it's going to be a, how about red for reduction? What about 2 to 3? Well, as a fraction, that would be 2 over 3. And that's going to be, is that bigger than 1 or smaller than 1? Smaller, so it's a reduction. That data student in my last class, they said, oh, so Mr. Duick, basically if the first number is bigger than the second number, it's an enlargement? Yes, because that'll make it a fraction bigger than 1. If the first number is smaller than the second number, that's a reduction? Yes, so this is a reduction. The deal, how does this affect me? Actually, it affects all of you but indirectly because you don't have to do the math. But anytime you're opening a video either on an MP3 player or an iPod or your laptop or your TV, whatever video program is running is very quickly doing some math because the perimeter of your screen might not have matched even in terms of similar triangles, similar rectangles, the perimeter of the original video. It's having to do a very quick enlargement or reduction on its own. Usually an enlargement although on an iPod, probably a reduction. All right, here we go. We're almost done the lesson. It's a short one today. It says, determine the scale factor that will transform diagram P to diagram Q and give your answer as a ratio. Okay, I think if I was tackling this one, I would ask how many squares long is the bottom of the original? Four, that's going to be the second number. How many squares long is the bottom of the new one? Three, this is a three to four reduction or enlargement. I know it's a reduction because I can just see the shape is smaller, but mathematically I've just proved it as well. I would probably on it. Now in my homework, I'd say I've counted carefully out of done. On a test or a quiz, I'd probably also say how high was the original four? How high is the new one? Three, I've checked it twice. Good, I'd normally. As a rational number, that means as a fraction, what about as a percent? Now Jordan is actually surprisingly, I know you look at it when you kind of, Jordan is actually doing some arithmetic in his head and some good arithmetic. You said 75%, you're right. How'd you get that? Because I've learned a lot of my students have forgotten their math eight and it was math eight. See, what sport do you play? Do you use percentages in basketball in practice and in free throw all the time? So Jordan has had to get good at percentages. What's your current goal as a team for free throws right now? Okay, so for example, if you ever go to a Mr. Goulet's practice, at the end they do a free throw drill where they're shooting foul shots and they have to hit 70% or they run. And all of them are looking at the scoreboard and doing the percentage math in their head because they want to know are they running or are they not? Self-interest. If you have forgotten, here's what you do. You get your calculator out and you would go three divided by four. As a decimal it's 0.75. How do I change that to a percent? Times by 100. Just in case it's a weird fraction and you can't remember what the heck it is as a percentage, you can actually change the fraction to a decimal. Times by 100. Remember math eight? You're all shorter? Well, except Jordan. Most of you are shorter? Five percent. This is a 75% reduction. You're keeping 75% of the original. How about you use Photoshop or some other graphic photo program? None of you, really. Only one. That surprises me. I thought you guys were into photo. I'm not a photo person. I've only used it because I'm a nerd to play with it, but I haven't gotten big time into it. With any good graphic photo program, you can crop, you can reduce, you can enlarge. So here's the math behind it as well. Sarah increased the length and width of a rectangular 8 by 10 photo. So she scanned a photo when originally it was 8 by 10 and she wants to increase it by a factor of 5 to 2. First of all, is this an enlargement or a reduction? Enlargement? I don't want to rewrite it. I'm lazy. I figure if I circle it, I'll clue it. Real question is, what are the new dimensions of this picture? Now, in real life, software does this for you, but I'm a math third. It's nice to know how it does this for you. If you have a 5 to 2 reduction, what's the 8 going to become and what's the 10 going to become? I'll give you a hint. It has something to do with multiplying or dividing with a 5 and a 2. What you're really going to do is you're going to go 8 inches times 5 over 2 and 10 inches times 5 over 2. Jordan, what did you suggest your answers were? 40 to 20? Let's find out. The next question is, how do I multiply by a fraction? Multiplying does not know. I got a pause and I got to go bent for a second here. My little rant is over. It's going to be 8 times 5 divided by 2, which I think I can do in my head. 8 times 5 is 40 divided by 2 is. I did hear you saying 20 and it's going to be 20. That's the abbreviation for inches to apostrophes or you can write inches, but I'm thinking most of you are willing to learn abbreviations because that's less writing. What about this one? Sorry, 25. And then the last thing it was wanting to reinforce is, if we have a 5 to 2 enlargement with the lengths, we also have a 5 to 2 enlargement with the new perimeter. So it says, show that the ratio of the new perimeter divided by the old perimeter is 5 over 2. We're dealing with a rectangle. Remember I said the easy way to find the perimeter was to go length plus width times 2. 32, I disagree. 36, I agree. And the new perimeter would be new length plus new width times 2. 20 plus 25 is 45 times 2 is. Now, does that reduce to 5 over 2? Well, what number is going to the top and bottom? 3? About 9, a little bigger. If I divide by 9, I'll get 10 over. If I divide by 9, I'll get 4. Does that even go into the top and bottom there? Get your calculators out. This is where we're going to find out if your calculators have this built in. I think I showed you the other day. Does anybody have a graphing calculator? I can't remember in this class. You do. So yours will be exactly, that's yours that you own. You can use it. I'll show you all sorts of neat little things you can do with it. To reduce a fraction really quickly on a graphing calculator, it's 90 divided by 36, enter. And then if you press the math button, the first option is to write it as a fraction. So what I really just teach my students is if you go math, enter, enter, because it does the first option by default, 5 over 2. Many of you have some kind of a fraction button. Looks like this, probably. So see if you have it. If you can't find it, call me over. I'm going to pause the recording right now. Continue. Homework! Turn to page 29, please. I already assigned 1, 2, and 3. Let's quickly talk about them so I can explain them a little bit better. So it says, determine the scale factor that will transform circle S to circle T. How wide is circle S? How many squares wide count? How many squares wide is circle S count? Four. How many squares, whoops. Then how many squares wide is circle T count? Yeah, it's a 4 to 5. Sorry, the new one always goes first. It's a 5 to 4 ratio because you've got an enlargement. I'll let you think about how you would write that as a rational number and how you would write that as a percent. You'll do something very similar for question 3. Count the length of the first one. Count the length of the second one. The second one always goes first in your ratio when you're writing it. And that will tell you the scale factor from A to B or from B to A. From A to C or from D to A. Here it wants it as a ratio. Here it wants it as a rational number, a fraction. Here it wants it as a percent. Turn the page. So I'm going to assign number 4. Number 4 wants me to figure out the linear scale factor. So this time instead of giving me the scale factor and saying what are the new dimensions, they're saying here's the new dimensions. What's the scale factor? Well, what did the 2 become? A 6. What's your scale factor if you turned a 2 into a 6? 3 to 1. And if you're not sure, this number divided by that number will always give you the scale factor. Your new measurement divided by your old measurement will always give you the scale factor. But Sidney, make sure you divide matching sides. Make sure you divide that by that or that by that. But don't go 15 divided by 2 because those two sides aren't paired up. Okay. By the way, enlargement or enlargement. Some of these decimal ones I'll let you think about. Look tougher. But number 4. Number 5 says diagram 2 is a reduction of diagram 1. What's the scale factor? What you're going to have to do I think in only one of these sides do they actually give you both numbers. In fact, I think it's here and here. Once you know the scale factor, see if you can fill in what the missing dimensions must have been. Either the originals or the new ones. So A, state the scale factor. B, use proportional reasoning. That'll be cross-multiplying by the way if you really want to know. Turn the page. 6 is good. 7 is good. 8 is good. I don't feel like doing the cartoon one. 10 is good. Now number 10. Most of you, myself included, are going to get number 10 wrong at first. You're going to go, why am I going to get number 10 wrong? Here's what I would like all of you to do right now if you're buying your book. Underline the word smaller. When you get to number 10, make sure you notice that word. That is the lesson.