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Pre-Algebra - 6.6 - Scale Drawings and Models

Added Apr 16, 2021 •

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Finding the Scale (Factor) Using Scale Factor to find measurements .

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so it all relates to proportions so two concerts are going to do they use scale drawings will go over what a scale is and construct a scale drawing construct you can do I'll say sketch sketch cuz we don't have rules we do have Rose but I don't know where they are so a scale drawing of the White House is drawn on the grid paper is there right now I'm assuming that's this the length of one square on the grid paper represents 7 ft so they're kind of okay I guess I imagined fix us so what we have scale drawing so just imagine I asked you had graph paper I don't so I'm going to pretend so we just going to do it sketch let's say I had graph paper I'm trying to make squares that's not a square but you imagine it it that's why you shut up so each soap one square represents so even though this is definitely not in a whatever each little square so here to here is 7 ft here here is 7 ft so if I actually have real grass paper you can sketch a diagram and find the six six did I not set it up on me go double-check it is published that's why alright try it now here let me go get the link for you all right there's a 6-6 the following right now it's all right you're here I haven't started my so just imagine so in a grid wants some of you guys when you take art with mr. Lee he'll always want to think she always does is a gridwork how you make a scale drawing using grid so you would actually block out make a grid put a grid on top of some teacher you have and then instead of just drawing the picture as a whole you fill in each little box of trying to replicate it and what you guys don't realize just my phone instead of focusing on a whole page going to drive this box right here where would match up in the real life thing it's actually hey you guys say you're not a good artist but you know what grading it out make focus on one little thing so a scale drawing of the White House has drawn on grid paper assume this is in the length of one square of the grid paper represents 7ft all right so we have an idea what it would be like graph paper what is the actual length of the White House if it's length is 24 Square so you got 24 squares I'm not going to draw 24 squares so the length of the White House 24 24 x 7 ft 24 * 728 + 140 168 ft long is that is really small man now I don't know what you want to call it 24 squares and each square is 7 ft * 7 * 2468 ft in real life 224 squares represent 160 ft what is the actual height of the White House if the height is 10 Square if its 10 squares 10 * 770 ft in real life that's that's believable trance 868 beat that doesn't seem like much but I guess it is so this right here is the use of proportion and scale that is a scale let's do that scale drawing so depending on which way you want to go so you always want to read yours want to read which one we're talking about so they're two different directions this is scale to IRL Android or Android to scale so scale 1 square is the 7 feet or 7 ft is to one square which one do you use so the whole thing is this right here you look at this with trinket down scale for a scale 1717 these restrict this is so just imagine a fraction this is what's called a reduction shrinking it down if we want to scale it up we know what's 7 times bigger this is an enlargement we'll go over this a few times don't worry so a fraction scales down even though this is a fractions the fraction bigger than one it's scales up we enlarge it so a couple of different ideas right here so notice how I set it up and notice how we find measurements to look at this we took we took the smaller thing and multiplied it by charging it supplied you guys would think alright which one would I use do I use 1/7 or 7 or one that's where the Lexile comes in when you read the word problem like it right here what is the actual length so I'm making it bigger if I'm making it bigger I have to use this one look at that's why it's 24 * 7 Watch What Happens right here I want to find how many squares I have if I have 75 I'm going to make up some other number if we know it's 28 ft long 17 ft High how many squares would BF in real life how far back the White House goes, I'm just making it up I'm going to say let's go 58 I just made it up as you can imagine we have a we have a we have a house the White House I'm using a cube represent so we we saw this right here the White House is 168 ft long how tall is it is 70 ft in real life but how far back does it go we don't have that I just made it up 58 feet how many cubes would that be so looking at this right here I'm taking in real life and I'm shrinking it down to how many squares it be this is where people get stuck with which one do I use so it's 58 and I'm sure keeping it down so many use the one 7th so 58 * 1/7 what is that I don't know 58/7 what is it 56 I would have been so much easier but I did I messed up imma stick with it I'm not going to change it so 58/7 is another way of writing division so 58 / 7 how many squares with because in this 856 we get to bring down a zero that would be 214 we get sick bring down the role that would be DW 5002 be about 8.3 squares in our 8.29 squares whatever I already went around a lot so you know about 8.3 squares and word problems I'm lazy and I let you guys be lazy that's my mistake I'm trying not to do that in word problems at all what are we trying to find that's why you want to write down this last little bit 8.3 squares 70 feet some type of a unit thing that helps you try not did I ask her what I'm looking for in a word problem that's the biggest mistake and we're proud we don't finish answering it so it wasn't shorts Canales best scale shrinking it bigger making it smaller scale drawing or a scale model is used to represent an object that is true large or two small to be drawn or built at actual size so you can make us bigger thing or smaller thing the length and width of objects on a scale drawing or model are proportional to the thanks and which of the actual object so things match up and their proportional I will do some of that in the second a scale is determined by the ratio fraction but another way of saying fresh scale determined by the ratio of a given length on the drawing or model to its corresponding length on the actual object so that's the way it should be the other way around it could be the actual to the model so that's the whole thing again which one is it I called its scale that use their words I'm going to cross that out model model are we the model 2 in real-life object or are we looking back and relaxing to the model read read read read and then we'll tell you which one that's the Lexile but so scale is a fraction were comparing and corresponding me matching course funny memes matching so that's the whole thing needs to match with the ones that I have a match with 20 resume out now that I can't see 168 length of the White House would have to match with 24 squares it can't match with 10 squares cuz that's this right here matching side so we're just going to do with food figures for now we'll do with triangles and triangles notice I got a big triangle and a small trying to label it a b c and I'm going to go in another Direction I'm going to go random letters mrq corresponding means matching make sure that your shapes whatever it is always facing the same way sometimes I'll do your dirty and flip it the other way and I remember you are so you're going to have to your whatever object you have redraw it and face it the same way you'll see right here if you guys are just looking old less to less angels with our but if we turn it around and face it the same way he goes with them that's the biggest mistake when they're not face the same way simple thing you could just by redrawing it spacing it in the same orientation soeed matches with M A corresponds with m b corresponds with r corresponds with Q notice I want larger to smaller but could you go smaller to larger yes you can't go back and forth but when you who is One Direction One Direction that you choose you got to stick with it don't change it up middle the way then things get all mixed up so corresponding corresponding lengths actual object considered as far as the one in is to 1 inch represents 3-ft in a diagram one centimeter represents to mmmm we cannot let the scale right there we're shrinking well this right here we're enlarging we're shrinking an inch is smaller than feet so if inch goes to feet enlarging it centimeters those were shrinking it down scales are written so that the unit length on the drawing model is listed first so they say this is according to them and let's stick with it scale and forget skill it's what's called I'm jumping ahead here it's a fraction your scale the call it the sea Factor your scale is model measurements over in real life object so we're doing this then we're shrinking it down in my opinion all right first example lot of explaining just to get to hear suppose a model of a dragonfly has a wing length of 4 cm that's really short for centimeters that like that that is a MEP engineer for centimeters if the length of the insect actual Wing is 6 centimeters play we suppose a model of a dragonfly has the length of okay and the show length is 6 / shrinking it down why would you shrink it down if it's already That's Amore I don't know if the length of the insects actual Wing is 6 centimeters what is the scale of the model Model Model S you can model 2 in real life remember scale is model 2 the real life thing so the model is what the model is 4 centimeters and then the actual is sixth sense when you have the same unit measurements Dashie cross them out you don't need to list the measurements is there the same that's only when do the same if you want to convert it you go to burn witches cuz I can you go but I always got to simplify fractions I had to take people test because they didn't read it even said write in the simplest form 4/6 the scale is 2/3 so the model is 2/3 the actual size of the dragonfly look at this right here model length overscaling you know why do they do that all of the Ratchet look so 2/3 I saw what they did all right if the length what is the scale of the month 46823 I think they decided to go with 2X equals 3 / x equals 1 did it even further they wanted the actual length is the length of what is the scale x equals 1.51 cm equals one point so they cut it straight so they kind of did a weird unit rate unit rate should be a 1 in the denominator but they decide to make it 1 so 2/3 was the scale they decided to make that she even I would have messed up on this one it's alright they wanted one as a one what is 1 cm what is in real life what is the one centimeter in the model my wife alright so using this as our model so they just went up this is an actual interest interesting point looking what they did they did for cm over six equals 1 cm / X so what is 1 cm in the model 2 in real life so if the weather in K what is the scale of the model so what would 1 Mach 1 in Wednesday so they went for six equals 1 over X I simplified it 2/3 and they just did the cross product 4 times x is equal to 6 times one so that's a cross product right there and then 4X equals 6 and all they did was divided by 4 and they at one point five same thing is what I did though I simplify didn't got two-thirds 2/3 equals 1 over X at the cross 2X equals 3 / 2 same answer I am a person that always liked likes to simplify when I can ease your mental math do you have to do that no this day in age of calculators it's actually not work simplifying for 6 if you have a calculator and you had some big John fraction would have been better just to use the calculator Steelers of the World War II Memorial in Washington DC are 17p tall a scale model of the memorial has pillars that are 5 in tall what is the scale of the model so it wants you to create a fraction what is the scale of the model so we know that it is a fraction of a side send a text as one of those things get it take time do it on your own let me know what your answer is so we can check her answers if it match up cuz I can mess up what is the scale of the model so it means we wanna one where the model would be what is 1 inch Amara visit scale so first world problems always listen to Tops what they say scale is model over the real life set up the first find the ratio of it then we'll deal with the rest so let's find our racial or model is 5 in tall and in real life is 17 ft now in this case our units are different would it be better to convert he's too the same units as this example of both in the same unit measure now we got true different units but they're related we'll go do that in a second so we want to find out what is so 5 in is 217 feet the model for real life now our whole goal is this right here find a proportion set up so the model what does one inch represents that's not Lynn that's one in do Jeremy Lin 1 inch model represents how many feet in real life is what it's saying so we can take across from change it to inches 5x equals 1 * 17 / 17 / 5 three-point something 3.4 x equals 3.4 ft so what it's saying is what Anton the model is 3.4 feet in real life sorry I didn't yes you could also flip it upside down but you also got a match so if you took the reciprocal you would have to make sure the cross product is it being the same so it needs to match up that needs to match up model in real if you went in real life to model this other one would have to be in real life the model so if you went 17 ft / 5 in x / 1 inch you have to match in the same day action that right there it does matter does matter we end up getting the same thing so 5 in 7 B * 17 * 12 204 so 204 4 inches so these containers go away so in real life what would one B12 what so five x equals 204 / 5 equals and then 40-48 so one in on the model represents 40.88 inches in real life so since these are both Inches I can get rid of the inch but one in in the model represent 40.8 what's what's 1 in inch represents 3.4 ft better to understand in real life in a models does 3.4 ft equal 40.88 3.4 ft let's change it to inches * 2 3.4 * 12 in converted to in what is at 868-0438 10. 1 for one decimal is 40.8 so it doesn't matter if you need do you need so when you have us scale you do not have to make matching units first it will convert later on just set up the proportion so both of these are equal 3.4 ft equals 40.8 in which one's better someone said I don't know I think this would because if you were going to go and talk about real life no one says you know my model airplane one is represents 168 in my one inch of my model airplane or what inch of my gundam model represents in whatever it is in real life don't hate on the Gundam we only got three examples I know these are all right if the cell drawing and model have the same unit measure the scale can be written without units this is called the scale factor and I guess you can are they both technically simplest yes they're both simplest but if you want the scale factor you want to get rid of the unit measures so pistol with you have the saying it the scale factor suppose a scale model has won Institute feet so 1 2 to feet that doesn't record a but if you decide to change it to a scale factor 1 in to 24 inches this inches in inches go away that means your mama so your model is 24 times smaller than the actual thing this right here inches to feet I'm smaller it's actually 24 x smaller do scale factor that's the scale factor right there 1 to 24 scale factor one unit of the model represents an actual distance of 24 units to the how tall is 1/24 the size of the actual object so we'll look at the alternative in a second a blueprint of a skateboard ramp shown shows that it's length is 11.4 in if the scale of the blueprint is 1 in equals 6 ft what is the length of the Astros skateboard ramp that's dangerous their people so let's look at this right here so the blueprint remember scale or scale factor did that in a second so scale remember they want us to go model over in real life so the bloop of a skateboard ramp shows that it's length is 11.4 in if the scale on the blueprint is 1 inch to 6 ft so 1 inch to 6 feet what is the length what is the actual length so look at this right here this is the model so here's our skip 1 inch to 6 ft we know that's going to be equal to so and have the same ratio proportion what's this in real life if 1 inches is 6 feet so the model needs to be sold this tomorrow so we set it up it's still model over real life so 11.4 over I don't know in real life inches notice inches to real-life feet let's just call it x x feet and 60 corresponding match in the mall one in that goes to 6ft in our dry we have this length of 11.1 11.4 in it needs to match up model to real life models real life models real life we don't know what the real life is we're looking for it we're looking for the corresponding lengths in real life so all we do is take the cross product this one's nice when we have the number one there one in which of the cross product X x equals 6 feet x 11.4 in the units don't matter real life all we got to do this X 6 * 11.4 so f equals 6 * 11.41 * we know what it's going to be it's across the whole thing the units just do they're already there in its place so all you want to take a cross multiply the numbers which is what for 68.4 and what's missing from them is fee cuz sure it would go in the cross product sorry so your diagram are diagram 11.4 in in real life is 68.4 that's a huge skateboard ramp that's nice that's a that's a half of a 1/2 pipe message to so that's using a proportion that's using a proportion and so someone asked you can also solve the proportion one and see if there's another way of doing it look at what they did to units this is called a property of proportions will go over that easier later inches to inches vs Feet 2 feet so in the model 1 in in are so we know we have one in in the model that represents 11.4 in so 1 inch goes to and then what would it be in real life so they might inches to inches feet to feet but look at the cross product 1 * X that's X and then the other cross product is 6 * 11.4 16.4 which one is correct is logic notice how they decide to decide to go here using the scale what is the 6ft that's what it sent up here and so we need to match up model in to real life feet but if you just want to go inches to inches 1 in to my model engine where it's related feet to real life feet proportions can be set up if your logic goes in the same direction that is key but that was using the proportion method they want us to use the scale factor method right here using the scale factor method the actual length is proportional to the length of the scale drawing with the ratio of 1 inch to 6 ft so let's change it and go scale factor way 1 inch to 6 feet so let's convert feet to inches in 6 feet that are what's 72 in 1 in 72 in insisted the same one to 72 22 times smaller that is the scale factor sorry I thank you for letting me know so let's do it again so they gave us this right here one in the 6ft let's convert it 1 in equals 72 in 6 ft equals 72 in visits 12in for every 6 ft but since the units are the same he could get rid of the inches so the scale factor 1/72 SF stands for scale factor it's the lazy way of writing scale factor he should simple and so what do we do with that 172nd we can see the scale factor is 1 / 72 the actual length is so look at this we know the scale factor is 70 to 170 so that means measurements is shrunken down 72 times that means in real life it's 72 times bigger so what is the drawing picture 11.4 so we know it's 7:00 this is 72 times smaller than the real life one think about logic backwards in real life it's 72 times bigger remember this is shrinking down a fraction but we won 72 seconds fractions multiply 72 * 72 * 11 point or 822 we get a zero we get 28 area to 97810 carrier 111 12 in 1 so 8208 inches but what is that in feet so we divided by 12 that's why this mess antenna from the circus divided by 12 16.4 I did put the decimal place so figure that 68.4 size is messed up that's my fault so this display this message right here using the scale factor so the actual like the 72 x the blueprint the actual length equals 72 times the blueprint length so they create an equation a equals 72 B 8472 b and we know the blueprint length is 11.4 820.8 and if we divided by 12 actual as in inches or 68.4 ft same thing which one is better I personally prefer the proportion is that easy Lodge but you guys will be doing those state test they're going to ask for multiple ways so even though you guys might know the proportion way some of these test questions are going to ask you to show show me a second way to do it and that's the second way is actually worth more than the first way I know it's poop but that's what they want you guys to do but I want to look this right here I'm going to ask you guys this right here so 70 or 172nd was the scale factor so y equals a equals 72 * b y equals MX y equals KX this is how it relates to what we've been doing I'm trying to connect it so our scale factor hey we are related to the everything we did remember how we started at that y equals KX or k equals y over X think the car a proportionality K as the constant the scale factor is just k just one of the guys to know that I'm jumping ahead cuz it's easier to build right now if you see it and I give it to you let's do one of these files make sure you know what you're doing a map of the Natural History Museum shows that's a dinosaur exhibit room is 7.25 in wide if the scale of the 1 inch 1080p what is the width of the actual exhibit room so that's the whole thing would you rather do a scale factor or proportion trying to the scale factor method just to practice it and we'll prove it using both methods someone said I do how did the proportion way alright do that and I'll do the other way check your answer but try to use the scale factor method yes I know the proportion method is easier scale factor everything is the same unit correct all right I got two answers your calculations skills aren't you the calculator right now then this is a test not a test just to check to see if you're not doing it I'm going to start setting it up start setting it up sorry what was the following ISO person so give this so but let me say this it gives you a scale 1 in 280 feet I'm going to use the scale factor method first so let's convert this the same units so if I'm going to convert feet to inches that's 8 * 12 what's 8 * 12 96 Sol inch represents 96-in in real life but let's just go 12906 that means the model this map is 96 times smaller then the actual building the museum so looking at this concept is 7.25 in do you want to hear what we're looking for what are we looking for we're looking for in real life what we have is the map the map is the model so you take scale factor time the model but here's the thing this right here is 196 I say scale factor but you got to understand scale factor again I went over to the beginning is it one over 26 / 96 / 1 that's where people get confused and that's why this book is kind of offenses you should always have the model first let's look at this I want it in real that means that I'm going to have to multiply to this model number and make it bigger If I multiply my model number by this fraction is actually making it smaller so this right here I have a fraction less than one that's a reduction this how you know which one to do but I want to enlarge it 96/1 is an enlargement in large and this is what I want I want be bigger in real life so I'm going to enlarge my model if I'm going to enlarge my model I need to use this one that's why I disconnected the scrum that we're doing right now so I want the in real life in real life that means I got a x 96 * what's the width of the room 7.25 so let's do that 96 7.25 that is equal to 696 inches sorry inches but we who who measures of rumen we measuring feet so what's / 12 bye-bye 12 gets US 58 you are totally correct those people that wrote so 58 in 58 feet or 696 inches hoping you didn't tell us did it want it in inches or feet these problems are funky that's why you want to write your unit measures so you could see this is an inches versus feet multiple-choice you got to watch out wrong answer would say 58 in or 696 ft but these are the choices to make sure we could set it up so one only got one in 8 feet and now we got this other 17.25 in how many feet is it in real life I don't know X fee take a cross product 1 * X as X and then we go 7.25 X ocho that is a 4160 005-6010. 185 two decimal places 58 speed with the cross Prada and we converted man that's it right there and see what we get let me try and skim through so right here construct a scale drawing of five minutes construct a scale drawing of an object use the actual measurements of an object is still alive wila is painting a mural on a wall at the community center that measures 18 ft long and 12 ft tall make a scale drawing on the mural use a scale of 1/4 inches to 3 feet use a 1/4 inch grid paper for the whole thing so we want to go so let's do a quick sketch so it's going 18 ft by 12 ft and we have this right here 1/4 inches is 235 ft kind of funky I don't like that at all horrible horrible so look at this let's go one in I got to multiply this by 4 cuz i x 4 I get one in let's find what one is in the model and multiply that by 4 * 1 inch equals 12 right 4 * 1 this right here they put 18th Street one-fourth of an inch and a quarter I got a x 4 3 x 4 doesn't get me that they multiply 2 by 6 that's funky I think they did it wrong she did it right correct here I get it done and I saw what they did forget it I'm not bothering with them so I have this right here here's my scale factor they decided to use a fraction I'm not going to bother with the fraction I'm getting rid of the fraction so here's to do a schedule I got to find this and that so it's 1 in 12 ft equals how many inches x inches over 18 ft and then I got to do it again one in over 12 ft equals x inches / 12 this right here I got to do two different conversion this right here that's already 12:00 so X is one so this right here is one in on my drawing this right here 18 feet equal 12x / 12 that is 1.5 inches so 1.5 in so she wouldn't make that making a scale drawing

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Pre-Algebra - 6.6 - Scale Drawings and Models

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