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Math 7 - Module 1D - Practice Test Problems

Added Feb 10, 2021 •

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Models of each problem on the Test

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let's do a que viste cures yes you may these figures are similar find the scale factor now there's a word right here that's totally different than anything I've used so far and that's the word similar so I put this off to the side right here let's put it on here similar is the same thing as scaled so the program I used to make the test so you know like you guys got Google Docs at the program so I have the program I used to make this test didn't let me use the word scale they couldn't they wouldn't let me change it so I'm letting you know right here similar it's the same as scale so you know zoom in zoom out whatever you want to call it so it is still so what are the figures let me draw the picture for you and we will go from there so I got two pictures find the scale factor now I'm going to do an extra bit because all tests the difference and everyone's going to be a slightly. different thing so there's going to be two different choices and everyone's going to get one of them some of you guys will get none this is important so the picture can be flipped around and whatnot but we'll help you out so fine the Phoebe's figures are similar find the scale factor yours will either say from larger 2 Mahler from smaller do larger you will not have both lby the other so yours is I was going to say larger to smaller or small it a larger and that is important because if you don't pay attention to the order and your answer is flipped around in a sentence while we do this I'm going to take away points depending on how much work or how little work you show the difference will be one point versus a half a point taken away so looking at this I'm already two sides I'll do it supposed to hit twice so give me a scale factor so distant on this side larger two smaller and this is easy you're just doing it twice and you see how easy it is it'll be easier on the test cuz I'm only asking for one of them alright so like I said you won't get both you're just going to get one of these now I'm going to give you I'm asking you to find the scale factor hurry up go ahead this is important so this right here scale factor set it up and give you some time set up the scale factor York rake leave it as an improper fraction don't know decimal leave it as an improper fraction cuz remember a scale factor is a well the decimal is you are correct with a decimal but trying to leave it as a fraction so that's one of them but make cuz on your test like I said some of you will get the word of phrase larger to smaller some of you get the price smaller to larger so flip the round yes that's fine Oklahoma Arkansas Texas I don't know whatever Southern Country you we we haven't used yet good good good again like the last person I said try to leave it as a fraction you are correct the same two numbers in the night I give you another 30 seconds cuz literally I'm giving you more time you need on this test question scale factor talks about the size pretty much pretty much so let's set this up set this up so looking at are triangles you can visually see this is smaller this one smaller this one's larger it will help it will totally help if you label them with the occult haven't used yet here's a color I haven't used it look at this one so let me read this last comment weed use all the numbers? Know that is a good catch you are not going to use all these numbers these other numbers were going to go over in the second for the rest of you some of these numbers are here to not confuse you but but make sure you understand which numbers you're going to use if you guys try and use 8 the corresponding side with 8 there's no number right here that corresponds with the eight members of what corresponds matches with doesn't matter that the blank it's nothing looking at this 28 right here just 28 should correspond with this side but there's no number there so we're not going to use 8 or 28 at all cuz there's no matching side to go with them look at that it goes this side doesn't match there's nothing that matches with it nothing that corresponds with corresponds with the 28th so there's no number but on this 12 + 42 they correspond with each other so we're going to set up scale factor a scale factor is just SF scale factor is just y over X but which is why an ex and that's where these come in the so we're only looking at 12 and 42 for going larger to smaller the scale factor for the larger to smaller is 42 212 and the scale factor setup from smaller to larger is 12 to 42 now if you flip these numbers around I'm going to take away points depending on how many steps and how much work to do but we're not done we are not done because we can simplify because we can simplify you have to simplify if you wrote 42 / 12 I would take away a full point because all fractions ratios need to be simplified right here hopefully you see that 42 and 12 can be divided by the GCF of 6 the greatest common factor 6 and 2 biggest number that divides both of them by 42 / 6 that is 712 / 6 that is 2 that is our scale factor 70 to 3.5 is odesza but leave it as a fraction please look at this it is the larger number over the smaller number is your answer what time is the only this part to answer but if you want to add that I'm not going to trip now we can have the other one look at all it is is the reciprocal you can / the same thing but I got a couple people here that said they didn't / 6 what if I / 2 birth what if I divide 3 first one said two different people said it so what's / to First Watch What Happens if you just divided by 2 12 / 264 / 2 is 21/6 + 20 10 / 3 if we divided by 3 look at this our scale factor 6 / 3 is 221 / 3 is all it is is the reciprocal but in this case this isn't the large over the small it's the small to the large so on your you better be careful and read that way it'll be literally the last statement on the problem it'll tell you which one to do question it's this easy this question is yes so yes you said it he said it was that easy so you should get four points on this question all questions are four points you're like what not yes I grade each question on a 4-point scale 4.0 is a 3.0 a B 2.0 a c on Plano Rd and then yes and I get half points to so you can get a 3.5 a 2.5 1.5 or 0.5 and even a zero goes all the way down so yes 28 points total on the test but your score will be a percentage 4 out of 100 at the end when I convert it so this one super easy excellent good job I'm glad you think it's easy not all questions over this is one that you know right now so what am I testing you on this question I'm texting you on do you know which two numbers I'm going to give you four maybe more numbers which two numbers do you use to make the sky factor and after you find out how to set up a skit are you reading do you know which scale factor to set up large to small or small to large that's reading and then after that do you know how to simplify a fraction that's what I'm testing you on on this I'm right here alright your copy. Hurry up I want to move on to the next one we used the same so on your test the difference is so on the test it won't have both of these on your test some of you guys the question be this these figures are similar find the scale factor from larger to smaller some of you will get that question but some of you guys will get the other question and said these figures are similar find the scale factor from smaller to larger instead so you're not going to get both of these are going to get one of those southbound showing both of them just to show you it's no different I'm not going to take away points if we use the decimal but try to stick with a fraction but if it's the if it's incorrect decimal then yes but make sure it's the correct equivalent son that I won't take away points to that all right I move on I move on everyone got this down yes so I'm not going to for the scale factor I'm going to go in reverse are they similar all right AR these figures set alarm and again I'm going to write it down the words similar because of the way my test setup came out my my form dead program it didn't let me use the word scale remember similar me and the scale drawing mean scaled similar is the same thing as scaled are these figures scaled is what I'm saying what are the drawings I'll do two of them but it went easy one first and then we'll do are these figures similar so here's the to the call them rectangles there ugly rectangle and if you just say yes or no I'm going to treat it like you didn't even do the problem at all you have to show me work all of these problems you need to show some calculation without calculation it's considered correctamundo are these similar are not all you got to do is I got to check on and the work is the checking hurry up you didn't come back cuz I'm going on with these notes weather here or not that is the work so let those people are stuck let me read this what this person say all I can show are the ratios I don't know how to show the work the ratios are the work the ratio is the word but the ratios plural are the work showing the ratios that's the work going to give you another 30 seconds so this person with a type perfect tint for you guys I only see a couple of you guys riding down those two guys that are practicing thank you for those that are not stopping it down you better be learning this is your last chance to learn Last Chance anytime there's a review for any class, last chance learning all right so we have four numbers we're actually going to use these p*** up these four numbers this time so I'm going to put it in the chat 24 corresponds with what number 24 corresponds with what number thank you one person to 3 I need a couple more 24 corresponds all right there 24 matches 24 corresponds 24 matches with what number 24 corresponds with what number excellent all right got enough answers good you have to choose a number so first how do you know these figures are similar scale factors need to be equal that's how you know that there's similar so SS need to be equal so if 24 matches with 10 so let's go 24 is 2:10 so I'm going large to small that means to match up with 12 / 5 good and all you need to do is see if they're still factors need to be equal so let's look at this first one we could divide top and bottom by 2 24 / 212 10 / 2/5 and we can't simplify any more look at these right here scale factors are equal so yes similar there's similar yes there's some of the scale factors of the same that's how you prove that they're similar someone said I did 10 / 24 does that work yes versus the last question it didn't say large or small small the large that is one of the things that makes this question a little bit harder you use as the mathematician need to decide which way you go I just went left to right cuz I'm lazy some of you guys though for some reason like they have the smaller number on top that works so let's go let's go check that out so this person said they went 10224 they want to check to see if that is if you go 10 to 24 then the ratio for the other one needs to be 5 to 12 are these equal let's check if I / 2 10 / 2 is 524 / 2 is 12 look at these equal scale factor equal scale factors equal plural yes similar it doesn't matter which way cuz I didn't tell you that's the thing I didn't tell you which way to say all right let's do one more but instead of a rectangle I'm going to give you a triangle all right here is the prime same thing are these triangles similar yes or no but you got to show the work if you just give me a yes or no I'm not going to give you any credit you got to show me some triangle only difference is you got it yes only difference is you got to do all three sides good job finish finish finish stay on as long as you can and if you can go on your phone go ahead go on your phone that's fine are you sure for that answer okay you good you checked it hurry up and come back you know I want you to follow follow along so you can see all these problems being worked out but have your phone ready though cuz I don't want you to miss any of this all right job setting it up almost all you guys are done I'll wait till this one last person comes back from Tennessee or Oklahoma to see if what they're answer is okay so rather than hear it like I said you could do one of the other I'm just going to go left to right the save time so look at this you need to match up your numbers I am going to go for this side I need to match with this size so I got four to eight now I'm in a switch up and go this side 10 needs to match with 20 notice I went here to hear I can't zig zag I go back and forth I went 428 that means I always got to start on this triangle as my top number if I do that I went for two 8 so I cannot do 2210 it is 10 220 and then my last one what color should I eat this one I'm going 15 the 28th now I just need to check and scale all of these down to the sky factor and see if they're equal 4/8 simplifies to 1/2 10/20 simplifies to Yas one good job what's 15 / 28 that's not 28-20 that's 18 my fault 15 / 28 I can't divide anything out 15 / 28 if I can't is just 15/28 I can't change it I can simplify it just by showing this around here just by showing this right here it's not the same this one is not equal I don't need to show it to both of this is what I just did to say to one of these not equal scale factor not equal if the scale factor is not equal for even one I don't care about these two being equal as long as one set of size one set of corresponding sides does not equal its not similar similar Seminole are now I'm going to give you a shortcut you if you could see that these two are equal you only need to show one of them you don't need to show both of them that's that's that's a shortcut for when it's similar for 8:10 a.m. I'll need to do one of them let me see the third side doesn't match up you don't you do not need to show me all 3 you just need to show me that one set or two different sets don't as long as there's one set that doesn't equal it's not similar but when they are similar and you need to show them all so not soon as I should less work less work for the symbol yet to show all the work I give you a chance to copy down yes go ahead so similar not similar little bit more work than the last one but not too much it's a she pretty easy work yeah be with you it's pretty easy work good job the next one goes up a little bit and difficulty but not too much but it involves calculate more calculations all right I'm about to switch over to the next one what I meant to ask you to do on this next question is find the missing thanks from these similar figures and remember again I'm going to write it down similar means scale 3/2 scale drawings oh yeah that's what are the Giants that all right find? So I got 830-270-2624? Find me the? Side now I'm going to give you a minute or two to figure it out on your own before I even try the South if you have if you have the answer and you're pretty certain of it put it in the chat let me see if you got it right I'll let you know right or wrong this will help you do all the other hard problems so make sure you pay attention to this one right here if you have the answer if you think you have the answer put it in the chat did you get up for lunch stretch around all my fault you were you got left hanging by generic lest you on left hanging ghosted you custody for the lunch date I know right I know Edwin Mississippi I left hanging close very close I know why you got that number check your calculations check how you did your Calculus that number it's closed I would give you and I know I would need to see the working but you would get maybe anywhere from one and a half to two and a half points with that answer depends on the work you're close with that one all right so I got an who answers I got two answers both of these are pretty close not quite alright so if you set it up if you set it up the most important if you set it up correctly and you mess up on the calculations I'll give you two and a half points if you set it up correctly but if your calculations are way way off in maybe two let's go with this so we got all these numbers and we're looking for the? First things first number one first step let's go right step 1 Step One find scale factor now here's the dangerous thing I didn't tell you which direction to go I'm going to do both ways and show you both ways so just to be clear so pay attention right here this find scale factor now we can do this to this or this to this it depends and then even then which numbers match up look at it h what's 6 32 matches with 2472 matches with a? So these two sides are the only things that don't have numbers that match up you you you the mathematician need to make a decision which set of corresponding numbers to connect I'll do both of them and show you it doesn't matter so I'm going to go start with the big numbers and I'll show you end up with the small numbers I'm going to go 32 to 2 94 32 / 24 but I can also set up 24 / 32 I'll show you will do will use both of them separately and show you same answer all right but these can be simplified so let me simplify it 32 + 24 even though I can / 88 I'm not going to / 8 I'm going to / 4 instead Jesse could see what's up if I / 432 / 4 end up with 8 24 / 4 end up with sticks look at this I have my two numbers right there so even if I chose the other numbers you can still end up with a bunch of the bigger numbers you still end up with a smaller numbers it's about setting it up so it doesn't matter which one's the same thing down here 24 / 46302 / 48628 I still end up with them so it didn't matter if I start the big number or not it's easier to start with smaller numbers yes if you see that go ahead but I'm not finished if I divided by 2 I get 4/3 and then down here 5 / 2 I get 3 / 4 both of these are scale factors going back to lesson number one in less than nothing less than 16 and 17 the first two lessons of module Wednesday are over three is different from 3/4 what's the difference though what type of scale do I have with 4/3 what type of scale do I have at 3 or just answer one of them what type of Gail do I have with 4/3 what type of scale do I have at 4:30 think about what we did with the pictures the two pictures when we compare them that's what I'm asking about if you have 4/3 what's up scaled you have and put it in the cat put it in the chat what type of scale do you have 4/3 if your scale factor is 4/3 what does that tell you about your scale drawing excellent one person for those who don't have it your three Force but what type of scale do you have right here if you have 4/3 NADA number all right let me do this part if you have four thirds this number is bigger than 1 if I have 3/4 this is 2 smaller than 1 in contempt good if you have the scale factor of 4/3 you have what's called an enlargement if you have a scale factor of 3/4 Which is less than one we have what's called a reduction this number makes a bigger number this number makes a smaller number you enlarge it you reduce it step 2 use the formula and what's the formula the formula is the original measurement times a scale factor equals the new measurement depending on which one you do coated it depending on which one you decide to do unit that's how you started your formula so if I'm going to do to a I'm going to do a reduction as a Dakshin the scale factor equals 3/4 because it is less than 1 as an enlargement scale factor equals 4/3 that's the only that's the main difference but it's a setup let's go look at this right here so we're going to use our equation OG * 3/4 equals new number do not let me Zoom and on this side it's OG * 4/3 equals our new measurement now this is where your love saw comes in you will decide which one you use depending on which formula now what number do you use for the OG in the newest zoom out in the second so we go back to our measurements we take our original number well we x 3/4 inch shrinks the number down we take original number and X 4/3 it enlarges the number that's why you need to understand this the OG versus the new that's where people mess up on the next step I'm going to wait a second so remember * 3/4 makes your new number smaller * 4/3 makes your number larger this is you understand the problem let me zoom out so we can look at back that are diagram all right look at this right here so if I'm going from this triangle to this triangle I make it smaller h 8 * 3/4 equals 6 I made it smaller 32 * 3/4 equals 24 it got smaller but what if I went the other way around if I went from this triangle does this triangle 6 is my original number 6 * 4/3 makes the number go bigger to become eight that's why it's an enlargement 24 * 4/3 in large is a 32 that's why I said enlargement so understanding which one goes where so that means you need to understand your equation down here so if I am multiplying a fraction is smaller than one to make it a smaller number that means this side right here is the larger number the larger number times the smaller the fraction that's less than one cuz it's reduction the smaller number going the other way if my fraction is bigger than one that's understanding fractions knowing that that's bigger than one my smaller number times a number bigger than one gets me a large now notice I did eight look at this let's do it again my larger number eight times as fraction that's less than 1 3/4 gets me this month 6 my larger number 32 x a small fraction of 3/4 gets me the number 24 which is smaller than 32 going the other way around my small number 8 kinds of scale factor bigger than one gets me the new number of eight six small 28 Millards numbers eight so understanding that will tell you which one you're going to do we're going to do both of them shows the same what's the only side we haven't dealt with we're looking for the? 72 m equal sign So based on this this this side is the larger one this side the smaller one so that helps to write it down larger and smaller I'm looking for the? I got a match it up with its Sunnyside to the large number is 72 72 * 3/4 equals my smaller number we don't know if that's what we're looking for that's why we're searching for the? all I need to do is multiply 72 * 3/4 will get her answer but let's set this up just to show you why I think this one might be better depending small number this time is it? Some number * 4/3 equals 72 corresponding side now that we have her quiz in let's go look at it what number times 4/3 equals 72 some number times four thirds equals 72 how do you find that some number u x is equal to how do you earn do it I had the * 4/3 to get 72 to undo it to get to the? It's the opposite think about this if you guys were going like this you start marching they did a video what was it if it was hurting you guys left left left-right-left but if you went backwards because I left left left right left going backwards to undo everything you'd go right left right right right cuz you have to go back or just be moving backwards and you be the opposite side just a reverse everything slow to go backwards you would have to divide 72 / 4/3 gets you back to the? I'm going to show you this right here is the same thing as this in a second let's do this cuz everyone understands this part all right fine let's finish it 72 divided by 4/3 equals a? So let's just finish it so we're going to divide again 72 / 4/3 we do not like dividing a fraction so let's change the division into multiplication and the fraction to the reciprocal of 4/3 the reciprocal of 4/3 is 3/4 this right here is 72 * 3/4 same thing is this 72 * 3/4 all you have to do is divide multiply your fraction and that's a skill you guys need to know how to multiply fractions and if you don't follow on will do that right now so even if you say stop this way you can still end up back this way that's why I need you guys to understand this before we move on when you find your scale factor you need to know to use the formula of the original measurement times a scale factor equals the new so if you know your scale factor you know what fits in there the next thing that you guys will trip up on which is the? And which is the number which is a? Which is the number which is the? Which is the number the ogier the new that's the Lexile understanding if you have the rate scale factor as a reduction the largest side goes here if you have the skill side as an enlargement the largest side goes there in the small go understand that one not quite yet but for this problem yes we are so instead of multiplying with 72 x 3/4 to change 72 into a fraction 72 over 1 x 3/4 and when we multiply that out we're going to get 72 * 3/4 with simplifies to 18/4 and you need to simplify that but when you know that this is just division let's just divide then 216 / 4 4 goes into 21 five times bring down to 20 subtract to get a 1 bring down the 6 4 goes in a 16 or X no remainder so you're in for both of these is 54 the numbers you guys gave me you messed up on the calculations you did the work right well that the work you did the setup right depending on how much work you showed me with the pain tell me how many points to give you but the correct answers 54 let's assume out 54 let's look at our picture it goes to 6 that's 3/4 the size 24 go into 32 that's for Thursday size enlarging but if I shrink down 72 3/4 time I shrink down 72 that equal 54 you could see that it's track down this will help you do this problem understanding this problem will help you do the rest of the problems that we're going to go into all right so too to be you're not going to do both you just do one of them figure out how to set it up this one's hard alright save this for your last question then you don't have to do all these problems in order just do the ones that you can do all right let's go to the next line all right let's look at this right here so let's take down some notes before I move on for this one right here so area Factor versus the scale factor the area factor is a ratio of areas so it is area 1 over area 2 it is not scale factor it is not scale it is more than scale it's a type of scale that's a scale of areas but it's not your scale factor so let's write this down area Factor does not equal your scale factor instead the area factor is equal to the scale factor x the scale factor this idea will help you on this next problem most people will only get half credit on this problem cuz they don't finish and listen I'm going to help you get full credit I want to show you how easy it is it's alright your back your back that's all that matter so look at this right here so let me buy your copy this down let me go through this again area Factor vs scale factor know that the area factor is the area over the area you're looking at area over area do the area faster does not equal the scale factor area factors equal to the scale factor x the scale factor so the question is how do you go from the area factor to the scalp that's this question right here I'll put that as a hint that's not that won't be on the test this is important notes that uses color going from area factor to scale factor that's what this problem that's the main idea for this problem going from the area affected to the scale factor how do you do that I'll give you a second trying to get as much as you can hurry up come back as much as you can everyone should at least you two points out of four on this one so what would this be as a question of course it's not as easy to join your hands on the test you for that is the only constant on every single problem I got it when you're doing this test Thursday I have to see your hands the whole time. I don't care about that has both hands yes while you're taking the test yeah but what's your desk. no no and no I got three answers at the same time you're all incorrect but I'll give you half points for that you just didn't finish I'm going to give you another 30 seconds if you got that far everyone else should be getting close you three got half credit at most depending on what work you showed you just gave me this you're not understanding this I'm going from area fast at the scale factor how do you go from area Factor just to scale factor you did was set it up and not even finish but you set it up and get some points for that that's good I'll give you credit for that alright let's get on with this so what these three people did and I don't get it I'm stuck here for their stuff pay attention now what these three people did right here so what did he say 72 + 128 represent look at this letter they represent the areas of these rectangle the area of the small rectangle is 72 the area the big rectangle is 128 so find the scale factor left to right that's not going to change what you guys did was just this 72 / 128 that's not the scale factor what you found was the area Factor but before we change it to the scale factor simplified first alright you divided you kept on the vine and you got a chance to do it one more time you can simplify it one more time but for the rest of the people that don't see it let me do by I'm going to go / 2 if I / 2 I end up with 36 / 64 I meant / 2 again I end up with 18 yes you can hurry up and come back if I / 2 end up with 18 / 32 keep on the bottom at 2 / to one more time so technically I could / 8 / 2 you end up with 9/16 that is still the area Factor 9 hour. Watch out cuz we can't do part of it right almost you're so close on that one almost now look at this so why do you guys will get that hair you divide the principal and you end up with the simplified version of 9/16 for your ear Factor 72 / 128 simplifies down to 9/16 that is still your area Factor I'm going to zoom out look up here the area Factor does not eat with a scale factor that's the first thing but what does the area Factory twill instead it is the scale factor times the scale factor so let me instead change the area factor to scale factor time scale factor so instead of area Factor it is El factor x the scale factor is equal to 2/16 now I'm not going to let some of these know square roots I'm not going to teach square roots just yet you got to think I got two twin fraction give me two twin fractions that multiply together to get 9/16 and here's how easy it is instead of going scale factor to make two fractions fraction line times fractions 1 equals 9/16 here's how easy it is cover the bottom number on give me to Twin numbers give me to Twin numbers that multiply to get 9 what are my twin numbers that multiply to get 9 3 3 x 3 there's my twin three times three Now cover the top number the numerator the bottom what are twin numbers that multiply to get 16 nope think about it what is 8 * 8 give me to Twin numbers that multiply to get 16 fix your hands are pigs or answer yeah little bit of a steak cost you come on you're so close two twin numbers that multiply to get 16 for x 4 and in the end what do I I just said find the scale factor find me the scale factor the scale factor equals League of this scale factor x scale factor 3/4 x 3/4 doesn't that just mean one of these is a scale factor yes so on this problem right here let's go back through and do a quick review I'm going to the areas of two objects you take your air as most of you guys will go left to right and you're going to give me not a scale factor and give me the area Factor fine once you're done setting up your area Factor you need to know how to simplify it all the way. Everyone is going to get a nice simple little number like this and then you set it up as twins scale factor x scale factor you need to figure out what the twin numbers are and I just need one of them one of the fractions so set up your area frat area Factor fraction ratio simplified all the way down all of them will simplify down to some that you can find twins of so 3 * 3 makes 9 4 x 4 make 16 you're going to get the results so you're going to have to reverse in and find the twins once you find what the I only need one of these fractions that's your answer that's how easy this one problem is yes sir-re all right that's fine try and go on my phone your phone I mean still got a couple more alright next problem what would he parameter and area if that's not an SSN SBS the scale is 8 Beach 1 inch and I'm just going to give you a diagram that gives you the perimeter and area of an object perimeter is 28 feet and the area is 40 yeah 40 feet squared you can tell she find the dimensions you should ask find the measurements by breaking apart you can do that that might help you that might help a lot of you find the perimeter find the area Factor we're shrinking it down two measurements 8 feet is 211 in so fine the new perimeter find the new area 851 inch for converting It Down 2 inches or can be converting feet to inches so we got 28 G we got 40 feet you got the kind of figure it out 28 feet is the perimeter of 40 ft squared is the area all right let's go look at this right here so we have eight p21 in so let's look at this right here we have the original right here we have the array we know it's in feet but we're trying to change it to inches so look at this rate first you have to find your scale factor and which one is the better one to use and to think about find the scale factor so we could go eight Beach 8 feet to 1 inch or 1 inch 1 inch 2/8 feet which one's better so you can see this right here if this is 8/1 that's 8 this is an enlargement 1 inch to 8 feet 2 1/8 that's a reduction no that's fine feet to inches we're reducing it down we're shrinking it down so even though this right here goes 8:50 to 1 in if we're going to do and use the formula we're going to use a reduction so we have to use this we are changing feet to inches so we have a reduction reusing this one here so then we go number two we use the formula OG time scale factor equals the new measurements and since we know it's a reduction we're going to use 1/8 we're going to take the perimeter and scale it down so to get our new perimeter 28 ft x 1/8 equals our new measurements someone said what's the perimeter the perimeter is the length around the thing about the fence around your house a house that's around the house but why it relates to this just imagine if it was like a paperclip and we unraveled it let's say we sold it out one side to side 3/4 size and becomes a straight line if you go to Home Depot and buy some fencing it's rolled up if you unroll the fence without making Corners it's just a straight line it's just like one wall one side you have to wrap it around the corner to make it close it up but if he unraveled the straight-line that's why we use scale factor with that 28 * 1/8 * that we end up with 28 / 8 that's our new number but let's simplify that we could divide top and bottom by 4 28 / 4 is 7/8 / 4 is 27 / 2 in 3 1/2 in sew the perimeter of model is going to be three and a half but now next thing we got to do to we got to find the area so that's three actually so two-part problem find the area factor to find the area Factor you got to remember it's a scale factor x a scale factor and our scale factor is 1/8 1/8 x 1/8 equals 1/64 which is your area faster so we're going to use OG area find the area Factor that equals our new area tomorrow G area or tea and we're done with this one after we finish 40 times your area Factory was just one 64 let's make this into a fraction we end up with 40/64 which we could divide both by 8 40 / 8 564 / 858 and then we can simplify that anymore this is our new area 5/8 square inches retract 40-gallon off all the weight of 5/8 of a square inch that's what's it's in there we've done this before but now it's a lot more interesting let me go set it up so a map has a scale I'm making stuff 3 inches 232 let's set it up 3 inches to how many miles I'm anime 3 in 222 that's all funky and doesn't really match up 22 miles I'm going to do with two different problems on these right here the first one we'll just do this one if 2 are let's see seven in seven two towns are 11 inches apart on the map what is the distance art and I will do another version what is so what if what if I give you the actual distance what is it on the map so let's do this one first I think this one's easier set up first and then we'll do another one after that so we're going to go through all the problems and if we go to the other problems again so on a map a map literally IMAP and you know you look at the park yellow cat that BART map that's not the actual distance that's what's a map its scale down a map has a scale of 3 in 2:20 to 3 inches on the map in real life is 22 MI if two towns are 11 inches apart on the map what is the actual distance apart in real life round to nearest one decimal place round to nearest 1 decimal so this is the only I think this is the only problem on your test that has decimals everything else should be a fraction that nice fraction or a whole number now this right here so let's look at it there's a scale so we first just like all those other problems first things first find the scale factor so number one step one find scale factor now here's a thing there's two different scale factors that depends on what we're doing so that's why Lex outcomes of my but first let's do both different scale factors so we can go 3 in 22 miles two different colors 3 inches 222 miles so using this one right here I'm gonna is a reduction 3/22 is a small fraction 3 out of two pieces that means we shrink it down that's why this is a reduction going the other way or 22 miles over 3 inches that right there is an enlargement because I got 22 pieces out of three that's more than a hole so this is an enlargement now before we go into this so that's why before we go on the step to step two is use the formula let me write it down first though original X your scale factor equals your new measurements now let's look at this right here let's read it this before we even do this we find two different scale factors using your Factor this will help set up your formula but you got to read this first on a map and map has a scale of 3 in to 22 Mi but let's go read this part we got a scale factor is two towns are 11 in apart on the map what is the actual distance so we're given that it's 11 in and we're going to make it bigger enlarging it to the actual real distance so we're going to use the enlargement we're we're looking for a new number that's how you tell the difference if you use the other way around you could still do it but you need to know where the place is so let's use our Alexa let me zoom in really close so we know that we have the math distance which is 11 inches apart but we want to find what it is when it's bigger in real life that tells us this the enlargements where are using the enlargement because we're making it making larger actual distance we're making a larger actual distance that's actually ugly Henry I'm sorry making larger actual distance so enlargements that tells us we use that scale factor 20 2 / 3 we're changing 11 inch on the map for changing 11 in on the map of by multiplying by the scale factor of 22 over 3 to get the larger real life distance Solstice overdoing 11 * 22 / 3 so that's our actual in real life how many miles is that so 11 * 22 / 311 * 22 is what 242 divided by 3 so now all we got to do is divide and that's how easy it is to find our real life distance so let's do that three / 200 North 242 / 3/8 * 3 * 8 that's 24 weeks we get a remainder of 0 we bring down the two Frida's not going to 2 so we got to put a zero down 80 bring down a zero we subtract we get it to you put a decimal place down bring that we get a 23 goes into 26 times 3 * 618 with a remainder of 2 even though it's one decimal place when you're rounding off to one decimal you always need to look at one extra if I say round to two decimal places if you look at 3 but they Round Up 5 decimal places you look at 6 it's always the decimal place asked that tells you how to round to the nearest place that you want so we want 80 point something if you cut her off at point six Watch What Happens I put another zero down bring it down 23 goes into 26 times now I got decimal places I'm done I don't care what it goes on anymore look at this right here think about it in terms of money $80.66 I don't want pennies one if you have a 1 decimal place is the nearest dime what's the nearest dime $80.70 but I can drop the zero off 80.7 see if you had stopped and just drove 80.6 I take away a point cuz you didn't roundoff you have to finish and round off cuz it wants one decimal place that's do you need an extra second decimal place this sixth tells you this this becomes a7rii Roundup so that right there is looking for the actual this look at it we're from 11 in to 80 mi in real life that's like going from Oakland to Sacramento so on the map on our map on our map Oakland to Sac is 11 inches apart but in real making it up it's actually less I don't know let's go look at it hey Siri what is the distance between Oakland and Sacramento Sacramento is about 80 miles from 82 miles buy cars 82 I'm a pretty good guesser so let's do the other way around now what if I asked you to find the map what if I asked you to find the map so I'm going to change this I'm going to rewrite it so we're going to do a different so and I'm going to show you what no different it's about how you set this up it's about 1 setting up the scale factor step to using the scale factor to write your equation and it involves reading and understanding your reading something to do another problem like this except we're looking for the math distance instead so let's do that let me copy tomorrow and we'll use the same scale to use the same scale take this down for your notes a map has a scale of what did I write down three in 22 MI I got 3 inches of 22 Mile if what is Oakland to Fremont is Oakland to Fremont and Oakland Oakland if two cities are 112 MI in real life how far are they apart on the map very similar except instead of looking for real life we're looking for math now so still step one I miss y'all Factor let's find the factor of the scale and again most people will not understand or you just look straight to this 3 in to 22 Mi 3 in 222 MI and 22 MI C3 in this will depend this will decide combining these two right here reading and setting it up will depend on how you smell will pretty much set up how pretty much will let you know set up your equation Step 2 so let's read it before we even do Step2 let's read it again so we got a map has a scale of 3 inches to 22 Mi so 3 in free answers about this in real life is 22 mi in real life two cities are 112 miles apart how far are they on the map so what the measurement on the map let's do I forgot to write this down set up your thing and one decimal place again round answer to one decimal sorry about that so looking at this right here we're taking so looking at this right here we're taking to see we're taking the actual miles apart and shrinking it down reducing it to a map size so let's review let's read again a map has a scale of 3 in 222 MI is two cities are 112 miles apart in real life how far are they apart on the map round answer to nearest one decimal find the scale factor because I didn't tell you which way to go write them both down and then do the next question so it's either 3in to 22 Mi or 22 Mazda 3 in which one do you use remember Riddell enlargement reduction 3/22 that's a fraction less than 1 so it's a reduction 22/3 that's an enlargement let's read what we're doing we're taking the dis since the two cities are actually apart and we're trying to see how far they are parked on the map so we're taking actual life and shrinking it down to a Mac so it's a rare using reduction so when you write your two scale factors ask yourself reduction or enlargement or enlargement let's write this little bit through since we are taking real life scaring down to a map it's a reduction so we use 3 / 22 scale factor that's first question people need to ask do I use 3/22 or 22/3 read it carefully and I'll tell you for reducing now Step 2 technically that's tough to get the mental stuff but let somebody was step one step to use formula used for me so it is the original number times the scale factor equals the new measurement original measurement times of scale factor gets us the new measurement and since it's a reduction since it's a reduction what is our original number we are reducing 112 miles we are reducing 112 MI down with the scale factor 3/22 C when you multiply by a fraction smaller than one we create a new measurement that's going to be smaller traduction original X reduction we get our map distance so we get 112 * 3/22 and all it is is the math now let's go do that calculation 112 * 3/22 what is that 336 I believe 300 36 / 22 and then I do not want to do long division with 22 I know I can divide by 2 if I divided by 2 115/60 168 168 / 11 I think let me just cheat music yes 168 this part I'm not going to cheat so now I got this this is what the map is its 168 / 11 in that's what the distance on the map but that's not acceptable we need it to one decimal place rounded to one decimal place so we got to do division now so this becomes 168 / 11 I notice I put two decimal places cuz I know round to one decimal you always need one extra decimal place when you're rounding so let's do the work 11 goes in a 16 one time let's subtract we get five we bring down at 8:11 goes in the face 85 * we subtract baguette 5503 we bring down a 0-11 goes into 32 * which is 22 subtract bring down this 11 goes into 87 times so it's 15.27 but we need to round it to one decimal place so how many inches on the map if in real life two cities are 112 miles apart with this scale factor 112 Mi scales down to 115 point 3 inches that's our scale factor finding so understanding how to set up the scale factor understanding one how to set up a scale factor one of two and then when you read it you got to see remember if the scale factor less than one at the reduction that the scale factor is bigger than one it's an enlargement so you want to take a second and go back and re-read this problem and ask yourself is this an enlargement or reduction and when you decide that that tells you which one so let's go do a quick reread if two cities are 112 miles apart in real life how far are they on the map taking real life shrinking it down to a map so it's a reduction so we use this scale factor 3/22 as their scale factor then next F1 plug it in the formula so since we know what's a reduction reused 3 / 22 what are we and that's the whole thing what are we we are reducing the hundred twelve miles so it's the original number reduced by 3/22 when we multiply this together we get our new measurement did all that work and found out it was 15.3 in that right there that's a word problem so if you were a little bit late best part one is pretty much picture problems part 2 is word problem yes we just started so we just did this one problem so far as we did to this is dissimilar so are so this one right here we decided to take real life map we would decide to take the real life distance and change it to the map distance the one we did before same problem pretty much except we change the map we wanted the math distance to become the actual distance so let's do a quick review and compare same thing a map has a scale of 3 in to 22 Mi if two towns are 11 pictures of park on the map what is the actual distance apart in real life round to nearest one decimal place no matter what first find the scale factor here's your scale what scale do we use so if I just left to right 3 in to 22 MI 3/22 is less than 1 so that's the reduction or something around 22 miles to 3in and enlargements before we move on you need to ask yourself is this an enlargement or reduction problem I'm taking 11in on the map and trying to change it and get the actual real life distance so I'm taking a nap and making it bigger into real life so what's an enlargement so we use this scale factor so making larger a natural distance to enlargement so Regional time scale factor equals new so we use a 22/3 as an enlargement scale factor but what are we in largening we are enlarging 3in on the map towns are 11 inches apart on the map enlarging 11in on the map by the scale factor so becomes 11 * 22/3 that gets us our new measurement we got to do the calculations right here 11 * 22 is 242 / 3 but that's not an answer we want one decimal place so we know that this is a division problem 242 divided by 3 we always need one extra decimal place more than it's asking to round off we divided it we found out it was 80.661 decimal places 80.7 so the difference of when which nail Factory set up and use that's what you guys need to know and the problem that's the that's the main difference between the problem on your test some of you will actually find the map to the actual life some of you are going to go ask your life to the map that is the main difference you have different numbers sure you're going to get different numbers but the only difference is which way are you going that's Lexile that is understanding what Multiplex last problem I did not have a chance to go over during regular class is the diagram floor plan let me make I made this one up yesterday and I'm going to use the same thing so you're going to have a floor plan on your problem somewhere and I just made it up this way so here's your bedroom is your bathroom is your living room and I have the kitchen here I'm asking to take out the kitchen I'm going to take out the kitchen okay let's go with them here to here is 5 in it is here is 6 inches here to here is or inches and then I went here to here 10 inches I'm making it slightly different than the one I had before now let me write down a question let me put on the scale first the scale is 7 feet to 1 in going to give you a chance to copy down before I move on on this one don't worry find dimensions the living room I give you a chance to copy this down so it should be pretty or on yours this is of the last problem of part 2 part 2 so I guess part 1 or picture problem even though this is a picture of me and there's a word problem technically the first one you got pictures and measurements and you're going to do calculations to find stuff part 2 as a bunch of word problems not about to just three give me a chance and I'll start in about a minute or so on first try now and see if he could do it I want the actual dimensions of the living room the actual dimensions of the living room yes find that find them find the measurement of the floor to find the measurement of the living room first you yes find the scale measurements of the living room first yes do that we don't care about the bedroom we don't care about the bathroom we just want the living room West Ashley of the living room give me another minute or so before I move on and start on alright let's get on with this so let me ask me pull out living room so so we can use this to set it up I'm going to do a small sketch off to the side right here of the living room so we want to find the real life living room but let's get rid of the bedroom in the bathroom that gets in the way so this is something that that will help you guys when you get into geometry throw away worthless information so this is the opposite of connecting Legos it's tearing them apart to the only piece that you want so we know the living room is a rectangle a long rectangle look at this right here we need to know where and we know it's a wrecking we need to know the length and the width look at this from here to here is how long the living room is that is the bedroom connected to the bathroom look at this up here the bedroom from here to here is 6 the bathroom is here to here for what is the length of the living room so look great and if you go down here the length of the bedroom here to hear 6 the length of the bathroom from here to here is for connect those two pieces that's the length of the living room yes the length of the living room that use a different color still stands out is also 10 in now look at this right here the bedroom from here so we need to find how wide the living room is from here to here it's 5 in going across that's 5 in wide so this is five and this is five look at this right here from here to here is 5 because it's across the look at this this whole thing is 10 if this whole thing is 10 and this is 5 this has to be yes thank you it's all so five put around this side just cuz 5 right here so it's 10 in five in 10 inches is a 10 x 5 in sketch what is it in real life you actually do maybe you could go you can think about what's 1 inch yeah what's 10 inches so you use the scale factor so all of these all we got to do is yeah that's right you got your gun that's how easy this problem was are those guys that don't see it I'm going to do it in the second let me play we just took a living room I don't care about the rest of it that we found out the measurements of the living room I want to find the length are the actual dimensions of the living room so what are the links and Whit's what are the length and width that's the question that's pretty much what this what's the length and width in actual life and we have the skill right here 1 in equals 7 feet if 1 in equals 7 feet and I got 10 in in real life how many feet is that yes I have one in is the seven I Got 5 in right here what's 1 inch worth 7 ft what's 5 feet worth how do you show that so I'm going to use the message formula remember you have the original measurements times the scale factor equals the new measurement and lot of guys are stuck on the scale factor don't get hung up on it so let's go look at it this is my diagram I want actual real life I want to go from inches to feet so let slip I'm growing so if I set up my scale factor let's go to the scale factor right here the scale factor equals 7 ft / 1 inch or 1 inch over 7 ft yeah this is just like that last problem we did are we growing or are we shrinking and that will tell you which one of these to use this right here for those you guys that are stuck look at this this right here is bigger than 1 so it's an enlargement this right here is 1/7 smaller then one so it's a reduction reduce so this one grows this one shrinks I am taking our 10 inch by 5 inch living room and work doing it to real life so we use an enlargement room diagram real life is an enlargement so that's why we use this scale factor so we got our scale factor * 7 ft 1 in and what's our original measurements we got two of them what are the dimensions are length is 10 or width is 5 you need to know you need to do you need to do spice you need to know you need to do it twice so let's put it down we got 10 inches and 5 inches and what we're going to do we're going to multiply both of these by 7 feet over 1 inch 10 * 7 70 so we got inches and feet over 1 inch inch and then inch over inch goes away it's a but that's a one right there leaving us with 70 ft so it's 70 ft long yeah you don't need to do all this if 1 in 7 ft I got 10 in 1 in 7 * 10 in * 7 hey 10 what's 7 / 1/7 I could have just X old measurement by 7 7 x 1070 hey look at this guy * 7 5 in * 7 ft 5 x 7 35 Watch What Happens step 5 in x 7 ft by 35 I got inches x feet over 1 in 1 inch / 1in goes away leaves us with 35 ft so what are the dimensions of our living room 20 feet by 35 feet that's is that Brian that's it yes that's it you don't even need to use the the formula if you understand the scale Once you pull out what you want you look at your scale but if your steps if your scales not a unit unit rate we're lucky it's over one what it's not over 1 what if it was uneven you would have to use the scale use the formula that's your scale factor you take your old number times your new number to get you take your old number times your scale factor and it comes out with your new number you can it'll always have my old number your OG number comes the scale factor get you your new measurement we turn 10 in into 70 feet return 5 in 35 ft we scaled up so our scale factor has to be bigger than one so that's technically all the problems right there all the testing example of every single problem that we have done

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