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Math 7 - Module 1D - Lesson 19 - the Rest of the Lesson

Added Jan 15, 2021 •

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These are the exercises in the Notes Packet (not an assignment but part of the notes) you were supposed to do and try on your own. It's for you to check to see if you can succeed on your own. Watch the video to check your own work.

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what is the thing the Latin these are the problems you were supposed to try and do on your own to make sure you could do the homework / problem set so let's go through this right here so we have the cover this up with start over the triangle depicted by the drawing has an actual area of 36 units so this is a this is a depiction is a drawing of an actual trial that supposed to exist but notice that pictures not there what can help you guys what you don't realize you can always make your own drawing and that helps you organize your thoughts so that second triangle that's not listed as you're right here we have an area of 36 that's what it said that right there what is the scale of this drunk what is a scaled is gray drawing right here so you need to know that each of these squares little squares is 1 units long so if I go top the Bob look at the hash marks three of them that means this is 3 units high that's why it's 3 how long is it that's why it's 6 so it's a 3 by 6 so we have the area of the real triangle but we only have the side lengths the second triangle now that's the information we have but it wants the scale of this gray drawing this gray one right here so want to find the scale scale factor from the Big Y Jose is going to be so let's find the area first so that's why we got this right here find the area of this triangle area of a triangle is base times height 6 * 3 / 2 6 * 3 is 1818 / 2 is 9 so now we have the area of both of these triangles who let's put that here cuz let's have a matching so the area equals a equals 9 equals 36/8 equals 9 so let's put the area factors as we have the two areas we can compare them what we want so the area affected what we want over what exist what we want is the scale picture drawing that what exists is the one the beer they weren't there so the area factor is 9 to 36 so 9 / 36 simplifies to 1/4 there's our area Factor right there so we know that the bigger triangle if we divided by 4 for X small color is this new one right here in terms of the area but it wants to scale area versus scale or two different things we showed that during the lesson so we know that the area factor is scale factor x scale factor and we're looking for the scale factor just one of these we just found at the area factor is 1/4 1/4 equals scale factor x a scale factor and you need to know the scale factor is the same for both of them scale factor scale factor the same so 1/4 equals scale factor time scale factor 1 * 1 equals 1 but what number times what number equals 4 and it has to be the same number 2 x 2 1/2 x 1/2 is 1/4 so if scale factor is 1/2 times what will area Factor scale factor time scale factor give me the scale factor that's what we're looking for so that means that this triangle from this We Shrunk it down by 1/2 to get this so that means If We Shrunk a day this is double the size so this side is 3 the side has to be 6 in this side is 6 this side has to be 12 we can check to see if the area of this triangle is 36 the triangle base times height divided by 2 base times height divided by 212 * 67272 / 2 boom 36 and we were given full circle so we found the scale factor how did this is just checking your answer knowing how to work backwards if you're given the area Factor can you find the scale factor so let's go look at this right here all right so let's go look at the next exercise so some of us got to this some of his dad but I'm going to move on and finish these I'm going to finish number to ABCD and then we'll do the homework all right so this is for notes right here we're finishing up you were hopefully you guys are able to do this on your own but if not that's alright let's do this together use the scale drawing set of two different apartments to answer the questions it's a 34 questions use a ruler to measure all right so scale scale not area scale scale 1 in a scale drawing corresponds to 12ft in real life so we can do this right here the scale factor is 12/1 to the scale factor is just 12 on this this one one inch on the scale drawing course bus to 16 feet in the actual apartment so the scale factor in this one is 16 I'm just jumping ahead this is the exercise questions from the notes that I asked you guys to try and do to see if you could do the homework so we'll get to this once we do this will start the homework but I just want to finish these up so people have notes if they want to try out the home Cameron so scale factor for both of these are different and you look at it there different shapes looks like they're different sizes and let's compare find the scale drawing are for both apartments in the area for both of these apartments scaled scale means was find the area of just the pictures so we got to measure this right here this right here is 2 + 0 did two and a half so this is two and a half inch I will choose the right color 2 + 1 + 12.5 2.5 in I don't need to find the top cuz we know it's a rectangle this side of the Define one of these sides and there's more sides a right with here let's find how tall this is this right here is 0 to 2 so that's 2 in 2 inches high all right now let's go to this next one right here what's fine I'll let you do the area first and then we'll measure this one after so the area of this I hear area equals base times height are bases 2.5 are height is 22.5 * 2 so the area is equal to $5 find the area of this one so here's a here's one there's two right in between is 1 and 1/2 so 1 and 1/2 in 1.5 in how tall is it a there are exactly the same height look at matches but all right fine let's check I wanted to go back but I'll make you happy 2 in the area of this one right here x height bass is 1.5 times are height of 21.5 * 2 is 3 so the area of our picture this one right here if we cut it up into a bun little squares there would be 5 Square I know how do you have five squares in it it's just the way things are measured so this right here as five squares in it or three equal units square units picture wise this one is bigger but let's compare areas so look right here so fine the scale are in for both apartments and then use it to find the actual area of both Apartments remember the formula I'm going to write it down up here I have the areas of this blueprint of I have the area blueprint areas of the blueprint yeah that's how I say it and then I have the scale factor for both of them so we're going to find the real life areas and here's how you do it area so old area find the area Factor equals the new area measurement one thing is missing so we got the older here's the old area here's the old area for this one but we want the area Factor instead we have the scale factor so in order to find the new area we need to find the area factor for so there's another piece of note need to know that the area factor is the scale factor x the scale factor which is scale factor squared another way of writing it so it's fine building scale factor that means our area factor is just 12 squared or 12 x 12 12 x 12 good 144 does anybody know what's 16 square it is 16 * 16 * 16 I get it what is 16 * 16 I'm waiting you can figure it out Tuesday going out their phone to punch up the buttons I don't have a calculator thank you one person to calculator 256 so the area factors to 56 after finished go through all this yes so old area X the area Factor equals the new area so will for both of these we're going to compare so let's look at this the picture the area of our diagram is 5 the area of this diagram is 3 but now can I look at the area in Real Lies so let's go plug it in Old area 5 find the area factor which is 144 that is equal to the new that is equal to real life area real not just new but real life area on that one this one right here the old area is three times the area factor which is to 56 that is equal to the real-life area of this apartment all right calculator on the phone 5 * 144 720 so this bourbon apartment is 720 square feet in real life 3 * 256 so in real life 768 square feet what different in the old ways the diagram in this diagram this is bigger you can see it's bigger than this so that's 5 versus 3 but when we find out the real life measurements by doing old Ariat Azaria Factor this smaller looking diagram in real life is actually a bigger apartment than this one that's just one of those things that prove it's like you know what is this is like a new version of the better by which is the better buy don't ever in this another way to say don't judge a book by it's cover cuz it might looks like but flipping pages don't judge a book by its cover which apartment has closets with more square footage justifier answers all right so I think we want to find all the closet so we got one closet two closets we got one closet we got two closets we got to measure it so these are two different lengths which apartment has closets with more square footage but let's just do all four of them but this looks this definitely is a bigger closet than this one this one this one looks like a bigger closet than this one but in real life which which bedroom has the bear claw that's a huge looking closet though but let's figure it out so this is 1 inch long how tall is this that's a quarter of an inch cuz that's a hat that's a quarter so let's put that so this is one inch long this is .25 in high let's look at this one that was also .25 in hysys put a .25 here but how long is this one that right there is 0 1 and 1/2 and 1/2 inch 1.5 inch switch colors that is .25 that is .25 so both of these have the same 125 right there noticed the same yet you don't know that this right here is only a half inch tall so point 5.50 this to have the same amount of decimal places must measure this one woo-hoo this is more than 25 so here is zero here's one here's point five and that's between .5 and 1 so that's .75 High you need a ruler I know so it's the same thing old area of old area tons the area fact we want to find the new area so these are definitely smaller so let's compare the two bigger why alright so someone said why am I the question is which apartment has closets with more square footage justify your thinking what's the biggest closet both of these 2.25 high but this one is one long this one so this is the biggest closet in this house I don't care about this one of those find the area for that one and let's look at this one right here officer .25 base this is .75 F-150 so this one's a bigger closet so that was a smaller let's get rid of that one so I'm only going to find the area for both of these and once I find which one has the bigger closet I'll say this apartment has the bigger closet overall let's do this one right here going to find the area old area so 1.5 x 2/5 that's our area area of the closet and then on this one here that closet were looking at that right there area of that closet .25 10.75 just to make things go faster I'm going to cheat music letter yes it's cheating 2.5 * 2 can I do it right one point five * 25 so that equals 0.3 75 that's the area let's do this 1.25 * 27.25. 2775 * 75 0.1875 this is the area of the drawing but in real life we got to do the same thing we need to convert it into real life picture this point three so just imagine this is $0.38 this if you rounded up is $0.19 38 senses more than $0.19 that's rowney I'm using rounding I just already got a question I knew you were going say that how did I get $0.38 so remember cents is two decimal places this is three so I have to round off 5 is bigger number if it's 5 or bigger the number before goes up one so this is five that's 70s become an eight that's why it's $0.38 I don't care about the five cuz my pennies on the 818 sense but the 7 is bigger than 5 so becomes 19 set rounding ski saves a time so this is supposed to be the bigger closet but that's only in the drawing we got to do real life again remember old area the area Factor equals new area where you got the area faster or right here right there so let's double-check this right here so using our area Factor old X area Factor equals new old is 0.375 X or area factor of 144 what is that and on this one times area Factor equals new old is 0.18 75 x Arya factor which is 256 equals Arnell is my calculator and cheat again yeah pretty much you can get your sense and Adizero place that totally works I want exact number so and I don't want to round so 18.75 I'll do this refers to the Sargon my calculator that was my old number I multiply these two together that equals 48 so my new area closet the big closet in this apartment is 48 square feet let's compare that to the closet right here .375 44 the area for this is 54 now some people don't care about that little bit so this house where is this condo just a little bit bigger what that means is we got a little bit bigger bigger bathroom and closet who knows bigger kitchen all those little things add up but some people like man I got a lot of clothes I got a lot of shoes I got a shoe collection so I mean big closets even though of this condo is smaller it's closet is bigger but that's a lot what you guys do realize that those was how much are those 6/6 square feet be at 6 square feet boring that's huge you can fit Harry Potter in that closet that's how big it is 6 ft space yeah that little crab space so even though this apart in a smaller its closets are bigger so in real life the city apartment is bigger but it got puny closets in real life this apartment is smaller than man that's a beautiful closet that you know who knows alright let's finish CND which same concept I'm asking to skip this which apartment has the largest bathroom cuz we do the same thing we measure it where's the bathroom so here look this one is hard for one this right here we got a perfect rectangle what's the size of this bathroom in real life but look at this bathroom there's a bathroom and Lotus right here what's that is that because they didn't didn't put in the doorway so that means if you're in the living room and use the bathroom everyone watching in on turns or what are you doing to close the door this right here what's a harder question because you need to realize the find the area of this one you got to close it up and make a rectangle so you got to find the area of this and compared to the area of this in real life and then let's see that's that one right there same thing a one year lease for the Suburban apartment cost $750 per month a one-year lease for the city apartment cost $925 a month which apartment offers the greater value in terms of cost per square footage this right here is a challenge question remember next week we're doing the reading STAAR math test this right here is considered question Sol math questions are on a difficulty level of 5 what's over that one level 1 is what can't do this what's wrong with you type of the question question to ask question 3 man that's okay that's alright that's an average question not super easy not super hard average level Forest man I actually broke a sweat trying to figure that one out and level five is all man my brain hurts this is kind of between if there was a halfway between four and five does a 4.5 level question because it involves a lot of steps but we've already done all these steps so if you know the parts it's actually a level 2 or 3 but it looks like a level 4 and 5 but let's get on with this in Finnish so who cares that it's a one-year lease we know the first apartment is 750 that's in the suburbs the one in the city is 925 but look at this right here what is the cost per square feet so it is money how use a different use black so it is money over square feet which is the better price so it's a better price things better problem money over square feet so let's look at this first apartment that's based on square footage all of the square footage so the first Suburban apartment is $750 a month that is over what was the square footage we found that out right here that's the Suburban Apartments Suburban square feet is 720 it's a little bit over a dollar per square foot that's not too bad now let's look at the next the city apartment cost $925 and the square footage is 768 all you got to do is divide just divide cuz we want a unit rate a unit rate is another way of saying just divide so this right here we can rewrite this as 7 gyro place holders cross out that right there 75 / 72 I could simplify the fraction some more but punching a calculating I don't know how many simplified so I'm just going to write it as 925 / 768 and again I'm going to cheat and use my calculator 75 / 72 5 / 72 for 1 square foot in the house when it breaks down to is 1.0 416ce 667 but we don't care about this long decimal for talking about money per square foot we just want one decimal place to decimal place is my fault dollar and $0.04 but we always got to go back one and check the one so I just so it's about a dollar and $0.04 a square foot I guess this right here 925 / 7925 / August 68 that's what shows up on the calculator but weekend we don't we don't go a dollar 24 for 4 to 7:08 since we round off two decimal places but we always got to go back one to see if we round up or just cut it off that's four or less so we just cut off so it's about a dollar twenty a square foot even though you're thinking I was only it's only $0.16 and 16 cents more is it worth it per square foot times it by how many more so cheaper to live here so it says which apartment offers the greater value in terms of cost per square foot Better Valu better value and which apartment is this is the first one better value in the suburbs SOB herbs play wait wait. It's not here so Marissa has to take that one place is all the filters I also do the homework together let's start that together all right so let's get on with this lesson

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Math 7 - Module 1D - Lesson 19 - the Rest of the Lesson

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