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Math 7 Module 1A - Lesson 4 - Proportional or Non-Proportional using a T-Chart

Added Sep 02, 2020 •

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Fill in T-Chart Values (using y = kx, when proportional) Prove data is proportional or non-proportional by finding/using k = y/x

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so it keeps kicking me out alright that's the point so what show for everybody. everyone who has issues Ray-Ban glasses shoes starting next class you should have no issues we've been saying it for the longest go to school if you can't go to school go and fill out that form on the Oak Hill. Org that says you got computer issues if you can't go to school because you cannot pick up a Chromebook one of the millstone or the people at school secretaries will delay one to you so if you say you your camera don't work your mic doesn't work starting next class wednesday it is no excuse why because I don't text class because turning next class doing uniform check everybody's hair everybody needs to have a uniform top uniform checks out camera Beyond got to check out you perform check and make sure you're there cuz when we do breakout sessions a lot of guys just sit here and it's it's in the room why because you're not there to click accept so was that just kick me out again. So was that once you fill out that form it also set you up you could do one of two James arbaugh what about what about that that's fine just keep on trying to stay on sign up for that on your own the extreme team, did you sign up for that so same thing like I said you go to school or fill out the if you can't go to school it is the Tech Exchange free computer all you got to do is fill it out so one or two things can still out and get a free computer and or get a hotspot Sephora body as a kid getting hit it says your internet is not stable so what that does there's a lot of different ways by different hotspots I'm not going to talk about it the people that will give you the hotspot or the person that school will talk to you about it and don't figure out which one's right for you so like I said I have internet at home so anybody who's using their phone right now you're going to eat no excuse anybody so once I take roll here's what's going to happen once I take roll if you don't have your camera on I'm pulling you out you're here but I'm going to send a message home I'm going to send a message to the TAC officers and I'm going to put it in Aries so uniform check that's next class Sergeant cotton went to a bunch of your last two classes I heard popped in a lot of your classes and pretty much said if y'all disappear from class we teachers can drop your or do something else I don't know what else but I'm not going to bother with that is just too much alright so if you do not have the packet don't worry just how long the video of this class will be posted I know I saw that's why I keep coming back like I said if you can take note and go did the video and follow along alright so listen for quick this does a review of so it's pretty much more practice of what we finished with on lesson 3 identify proportional non-proportional so check if proportion proportional is a yes non-proportional is a no and based on tables how do we do that so how do we do that we pretty much do that sell a lot if you ask when do we take me out again just watch the video later how long take notes identify proportional and non-proportional relationships in tables check if a proportion yes so we got things so a lot when do you use which one for the one person that came to tutoring tutoring every Friday 1:30 to 2:30 all right and I'll give you the two different versions so use k equals y over X when checking if proportional and how do you use this call Kay's equal or all Kay's are equivalent lot of people are saying well they got that one when do you use y equals KX use y equals catfish people are saying I'm getting these two mixed up when do I use which one for which so you use k equals y over X when you're checking to see if all case has to be equal that's what you're looking for you use y equals KX when filling in teeth chart T charts a short word for table chart so when your bunny missing stuff you use that soap to cases sometimes in a prom you use both of them you're used one before the other that's where the Lexile comes in all you got to do is read so let's look at this right here one right here is understanding so this is not just about proportion or not proportion it's also about learning how to read the table this leads into your science class so you were doing stuff for mr. flemister when you make chart and learn how to read and look at results so this will lead into that and this will help so we're going to fill in these charts answer ABCDEFG these questions relate to these two charts right here all right so let's listen together read the story first you have decided to walk in a long distance race a walking race there are two teams that you can join so it's up to you to decide DJ in the blue or green or orange whatever colors they are walks at a constant rate of 2.5 miles per hour read that team walks at a constant rate of 2 miles per hour Team B walks 4 miles the first hour 2 miles per hour after that they get in a nice little run use up all their energy they walked for miles and that first hour but after that every hour they do it's two hour to miles for every hour I asked create table saw a lot of people having issues how do you create a table what and we're just follow the instructions create a table for each team that's showing the distance that would be walked for x 1/2 3 4 5 6 hours so far both of these H is the same o let's do this X why Frozen X Y member anytime have a t chart organize yourself keep it simple and it's for both of them 1 2 3 4 5 6 use the table to answer the question so let's fill this in thank you to people prefer jumping already but let's do the easiest why do guys want to go into past great three people all right did the first one for this perfect hold on so for all these look each team both of them both of them were looking at x 1 3 4 5 6 1 2 3 4 5 6 same for both of them all right now that looks easy but that's why you want to read this class you guys don't realize is so much reading it's like an English class with questions except we're looking for numbers instead of why the dog ate the cat the first one team a is you a hint how to figure it out teenager walks in a constant rate of 2.5 miles per hour now the fourth person four of you guys figured it out in my first hour 40 minutes a I walk 2.5 miles an hour show me cuz I am looking for why I'm looking for why so how do I do which one do I use if you're looking for why use y equals KX when stealing in the teacher I'm feeling in the teacher I'm missing information so all I'm doing we're going to be later so so what am I doing to each one of these at 5 to get to be blank 3456 what do I do what say again you had it you had it good * 2.5 read let's read this for those you guys that gave me a? Seeing a wasp at a constant rate of 2.5 miles per hour so for however many miles hours you walk each one of those hours is 2.5 so it's the number times to that is your K so for this one x / 2.5 x * 2.5 decimal y x * 2.5 that's why we fill it in good 2 * 2.5 is 5 3 * 2.5 yes 7.54 * think about quarters quarters but the decimals on this is $2.50 how much a hundred so you got to take one decimal place 10 5 * 5 quarters is thousand five good 12.5 and then 6 * 2.5 15 excellent so this one super simple accept it just took us a little bit time there's some Mental Math but that's alright make these decimals bigger now let's match up. Don't have decimals some people are saying what what are you do you can if you want match all these up with a decimal place put a .0 number have decimal can always add zero placeholder all right this is supposed to be distance in miles 2.5 Mi 5.0 miles is just five miles 7.5 10.00 10-0 place which is okay so all these we use y equals KX to find the wise to fill in because this two people came through so far and said number one has to be for because in the first Mile right here TV walks 4 miles the first hour every what do we got to do then after that every mile every hour is too so 6 add two more a add two more 10 add two more 12s more for 10 all right so let's compare before we move on so this is something that you should do in science so right now they're going to walk us through it will come back to it but in science that he's going to set YouTube be able to compare hey look at this and that first hour you were talking about how far we walked him he's a better walk in one in one hour 4 miles vs 2.5 in 2.5 MI vs6 still better but not as good and 37.5 it was just a half-mile better in 4 miles they both locked n tide look at this you could see a pattern 5 hours 12.5 12 so now this is slower this becomes faster in six hours they want 15 Mile Walk only 14 so they're getting slower and Lauren they're getting for the way they're taking off so this is about pattern recognition even though it asked a proportional or non all right so what's up with these questions which team is distance before tional to time explain your reasoning explain how you know distance for the other team is not proportional to time is proportional or not good yes yusuke use can cause y over X when checking if proportional and yes I'm using caveman speak up here but that's all right all cases need to be equal if it's before Channel what's a good team a which team is proportional sof4 V's with a different color so even though we use it the film you don't need to fill in the Box anymore so we don't need to use this so let's look at our case y over x equals k 2.1 * 2.5 / 1 5.0 / 27.5 / 3 10.0 / 4 12.5 / 5 15.0 / 6 alright this first one is super easy yes you can Anthony looking for K choose a different color for that too it's okay to 25 / 12.5 simple 5.0 oz silver $5 / $5 good massage even though decimals in the wrong place think about this I got $0.75 and I / 3 how much do I have what's a dollar divided by 4 quarterback the decimals in the wrong place what do you think all of this stuff is a dollar 25 / 5 2.525 and then a dollar 50 decimal place in the wrong spot but you can fix that dollar fifty divided by 6 quarters we go wild for x-ray here let's check versus bouquet all right so this first one y over X 4/1 I know I know I know let me got 6 over to we can stop right there we weren't even need to do the rest is this look at this 4/1 that's a for 6/2 that's 3 4 does not equal 3 what all This Means War and then the long answer for notes so we can stop as long as you see one example where they're not equal you can stop for doesn't equal 3 not proportional so let's go and fill this out right here for which team is des is proportional to time explain your reasoning so I would give you folks this right here so cine is proportional call Kay's equivalent that's the reason I fall Kay's your constant of proportionality is the same that means in proportion now here's the notes version explain the reasoning does all y over x equals k simplifies to the same number 2.5 the constant Pro portion ality and that letter is K since all y over x equals K simplify soda same number 2.5 the constant of proportionality K is the same for all we have a proportion okay that's what's right and you did this work right here man that's perfect answer to who this notes explaining why now look at this right here this one's even the simple note that the note answer is the same as the regular answer because this explain how you know the distance for the other team is not proportional so 2 Kay's I / X are shown to be not equal not all equal not proportional simp alright so this way let me zoom out and give me a chance to finish hockey so somebody you guys to read ahead and read ahead to the next page I'm going to call my name's to answer questions Surrey BC to with a G and then we're going to have a couple questions what's up Kenzie can you like push the paper like up give me a minute or two of us 2 minutes so I can write but for those you guys that have already gotten this and start looking at observing our table learn how to read read carefully cuz I messed up in the first class the last two questions and I had to go back and fix it trying on your own to read chart answer these questions in a science class you guys another minute then I'm Movin On this is like way more combo it is in the problem set go to the problem set before we jump to break out room all right so I'm going to keep on going back and forth but right now I'm going to scoot this down so we can read the so I'll read it follow along and slightly so we can read it at what distance in the race would it be better to be on NB Zante may explain so this right here when is it better to be on Team B it's a race who goes first all right if you go further Austin means you go faster so in one hour you go for miles vs 2.5 out of TVs better at 1 hour and 2 hours 5 hours vs 660 still bigger than 5 so that means we still go further and faster 3 hours 7.5 vs 8 not as much but still bigger than 8 750 cenotes how I switched in terms of distance to money I always think about money cuz it helps me understand I got more money I got less money but we'll talk about distance Air Miles not money is code switching now look at this right here at 4 miles both of them are 10 there Thai so if I was going to be in the race anything less than four hours anything less than 4 hours is when I want to be on TV for the question I hear what distance at what distance does it talk about time distance at what distance do anything it's the race is less than 10 miles it's better to be on team be because based on the rates the distance is the data Team B is better when it's 10 miles or less less than 10 miles so good to people type that in the job you too so what's our answer and why do guys think we talked about it but I don't know what to put down guess what we just said same thing in English class when you guys are writing a paragraph I don't know what to put down just write down what you just said when you guys give good answers you know I got a lot of you guys and say the same I got people that typed up stuff told me the exact right answer and I'm like what do I put down to the answer what you just typed in look at this when is it better to be on Team B the data shows the table shows that Team B is faster when it's less than 10 miles what at what distance 10 miles explain the chart chose teen B traveling further when it's less than 10 miles there's no easy web shorting that out all right so look at this if a member of each team walk 10 hours how far would each of them walks look at this we're filling in an extra spot if it was 10 hours this one is easy we already did it look if we're feeling in all we're doing is a time is it by 2.5 if we're walking 10 Savannah plug it in 10 * 2.5 25 T made 25 but this right here what is 10 there's no pattern notice it's not consistent but we know it's true miles each time so I'm going to make a separate T chart listen to down here let's just put it in this one I hear Richmond walk 10 hours so this right here we're looking for what y equals KX so K is 2.5 ex was 10 so y equals 20 that's not a 2 this is a 2 25 miles now for this one let's make a t chart we got to finish out fine the rest of it we're looking for the pain so in order find rewrite the six six seven eight nine and then we want this spot right here what is it at 10 so 6 is 14 and remember restart 4 and every mile every hour is two more show at 7 it would be 16 and 18 date it would be 18 at 19 would be 20 + 10 22 so how far would each member if it was 10 to look at the difference if there's a look at how much less work this way this is what is trying to say when you have a proportion any number you want cuz you know it's going to be the same pattern this right here what if I said how far would they walk if it was a whole day 24-hour race 24 * 2.5 boom you find this this right here I got a calculator don't worry when we get to the algebra part of the work in the class she's going to figure out there is a way to figure out what if it was 24 how did he figure that out 24 x what do you get for why on this one instead of just fine which one alright next one will there always be a winning team why or why not answer somebody one person put it in you are correct anybody is there always a winning team is there always a winning team it's a yes or no question how do you know why or why not what does it mean to be a winning team it means that one person goes further than the other one it goes faster than the other one team is better this case so time is the same in this case TV is better team B has better team B has better look at is there Thai team becomes better starting at five teams is better 7 we already got 25-22 becomes better but is there a time when no team is better they're tied at 4 will there always be a winning team no 4 hours team A and B are tied 10 miles so they're the same got to watch out watch out for that reading day this is table all right this is what I messed up so this includes reading if the race is 12 miles long which team should you choose to be on if you wish to win why would you choose this team so this is why I messed up so look at this it's 12 I put the 12 in hours for the last class but look at this it's a 12-mile that's distance so the other way we can right here it's 12 here show so X why it's saying what's 12 esteem a B we're looking for X when 12 so which one is better to be a which team is better to be on sew-in 12 we are at 12 12 this team would finish in 5 hours Team B finishes in five cuz we already have that information but is there 12 on just right here this we have 10 versus 12.5 so somewhere in the middle is 12 what number do you think we plug in to try and get 12 Burt Reynolds live at 12 what's a 12 incircle what number do you think what number * 2.5 do you think would get 12 guess what number is it goes in the middle what number goes in the middle Lord in the middle Rita's up here okay two people what number is between 4 and 5 as a decimal 4.5 Let's test shout out to remember I'm cheating a all it is is your K which is 2.5 times that number so let's test it out 4.5 * 2.5 we want to check to see if it equals 12 what's 5 * 5 is 25 * 4 is 20 we get 22 so here is zero we get 2 * 5 is 10 carrier one 289 511 and we got two decimal places for answering is 11 point 25 not quite there it's quite there so but we got to get us 4.5 we get 11.25 so we needs to think so 4.5 week so we got to get clothes dryer now so 4.5 between 4.5 and 5 to get to 12 but that's complicated so this right here's a challenge question but we already got the answer if this was a 12-mile race which one would you rather be on email because here's an easier answer because after 4 hours team is always the fast 13 and our data showed that that's how simple it was but here's the thing how much sooner would you finish the race compared to getting this is specific because I put 12in the X instead of the Y that's why I messed up but again we're looking for this remember what I said in the beginning k equals y over X when you use a to check the sea proportional use y equals KX when filling in a t chart we're trying to find that missing piece y equals KX in this case we're looking for X ax equals? Cuz what k equals 2.5 + y equals 12 anytime has situation like this substitute in which just plug in the information you have into the equation Y is 12 is 2.5 and we're looking for X 2.5 * number equals 12 I'm a cheat the cheat help you guys working use a calculator so I'm going to tell you what to do so I'm five times some number equals 12 what's the opposite of X division show its 12 / 2.5 that equals 4.8 that equals x so how much sooner though so how much quicker so if it took TV 5 hours and it took team a 4.8 hours just subtract 5.00 -4.85 hours notice we have zero placeholder the line up your decimals .2 ask by 22 hours what is 2 hours of what is 2 to Tenth is 1/5 what's one fifth of an hour so an hour is how many minutes 6060 divided by 5 12 minutes to hours 12 minutes faster excellent both of these are correct cuz it doesn't say doesn't want your answer in hours or more minutes is nicer because it's not a whole number that's a conversion thing that's the next level that would be two chapters from now we're not doing that yet but Point 2 hours will be the answer I want right here so let's go these last two questions which account has questions how to learn how to interpret the table now it's super super simple much simpler look at this we have a chart and look at this one 23660 information is already given to us look at this XY I will keep on saying that what are we looking to fill in on the table before reading the story what's missing what is missing for Aldi's excellent if we're looking for Y which equation do we use if we're looking to fill in the table which equation do we use I was beginning which equation do I use if I'm looking to fill in the Box which equation. Which operation remember we have two equations we got k equals y over X and we got y equals KX they're both very similar and then she wasn't remember I'm going to show that part of the notes again when do you use one versus the other this is something you guys got to know for the quiz quiz is nice and simple short test this is something to know for the test next I'm not sure if it's next week or the week so if you're looking to fill in your charge when filling in teeth chart use why was KX we're looking to fill this in so we got to use y equals 8 * X to fill in chart so for all these let's go read let's go read cuz we could get information now Bella types at 8 constant rate of 42 words per minute key words right there this is how come back to that is the number of words she typed she can't I proportional to the number of minutes she can type that's totally different is checking to see if proportion or not create a table to determine the rate if it's it's the same 42 words per minute so this says k 42 this right here though is the number of words you typed is proportional if it's proportional we're going to check call Kay's equal are all Kay's equal That's What proportion of me so I have to refill in all these it's a Sciences make a plan all the stuff you guys in science this year's and what kind of plan do I do to think about this process the scientific process this hypothesis testing so we got to do what we got to do this first so y equals KX we're looking for why y equals 42 X is one look X is 1 y equals 42 times to all of these r y equals US do that 42 * 342 * 642 * 60 all right my sister book what's 42 * 142 + 42 * 2 Double it what is 42 * 3 106 126 stop for second patterns notice it went 1-2-3 you can think about it was for be nice but now its 6 look at the relationship between 3 and 6 6 is just doubled three you can just double your answer right here what's a double 126 250d excellent look at patterns. Stop for second are you guys has participated excellent and thank you no one had a problem figure out what the Y 1 * 42 * 42 * 3 BC student the C student can still get this right to multiply 42 x 6 I don't need to do much this is just double to get so I just double my answer look at this from here to here is ten times my answer what do you think I just do to the 252 to get my answer put in a zero a different kind of just so you can see notice I didn't even multiply 42 * 60 I didn't bother with the algorithm all right the question was alright so now we got all this the question was are all is this General Tso for all of these check your k use k equals y over X Sissy if proportional so far all of these make a y over X 42 / 184 / 211 6 / 3 252 / 6 252 / 2520 / 60, show you this right here quick and easy way Mental Math I could cross out the zeros right here that's like to buy thing out of 10 if I cross out these 10 I get the same one I can say that equal if I divide both these by to hear these are equal this right here I know these two are equal cuz it's double this too can become 3 that easily but I can divide top and bottom by 3 which equals the show it 42 / 1 which ends making this equal to this if this is equal to this and this is equal to this these have to be equal also I've just blogical to prove that all of these are equal if they're all equal all pays equal you can say it's proportional yes alright read this I'm going to read this those you guys that have gotten ahead already try and fill this out on your own do as much as you can I'm going to say the last row is a challenge question while I read Mark recently moved to a new state and based on this  thing is like Montana during the first month he visited 5 State Parks after he visited two more state parks complete the table below use the result to determine the number that's of the parks visited the number of parts is it it is proportional to the number of months so is it a proportion or not that's the last thing you check the fill in the Box first things first in the Box first month five Parks every month after that two more parts on top so you should be able to do the first one and the last one do what you can I'm going to give you gas minute and a half we're still ahead of our pace trying to finish our lesson by 3 if you guys a chance to work together on the problem correct and Homewood only thinks a lot of you guys were asking what's homework the homework is always the problem set unless I say it something else that is the only thing you need to turn in on 10 best do it on a separate piece of paper because there's not enough room but if you can fit it on and scan that last page in you're more than welcome to do that but turns you on a separate piece of paper all right so let's look at it and talk it through the first month marked got to I said Wyoming or Montana how many parts did he visit it even tells you how many City visit 5 send a gave you a clue didn't tell you exactly how what the total was but they told you each month after that how many parts you decide to go to sew first what was 5 Second month every month after two more parts after that what's 2 more urban and then the third one two more 9 excellent 579 but look at this it jumps to 23 what is this right here how do you figure it out so a lot of people were stuck on the algebraic way I'm going to just use basic take to help you figure it out so we don't even need this last one yet but let's check proportional if we're checking to see if it's proportional we're looking at k check 4 proportion pro-poor shun so for the first time 5/1 for the second one 7/2 for the third one 9/3 I don't want to deal with this metal one I'm just going to use first in the first 5 / 1 does not equal 9/3 what's 9 / 3 when you simplify your razors that's how you check so how do you know they're not portional you take your ratios simplify them 5 doesn't equal 3 I don't care about this 7/2 you can do that 7 / 3 and 1/2 cares I want to waste time doing these two are super simple you don't even need to show the rest as long as you have to ratios that are not equal that's good enough not proportional because Hayes are not equal to say all of them you just need to say it enough why do guys are asking what does this mean that's an equal sign with a slash through it not equal so don't answer if he were stuff right here though I find that right there so you got to think let's go to logic how do you find this 23 -5 CM minus the first month something to use a no-sew Pickaway first month if I take away the first month cuz you want five five parks 23 - 5 what's 23 - 5 18 thank you show for the rest of the months went 18% each month how many parts did he go to after the first month for each month what's how many parts do you go to accept the first one good exit visa to park some months if you want to park some months but total of 18 show 18 / 2 is what's 18 / 2 time do the different color, he must 9 months 9 months ago 18 Parks but here's it here is the challenge question what makes this hard even though it says 9 that's for the 18 Parts he went 23 cuz that was one Park also Plus equals a total of 10 months there's an easier way we're not there yet some of you guys know it we're not going to do it that is closer to me rule a law in equation I'm just showing this to say that even if you don't think you can do Algebra you can do logic alright last one take 2 minutes to fill in as much as you can the first two are already done for you you need a lid prior knowledge and I'm going to read this and give you the prior knowledge the table below shows the relationship between the side length of a square and the area of the square complete the table then. when is the length of the sides is proportional to the area need to know how to find the area of a square I'm going to go the long way there's a much easier way but I'm going to Longway nice times with WhatsApp the square so you can imagine how to find the area of a square for all of these and I'll draw a picture so fill in the area they already gave you for one the side is too long it's for what is this length of 3in what's that 45 skip go to 8 and 12 what is the area you need that bit of knowledge I'll give you two minutes behind schedule alright keep on working I'm going to go over to how to find the area of a square you got to sink a square is a four-sided figure not a rectangle it's a special rectangle where the sides are the same length and the area is length times width so you need to know that formula length times width and since this thing about a square the length and the width of the same all in this is 1 * 1 were they got one on the next one I'm going to write them the same size yes you can draw them the same size but I'm just put the numbers down it's just a visual way to * 2 that's where they get the four thing about this the area 3 Square 3 * 3 is what we have Siri next time with 9 if I had a 4 by 4 4 * 4 16165 * 5 25 we don't need the ones in the middle eight times thank you 12 x 12 144 notice this is something that said thing that helps people a visual aid draw a pig some form even if it's a line diagram helps you visualize what the fill-in alright we sold it in that was simple but you needed to know this need a prior knowledge how to find the area of a square now we're checking see if it's proportional y over X there's a thing I don't even need these down here look at this one and the other one is 4/2 I am. 1 over 1 does that equal 4/2 what's 1/1 what's 1 divided by 1 good one what's 4 / 2 two are these no hey Kay's not equal so not proportional all right use these last couple on sub non-proportional ones super easy all you got to show is them not being equal if it's before some of them all so let's visually go through all these let me just read through all of this the boxes are blank you got to fill them both in I'm going to give you a hint for both of these for the X but a while I put the x or the Y even on these X and Y they're all different problems if you're feeling it in remember which equation to use if your filling it in versus when you're checking for proportionality which one do you use slow down now let's look at this they don't have anything up here for your ex cuz it's always nice if we have an X what do you plug in read Joseph earns $15 for every lawn he mows is the amount of money he earns proportional to the number of Lawns he mows make a table to how identify the type of relationship so the last page of in a bit number of Lawns Moe what's the easiest one to plug in 1 what's the next easiest what's the next one and done Maria's freak next chapter 4 but sometimes it's not the best next chapter will start practicing learning strategies how to identify which are the best numbers but there's there's nothing sitting right here at the end of summer Caitlin had saved a hundred twenty bucks from her summer job this was her initial deposit into a new savings account in the bank has the school year starts Caitlin going to deposit another $5 each week from her allowance is her account balance proportional to the number of weeks but this time in weeks 1 week 2 weeks 3 weeks 4 weeks how to find the Y read carefully the song right here Luke send Brianna read three books last month the table shows the number of pages in each book and the length of time it took to read the entire book which table if any shows a proportional relationship the gave you the data already how do you check to see if proportional which equation do you use B we cannot answer I'm telling you now both Lucas and Brianna had specific reading goals they needed to accomplish what different strategies did each per employ and reading those goals give us no story for that so we can ignore be but a which one of these is proportional and non-proportional fill it learn how to fill it in and check to see if before so or not your quiz will look like this one two three problems so I'm going to throw you in your groups together as much as you can some guys wanted this I'm going to see how many people I'm still going to be for groups yes go to your room help each other out you guys when you're done if you are done before your group members help them out talk to them please but once you're done you're going to you as a group or done yes you can go bye bye study groups Muhammad join your group

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Math 7 Module 1A - Lesson 4 - Proportional or Non-Proportional using a T-Chart

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