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Math 7 - Module 2A - Lesson 2

Added Feb 23, 2021 •

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Modeling Addition of Integers on a NumberLine

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answered your game remember manager game would be a stack of cards a stack of number cards Visa those Janke not playing cards he should be like homemade number cards 1 through 12 -1 to -12 and a bunch of zeros so you know I'm asking you guys to put a bunch of cards together I'm just putting all right by someone said use 8muse 8U funny okay then I'll go with it is 10 then we'll go with lucky number not lucky number 7 let's go -3 so this we're going to eventually change with some people if you noticed the title of today's lesson adding use a number line to represent addition this right here is an addition problem we're going to do on a number line all right before we begin as a quick review number do we always start at on the number line what number thank you I got one person what number do we always start on the number line yes good job so zero that's three people that have been penitent we always start at zero and we go to the first number so now there's two ways to do it I'm going to do the finger counting way this is called the counting by Method on a number line counting by going up counting by going down so first thing positive a positive number means you up upwork right so f means to the right so this this even though we're going left or right this packet these people that make these are these these know they're saying light going is going up going left or negative is going down down toward the negative side down the depths of nothing less than nothing cuz they're as technically nothing but negative is less than nothing that's a concept where so many guys get lost I do have a negative number so if you if we had a whole chocolate cream pie from a man who makes a good pie around here no don't even say Nations Nations has gone downhill Bakers Square is there a baker around here anymore I don't think so little the one in in in in San Leandro is Don that was my favorite one cuz no one went there whoop someone's fancy you know Shari's in Castro Valley reuse fake cream racing timer not forget 5 if we had a chocolate cream pie forget where it's from and we cut it up how many people are in this class we cut it up 20 20 slices of 23 people here that means three of you don't get a slice that's a zero that's nothing so yeah e 21 out of 20 slow those of you gots Supply one out of 20 will get a slice of pie cuz it's easy to cut 20 slices 23 not so much so you might get 0 out of 23 but negative numbers you're not an egg you just don't have a piece but a negative number is less than having nothing so that concept of a negative number is messing with a lot of guys but anyways let's go back to the number game so positive goes up into the right negative down into the do we have a positive number we always start at 0 we go left to right right now so we go 0 to 8:32 ways to do it I prefer you guys not to do either method I prefer today's method which will get you in about 5 but what one lesson one you counted so you could do the hopping method counting up by one unit each time one two three four five six seven eight so notice right here the arrow and is where the number where you end up at so right now we're at 8 but we're County each one of these represents a hop and a unit and this is the beginning noticed right here is where you begin and the arrow tip is where you end up but we can't all these hops what if I gave you the number 75 would you do 75 hops no you can give you a cut what we would represent is this then instead of taking multiple little hops you to take one big giant leap so we end up at 8 and then at 8 this is the new starting point we start at zero but we stay now at 8 so you understand how to move back and forth that was the main point of what all that was one of the main points of less than one how do you move with what numbers so it is a positive number so we go to the next number is -10 so it's a the number we go ten spaces back left let's use a different color let's go use Brown so we don't start at zero again zero is starting for the first number the next number start where you ended up and we ended up at 8 I don't want to do 10 little house but you get the idea we know we got a 10 hops back here so if you look at this like a ruler 028 that's 8 units long if this is 8 units long from here to here I need to go 10 units to the left so you need to know that this is why we do a number line it helps you understand where you end up so let's go one big leap back here and instead of adding on all these little hops if you know that here to hear is 8 but this hop is supposed to be and units long so we're going negative 10 the brown Heroes Tessa Brown is 10 Arrows Long 10 units long ear to hear is 8 good good two more someone so two more spaces and this is -2 and I'm going to stop for second this person just said you need to go to more spaces notice they didn't say I need to go - spaces this person right here man so after that you need to go to more spaces from zero and since we're going this direction I'm going to assume you meant left I noticed you didn't say negative spaces ranks is always counted as a positive number as a quick Butte County spaces absolute value distance is always a positive value we just so happen by going left and it up in the negative side cuz it's two units now look at this here to hear is 8 to hear is 2/8 + 2 is 10 units long so that number helps keeps us in check how much and now the next number good 7 is a positive number so we start at -2 and we go seven Yuna this way but where does 7n we know here to hear is too good new person thank you so here to hear is two spaces but we need to go 7 spaces so here's to we need to go far five more spaces so 1 2 3 deep so we end up right here so here we got another arrow and we end up at 5 so that's a plus 7 and then on our last Arrow we start at 5 cuz now we're going here we subtract 7 subtract 7 subtract 3 my fault so we go back and just and that's why I don't like this method that's why I like you guys got mixed up we started zero here's the arrow tip and then the next one from there -10 here's the arrow tip and then we start here again and we end up here there's a narrative and finally we start at 5 and we go back three but we're always kind of moving up so we got to make a big John R end up down here good and you said it was too thank you 5 - 3 units going back left 3 units is at 2 and here's our final answer I'm Circle that number yeah that's like zigzagging back and forth that's like looking at all these yeah who knows what that is so we're going to do a different today but the main thing is no how do the number line know that positive goes to the right negative goes to the left and we're combining numbers and we're combining using addition so one thing we're going to add if you are going to make some make an expression of a sub with the cards it looks like this it's 8 plus the negative 10 card so we don't have a card and we're going to put it in parentheses 8 + -10 + 7 + -3 and We Know It equals to now number to the number to is some so love you guys and years prior have misuse the word some some is the result of adding numbers together so I'm not going to use the word answer I like the word result the sum is the result adding a group numbers so the sum I'm going to use it in front of that right now the sum is the answer it's it's not process it's when you says find the sum find the answer find the result an adding a bunch of numbers together all right so let's get on with today's lesson super easy no problem how do you fix that all right so let's move on right here so lesson 2 using the number line to model the addition integers and I want you guys to think we're doing this because when we get to two parts when we get two negative numbers more negative numbers combining negative numbers and then we're going to bring in fractions that's like 5/8 who knows further down understanding where numbers are on a number line thinking using a number line will help you visualize a number line right now we have a picture we actually do stuff on a number line the end of this module we're going to say think about the number line we don't want you to use a number line we're going to eventually fade away from the number line and you're going to picture it in your head that's why we're doing this so you can visualize in your head how the result is most people make a mistake just by doing the mass and not understanding it so we're going to understand it first with number lines so using the number line to model the addition of integers so hate 2 minutes going to give you two minutes and do you do exercise one and I'm going to go over it with you guys after 2 minutes but I want you guys to try it out on your own first do it on separate piece of paper if you didn't print it out exercise 1 real world introduction to integer addition answer the questions below suppose you received $10 from your grandma for your birthday you spend $4 on snacks MSRP Houston condition how would you write an equation to represent the situation think about what I just did so write an equation to represent not if you're stuck with that juubi first be how would you model do your equation on a number line to show your answer a number line can actually help you do word problems helps you model it if you're stuck on a doobie first so let me read it again and start doing this suppose you receive $10 from your grandma for your birthday you spent $4 on snacks using addition how would you write an equation to represent the situation be how would you model your equation on a number line to show your answer so let's all be like a test question ex who I like yours cuz it says using addition great job now doing on the number line I know you can't type in the number line but we'll do that together let me give you a minute and a half now to finish this and literally all we're doing today at following directions it's like a cookbook that's why the beginning is so important for you guys and get the basics yes go ahead hurry up come back later screen on can I get to work I guess you're not writing anything down all right get your crayon and start doing this get the worst color pink magenta is that your favorite color picture pink magenta crayon hey don't hate on crayons just because makhi is fancy enough to have the giant country 28 crayon box I was jealous of people that have the 64 crayon box but you know I'm a hater on him cuz he has a hundred twenty-eight bucks It's homework man come on alright so one person gave me a great answer some people gave me a subtraction problem almost everyone gave me some traction prom except for one person we are not doing subtraction yet for now we're doing addition we will transition to subtraction eventually so it says using addition so 10 you got $10 from your grandma so that means you have $10 if you spent that vocab right there a lot even though you guys said subtract I like it cuz you saw the Lexa means spent means subtract or minus minus I put in parentheses but negative is better if we're using addition you see that as a negative for great job and some of you guys kind of messed up right here that's why you wanted to use the number line to check your answer my two guys are messing up for mining what are the negative numbers so let's look at this so 0 we start at 0 we hop all the way to 10 and from 10 week go back to the left down 4 units if you want a cop for Eunice but that's the whole thing 14 that's a negative so we can't go further hear something no understanding that negative goes left so then we go back for more units we end up at 6 now look at this criss-crossing stuff is where people got messed up so we're going to slightly change that today but good job was so let's go do this so if you have this printed out we're going to do exam one but we should have this right here because the next page so we're going a through F but the people that made this PDF didn't realize that's kind of messed up what is the next page Google one by one will so we need the number line to do it so complete the steps to find -2 + 3 by filling in the blanks model the equation using Straight arrows called vector so how many so follow along and I'm sure it's the same thing we're doing but instead of doing Rainbow hops we're doing vectors and these are straight arrows and yes do a straight as you can you see my ugly writing in this is straight as you can on the number line below so place the tail of the arrow on so this is saying where do we start out again so again on a number line where do we always start at and that's what this is where do we start at thank you one person to pee stings re and for good you're paying attention so these four people 5-6 have said we start at 0 7 people instead 0 but instead of starting on the number line of 0 should we place the tell him so it should be above a little bit above you don't want to draw actually on the line we don't want to draw on the line so place to tell in a little bit above 0 and if you want to put the word zero cuz that might be a no but zero so we start at 0 put the tail end of The Arrow I always put a. does it say okay that's not my aerotip this is where I begin my arrow so we're start at 0 that's easy next one we are doing we're trying to model -2 3 by filling in the blanks so draw the arrow two units to the left on zero and stop at so if we draw the arrow two units to the left what number do we stop over what's the first blank 2 units to the left so we start aerotip right here we tell the tale of the are we starting here we go left on the number line what number do we end up on top over okay excellent one person 223 good job so for those that are following long check your answer we end up at -2 so look at this 0 to negative 2 start at 0 then go to the first number and since its -2 units to the left that's what it's saying and we end up over negative two I'm going to change color next when it says direction of the arrow is to the left and it's redundant I know we're just saying all these things over again it's to the left since you were counting down from zero going negative to we're going to the left left also means down the direction of the arrow is to the left as you are counting down from zero but we go to the units think about that Burbage right they're removing two spaces space is positive we're going to the left that's how we end up over and negative alright next one start the next Arrow at the end of the first Arrow so we start the next Arrow at the end of the next round so what not where do we start at good we start at negative 2 we start above where we ended at so we went 0 the negative two two spaces and we start there where the end tipis and look we're adding three what's up with the next line draw the second Arrow how many units to the right since you are counting up from negative to how many units are we going good free went on the negative two were adding three but that's a positive Mazda 3 music go to the right draw the second Arrow three units to the right since your accounting up from negative to before I draw the next era if I'm going 3 units to the right what number do we end up over if we're going 3 units to the right from -2 what number are we over excellent good good how many units so listen to the blue forget unit was thinking about a ruler. Spaces how many spaces from 0 to -2 that's 2 and if we go back over the blue right here that's too but we need to go 3 so we need to go one more one more we end up at over 1 so good I love you. at or above 1 Inlet Circle that you start at zero we go back to and then we go 3 over so we can actually go past our route we go past our original line and we at 1 so there's our answer now I want you guys to take 1 minutes and do the opposite of what they're asking thank you look at this one right here repeat the process what we just did except so the first time we did -2 + 3 right here on your number line I want you guys to do this right here do 3 + -2 using vectors do 3 + -2 using vectors and in one minute we're going to go over it check your work to see if you have the same thing Kenzie Elias joined Rogan Jones Rogan yeah good job same thing yes same what's the difference what's the so now let's look at this what's the same what's different all right you guys see that so think what that's the next couple of months done so good job so we start at 0 we start at 0 and we go to 37023 so go to 3 and at 3 at 3 we go from well we go back to we go to the left 2 units but we still end up at 1 so looking at this right here so this one went to the negative side and then we came back and we ended up at 1 so we didn't even go to the negative side but we ended up back at 1 so the difference is where we started but what's the same as we ended up in the same place so right here next question what can you say about the sum of -2 + 3 + 3 + -2 so right there let's just leave it will answer the second part after so what can you say about the Sun AR the same equals 1 does order matter when adding numbers so this right here is what we just did we just did two different addition problems did it matter what order we added the numbers in know we got the same answer order not that's not not matter with addition why or why not that's the complicated things so there is a term for this we'll get to that in a second so why or why not order does not matter with addition because and I'll change colors right here addition is and here's a key word which we're going to learn and I'm supposed to show you guys even though it's not printed ear addition is commutative and I'll do it on a separate piece of paper and explain what commutative is so using that last piece of pie commutative yes commutative so let's look at this right here addition is commutative what it's saying it doesn't matter what order you add and then I'm going to use example 8 + 4 equals 12 4 + equals 12 we've have the negative number in this example but who cares if it's a day it doesn't matter what order as long as you add them together you get the same some the same some so it does not matter and what is the commutative property that is the commutative property of admission this also works for multiplication but we're only doing addition right now commutative property what it means is you can add one way to add the other way to same thing and to help you understand let's make this English class but you said lights out right here what is the root word what is the root word in commutative what is the root word in commutative I want to see who knows this what is the root word in commutative this is stuff you guys are going to do in that standardized test the state standardized test what's the root word I like that one like a first one it's okay it's close and I like this last one yes the one you just need good so all right so Community I can see where you can get community community if we're in a community we're as a group but it's somewhat as a group but in a community in a community it's just a group that you stick together with now the better root word where commuters them is commute as you commute is to travel back and forth usually home to work so here for you guys if this was a normal year which they're saying probably at the end of March maybe April you start at home every day and you go to school physicals school everyday so you go home to so here's our Vector I should use a different color ears are vector in the morning home to school considered H your home does Darrow school and once you're done with school I don't care if you stop for a in and out or something or Chick-fil-A I don't care if you stop for a little snack keys but no matter what you started school and you end up back at home so it doesn't matter which way it ends up being the same spots I forget forget stopping for a break you go straight home cuz you know your mom is overprotective everything I don't trust you so you go from home to school and then because you're scared of her mom and she'll throw her slipper at you and beat you with her slipper if you don't shop at home I don't need to know she's super overprotective and scared that something to happen you have to go straight home so home to school school to home that's the commutative property it doesn't matter which what will you go first it's the same distance so that's mute so adding subtracting no difference my fault adding there's no difference in the order subtracting we'll get there we will get there soon if there is a difference when we bring it up show example to I will start this together and then start this together and let's do this right here how does absolute value determine the arrow length for negative to use the number line provided to support your answer all right draw an arrow to -2 that will do Kenzie Kenzie go to Dragons alright thank you so right here draw an arrow to -2 John aaroe two- to how do you know that's two units long how does the absolute determine the arrow how do you know okay that's fine that's fine doing this now so draw an arrow to naso 0 to -2 now right now I answered it for you you guys are just complicated so I asked how does absolute value turn on the Arrow length for negative to so absolute value negative to remember absolute value let's review that I forgot about that we talked about absolute value less than 1 remember make sure these parentheses are bigger so you what's absolute value parentheses you don't want to see this as a 1 - 21 absolute value of -2 someone just said what do you mean one my man Hector fast all right so if you messed up on your absolute value parentheses and you wrote it the same size as your numbers it looks like 1 - 20 right here that's why you want to make your to the value parentheses a little bit bigger so that's not 1 - 21 it's the absolute value of -2 and I said how do you know your arrow is because if we treated like a ruler and that's why that's why I don't know why that's my key why we use the absolute value parentheses like that we're saying from here to here so here's the book and the two bookends what's the length that's two units long so the arrow just shows the distance 2 units long length is always positive measurements so absolute value of -2 is 2 we're saying if I had an arrow that from 0 to -2 how long is that arrow and that's the whole thing it says ignore that is going to the negative how long is it and that's how we're starting with a negative absolute value first get you guys understand it has nothing to do with negative or positive it's just how long is that Arrow it just so happens the arrow went to the negative side all right next to page and we're almost done that last page is super short so don't worry too much all right so let's look at this how does the absolute value determine the arrow length of three John Arrow from 0 to 3 super simple and use the number line provided to support your answer what how does absolute value next toll same thing good job so here we start at 0 or tail to the A which is the arrow tip we end up at 3 what is the absolute value of 3 what it means is what is the length from here to here notice we don't care about which direction when we talked about Havasupai we're just going from here to here how long is that so that's three units Farm and 3 units you know nothing super complicated it's just that so the absolute value of 3 is just free nothing all that different so let's think of this describe how the absolute value half-elves you represent -10 on a number line alright so this right here we're asking you this is Lexile Lexile them play this is like you understanding English now do not use a number line picture the number line in your head and if you're able to write this down in a sentence it helps you understand and says you get this idea described in one sentence to if you need how the absolute value help represent -10 on the number line write a simple sentence I'll give you 30 seconds how does an absolute value how does the eye do you have an absolute value just this right here help you understand the number line you type really fast and that's a long paragraph your answer is correct but let's cut it down to this person super fast typer gave me a great answer but it's just too long but I do like your answer what was the question again without the number line without using a number line what we just did try and write a sentence to help you understand how does the absolute value the eye city of just writing this help you understand how to write or Draw -10 on a number line this is why English is so important I got another essay answer what's great about Alexa why we want you guys to keep on reading how do you describe something in the shortest amount of words East amount but still say the Saints pay the right thing when you guys give us a paragraph that's longer and bigger than the story that's too much excellent so good I'm glad you guys are thinking though so these two answers they are correct but they're just super long so here's how describe how the absolute value helps your the absolute value pretty much helps shrink you too short helps because it tells you the links and I used to work distance also distance your arrow is from zero and I put that losing their absolute value of -10 got to make it bigger as we got -10 equals 10 so 10 units from 0 I just think about this absolute value of -10 we know it's the arrows going to go to the left we know it's 10 units to the left cuz we know it's just ten spaces that's what Alice is value is so if we're on a number line just thinking about you no spaces all right so exercise to almost done almost done I want you to do a and b on her own I'm trying to do a first and if you can finish super quick do be we're going to go over these together I want you to check to see if you Master but we done using vectors not the Hop knot the Hops and I'll show you and we'll go to the vectors again and we'll explain why mobetta create a number line model to represent each of the Expressions below on a do -6 + 4 when you finish Circle the number above you end up at 3 + -8 Circle the number you end up at this right here moving left then right up and down helps you understand addition right now it will help you understand negative numbers and fractions later please do this good see two people already done good job I don't need you to tell me it's easy it's easy for now but this easiness will help you have a better understanding of everything good job o third person 456 don't forget to circle the number where the arrow ends up all right so always start at 0 so 0 to -6 so the first one's always easy so we're here is the end of our tail and we go to negative 6 is where we end up don't forget to draw the arrow cuz that's where you end up for first number and then from there from there we add for so you got to think 6 negative 6 is 6 units long 4 is 4 units long there is no way I'm going to get back to the zero that's why the number line is so important it tells you how far do I go do I go pass do I need up or do I need to make it back think about that do you think about having gas for the car we went six units this way but we didn't have enough gas to even get us back home we ran out of gas part of the way cuz this is shorter so we go here the wine is shorter so we go back for units and we end up right here think about distance all right good job so we're at -2 this is Margaret knows we're not jumping over each other like a hop it's like we're building a building a skyscraper building a mountain we're always going up where does our tip on the highest point and up above and we look at that point so let's do it the next one so let's look at we go to 370 to 3 all right we're here that's where the tip is but now have a new era new Vector going 8 units long do we know it's 8 units long but notice right here the eight units is longer than the three units so from 0 to 3 is 3 unit if I'm going to the left 8 I go past so it lets you know you go past 0 so you're going to be in the negative Zone the negative side of number line but the question is to start thinking how much further good so you go to five on this side not just five five negative to look at this we start here for a new era cuz we got to go 8 to the left I'm going to stop part of the way so we have gas that was dirty now we went back we're going to the trip that's three already we're back home but that's only three we need to go a total of 8 so if this is three we need to go 5 more a total of 8 units so that helps you understand that you end up look how crooked that is but we still know it's a vector we know we end up over negative five so this is + 3 and this helps also I'm done right here if you need to drop put a number and plus sign saying you're going to the right and this side is -8 less than 1/8 this is an eighth so we know it's -8 units is 8 units to the left and we end up at -5 and look at this right here I'm going to use this so here to here we know is 3 if we go back we know here to here is also three but if we go further out that's 5 units what's 5 + 3/8 absolute value is 8 so adding is like thinking Legos so here to here is 3 and then we go back to hear it's 3 but then we know we need to go 8 units total so we got to go five more so we know it's a total of 8 so you want to match things up this part down here what I'm doing is just a way to check your work you do not this right here is super messy you do not need it that right there is pretty much what you should do this is just a all right let's go to 3 last page we can be done Super Shoes all right now look at this one right here going backwards going backwards so can you write an addition problem so you just do a write the addition problem that this Arrow represents remember we always start out at zero there's a hint what is the addition problem for a few that I give you 20 seconds more than enough stop talking yourself Mekhi write down the equation good good good good like it yes just like crazy I don't want the song I'm not the same yet yes you can this is if you could this new see where this going you're good alright so we got a couple so we start out at 0 so 0 says we go too far so it's 5 and then what's the next number we add since we're going to the left and that tells you how many spaces + -2 and then we add three that is the equation to express the sum but where's the thing where do we end up at we end up at 6 that's what they didn't have so sometimes they don't put that so we could put equals 6 so let's think about this what is 5 - 2.33 + 3 + 6 in what three cards are represented in this model how do you know remember the arrow length so the five the three cars that are represented so when I say cards if we have the card game this is the five card you have the -2 card and you have the three card how do you know remember the vectors and I put arrows in parentheses cuz it's a new vocabulary word be vectors each let's go eat each and parentheses each vector represents each card car just represents the length in a different way it's just other ways of writing for some reason why we like this is a visual thing that's somebody's Wendy's math people that made this thing realized if we make things out cards people for some reason understand it it's wait to visual aid the block we box it out so we see each of these individually some people don't like to see cards they like to see arrows arrows are better for one reason cuz they show movement the arrow tips shown and can use this on a number line This doesn't really show and it gives you an idea of the units but it doesn't show direction in position so this shows Direction and position so you figure out how to move all right in what ways does this mod differ from the ones we used in lesson 1 in less than one week work as hops in this lesson movements are shown as Vector arrows I'm going to change it movements are shown as Direct vector arrows direct me to go straight there we don't do little Hops and count one by one it literally tells us you know if you're on a trip what are the pit stops du Bist so I start here and I go all the way to 5 that's my pit stop for my pit stop I go back and I visit here let's go this I'm going down to I'm going down to Magic Mountain I go 0 so I go and I go to Tommy Burgers you know Soca I go to Tommy Burgers but then I go Tommy Burgers a little past Magic Mountain so now I got to go back and go to Magic Mountain and then some I want to go to Universal so then pit stop right now I go end up at Universal so it's like pit stops you go directly there little hops he's not one by one you see it's like on the trip you're looking at your phone you don't even know what's outside your telling one by one you looking at one little minutiae at a Time Rush direct to go straight there boom back. every Pit Stop So in this lesson movements are shown as direct bector arrows representing movement movement can you make a connection between the sum of 6 member the sum is the app the result of adding a group of numbers come by any of your can you make a connection between the sum of 6 and where the third Arrow ends up on the number line so what what does it mean that your answer is 6 and your third Arrow pretty much this the third Arrow third Arrow ends at 6 this means the sum of the numbers R6 so the arrow ends at 6 that means add all of these numbers up is 6 so look at this let's go back to this so work and it's a trip we're starting here going to 5 subtract to we end up at 3 and at 3 we add three more we end up at 6 it's a trip rotary combine the arrow sure movements it shows us adding and combine each step of the way and wherever we end up the arrow tip is the six we want you to use your head for now we want you to visualize it and do it eventually wants you only visualize it that's our goal so know that we're going to get rid of the number lines after a few lessons we will always say visualize the number line what does change if we change the order in which we added the numbers for example -2 + 3 + 5 we went over this would the song change if we change the order you good no we already went over then no no and I'll show that visually before we finished no and this is a simple answer because addition is commutative remember it doesn't matter what order we add numbers in will still get the same answer with a diagram change if so how well let's draw it diagram and see and will finish with this today so let's draw a diagram what number do we start at let's finish this up together what number should you always start at on a number line thank you good job 0 so we start at zero and noticed I'm not going to put all these other numbers for I want arrows and think where we end up so first number we go to is -2 so here's our tip we go to is -2 from -2 we draw the arrow 2 won't we don't draw the arrow to three remove three units think about this is 2 units long the next Arrow needs to be three units long going to the right what number am I over so I'm using red what number will I end up being over for think about it I'm at you have two and I need to move over 3 to the right 2 here's one unit here's to you in it here's three units what's this number right here 00 is right here remember so we went so here's another lie good I'm glad you guys do this together so we know that this is -2 so we know this is two units long so forget mom's but negative 2 absolute value of -2 equals two units so do you understand how long the arrow is now we're going 3 so it's a plus 3 absolute value of + 3 so we're going 3 units over but here to hear is too if your to hear is to how much longer is this one so 021 we end up over one and then our last one we start here and we go fight 5 units over if we're at 1 and I go 5 units over what is the absolute value of 5 what is the absolute value of 5 5 thank you good job think about this we're at 1 and I go five more units over what number is this right here what number should I Circle good job yes yes all right the answer you have told me is 6 now let's look at this this is why this method is better than the Hop but I'll show you why it's not as good where are the Hops with zig zag on top of each other so they got mixed up but this were always building upward so we always go higher like a Skies what what what are the top of the mountain what are we over so our first Arrow we go to -2 two spaces to the left so we're here then we move up and start again going over we add three spaces to the right and we go up and we add again so we're going to the right end up over 6 what's bad about this some of you guys actually need to be able to count the spaces cuz you guys need practice that's all right the Hops provide you guys the ability to count how many spaces over and so you find the exact number but that slows you down we're trying to get you guys to get to the vectors vectors are clear and they I want you to start thinking about where you end up but notice right here let me zoom out and finish with this right here so the question was does the order change what the sum is so negative 2 + 3 + 5 + stead of 5 + -2 + 3 it's the same added it was it's the same numbers being added in a different order we just move 5 to the back so we start at -2 + 3 + 5 remove the five card to the back the Edition did not change the sum the order did not change the sum that Synthroid

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Math 7 - Module 2A - Lesson 2

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