Adding Integers with Models

hi and welcome to today's lesson adding integers with models before we can add integers we need to first remember what zero pair is we talked about zero pairs when we were discussing opposites and here we have key of some counter chips that we are going to be using today to represent are adding integer problems so whenever see yellow know that that's going to be positive one and red is going to be negative one zero pair is just when you have both positive and negative they come together to make zero this is because one and negative one are opposites so on the number line they would both end at zero this is true no matter how many sets of zero pairs you have here have three positive ones so have positive three and here have three negative ones so have negative three each of these is going to make zero pair so this problem if was to write it out is three plus negative three equals zero if think about this in terms of money if had three dollars and spent three dollars i'll have zero dollars let's refresh little bit for our number line know that when am traveling to the right that of 0 that am going positive and if i'm traveling to the left of 0 i'm going negative this will be important when we look at our number line models let's get started now we're going to start out with very very basic problem one plus two we all know the answer is three but the point here is to learn how to use the models in order to add up numbers that are not all positive so my first step when i'm using counters is to first show the first number so have one here so have one yellow then i'm going to add whatever the second number is so because it's positive two added two yellows then i'll always follow the same steps will eliminate any zero pairs and remember zero pair has to have both colors since there's only one color here i've skipped to the next step which is count what is left so have one two three and we know that the answer there is 3. let's look at this on number line this first number this time instead of putting out one counter we have to show it on number line we're going to start at zero and then what positive or negative is going to tell me which direction to go so because one is positive i'm going to go one right i'm just drawing these little lines to show where started and stopped here have positive 2. we know that that is going to be continuing to go right because right is positive and left is negative so i'm going to travel another two right notice that did not travel to the number two traveled distance of two that's important for number lines where my second line ends or lands is going to be my answer so here we go again with three now let's try this with some integers in this problem have negative three plus five i'll start with three negative chips which are red and i'm going to add five yellow chips i'm gonna do this in very organized way where i'm going to stack any yellows underneath the red let me show you what that looks like i'm doing this because it makes eliminating my zero pairs much easier that is my next step so can see here actually have three sets of zero pairs you can box them like this and cross them out or since we're using hands-on manipulatives can simply just get rid of them and whatever is left is going to be my answer so here have two yellow chips and yellows are positive so have positive two as an answer let's look at the same problem on the number line i'm going to start at zero and this negative is telling me to travel left three so that's what i'll do first here have positive five which know that that means travel to the right if start at negative three because i'm always going to be starting where my last number line left off i'm going to go backwards 1 2 3 4 5 from the direction that came from and that's going to actually have me land at 2. 2 is the answer here because wherever the last number line stops is your answer for the problem if we try this again with another problem this time the second number is going to be negative we will first count out our four yellow chips and then we're going to add to it two red chips remember to line up any reds and yellows you have and then eliminate zero pairs so here have two sets of zero pairs i'm going to eliminate them and end up with positive two so that's my answer for this problem on my number line i'll start at zero and because this is positive i'm going to go four to the right my second number line is going to start right here but this is telling me to go 2 to the left when stop get to an answer of 2. my final example is negative two plus negative three so how have both negative numbers now i'm going to start with my two red counter chips and add three red counter chips to that i'll eliminate any zero pairs but notice that don't have two different colors so there are no zero pairs here so i'll just count what's left one two three four five which is negative five here i'm going to go two to the left so i'll start at my origin and go 2 to the left and then from there i'm going to go 3 to the left and just put them in straight line but you could stack this one if you wanted to and my answer is going to give me negative 5. so that is how we add with models let's recap we know with counters we want to make sure we stack any zero pairs so any different colors we want to eliminate our zero pairs before we count our answer for number lines we know that the number in the problem is going to tell us the distance but that the sign will tell us the direction and the answer is where you end up that wraps up this lesson thanks so much for watching feel free to click to subscribe so you can see this and other lessons until next time