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I'm here with bill mccollum again and I i thought today bill we could talk about up have the build-up love expressions and equations as we go into algebra and always I just wanna start this what's your sense of how the Common Core approaches this might be the same or different what one might think that does feel like the a the algebra or the pre algebra starting to happen sooner yeah a that's probably true I'm in the sense that we get kids using symbols family only arm arm there's also another sense in which that's true which is that there's a very conscious attention to using arithmetic to prepare for algebra and to make sure our making sure that we have many just during admission on poll numbers are any your multiplication whatever I but you're attending to the properties of operations that you're using and consciously using a mi which really prepares for dinner way you manipulate algebraic expressions a home Terry particular the distributive law plays a big role I'm understanding that rule I in irrationality hopes you prepare for algebra where plays a big role yeah you up and we see that in up as early as fifth and sixth grade right through these early standards right over here where you know once again the students they they they should actually be able to interpret this as your two times this other thing ridding the product of two things the second that happens to be a psalm and the really understand these things then in and then sanded in six grade you have the a standard literally expressed 36 per se as four times nine postdose was really kinda internal I'm there's an intention to looking at expressions and seeing what they mean I'm an as a partner in addition to simply being able to calculate them so if you see two times a class 70 I'm a lot of students who were brought up on the hors d'oeuvres operations parried ass that's what I've I drill will think our have to add a 10.7% then I have to multiply by two which I suppose is true if you want to find the value this expression but that's another thing is you want students just be able to see all this is two times the sum of two numbers when she gets her looking at two times X plus Y recognizing the structure expression is as important as calculating are evaluating the expression which brings up an interesting question job where goes order operations just got the classic P serve pre-algebra well bitch in there as a footnote in the their I'm earlier Standard Time under from a rip I'm the operations and algebraic thinking standards case you fire we tried to :d elevator as a substrate for had to Cal arm not to trust him he shouldn't be able to read and right numerical expressions but over operations I became really be goma curriculum that includes service the more important understanding of the properties and operations or operations is just a convention about how you read so I'm when we read English language text me reading from left to right everybody learns that he knows that I'm you don't make a big deal about that we don't have a %uh we don't have a topic in English language arts class a small reading from left to right I just use a certain and and and and meeting numerical expression is a little bit more complicated done reading from left to right and it certainly you should be given to use practicing during that but calling it a topic is weird it's more just to content tune about how we treat community distinguish that from but properties operations like the fact that you can add numbers in any order on the fact that the distributive law glad you when the multiplier psalmist the same this I'm multiplying separately and adding all those things those early foundational for algebra I a mix 2012 imprecise honors as being the basic got the more important foundations for algebra and while still not not to focus too much on penalties the standard version 6 gray be a one thing that went when I first read the standards you know this terror here find the greatest common factor of two whole numbers elliptical 100 least common multiple use the distributive property to express the sum of two whole numbers Bob so to me I'm like why they feel like you know at least two different things maybe three different things i mean i i Series cum multiple and andrew is coming back to our can be related based on the factors the you have distribute distributive property in the same standard was the was gonna the connective tissue by these things well connective tissue is the distributive Lauren this is a twist on the normal treatment greatest common factor her release from a model Paul which is often another one of those topics that occupies I'm can occupy huge part of the curriculum for no apparent reason arm been one important thing is the ability especially a game when you get algebra to see that you can pull a factor out of an expression like that for the people out of 36 besides so when students getting looking expression lie I'm borax numb lime Forex class 4y for example spot forex plus 8y they see if they can pull that for a fact and they've had the habit of doing that from during this part numerically arm so I have decided the greatest common factor industry and the least common multiple are also deemphasized topics in the Common Core compared to previous standards but they do have this place in this little standing here about it's a sort of a rehearsal for algebra if you like bright and I see the greatest common factor mean if your factory things out a multiple terms if you wanna factors much as possible as you care about the greatest common factor I am Ohio the least common multiple connection between that the distributive property is that I mom's not explicitly stated out there in that standard you can imagine the I'm a similar sort of activity I'll where you have two numbers you want to find at least common multiple at me it's not going to look like bad but it's related to the greatest common factor is the same idea looking at the factor structure right numbers I guess GTA is a bit but there's some hot they have in common rite II nothing I'm in this particular sort of list standard I back gives you an analysis activity right I guess the connective tissues the greatest common factor is a tool that can be used either for lease con multiple or for factoring things out I am is one way to yeah I am I mean once you see look at two numbers and you see what the greatest common factor is that also a Naples you to figure out the least common multiple that's right by me we were trying to limit back here with just by putting those two in one standard I don't think people should be spending a huge amount my mom this arm but it would have been a bit ought to mention the least common factor without mentioning least common multiple just because international connection just mention right now that makes makes a lotta sense and then as we get the get further in the sixth grade the others will love a whole number expression through were adding exponents to kinda what's fair game in expressions and there what's really interesting is %uh this is where we're starting to do some other preliminary algebra are starting to you know subtract why from five that's five minus why and as you look for common core take a lot of care to the bill that building baca not a really understanding what five minus why means that's right you want to see that exactly as you saw heart my wrists read when you're in great 3 a great one arm namely I you wanna see that this there's a number five minus about another number called why um as much as possible connect back to the arithmetic make clear that these letters were riding into town I just numbers me not specify what numbers their job but apart from that we operate on them exactly the same way yup and there's more about kinda really understand how to the structure of an expression saying that look this is too the product of two and at the summer 8&7 and then your you know kind of getting familiar with at least formulas I am substituting things like that yeah panini and that seemed a structure going back to that conversation we had about pro I'm order of operations so looking at two times a par 72 order of operations paradise way is all I have to admit 7i have to multiply by two well um if you see the structure that expression if you see that this procedure grouping a piece about its to times that repeat 857 inside a crib you gotta some you don't need to have memorized penny last today know what to do in fact if you see that structure so that's part of the I here in moving from some memorize rules which is a sort of like lohr someone's giving you that you don't understand why to interpretation saying structure and then being able to use that in common right right and then at once again in six grade you know equivalent expressions a bit over an hour written we're really talking about equations now not just I not just I'm equivalent expressions that have become the building blocks for an equation we got to standards worry if we start about solving an equation are black and a this is just kind of trying out values are kinda trying to reason through it but eventually kinda starting to do some of the war I am kinda you know methodically solving from the more basic equations using kind of ballad operations so we do try and make your brain for distinction between expressions and equations expressionist art have equal signs and basically people often use those words interchangeably almost nothing confuses students and so we do want you dance to be able to see an expression an interpreter as representing some population with numbers I'm then later on when they see an equation they'll see that ask your expressions be set equal to each other and you are solving equation means finding the value of the variables that makes that a quality troops sorrow building from the expression work for simply interpreting expressions that helps you any solving equations if you can look at it the expressions on each side of the equation pick up things to to do anything that helps you solve the equation yeah then so it's getting kinda more familiar as much coming out to break terms with the notion that up kinda inequality X greater than CX lesson see and kinda constraints on on on a I guess you could say we were not using the term at this point but kind of a what constraints on a variable are you and then and then I am and then starting to really kind of think about I guess you can start to say I'm is starting to build the late the Billy much for functions a independent variable dependent variable arlen year relationships things like that that's right yeah I and that from stocks in grade 6 I'm would but really just the night here using an equation to rate mister express a relationship between two parties not trying to get too heavily into the the idea of a functioning on the congregation at those parties but just the idea of using that language up immigration into variables to express that then grade 7 students totten I'm riding equations for proportional relationships downright white post KX to express a proportional relationship where the constant of proportionality is K and then a great day which was gonna get you later I guess I still have a full-blown exposure to the idea of function right right an area and I just wanna kinda doubly underlie this I mean already in grades 7 up you know solve solve the equations like this I and and inequalities like this I mean the evenings that at least I remember these were really introduced in algebra 1 %uh this is now not only not having an outer why this is happening in seventh grade that's right elbow it I think it is worth retention shifted to the limitation on the complication of the equations here arm backed these are not the most complicated near rations that you can write down even in grade 6 there are some simple ones next class P will skew or key times exit polls cue and so it's a very careful building up I'll um their at the level of complexity I in the equation you're solving and it's not until grade A you would expect students to solve an equation reticent X on both sides of the I'm a question for example United supposedly is just have the Exxon on the left started to be on the right but you don't want it on both sides mom I there's no nothing here is taking kids to try to like terms: bizarre this preacher communication solutions slowly build up their not make sense well thank you I think this message was very very helpful okay you