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this is Sal here and I'm here with Bill McCollum who's one of the lead authors UHV math portion of the Common Core and founder illustrative mathematics amongst many other math accolades and what I thought would be interesting is to because he's though one of the leading experts here to discuss the the Common Core and and and and go into much more detail that is is kinda typically had in these types of conversations so Avila other start with him a very high level question that I get a lot is you know what what do you think is the essence of the Common Core in and what was that the underlying motivation for well the s into becoming participate in this Friday water me one kids to know and understand the BF gay the B&B radio in mathematics and I huge part motivation wires that have in common standards set among states solves a lot of problems we have any mathematics education these days the fact that different states have different standards result incoherent exports in unfocused exports curriculum that was a mile wide and an inch deep in the in the world among raise and having common standards enable stakes for companies to focus on one set of standards and designed to prepare it expects any materials that assesses that that pete has no status and one thing that I think there is some confusion on as these are standards and then there's kinda the other notion of Kirk curricula and how are they the same thing like if you know and we're gonna talk about the Santa Ana few seconds with you know I look at these standards for you know this is the fifth grade standard around exponents I does this say that I have to do this on a certain day or have to be taught using a certain set of problems our house has a similar different than curricula a so it certainly does not dictate the order impeaching it does not dictate what happens day-to-day on page five min standards there's a state says exactly that we want people to be very clear and understandable standards are not any order ordered list that you have to teach in that order in fact I would say that you don't teach standards you teach mathematics in standards have descriptions of the achievements you want children to have a BF Goodrich radial curriculum is a sequence of day by day learning experiences that guides them those achievements it's not necessarily a one-to-one mapping between standards and what goes on there that day today and the region but you can design activities that might address many different standards that might be building skills reactivity not obviously related withstand result usual mediators there there's still plenty of green get into history so so in in your ideal world up an educator wouldn't Canada seles the standards and say I better you know there's this twenty standards I better do standard won the first week of school standard to the second week of school and just look all only that standard you'd rather them kinda design broader deeper experience is that it the Deathly should cover all the standards by the end of the year well they should feel confident that by doing these experiences the students will be able to achieve the standards correct and different people have different ideas on what those experiences should be and I think that in common standards gives room for innovation on that people have an idea inspired now and the trust everybody's working from the same standards you can dip some sensible comparison I don't think speeches should be saying today I'm gonna each five-point in the heat wave 8.2 I think they should be saying today I'm gonna work with exponents the over time that will address that standard on their various situations and standards where I you have connections are between different standards for example when you remember an Operations you doing modification in grade 3 that's the same great work it learning about area there's an obvious opportunity there too but I area to publication in fact the center designed that way people to make those connections they'll have an activity which is especially mobile stand right right and make it all work and live I've I've copy and pasted some %uh the standards here these are the standards around exponents and so the first number here this is the the graded which this is supposed to buy if the end of that great the students oppose to have person she mastered the standard and the one thing that I found interesting is you know exponents a which I always imagine love you discover middle school concept in the Common Core does start as early as as fifth grade what what's the rationale behind that we see and i'll read out explain patterns in the number of zeros on the product will multiply and a number by powers of 10 and explain patterns in the placement of the decimal point wanna decibels multiplied or divided by power 10 use whole number use whole number exponent to denote powers up ten so this is just a light introduction to respond rates and there's a good reason for it children have been learning about the base 10 system miss it there kindergarten really are great one and I day have lots of different ways of understanding the based in system when you see a number like 352 your mind's ear hurts is $300 plus 50 bucks to good excuse me but if you but if you want to understand the real structure at the base 10 system you then begin to see that in each place be units are worth ten times more in the place to the right and so that's an important I understanding their lives um study rates 283 and then the its employees you want kids to go to find that understand me this powerful notation from a exponent notation release other brings out this weighed about progressive structure basin system with each and what units the ten times the size on wall one lower than because then you see that and 23 or locking up in the exponents arm now this is really this ready just that little locational wives it's not me and then that's going to grow into something much more powerful in the subsequent expand but seeing you really just the ATP way eighty-something you know the he had a right canada beat analyst I and smile but yeah then notification the white speaks on a white one if you want to get out here right and and this is earlier I mean at least in my memory serves me this is earlier than is typically a dance tunes are have been historically been exposed to sponsor was in the US right bear in mind that in grade five min up during the properties are responding right doing anything other than using this notation and sorrow it's an early explorers it means that by the time they have to deal with these wheels respondents not being overloaded by strangers that this mutation right right and that takes you into six grade where I guess you start in a you know broadening your understanding response writing about numerical expressions involve in involving whole number exponent so now you know you're kinda breaking into the to the third power is able to times two times two were expanding the number bases that we're dealing with now actually so first we introduce the exponent made you realize I could put something else in the basal expectable right other other than a 10 and then also in 6th Grade you you start applying it in in the use a formula that have exponent a new start you know it in the famous you know order operations and Pam bossy start using the EM panda speech wired why although I have to say instead he tried to play down already operations arm as much as possible and ass takes on a life of its own which is lucky while eat eight and a half minutes long I it seems to suggest you can always do modification what division that's right it as on my right as as him Pandyas yeah a should be yeah I mean everything is about paradise is what you get algebra it's actually perspective for cuz if you give a here a expression like I'm open parenthesis 3x wants to impose but this is only a vote by the whole thing by a they don't know what to do because there's nothing to do in sight read it seems that way the expected be right and so so and I I did notice that as you know if your cock n me we've tried to go to the standards and make sure that we we were we were addressing them there is no order operations debtors is really sprinkled through a lot of a middle school and even some some high school standards yeah yeah kids should know how to read I numerical algebraic expressions that includes under study have parentheses the years and that includes understating the conventions that really does I'm there's a difference between conventions are how you read notation and properties and operations and we try to promote the importance of understanding properties of operations for example distributed war about I'll I'm thinking of the conventions as being somehow essentially mathematical now worst students do need to know how we do things but there used to be in the creek and also to treat restrooms like you or I wouldn't be able to get right you know they have like five my patience I'm 3 vision science through on our site and again what was that allegedly do a different one like five multiplication sign three a 4 division sign to 34 yeah I just just just so that the division is gonna be worked out twice that right now yeah um it back and see if your you could be division is sorry I'm yeah list for the division sign first okay for 25 division sign 34 multiplication to right okay now I see what a pandora's if someone take him to sleep early today would mistakenly well this is you know I guess could be with they might tried to 34 times to first and then ride only know you know this is a case where mathematicians we just put parentheses right you know exactly what I no sane person is gonna leave that expression I'm expected to be unambiguously that by everybody in the world the anybody can generate static you can share right armpit but at these per country questions that students have throughout have to you be n bass takes supremacy over or I'm happy to operate as necessary base is he getting that make sense then you noticed you know kinda completing or I guess at least the middle school portion of the sex was progression you know what jumps out at you is fifth grade 6 grade and the weed up to eighth grade you know what happened to seventh-grade is this and is not saying that you shouldn't do explode in seventh grade just our part I'm so a lot of the focus of the algebra in middle school is on linear a functions near rations and their expressions so there's not a lot of development a these formulas beyond six radio markets will keep using formulas that have exponent in them the a the may rusticated to be working here lazy so this really liked how to respond all the way through out there one of the things we try to avoid um when you look at standards better written a eventually there tends to be when I full matrix thinking if you have like topic you grade levels we have a list topics listed right little so to be like after the all year matrix black also need to put in a great seven standard is what result in a smile widened HD regional if there's nothing more to say until grade A unique make up a great certain standard it's a trip it but some other things that might happen you know we don't see it on the screen right over here but in 7th Grade you do have Padova a deeper you serve negative numbers now and you understand negative multiplication and so you could start using negative numbers as your bases in your opponents white and so at like its once again because there's a black doesn't mean you don't addresses you can start addressing it using more your tools that you have exactly I CNN and then is he going to eighth grade that that's when you actually start using integer exponents where I low on the other be a great day is where you start to get out the exponent we'll mmm-hmm right right over here which is not which hasn't happened right very cool iraqi I could talk to you for an hour about the stuff goes we've it's been a hard time on it but I thank you so much for this is a very very very helpful share you're welcome my skin