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# Common Core Standards: Exponents

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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