Embed Size (px)
Citation preview
Scott%County%Public%Schools%!!
!
Sixth&Grade&Mathem
atics&Revised&2013&
&&&&
Pacing&Guide&and&Curriculum&M
ap&
Scott County Pacing Guide 6th Grade Math
Unit Suggested Time Standards Content
Basic Skills I 2 weeks Review Place value of whole numbers
+ - x multi-digit whole numbers Divisibility rules
Chapter 1 3 weeks
6.NS.2 6.EE.1 6.EE.2c 6.NS.4 6.EE.3
Estimating with whole numbers \ multi-digit whole numbers
Exponents Order of operations
Properties
Chapter 2
3 weeks
6.EE.2 6.EE.2a 6.EE2b 6.EE.3 6.EE.4 6.EE.5 6.EE.6 6.EE.7
Variables Expressions Equations
Chapter 3 5 weeks 6.NS.3 6.EE.7 6.EE.6
Decimals
Chapter 4 3 weeks
6.NS.4 6.EE.2b 6.EE.3 6.EE.4 6.NS.7
Fraction Basics
Chapter 5 4 weeks
6.NS.4 6.EE.6 6.EE.7 6.NS.1
Fraction Operations
Chapter 6 3 week
6.SP.2 6.SP.3 6.SP.1 6.SP.5c 6.NS.7c 6.NS.7d 6.SP.4 6.SP.5 6.SP.5a 6.SP.5b 6.SP.5d
Data Collection & Analysis
Chapter 7 4 weeks
6.RP.1 6.RP.2 6.RP.3 6.RP.3b 6.RP.3a 6.NS.6c 6.RP.3c
Proportional Relationships
Chapter 8 2 weeks
6.RP.3d 6.EE.2c 6.G.1 6.G.2 6.G.4
Measurement & Geometry
Chapter 9 2 weeks
6.NS.5 6.NS.6 6.NS.6a 6.NS.6c 6.NS.7 6.NS.7c 6.NS.7d 6.NS.7a 6.NS.7b 6.NS.6b 6.NS.8 6.G.3
Integers & the Coordinate Plane
Chapter 10 2 weeks
6.EE.2c 6.G.1 6.EE.9 6.RP.3 6.EE.8
Functions
Scott County Pacing Guide 6th Grade Advanced Math
Unit Suggested Time Standards Content
Basic Skills I 1 week Review *Place Value
*+ - X multi-digit whole numbers *Divisibiltiy rules
Chapter 1 2 weeks
6.NS.2 6.NS.4 6.EE.1 6.EE.2c 6.EE.3
*estimating with whole numbers */ multi-digit whole numbers
*Exponents *Order of Operations
* properties
Chapter 2 3 Weeks
6.EE.2 6.EE.2a 6.EE.2b 6.EE.3 6.EE.4 6.EE.5 6.EE.6 6.EE.7
*variables *expressions
*equations (1 and 2 step)
Chapter 3 3 weeks 6.NS.3 6.EE.6 6.EE.7
*decimals
Chapter 4 2 weeks
6.NS.4 6.NS.7 6.EE.2b 6.EE.3 6.EE.4
*fraction basics
Chpater 5 3 weeks
6.NS.1 6.NS.4 6.EE.6 6.EE.7
*fraction operations
Chapter 6 3 weeks
6.NS.7c 6.NS.7d 6.SP.1. 6.SP.2 6.SP.3 6.SP.4 6.SP.5 6.SP.5a 6.SP.5b 6.SP.5c 6.SP.5d
*data collection and analysis
Chapter 7 3 weeks
6.NS.6c 6.RP.1 6.RP.2 6.RP.3 6.RP.3a 6.RP.3b 6.RP.3c
*proportional relationships
Chapter 8 4 weeks
6.RP.3d 6.EE.2c 6.G.1 6.G.2 6.G.4
*measurement *geometry
*angle types *angle measures
*circle graphs *area of circles
Chapter 9 4 weeks
6.NS.5 6.NS.6 6.NS.6a 6.NS.6b 6.NS.6c 6.NS.7 6.NS.7a 6.NS.7b 6.NS.7c 6.NS.7d 6.NS.8 6.G.3
*integers *+/-/x// integers *coordinate plane
Chapter 10 4 weeks
6.EE.2c 6.EE.8 6.EE.9 6.G.1
6.RP.3
*functions *slope
*inequalities *solving inequalities (+/-)
Probability 2 weeks Probability
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Expr
essi
ons
and
Equa
tions
W
rite
and
eval
uate
num
eric
al e
xpre
ssio
ns in
volv
ing
who
le-n
umbe
r exp
onen
ts.
Clu
ster
A
pply
and
ext
end
prev
ious
und
erst
andi
ngs
of a
rithm
etic
to a
lgeb
raic
ex
pres
sion
s.
Tar
get
Typ
e St
ate
Tar
get
Stud
ent F
rien
dly
Tar
get
K
Writ
e nu
mer
ical
exp
ress
ions
invo
lvin
g w
hole
num
ber e
xpon
ents
Ex
. 34
= 3x
3x3x
3
I can
writ
e ex
pone
nts
in e
xpan
ded
form
usi
ng re
peat
ed fa
ctor
s.
K
Eval
uate
num
eric
al e
xpre
ssio
ns in
volv
ing
who
le n
umbe
r exp
onen
ts
Ex. 3
4 =
3x3x
3x3
= 81
I can
find
the
valu
e of
an
expo
nent
.
K
Solv
e or
der o
f ope
ratio
n pr
oble
ms
that
con
tain
exp
onen
ts
Ex. 3
+ 2
2 –
(2 +
3) =
2
I can
follo
w th
e co
rrec
t ord
er o
f ope
ratio
ns to
sol
ve a
pro
blem
co
ntai
ning
exp
onen
ts.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.EE
.1
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Expr
essi
ons
and
Equa
tions
W
rite,
read
and
eva
luat
e ex
pres
sion
s in
whi
ch le
tters
sta
nd fo
r num
bers
. a.
Writ
e ex
pres
sion
s th
at re
cord
ope
ratio
ns w
ith n
umbe
rs a
nd w
ith le
tters
sta
ndin
g fo
r num
bers
. Fo
r exa
mpl
e, e
xpre
ss th
e ca
lcul
atio
n “S
ubtra
ct y
from
5”
as 5
– y
. C
lust
er
App
ly a
nd e
xten
d pr
evio
us u
nder
stan
ding
s of
arit
hmet
ic to
alg
ebra
ic
expr
essi
ons.
T
arge
t T
ype
Stat
e T
arge
t St
uden
t Fri
endl
y T
arge
t
K
Use
num
bers
and
var
iabl
es to
repr
esen
t des
ired
oper
atio
ns
I can
use
num
bers
and
var
iabl
es to
repr
esen
t des
ired
oper
atio
ns. (
For
exam
ple:
3 le
ss th
an 4
tim
es a
num
ber (
j) =
4j –
3.
R
Tr
ansl
atin
g w
ritte
n ph
rase
s in
to a
lgeb
raic
exp
ress
ions
. I c
an w
rite
an e
quat
ion
for a
wor
d pr
oble
m.
R
Tr
ansl
atin
g al
gebr
aic
expr
essi
ons
into
writ
ten
phra
ses.
I c
an e
xpre
ss a
n eq
uatio
n as
a w
ord
prob
lem
.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.EE
.2a
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Expr
essi
ons
and
Equa
tions
W
rite,
read
and
eva
luat
e ex
pres
sion
s in
whi
ch le
tters
sta
nd fo
r num
bers
. b.
Iden
tify
parts
of a
n ex
pres
sion
usi
ng m
athe
mat
ical
term
s (s
um, t
erm
, pro
duct
, fac
tor,
quot
ient
, co
effic
ient
); vi
ew o
ne o
r mor
e pa
rts o
f an
expr
essi
on a
s a
sing
le e
ntity
. For
exa
mpl
e, d
escr
ibe
the
expr
essi
on 2
(8 +
7) a
s a
prod
uct o
f tw
o fa
ctor
s; v
iew
(8 +
7) a
s bo
th a
sin
gle
entit
y an
d a
sum
of t
wo
term
s.
Clu
ster
A
pply
and
ext
end
prev
ious
und
erst
andi
ngs
of a
rithm
etic
to a
lgeb
raic
ex
pres
sion
s.
Tar
get
Typ
e St
ate
Tar
get
Stud
ent F
rien
dly
Tar
get
K
Iden
tify
parts
of a
n ex
pres
sion
usi
ng m
athe
mat
ical
term
s (s
um, t
erm
, pr
oduc
t, fa
ctor
, quo
tient
, coe
ffic
ient
)
I can
iden
tify
the
mat
h te
rms
in a
giv
en e
xpre
ssio
n (F
or e
xam
ple:
sum
pr
oduc
t, et
c….
K
Iden
tify
parts
of a
n ex
pres
sion
as
a si
ngle
ent
ity, e
ven
if no
t a
mon
omia
l.
I can
bre
ak d
own
expr
essi
ons
into
indi
vidu
al s
teps
by
usin
g th
e pr
oper
or
der o
f ope
ratio
ns.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.EE
.2b
K
R
S
P
Mak
e se
nse
of
prob
lem
s and
pe
rsev
ere
in so
lvin
g th
em.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s. U
se a
ppro
pria
te to
ols
stra
tegi
cally
. A
ttend
to p
reci
sion
. Lo
ok fo
r and
mak
e us
e of
stru
ctur
e.
Look
for a
nd e
xpre
ss
regu
larit
y in
repe
ated
re
ason
ing.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Expr
essi
ons a
nd
Equa
tions
W
rite,
read
and
eva
luat
e ex
pres
sion
s in
whi
ch le
tters
stan
d fo
r num
bers
. c.
Eva
luat
e ex
pres
sion
s at s
peci
fic v
alue
s of t
heir
varia
bles
. Inc
lude
exp
ress
ions
that
aris
e fr
om
form
ulas
use
d in
real
-wor
ld p
robl
ems.
Perf
orm
arit
hmet
ic o
pera
tions
, inc
ludi
ng th
ose
invo
lvin
g w
hole
num
ber e
xpon
ents
, in
the
conv
entio
nal o
rder
whe
n th
ere
are
no p
aren
thes
es to
spec
ify a
pa
rticu
lar o
rder
(Ord
er o
f Ope
ratio
ns).
For e
xam
ple,
use
the
form
ulas
V =
s3 a
nd A
= 6
s2 to
fin
d th
e vo
lum
e an
d su
rfac
e ar
ea o
f a c
ube
with
side
s of l
engt
h s =
1/2
.
Clu
ster
A
pply
and
ext
end
prev
ious
und
erst
andi
ngs
of a
rithm
etic
to a
lgeb
raic
ex
pres
sion
s. T
arge
t T
ype
Stat
e T
arge
t St
uden
t Fri
endl
y T
arge
t
K
Subs
titut
e sp
ecifi
c va
lues
for v
aria
bles
.
I can
solv
e fo
rmul
as b
y su
bstit
utin
g va
lues
for t
he v
aria
bles
.
K
Eval
uate
alg
ebra
ic e
xpre
ssio
ns in
clud
ing
thos
e th
at a
rise
from
real
-w
orld
pro
blem
s.
I can
use
alg
ebra
to so
lver
real
-wor
ld p
robl
ems.
K
App
ly o
rder
of o
pera
tions
whe
n th
ere
are
no p
aren
thes
es fo
r exp
ress
ions
th
at in
clud
e w
hole
num
ber e
xpon
ents
I can
use
the
corr
ect o
rder
of o
pera
tions
to so
lve
an e
quat
ion.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.EE
.2c
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Expr
essi
ons
and
Equa
tions
A
pply
the
prop
ertie
s of
ope
ratio
ns to
gen
erat
e eq
uiva
lent
exp
ress
ions
. For
exa
mpl
e, a
pply
the
dist
ribut
ive
prop
erty
to th
e ex
pres
sion
3 (2
+ x
) to
prod
uce
the
equi
vale
nt e
xpre
ssio
n 6
+ 3x
; ap
ply
the
dist
ribut
ive
prop
erty
to th
e ex
pres
sion
24x
+ 1
8y to
pro
duce
the
equi
vale
nt e
xpre
ssio
n 6
(4x
+ 3y
); ap
ply
prop
ertie
s of
ope
ratio
ns to
y +
y +
y to
pro
duce
the
equi
vale
nt e
xpre
ssio
n 3y
. C
lust
er
App
ly a
nd e
xten
d pr
evio
us u
nder
stan
ding
s of
arit
hmet
ic to
alg
ebra
ic
expr
essi
ons.
T
arge
t T
ype
Stat
e T
arge
t St
uden
t Fri
endl
y T
arge
t
K
Gen
erat
e eq
uiva
lent
exp
ress
ions
usi
ng th
e pr
oper
ties
of o
pera
tions
. (e.
g.
dist
ribut
ive
prop
erty
, ass
ocia
tive
prop
erty
, add
ing
like
term
s w
ith th
e ad
ditio
n pr
oper
ty o
f equ
ality
, etc
.)
I can
use
the
corr
ect p
rope
rty to
rew
rite
an e
quiv
alen
t exp
ress
ion.
R
App
ly th
e pr
oper
ties
of o
pera
tions
to g
ener
ate
equi
vale
nt e
xpre
ssio
ns.
I can
use
the
corr
ect p
rope
rty to
rew
rite
an e
quiv
alen
t exp
ress
ion.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.EE
.3
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Expr
essi
ons
and
Equa
tions
Id
entif
y w
hen
two
expr
essi
ons
are
equi
vale
nt (i
.e.,
whe
n th
e tw
o ex
pres
sion
s na
me
the
sam
e nu
mbe
r reg
ardl
ess
of w
hich
val
ue is
sub
stitu
ted
into
them
). Fo
r exa
mpl
e, th
e ex
pres
sion
s y
+ y
+ y
and
3y a
re e
quiv
alen
t bec
ause
they
nam
e th
e sa
me
num
ber r
egar
dles
s of
whi
ch n
umbe
r y
stan
ds fo
r. C
lust
er
App
ly a
nd e
xten
d pr
evio
us u
nder
stan
ding
s of
arit
hmet
ic to
alg
ebra
ic
expr
essi
ons.
T
arge
t T
ype
Stat
e T
arge
t St
uden
t Fri
endl
y T
arge
t
K
Rec
ogni
ze w
hen
two
expr
essi
ons
are
equi
vale
nt.
I can
cha
nge
a va
lue
in a
n ex
pres
sion
to d
eter
min
e if
it is
equ
ival
ent
(For
exa
mpl
e: y
+y+y
= 3
y)
R
Pr
ove
(usi
ng v
ario
us s
trate
gies
) tha
t tw
o eq
uatio
ns a
re e
quiv
alen
t no
mat
ter w
hat n
umbe
r is
subs
titut
ed.
I can
sho
w th
at tw
o eq
uatio
ns a
re e
qual
by
usin
g di
ffer
ent t
ypes
of
stra
tegi
es.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.EE
.4
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Expr
essi
ons
and
Equa
tions
U
nder
stan
d so
lvin
g an
equ
atio
n or
ineq
ualit
y as
a p
roce
ss o
f ans
wer
ing
a qu
estio
n: w
hich
val
ues
from
a s
peci
fied
set,
if an
y, m
ake
the
equa
tion
or in
equa
lity
true?
Use
sub
stitu
tion
to d
eter
min
e w
heth
er a
giv
en n
umbe
r in
a sp
ecifi
ed s
et m
akes
an
equa
tion
or in
equa
lity
true.
C
lust
er
Rea
son
abou
t and
sol
ve
one-
varia
ble
equa
tions
an
d in
equa
litie
s T
arge
t T
ype
Stat
e T
arge
t St
uden
t Fri
endl
y T
arge
t
K
Rec
ogni
ze s
olvi
ng a
n eq
uatio
n or
ineq
ualit
y as
a p
roce
ss o
f ans
wer
ing
“whi
ch v
alue
s fr
om a
spe
cifie
d se
t, if
any,
mak
e th
e eq
uatio
n or
in
equa
lity
true?
”
I can
dec
ide
whi
ch v
alue
from
a s
peci
fied
set w
ill m
ake
the
equa
tion
or
ineq
ualit
y a
true
stat
emen
t
K
Kno
w th
at th
e so
lutio
ns o
f an
equa
tion
or in
equa
lity
are
the
valu
es th
at
mak
e th
e eq
uatio
n or
ineq
ualit
y tru
e.
I can
und
erst
and
the
solu
tion
to a
n eq
uatio
n or
ineq
ualit
y m
akes
it a
true
st
atem
ent
K
Use
sub
stitu
tion
to d
eter
min
e w
heth
er a
giv
en n
umbe
r in
a sp
ecifi
ed s
et
mak
es a
n eq
uatio
n or
ineq
ualit
y tru
e.
I can
use
sub
stitu
tion
to d
eter
min
e w
hich
val
ue w
ill m
ake
an e
quat
ion
or
an in
equa
lity
a tru
e st
atem
ent.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.EE
.5
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Expr
essi
ons
and
Equa
tions
U
se v
aria
bles
to re
pres
ent n
umbe
rs a
nd w
rite
expr
essi
ons
whe
n so
lvin
g a
real
-wor
ld o
r m
athe
mat
ical
pro
blem
; und
erst
and
that
a v
aria
ble
can
repr
esen
t an
unkn
own
num
ber,
or,
depe
ndin
g on
the
purp
ose
at h
and,
any
num
ber i
n a
spec
ified
set
. C
lust
er
Rea
son
abou
t and
sol
ve
one-
varia
ble
equa
tions
an
d in
equa
litie
s T
arge
t T
ype
Stat
e T
arge
t St
uden
t Fri
endl
y T
arge
t
K
Rec
ogni
ze th
at a
var
iabl
e ca
n re
pres
ent a
n un
know
n nu
mbe
r, or
, de
pend
ing
on th
e pu
rpos
e at
han
d, a
ny n
umbe
r in
a sp
ecifi
ed s
et.
I can
reco
gniz
e th
at a
var
iabl
e re
plac
es a
n un
know
n nu
mbe
r(s)
.
R
Rel
ate
varia
bles
to a
con
text
.
I can
rela
te th
e va
riabl
e in
an
expr
essi
on to
a re
al li
fe s
ituat
ion.
R
Writ
e ex
pres
sion
s w
hen
solv
ing
a re
al-w
orld
or m
athe
mat
ical
pro
blem
.
I can
writ
e an
exp
ress
ion
usin
g va
riabl
es fr
om a
real
-life
situ
atio
n.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.EE
.6
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Expr
essi
ons
and
Equa
tions
So
lve
real
-wor
ld a
nd m
athe
mat
ical
pro
blem
s by
writ
ing
and
solv
ing
equa
tions
of t
he fo
rm x
+ p
=
q an
d px
= q
for c
ases
in w
hich
p, q
and
x a
re a
ll no
nneg
ativ
e ra
tiona
l num
bers
. C
lust
er
Rea
son
abou
t and
sol
ve
one-
varia
ble
equa
tions
an
d in
equa
litie
s T
arge
t T
ype
Stat
e T
arge
t St
uden
t Fri
endl
y T
arge
t
K
Def
ine
inve
rse
oper
atio
n.
I can
sta
te th
at th
e in
vers
e of
an
oper
atio
n is
its
oppo
site
ope
ratio
n.
K
K
now
how
inve
rse
oper
atio
ns c
an b
e us
ed in
sol
ving
one
-var
iabl
e eq
uatio
ns.
I can
use
the
inve
rse
oper
atio
n to
sol
ve fo
r a v
aria
ble.
R
App
ly ru
les
of th
e fo
rm x
+ p
= q
and
px
= q,
for c
ases
in w
hich
p, q
and
x
are
all n
onne
gativ
e ra
tiona
l num
bers
, to
solv
e re
al w
orld
and
m
athe
mat
ical
pro
blem
s. (T
here
is o
nly
one
unkn
own
quan
tity.
)
I can
use
the
corr
ect r
ules
to s
olve
a re
al w
orld
mat
hem
atic
al p
robl
em
whe
re I
mus
t rep
lace
one
var
iabl
e w
ith th
e co
rrec
t non
-neg
ativ
e ra
tiona
l nu
mbe
r.
R
Dev
elop
a ru
le fo
r sol
ving
one
-ste
p eq
uatio
ns u
sing
inve
rse
oper
atio
ns
with
non
nega
tive
ratio
nal c
oeff
icie
nts.
I c
an w
rite
the
rule
for s
olvi
ng o
ne-s
tep
equa
tions
by
know
ing
to u
se th
e in
vers
e op
erat
ion
to s
olve
the
equa
tion
(For
exa
mpl
e: C
+ 2
= 1
0 w
ill b
e so
lved
by
subt
ract
ing
2 fr
om b
oth
side
s of
the
equa
tion)
.
R
Solv
e an
d w
rite
equa
tions
for r
eal-w
orld
mat
hem
atic
al p
robl
ems
cont
aini
ng o
ne u
nkno
wn.
I c
an w
rite
and
solv
e an
equ
atio
n fo
r one
unk
now
n fr
om a
real
-wor
ld
situ
atio
n.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.EE
.7
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Expr
essi
ons
and
Equa
tions
W
rite
an in
equa
lity
of th
e fo
rm x
> c
or x
< c
to re
pres
ent a
con
stra
int o
r con
ditio
n in
a re
al-
wor
ld o
r mat
hem
atic
al p
robl
em. R
ecog
nize
that
ineq
ualit
ies
of th
e fo
rm x
> c
or x
< c
hav
e in
finite
ly m
any
solu
tions
; rep
rese
nt s
olut
ions
of s
uch
ineq
ualit
ies
on n
umbe
r lin
e di
agra
ms.
C
lust
er
Rea
son
abou
t and
sol
ve
one-
varia
ble
equa
tions
an
d in
equa
litie
s T
arge
t T
ype
Stat
e T
arge
t St
uden
t Fri
endl
y T
arge
t
K
Iden
tify
the
cons
train
t or c
ondi
tion
in a
real
-wor
ld o
r mat
hem
atic
al
prob
lem
in o
rder
to s
et u
p an
ineq
ualit
y.
I can
writ
e a
sim
ple
ineq
ualit
y to
repr
esen
t a re
al-li
fe s
ituat
ion.
K
Rec
ogni
ze th
at in
equa
litie
s of
the
form
x >
c o
r x <
c h
ave
infin
itely
m
any
solu
tions
.
I can
nam
e m
ore
than
one
sol
utio
n to
an
ineq
ualit
y
R
Writ
e an
ineq
ualit
y of
the
form
x >
c o
r x <
c to
repr
esen
t a c
onst
rain
t or
cond
ition
in a
real
-wor
ld o
r mat
hem
atic
al p
robl
em.
I can
writ
e a
sim
ple
ineq
ualit
y to
repr
esen
t a re
al-li
fe s
ituat
ion.
R
Rep
rese
nt s
olut
ions
to in
equa
litie
s or
the
form
x >
c o
r x <
c, w
ith
infin
itely
man
y so
lutio
ns, o
n nu
mbe
r lin
e di
agra
ms.
I can
cre
ate
a nu
mbe
r lin
e to
sho
w a
ll po
ssib
le s
olut
ions
to th
e in
equa
lity.
(I c
an g
raph
ineq
ualit
ies
on a
num
ber l
ine)
.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.EE
.8
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Expr
essi
ons
and
Equa
tions
U
se v
aria
bles
to re
pres
ent t
wo
quan
titie
s in
a re
al-w
orld
pro
blem
that
cha
nge
in re
latio
nshi
p to
on
e an
othe
r; w
rite
an e
quat
ion
to e
xpre
ss o
ne q
uant
ity, t
houg
ht o
f as
the
depe
nden
t var
iabl
e, in
te
rms
of th
e ot
her q
uant
ity, t
houg
ht o
f as
the
inde
pend
ent v
aria
ble.
Ana
lyze
the
rela
tions
hip
betw
een
the
depe
nden
t and
inde
pend
ent v
aria
bles
usi
ng g
raph
s an
d ta
bles
, and
rela
te th
ese
to th
e eq
uatio
n. F
or e
xam
ple,
in a
pro
blem
invo
lvin
g m
otio
n at
con
stan
t spe
ed, l
ist a
nd g
raph
ord
ered
pa
irs o
f dis
tanc
es a
nd ti
mes
, and
writ
e th
e eq
uatio
n d
= 65
t to
repr
esen
t the
rela
tions
hip
betw
een
dist
ance
and
tim
e.
Clu
ster
R
epre
sent
and
ana
lyze
qu
antit
ativ
e re
latio
nshi
ps
betw
een
depe
nden
t and
in
depe
nden
t var
iabl
es.
Tar
get
Typ
e St
ate
Tar
get
Stud
ent F
rien
dly
Tar
get
K
Def
ine
inde
pend
ent a
nd d
epen
dent
var
iabl
es.
I can
def
ine
that
an
inde
pend
ent v
aria
ble
does
not
eff
ect t
he o
utco
me
of
an e
vent
whi
le a
dep
ende
nt v
aria
ble
does
.
K
Use
var
iabl
es to
repr
esen
t tw
o qu
antit
ies
in a
real
-wor
ld p
robl
em th
at
chan
ge in
rela
tions
hip
to o
ne a
noth
er.
I can
use
var
iabl
es to
repr
esen
t tw
o qu
antit
ies
in a
real
-wor
ld p
robl
em
that
cha
nges
in a
rela
tions
hip
to o
ne a
noth
er.
(For
exa
mpl
e: th
e tim
e in
w
hich
you
trav
el e
ffec
ts th
e di
stan
ce th
at y
ou tr
avel
). R
W
rite
an e
quat
ion
to e
xpre
ss o
ne q
uant
ity (d
epen
dent
) in
term
s of
the
othe
r qua
ntity
(ind
epen
dent
). I c
an w
rite
an e
quat
ion
to e
xpre
ss o
ne q
uant
ity (d
epen
dent
) in
term
s of
th
e ot
her q
uant
ity (i
ndep
ende
nt).
(For
exa
mpl
e:d=
65t,
whe
re d
ista
nce
is
depe
nden
t on
the
time
you
trave
l. R
A
naly
ze th
e re
latio
nshi
p be
twee
n th
e de
pend
ent v
aria
ble
and
inde
pend
ent v
aria
ble
usin
g ta
bles
and
gra
phs.
I c
an c
reat
e a
func
tion
tabl
e to
ana
lyze
and
gra
ph th
e re
latio
nshi
p be
twee
n th
e de
pend
ent a
nd in
depe
nden
t var
iabl
es.
R
R
elat
e th
e da
ta in
a g
raph
and
tabl
e to
the
corr
espo
ndin
g eq
uatio
n.
I c
an w
rite
an e
quat
ion
to re
pres
ent t
he d
ata
from
a g
raph
or t
able
.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.EE
.9
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Geo
met
ry
Find
the
area
of r
ight
tria
ngle
s, o
ther
tria
ngle
s, s
peci
al q
uadr
ilate
rals
, and
pol
ygon
s by
co
mpo
sing
into
rect
angl
es o
r dec
ompo
sing
into
oth
er s
hape
s; a
pply
thes
e te
chni
ques
in th
e co
ntex
t of s
olvi
ng re
al-w
orld
and
mat
hem
atic
al p
robl
ems.
C
lust
er
Solv
e re
al-w
orld
and
m
athe
mat
ical
pro
blem
s in
volv
ing
area
, sur
face
ar
ea, a
nd v
olum
e.
Tar
get
Typ
e St
ate
Tar
get
Stud
ent F
rien
dly
Tar
get
K
Rec
ogni
ze a
nd k
now
how
to c
ompo
se a
nd d
ecom
pose
pol
ygon
s in
to
trian
gles
and
rect
angl
es.
I can
div
ide
poly
gons
into
tria
ngle
s an
d re
ctan
gles
. I c
an c
ombi
ne tr
iang
les
and
rect
angl
es to
geth
er to
mak
e po
lygo
ns.
R
C
ompa
re th
e ar
ea o
f a tr
iang
le to
the
area
of t
he c
ompo
sted
rect
angl
e (d
ecom
posi
tion
addr
esse
d in
pre
viou
s gr
ade)
. I c
an c
ompa
re th
e ar
ea o
f a tr
iang
le to
the
area
of t
he c
ompo
sted
re
ctan
gle.
R
A
pply
the
tech
niqu
es o
f com
posi
ng a
nd/o
r dec
ompo
sing
to fi
nd th
e ar
ea
of tr
iang
les,
spe
cial
qua
drila
tera
ls a
nd p
olyg
ons
to s
olve
mat
hem
atic
al
and
real
-wor
ld p
robl
ems.
I can
find
the
area
of t
riang
les,
spe
cial
qua
drila
tera
ls, a
nd p
olyg
ons
by
divi
ding
them
into
tria
ngle
s, re
ctan
gles
.
R
Com
pare
the
area
of a
tria
ngle
to th
e ar
ea o
f the
com
post
ed re
ctan
gle.
(D
ecom
posi
tion
addr
esse
d in
pre
viou
s gr
ade.
) I c
an c
ompa
re th
e ar
ea o
f the
two
trian
gles
that
mak
e up
the
rect
angl
e to
th
e ar
ea o
f a re
ctan
gle.
Dis
cuss
, dev
elop
and
just
ify a
rea
form
ulas
for
trian
gles
and
par
alle
logr
ams
(6th
gra
de in
trodu
ctio
n)
R
Dis
cuss
, dev
elop
and
just
ify a
rea
form
ulas
for t
riang
les
and
para
llelo
gram
s (6
th g
rade
intro
duct
ion)
I c
an c
reat
e an
d ex
plai
n a
form
ula
for f
indi
ng th
e ar
ea o
f a tr
iang
le a
nd
para
llelo
gram
.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.G
.1
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Geo
met
ry
Find
the
volu
me
of a
righ
t rec
tang
ular
pris
m w
ith fr
actio
nal e
dge
leng
ths
by p
acki
ng it
with
uni
t cu
bes
of th
e ap
prop
riate
uni
t fra
ctio
n ed
ge le
ngth
s, a
nd s
how
that
the
volu
me
is th
e sa
me
as
wou
ld b
e fo
und
by m
ultip
lyin
g th
e ed
ge le
ngth
s of
the
pris
m. A
pply
the
form
ulas
V =
l w
h a
nd
V =
B h
to fi
nd v
olum
es o
f rig
ht re
ctan
gula
r pris
ms
with
frac
tiona
l edg
e le
ngth
s in
the
cont
ext o
f so
lvin
g re
al-w
orld
and
mat
hem
atic
al p
robl
ems.
Clu
ster
So
lve
real
-wor
ld a
nd
mat
hem
atic
al p
robl
ems
invo
lvin
g ar
ea, s
urfa
ce
area
, and
vol
ume.
T
arge
t T
ype
Stat
e T
arge
t St
uden
t Fri
endl
y T
arge
t
K
Kno
w h
ow to
cal
cula
te th
e vo
lum
e of
a ri
ght r
ecta
ngul
ar p
rism
I c
an fi
nd th
e vo
lum
e of
a ri
ght r
ecta
ngul
ar p
rism
R
App
ly th
e vo
lum
e fo
rmul
as fo
r rig
ht re
ctan
gula
r pris
ms
to s
olve
m
athe
mat
ical
and
real
-wor
ld p
robl
ems
invo
lvin
g re
ctan
gula
r pris
ms
with
frac
tiona
l edg
e le
ngth
s.
I can
cor
rect
ly a
pply
the
form
ulas
for f
indi
ng th
e vo
lum
e of
a ri
ght
rect
angu
lar p
rism
to s
olve
real
wor
ld a
nd m
athe
mat
ical
pro
blem
s, fo
r ex
ampl
e: fi
nd th
e vo
lum
e of
a c
erea
l box
with
a h
eigh
t of 7
inch
es,
wid
th o
f 2 ¾
inch
es a
nd a
hei
ght o
f 10
inch
es is
7 x
2 ¾
x 1
0 =
192 ½
in
ches³.
S
Mod
el th
e vo
lum
e of
a ri
ght r
ecta
ngul
ar p
rism
with
frac
tiona
l edg
e le
ngth
s by
pac
king
it w
ith u
nit c
ubes
of t
he a
ppro
pria
te u
nit f
ract
ion
edge
leng
ths.
I can
mod
el th
e vo
lum
e of
a re
ctan
gula
r pris
ms
with
frac
tiona
l edg
e le
ngth
s us
ing
unit
cube
s.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.G
.2
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Geo
met
ry
Dra
w p
olyg
ons
in th
e co
ordi
nate
pla
ne g
iven
coo
rdin
ates
for t
he v
ertic
es; u
se c
oord
inat
es to
find
th
e le
ngth
of a
sid
e jo
inin
g po
ints
with
the
sam
e fir
st c
oord
inat
e or
the
sam
e se
cond
coo
rdin
ate.
A
pply
thes
e te
chni
ques
in th
e co
ntex
t of s
olvi
ng re
al-w
orld
and
mat
hem
atic
al p
robl
ems.
C
lust
er
Solv
e re
al-w
orld
and
m
athe
mat
ical
pro
blem
s in
volv
ing
area
, sur
face
ar
ea, a
nd v
olum
e.
Tar
get
Typ
e St
ate
Tar
get
Stud
ent F
rien
dly
Tar
get
K
Dra
w p
olyg
ons
in th
e co
ordi
nate
pla
ne.
I c
an d
raw
a p
olyg
on in
the
coor
dina
te p
lane
.
K
Use
coo
rdin
ates
(with
the
sam
e x-
coo
rdin
ate
or th
e sa
me
y-co
ordi
nate
) to
find
the
leng
th o
f a s
ide
of a
pol
ygon
.
I can
find
the
leng
th o
f a s
ide
of a
pol
ygon
usi
ng c
oord
inat
es.
R
App
ly th
e te
chni
que
of u
sing
coo
rdin
ates
to fi
nd th
e le
ngth
of a
sid
e of
a
poly
gon
draw
n in
the
coor
dina
te p
an to
sol
ve re
al-w
orld
and
m
athe
mat
ical
pro
blem
s
I can
app
ly th
e kn
owle
dge
of d
eter
min
ing
the
side
leng
ths
of a
pol
ygon
pl
aced
on
a co
ordi
nate
grid
to h
elp
solv
e re
al-w
orld
pro
blem
s, (f
or
exam
ple:
to d
eter
min
e th
e si
ze o
f rug
nee
ded
in a
room
to le
ave
a de
term
ined
am
ount
of f
loor
spa
ce a
roun
d th
e ru
g.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.G
.3
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Geo
met
ry
Dra
w p
olyg
ons
in th
e co
ordi
nate
pla
ne g
iven
coo
rdin
ates
for t
he v
ertic
es; u
se c
oord
inat
es to
find
th
e le
ngth
of a
sid
e jo
inin
g po
ints
with
the
sam
e fir
st c
oord
inat
e or
the
sam
e se
cond
coo
rdin
ate.
A
pply
thes
e te
chni
ques
in th
e co
ntex
t of s
olvi
ng re
al-w
orld
and
mat
hem
atic
al p
robl
ems.
C
lust
er
Solv
e re
al-w
orld
and
m
athe
mat
ical
pro
blem
s in
volv
ing
area
, sur
face
ar
ea, a
nd v
olum
e.
Tar
get
Typ
e St
ate
Tar
get
Stud
ent F
rien
dly
Tar
get
K
Kno
w th
at 3
-D fi
gure
s ca
n be
repr
esen
ted
by n
ets
. I c
an id
entif
y 3
dim
ensi
onal
figu
res
and
thei
r net
s.
R
R
epre
sent
thre
e-di
men
sion
al fi
gure
s us
ing
nets
mad
e up
of r
ecta
ngle
s an
d tri
angl
es
I can
use
rect
angl
e an
d tri
angl
es to
cre
ate
a ne
t for
3-D
figu
res.
R
App
ly k
now
ledg
e of
cal
cula
ting
the
area
of r
ecta
ngle
s an
d tri
angl
es to
a
net,
and
com
bine
the
area
s fo
r eac
h sh
ape
into
one
ans
wer
repr
esen
ting
the
surf
ace
area
of a
3-d
imen
sion
al fi
gure
.
I can
use
the
net o
f a 3
-D fi
gure
to c
alcu
late
the
area
of t
he fi
gure
. Thi
s m
eans
I w
ill c
alcu
late
the
sepa
rate
rect
angu
lar a
nd/o
r tria
ngul
ar a
reas
of
the
nets
and
tota
l tog
ethe
r to
get a
sur
face
are
a.
R
So
lve
real
-wor
ld a
nd m
athe
mat
ical
pro
blem
s in
volv
ing
surf
ace
area
us
ing
nets
.
I can
sol
ve re
al-w
orld
and
mat
hem
atic
al p
robl
ems
usin
g ne
ts.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.G
.4
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Num
ber S
yste
m
Inte
rpre
t and
com
pute
quo
tient
s of
frac
tions
, and
sol
ve w
ord
prob
lem
s in
volv
ing
divi
sion
of
frac
tions
by
frac
tions
, e.g
., by
usi
ng v
isua
l fra
ctio
n m
odel
s an
d eq
uatio
ns to
repr
esen
t the
pr
oble
m. F
or e
xam
ple,
cre
ate
a st
ory
cont
ext f
or (2
/3) ÷
(3/4
) and
use
a v
isua
l fra
ctio
n m
odel
to
show
the
quot
ient
; use
the
rela
tions
hip
betw
een
mul
tiplic
atio
n an
d di
visi
on to
exp
lain
that
(2/3
) ÷
(3/4
) = 8
/9 b
ecau
se 3
/4 o
f 8/9
is 2
/3. (
In g
ener
al,
(a/b
) ÷ (c
/d) =
ad/
bc.)
How
muc
h ch
ocol
ate
will
eac
h pe
rson
get
if 3
peo
ple
shar
e 1/
2 lb
of
choc
olat
e eq
ually
? H
ow m
any
3/4-
cup
serv
ings
are
in 2
/3 o
f a c
up o
f yog
urt?
How
wid
e is
a
rect
angu
lar s
trip
of l
and
with
leng
th 3
/4 m
i and
are
a 1/
2 sq
uare
mi?
Clu
ster
A
pply
and
ext
end
prev
ious
und
erst
andi
ng o
f m
ultip
licat
ion
and
divi
sion
to d
ivid
e fr
actio
ns b
y fr
actio
ns
Tar
get
Typ
e St
ate
Tar
get
Stud
ent F
rien
dly
Tar
get
K
Com
pute
quo
tient
s of
frac
tions
div
ided
by
frac
tions
(inc
ludi
ng m
ixed
nu
mbe
rs).
I can
det
erm
ine
the
quot
ient
of a
frac
tion
by d
ivid
ing
the
num
erat
or b
y th
e de
nom
inat
or.
I can
mod
el a
frac
tion
or e
quat
ion
to s
olve
wor
d pr
oble
ms
invo
lvin
g di
visi
on o
f fra
ctio
ns.
R
In
terp
ret q
uotie
nts
of fr
actio
ns.
I can
iden
tify
wha
t the
quo
tient
of t
he fr
actio
n is
repr
esen
ting.
R
Solv
ing
real
-wor
ld p
robl
ems
invo
lvin
g di
visi
on o
f fra
ctio
ns b
y fr
actio
ns, e
.g.,
by u
sing
vis
ual f
ract
ion
mod
els
and
equa
tions
to
repr
esen
t the
pro
blem
.
I can
mod
el a
frac
tion
or e
quat
ion
to s
olve
wor
d pr
oble
ms
invo
lvin
g di
visi
on o
f fra
ctio
ns in
real
wor
ld s
ituat
ions
.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.N
S.1
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Num
ber S
yste
m
Flue
ntly
div
ide
mul
ti-di
git n
umbe
rs u
sing
the
stan
dard
alg
orith
m.
Clu
ster
C
ompu
te fl
uent
ly w
ith
mul
ti-di
git n
umbe
rs a
nd
find
com
mon
fact
ors
and
mul
tiple
s T
arge
t T
ype
Stat
e T
arge
t St
uden
t Fri
endl
y T
arge
t
K
Flue
ntly
div
ide
mul
ti-di
git n
umbe
rs u
sing
the
stan
dard
alg
orith
m w
ith
spee
d an
d ac
cura
cy.
I can
div
ide
any
num
ber l
arge
r tha
n 9
by d
eter
min
ing
the
num
ber o
f tim
es th
e di
viso
r will
fit i
nto
the
divi
dend
unt
il 0
or a
rem
aind
er s
mal
ler
than
the
divi
sor h
as b
een
reac
hed.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.N
S.2
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Num
ber S
yste
m
Flue
ntly
add
, sub
tract
, mul
tiply
, and
div
ide
mul
ti di
git d
ecim
als
usin
g th
e st
anda
rd a
lgor
ithm
for
each
ope
ratio
n.
Clu
ster
C
ompu
te fl
uent
ly w
ith
mul
ti-di
git n
umbe
rs a
nd
find
com
mon
fact
ors
and
mul
tiple
s T
arge
t T
ype
Stat
e T
arge
t St
uden
t Fri
endl
y T
arge
t
K
Flue
ntly
add
, sub
tract
, mul
tiply
and
div
ide
mul
ti-di
git d
ecim
als
usin
g th
e st
anda
rd a
lgor
ithm
for e
ach
oper
atio
n w
ith s
peed
and
acc
urac
y.
I can
com
pute
mul
ti-di
git d
ecim
als
with
eas
e w
hen
addi
ng a
nd
subt
ract
ing
usin
g th
e st
anda
rd a
lgor
ithm
. Thi
s m
eans
that
I w
ill
corr
ectly
line
up
the
deci
mal
pla
ces
whe
n ad
ding
and
sub
tract
ing.
I c
an c
ompu
te m
ulti-
digi
t dec
imal
s w
ith e
ase
whe
n m
ultip
lyin
g us
ing
the
stan
dard
alg
orith
m. T
his
mea
ns th
at I
will
cor
rect
ly p
lace
the
deci
mal
poi
nt in
the
prod
uct.
I can
com
pute
mul
ti-di
git d
ecim
als
with
eas
e w
hen
divi
ding
usi
ng th
e st
anda
rd a
lgor
ithm
. Thi
s m
eans
that
I ca
n re
cogn
ize
whe
n I n
eed
to
mov
e th
e de
cim
al p
oint
and
whe
re to
pla
ce it
in th
e di
viso
r or t
he
quot
ient
.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.N
S.3
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Num
ber S
yste
m
Find
the
grea
test
com
mon
fact
or o
f tw
o w
hole
num
bers
less
than
or e
qual
to 1
00 a
nd th
e le
ast
com
mon
mul
tiple
of t
wo
who
le n
umbe
rs le
ss th
an o
r equ
al to
12.
Use
the
dist
ribut
ive
prop
erty
to
exp
ress
a s
um o
f tw
o w
hole
num
bers
1–1
00 w
ith a
com
mon
fact
or a
s a
mul
tiple
of a
sum
of
two
who
le n
umbe
rs w
ith n
o co
mm
on fa
ctor
. For
exa
mpl
e, e
xpre
ss 3
6 +
8 as
4 (9
+ 2
).
Clu
ster
C
ompu
te fl
uent
ly w
ith
mul
ti-di
git n
umbe
rs a
nd
find
com
mon
fact
ors
and
mul
tiple
s T
arge
t T
ype
Stat
e T
arge
t St
uden
t Fri
endl
y T
arge
t
K
Iden
tify
the
fact
ors
of tw
o w
hole
num
bers
less
than
or e
qual
to 1
00 a
nd
dete
rmin
e th
e G
reat
est C
omm
on F
acto
r I c
an fi
nd th
e G
reat
est C
omm
on F
acto
r of t
wo
who
le n
umbe
rs le
ss th
an
or e
qual
to 1
00 b
y co
mpa
ring
the
fact
ors
of e
ach
num
ber.
For e
xam
ple:
I ca
n lis
t all
the
fact
ors
of th
e 2
who
le n
umbe
rs a
nd th
en fi
nd th
e gr
eate
st
num
ber t
hat i
s th
e sa
me
in b
oth
lists
.
K
Iden
tify
the
mul
tiple
s of
two
who
le n
umbe
rs le
ss th
an o
r equ
al to
12
and
dete
rmin
e th
e Le
ast C
omm
on M
ultip
le.
I can
find
the
Leas
t Com
mon
Mul
tiple
of t
he 2
who
le n
umbe
rs le
ss th
an
or e
qual
to 1
2 by
com
parin
g th
e m
ultip
les
of e
ach
num
ber,
(for
ex
ampl
e: I
can
list t
he m
ultip
les
of th
e 2
num
bers
unt
il I f
ind
the
first
co
mm
on n
umbe
r bet
wee
n th
e 2
lists
.)
R
App
ly th
e D
istri
butiv
e Pr
oper
ty to
rew
rite
addi
tion
prob
lem
s by
fa
ctor
ing
out t
he G
reat
est C
omm
on F
acto
r. I c
an fi
nd th
e G
reat
est C
omm
on F
acto
r of t
wo
who
le n
umbe
rs a
nd I
can
fact
or o
ut th
e G
reat
est C
omm
on F
acto
r usi
ng th
e di
strib
utiv
e pr
oper
ty,
(for
exa
mpl
e: to
sim
plify
the
addi
tion
of m
ulti-
digi
t num
bers
.)
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.N
S.4
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Num
ber S
yste
m
Und
erst
and
that
pos
itive
and
neg
ativ
e nu
mbe
rs a
re u
sed
toge
ther
to d
escr
ibe
quan
titie
s ha
ving
op
posi
te d
irect
ions
or v
alue
s (e
.g.,
tem
pera
ture
abo
ve /b
elow
zer
o, e
leva
tion
abov
e/be
low
sea
le
vel,
cred
its/d
ebits
, pos
itive
/neg
ativ
e el
ectri
c ch
arge
); us
e po
sitiv
e an
d ne
gativ
e nu
mbe
rs to
re
pres
ent q
uant
ities
in re
al-w
orld
con
text
s, e
xpla
inin
g th
e m
eani
ng o
f 0 in
eac
h si
tuat
ion.
Clu
ster
A
pply
and
ext
end
prev
ious
und
erst
andi
ngs
of n
umbe
rs to
the
syst
em
of ra
tiona
l num
bers
T
arge
t T
ype
Stat
e T
arge
t St
uden
t Fri
endl
y T
arge
t
K
Iden
tify
an in
tege
r and
its
oppo
site
I can
writ
e an
inte
ger a
nd it
s op
posi
te.
R
Use
inte
gers
to re
pres
ent q
uant
ities
in re
al w
orld
situ
atio
ns(a
bove
/bel
ow
sea
leve
l, et
c).
I can
writ
e an
inte
ger t
o re
pres
ent a
giv
en s
ituat
ion.
R
Expl
ain
whe
re z
ero
fits
into
a s
ituat
ion
repr
esen
ted
by in
tege
rs.
I c
an u
nder
stan
d th
at z
ero
is n
eith
er p
ositi
ve o
r neg
ativ
e.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.N
S.5
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Num
ber S
yste
m
Und
erst
and
a ra
tiona
l num
ber a
s a
poin
t on
the
num
ber l
ine.
Ext
end
num
ber l
ine
diag
ram
s an
d co
ordi
nate
axe
s fa
mili
ar fr
om p
revi
ous
grad
es to
repr
esen
t poi
nts
on th
e lin
e an
d in
the
plan
e w
ith n
egat
ive
num
ber c
oord
inat
es.
a. R
ecog
nize
opp
osite
sig
ns o
f num
bers
as
indi
catin
g lo
catio
ns o
n op
posi
te s
ides
of 0
on
the
num
ber l
ine;
reco
gniz
e th
at th
e op
posi
te o
f the
opp
osite
of a
num
ber i
s th
e nu
mbe
r its
elf,
e.g.
, -(-
3) =
3 a
nd th
at 0
is it
s ow
n op
posi
te.
b. U
nder
stan
d si
gns
of n
umbe
rs in
ord
ered
pai
rs a
s in
dica
ting
loca
tions
in q
uadr
ants
of t
he
coor
dina
te p
lane
; rec
ogni
ze th
at w
hen
two
orde
red
pairs
diff
er o
nly
by s
igns
, the
loca
tions
of t
he
poin
ts a
re re
late
d by
refle
ctio
ns a
cros
s on
e or
bot
h ax
es.
c. F
ind
and
posi
tion
inte
gers
and
oth
er ra
tiona
l num
bers
on
a ho
rizon
tal o
r ver
tical
num
ber l
ine
diag
ram
; fin
d an
d po
sitio
n pa
irs o
f int
eger
s an
d ot
her r
atio
nal n
umbe
rs o
n a
coor
dina
te p
lane
.
Clu
ster
A
pply
and
ext
end
prev
ious
und
erst
andi
ngs
of n
umbe
rs to
the
syst
em
of ra
tiona
l num
bers
Tar
get
Typ
e St
ate
Tar
get
Stud
ent F
rien
dly
Tar
get
K
Iden
tify
a ra
tiona
l num
ber a
s a
poin
t on
the
num
ber l
ine.
I can
pla
ce a
poi
nt o
n a
num
ber l
ine
K
Iden
tify
the
loca
tion
of z
ero
on a
num
ber l
ine
in re
latio
n to
pos
itive
and
ne
gativ
e nu
mbe
rs.
I can
pla
ce z
ero
corr
ectly
bet
wee
n th
e po
sitiv
e an
d ne
gativ
e nu
mbe
rs o
n a
num
ber l
ine.
K
Rec
ogni
ze o
ppos
ite s
igns
of n
umbe
rs a
s lo
catio
ns o
n op
posi
te s
ides
of 0
on
the
num
ber l
ine.
I c
an re
cogn
ize
that
opp
osite
val
ues
are
equa
l dis
tanc
es fr
om z
ero
on
oppo
site
sid
es o
f zer
o.
K
R
ecog
nize
the
sign
s of
bot
h nu
mbe
rs in
an
orde
red
pair
indi
cate
whi
ch
quad
rant
of t
he c
oord
inat
e pl
ane
the
orde
red
pair
will
be
loca
ted.
I c
an re
cogn
ize
that
the
sign
s of
an
orde
red
pair
tells
me
whi
ch q
uadr
ant
a po
int i
s go
ing
to b
e lo
cate
d.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.N
S.6
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
K
Find
and
pos
ition
inte
gers
and
oth
er ra
tiona
l num
bers
on
a ho
rizon
tal o
r ve
rtica
l num
ber l
ine
diag
ram
. I c
an lo
cate
and
pla
ce a
ratio
nal n
umbe
r on
a ho
rizon
tal a
nd v
ertic
al
num
ber l
ine
diag
ram
.
K
Find
and
pos
ition
pai
rs o
f int
eger
s an
d ot
her r
atio
nal n
umbe
rs o
n a
coor
dina
te p
lane
.
I can
find
or p
lace
inte
gers
and
ratio
nal n
umbe
rs o
n a
coor
dina
te p
lane
.
R
Rea
son
that
the
oppo
site
of t
he o
ppos
ite o
f a n
umbe
r is
the
num
ber
itsel
f. I c
an u
nder
stan
d th
at th
e op
posi
te o
f the
opp
osite
of a
num
bers
is th
e nu
mbe
r its
elf.
(For
exa
mpl
e: -
(-5)
is th
e sa
me
as 5
.)
R
Rea
son
that
whe
n on
ly th
e x
valu
e in
a s
et o
f ord
ered
pai
rs a
re
oppo
site
s, it
cre
ates
a re
flect
ion
over
the
y ax
is, e
.g. (
x,y)
and
(-x,
y)
I can
und
erst
and
that
mov
ing
from
a p
ositi
ve x
to a
neg
ativ
e x,
cro
sses
th
e y
axis
.
R
Rec
ogni
ze th
at w
hen
only
the
y va
lue
in a
set
of o
rder
ed p
airs
are
op
posi
tes,
it c
reat
es a
refle
ctio
n ov
er th
e x
axis
, e.g
., (x
,y) a
nd (x
,-y).
I can
und
erst
and
that
mov
ing
from
a p
ositi
ve y
to a
neg
ativ
e y,
cro
sses
th
e x
axis
.
R
Rea
son
that
whe
n tw
o or
dere
d pa
irs d
iffer
onl
y by
sig
ns, t
he lo
catio
ns o
f th
e po
ints
are
rela
ted
by re
flect
ions
acr
oss
both
axe
s, e
.g.,
(-x,
-y) a
nd
(x,y
)
I can
und
erst
and
that
and
ord
ered
pai
r with
the
sam
e nu
mbe
r but
di
ffer
ent s
igns
is a
n ex
ampl
e of
a re
flect
ion.
Mak
e se
nse
of
prob
lem
s and
pe
rsev
ere
in so
lvin
g th
em.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of st
ruct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Num
ber S
yste
m
Und
erst
and
orde
ring
and
abso
lute
val
ue o
f rat
iona
l num
bers
. a.
Inte
rpre
t sta
tem
ents
of i
nequ
ality
as s
tate
men
ts a
bout
the
rela
tive
posi
tion
of tw
o nu
mbe
rs o
n a
num
ber l
ine
diag
ram
. For
exa
mpl
e, in
terp
ret -
3>-7
as a
stat
emen
t tha
t -3
is lo
cate
d to
the
right
of
-7 o
n a
num
ber l
ine
orie
nted
from
the
left
to th
e rig
ht.
b.W
rite,
inte
rpre
t, an
d ex
plai
n st
atem
ents
of t
he o
rder
of r
atio
nal n
umbe
rs in
the
real
-wor
ld
cont
exts
. For
exa
mpl
e, w
rite
-3 d
egre
es C
elsi
us >
-7 d
egre
es C
elsi
us to
exp
ress
the
fact
that
-3
degr
ees i
s war
mer
than
-7 d
egre
es C
elsi
us.
c. U
nder
stan
d th
e ab
solu
te v
alue
of a
ratio
nal n
umbe
r as i
ts d
ista
nce
from
0 o
n th
e nu
mbe
r lin
e;
inte
rpre
t abs
olut
e va
lue
as m
agni
tude
for a
pos
itive
or n
egat
ive
quan
tity
in a
real
-wor
ld
situ
atio
n. F
or e
xam
ple,
for
an a
ccou
nt b
alan
ce o
f -30
dol
lars
, wri
te |-
30| =
30
to d
escr
ibe
the
size
of t
he d
ebt i
n do
llars
. d.
Dis
tingu
ish
com
paris
ons o
f abs
olut
e va
lue
from
stat
emen
ts a
bout
ord
er. F
or e
xam
ple,
re
cogn
ize
that
an
acco
unt b
alan
ce le
ss th
an -3
0 do
llars
rep
rese
nts
a de
bt g
reat
er th
an 3
0 do
llars
.
Clu
ster
A
pply
and
ext
end
prev
ious
und
erst
andi
ngs
of n
umbe
rs to
the
syst
em
of ra
tiona
l num
bers
Tar
get
Typ
e St
ate
Tar
get
Stud
ent F
rien
dly
Tar
get
K
Ord
er ra
tiona
l num
bers
on
a nu
mbe
r lin
e I c
an c
orre
ctly
pla
ce ra
tiona
l num
bers
on
a nu
mbe
r lin
e.
K
Id
entif
y ab
solu
te v
alue
of r
atio
nal n
umbe
rs.
I can
writ
e th
e ab
solu
te v
alue
of a
ratio
nal n
umbe
r.
R
Inte
rpre
t sta
tem
ents
of i
nequ
ality
as s
tate
men
ts a
bout
rela
tive
posi
tion
of
two
num
bers
on
a nu
mbe
r lin
e di
agra
m.
I can
com
pare
two
inte
gers
on
a nu
mbe
r lin
e by
thei
r dis
tanc
e fr
om z
ero.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.N
S.7
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
R
Writ
e, in
terp
ret,
and
expl
ain
stat
emen
t of o
rder
for r
atio
nal n
umbe
rs in
re
al-w
orld
con
text
s.
I can
writ
e an
d ex
plai
n th
e m
eani
ng a
nd o
rder
of a
ratio
nal n
umbe
r with
a
real
life
situ
atio
n. (F
or e
xam
ple:
-3 D
egre
es C
elsi
us >
-7 D
egre
es
Cel
sius
.)
R
Inte
rpre
t abs
olut
e va
lue
as m
agni
tude
for a
pos
itive
or n
egat
ive
quan
tity
in a
real
-wor
ld s
ituat
ion.
I c
an in
terp
ret a
bsol
ute
valu
e as
mag
nitu
de fo
r a p
ositi
ve o
r neg
ativ
e qu
antit
y in
a re
al-w
orld
situ
atio
n.
R
D
istin
guis
h co
mpa
rison
s of
abs
olut
e va
lue
from
sta
tem
ents
abo
ut o
rder
an
d ap
ply
to re
al w
orld
con
text
s.
I can
com
pare
the
abso
lute
val
ues
in re
al w
orld
situ
atio
ns.
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Num
ber S
yste
m
Solv
e re
al-w
orld
and
mat
hem
atic
al p
robl
ems
by g
raph
ing
poin
ts in
all
four
qua
dran
ts o
f the
co
ordi
nate
pla
ne. I
nclu
de u
se o
f coo
rdin
ates
and
abs
olut
e va
lue
to fi
nd d
ista
nces
bet
wee
n po
ints
w
ith th
e sa
me
first
coo
rdin
ate
or th
e sa
me
seco
nd c
oord
inat
e.
Clu
ster
A
pply
and
ext
end
prev
ious
und
erst
andi
ngs
of n
umbe
rs to
the
syst
em
of ra
tiona
l num
bers
T
arge
t T
ype
Stat
e T
arge
t St
uden
t Fri
endl
y T
arge
t
K
Cal
cula
te a
bsol
ute
valu
e.
I can
det
erm
ine
a nu
mbe
rs d
ista
nce
from
zer
o.
K
G
raph
poi
nts
in a
ll fo
ur q
uadr
ants
of t
he c
oord
inat
e pl
ane.
I c
an w
rite
the
abso
lute
val
ue o
f a ra
tiona
l num
ber.
R
So
lve
real
-wor
ld p
robl
ems
by g
raph
ing
poin
ts in
all
four
qua
dran
ts o
f a
coor
dina
te p
lane
. I c
an s
olve
real
wor
ld p
robl
ems
by g
raph
ing
poin
ts in
all
four
qua
dran
ts
of a
coo
rdin
ate
plan
e.
R
G
iven
onl
y co
ordi
nate
s, c
alcu
late
the
dist
ance
s be
twee
n tw
o po
ints
with
th
e sa
me
first
coo
rdin
ate
or th
e sa
me
seco
nd c
oord
inat
e us
ing
abso
lute
va
lue
I can
det
erm
ine
the
dist
ance
bet
wee
n 2
poin
ts b
y us
ing
abso
lute
val
ue.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.N
S.8
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Rat
io a
nd P
ropo
rtion
al
Rel
atio
nshi
ps
Und
erst
and
the
conc
ept o
f a ra
tio a
nd u
se ra
tio la
ngua
ge to
des
crib
e a
ratio
rela
tions
hip
betw
een
two
quan
titie
s. F
or e
xam
ple,
“Th
e ra
tio o
f win
gs to
bea
ks in
the
bird
hou
se a
t the
zoo
was
2:1
, be
caus
e fo
r ev
ery
2 w
ings
ther
e w
as o
ne b
eak.
” “F
or e
very
vot
e ca
ndid
ate
A re
ceiv
ed,
cand
idat
e C
rec
eive
d ne
arly
thre
e vo
tes.
”
C
lust
er
Und
erst
and
ratio
con
cept
s an
d us
e ra
tio re
ason
ing
to
solv
e pr
oble
ms.
Tar
get
Typ
e St
ate
Tar
get
Stud
ent F
rien
dly
Tar
get
K
Writ
e ra
tio n
otat
ion-
__
:__,
__
to _
_, _
_/__
I can
det
erm
ine
that
the
first
num
ber i
s a
com
paris
on to
the
seco
nd
num
ber w
hen
give
n th
e fo
llow
ing
nota
tions
(:, t
o, /)
K
Kno
w o
rder
mat
ters
whe
n w
ritin
g a
ratio
I can
reco
gniz
e th
at w
hen
writ
ing
ratio
s th
e or
der i
n w
hich
I w
rite
the
first
num
ber,
com
pare
d to
the
seco
nd n
umbe
r tha
t I w
rite
will
mat
ter;
for e
xam
ple
whe
n co
mpa
ring
cats
to th
e to
tal n
umbe
r of a
nim
als,
the
num
ber o
f cat
s sh
ould
be
writ
ten
first
K
K
now
ratio
s ca
n be
sim
plifi
ed
I c
an s
impl
ify th
e ra
tio b
ased
on
the
proc
ess
used
to s
impl
ify th
e fr
actio
ns. T
his
mea
ns I
will
find
the
GC
F of
the
first
and
sec
ond
num
ber
to s
impl
ify th
e ra
tios.
K
Kno
w ra
tios
com
pare
two
quan
titie
s; th
e qu
antit
ies
do n
ot h
ave
to b
e th
e sa
me
unit
of m
easu
re
I can
iden
tify
that
the
ratio
is th
e co
mpa
rison
of t
wo
sepa
rate
num
bers
by
div
isio
n.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.R
P.1
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
K
Rec
ogni
ze th
at ra
tios
appe
ar in
a v
arie
ty o
f diff
eren
t con
text
s; p
art-t
o-w
hole
, par
t-to-
part,
and
rate
s
I can
tell
you
the
diff
eren
ce b
etw
een
part
to p
art a
nd p
art t
o to
tal,
as w
ell
as ra
tes.
R
Gen
eral
ize
that
all
ratio
s re
late
two
quan
titie
s or
mea
sure
s w
ithin
a
give
n si
tuat
ion
in a
mul
tiplic
ativ
e re
latio
nshi
p
I can
exp
lain
how
two
num
bers
in a
ratio
are
rela
ted.
R
Ana
lyze
you
r con
text
to d
eter
min
e w
hich
kin
d of
ratio
is re
pres
ente
d
I c
an te
ll yo
u th
e di
ffer
ence
bet
wee
n pa
rt to
par
t and
par
t to
tota
l and
ra
tes.
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Rat
io a
nd P
ropo
rtion
al
Rel
atio
nshi
ps
Und
erst
and
the
conc
ept o
f a u
nit r
ate
a/b
asso
ciat
ed w
ith a
ratio
a:b
with
b ≠
0, a
nd u
se ra
te
lang
uage
in th
e co
ntex
t of a
ratio
rela
tions
hip.
For
exa
mpl
e, “
This
rec
ipe
has
a ra
tio o
f 3 c
ups
of
flour
to 4
cup
s of
sug
ar,
so th
ere
is 3
/4 c
up o
f flo
ur fo
r ea
ch c
up o
f sug
ar.”
“W
e pa
id $
75 fo
r 15
ham
burg
ers,
whi
ch is
a
rate
of $
5 pe
r ha
mbu
rger
.”
Clu
ster
U
nder
stan
d ra
tio c
once
pts
and
use
ratio
reas
onin
g to
so
lve
prob
lem
s.
T
arge
t T
ype
Stat
e T
arge
t St
uden
t Fri
endl
y T
arge
t
K
Iden
tify
and
calc
ulat
e a
unit
rate
I can
sim
plify
a ra
tio to
a d
enom
inat
or o
f 1.
K
Use
app
ropr
iate
mat
h te
rmin
olog
y as
rela
ted
to ra
te.
I c
an c
orre
ctly
sta
te th
e co
rrec
t am
ount
com
pare
d to
one
uni
t.
R
Ana
lyze
the
rela
tions
hip
betw
een
a ra
tio a
:b a
nd a
uni
t rat
e a/
b w
here
b
≠ 0.
I can
cor
rect
ly a
naly
ze th
e re
latio
nshi
p be
twee
n a
ratio
and
a u
nit r
ate
(for
exa
mpl
e, 1
80 m
iles
in 3
hou
rs is
com
pare
d to
60
mile
s in
1 h
our)
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.R
P.2
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Rat
io a
nd P
ropo
rtion
al
Rel
atio
nshi
ps
Use
ratio
and
rate
reas
onin
g to
sol
ve re
al-w
orld
and
mat
hem
atic
al p
robl
ems,
e.g
., by
reas
onin
g ab
out t
able
s of
equ
ival
ent r
atio
s, ta
pe d
iagr
ams,
dou
ble
num
ber l
ine
diag
ram
s, o
r equ
atio
ns.
a. M
ake
tabl
es o
f equ
ival
ent r
atio
s re
latin
g qu
antit
ies
with
who
le-n
umbe
r mea
sure
men
ts, f
ind
mis
sing
val
ues
in th
e ta
bles
, and
plo
t the
pai
rs o
f val
ues
on th
e co
ordi
nate
pla
ne. U
se ta
bles
to
com
pare
ratio
s.
b. S
olve
uni
t rat
e pr
oble
ms
incl
udin
g th
ose
invo
lvin
g un
it pr
icin
g an
d co
nsta
nt s
peed
. For
ex
ampl
e, if
it to
ok 7
hou
rs to
mow
4 la
wns
, the
n at
that
rat
e, h
ow m
any
law
ns c
ould
be
mow
ed
in 3
5 ho
urs?
At w
hat r
ate
wer
e la
wns
bei
ng m
owed
?
c. F
ind
a pe
rcen
t of a
qua
ntity
as
a ra
te p
er 1
00 (e
.g.,
30%
of a
qua
ntity
mea
ns 3
0/10
0 tim
es th
e qu
antit
y); s
olve
pro
blem
s in
volv
ing
findi
ng th
e w
hole
, giv
en a
par
t and
the
perc
ent.
d.
Use
ratio
reas
onin
g to
con
vert
mea
sure
men
t uni
ts; m
anip
ulat
e an
d tra
nsfo
rm u
nits
ap
prop
riate
ly w
hen
mul
tiply
ing
or d
ivid
ing
quan
titie
s.
Clu
ster
U
nder
stan
d ra
tio c
once
pts
and
use
ratio
reas
onin
g to
so
lve
prob
lem
s.
Tar
get
Typ
e St
ate
Tar
get
Stud
ent F
rien
dly
Tar
get
K
A1:
Mak
e a
tabl
e of
equ
ival
ent r
atio
s us
ing
who
le n
umbe
rs
I c
an m
ake
a ta
ble
of e
quiv
alen
t rat
ios
usin
g w
hole
num
bers
(for
ex
ampl
e 4:
1 is
equ
ival
ent t
o 8:
2)
K
A
2: F
ind
the
mis
sing
val
ues
in a
tabl
e of
equ
ival
ent r
atio
s
I can
find
the
mis
sing
val
ues
in a
tabl
e of
equ
ival
ent r
atio
s. T
his
mea
ns I
com
pare
the
give
n eq
uiva
lent
ratio
s to
det
erm
ine
the
mis
sing
ratio
s.
K
A3:
Plo
t pai
rs o
f val
ues
that
repr
esen
t equ
ival
ent r
atio
s on
the
coor
dina
te p
lane
.
I can
cor
rect
ly p
lot t
he o
rder
ed p
airs
from
a ra
tio ta
ble
onto
a c
oord
inat
e pl
ane.
Thi
s m
eans
I w
ill p
lot t
he n
umbe
rs o
n th
e co
rrec
t x-a
xis
or y
-axi
s ac
cord
ing
to th
e ta
ble.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.R
P.3
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
R
A4:
Use
tabl
es to
com
pare
pro
porti
onal
qua
ntiti
es.
I can
use
tabl
es to
com
pare
pro
porti
onal
qua
ntiti
es. T
his
mea
ns I
unde
rsta
nd th
e re
latio
nshi
p be
twee
n th
e pr
opor
tiona
l val
ues
to m
ake
a ta
ble
R
A5:
Sol
ve re
al-w
orld
and
mat
hem
atic
al p
robl
ems
invo
lvin
g ra
tio a
nd
rate
, e.g
., by
reas
onin
g ab
out t
able
s of
equ
ival
ent r
atio
s, ta
pe d
iagr
ams,
do
uble
num
ber l
ine
diag
ram
s, o
r equ
atio
ns
I can
app
ly m
athe
mat
ical
ope
ratio
ns, u
sing
pro
porti
onal
reas
onin
g,
invo
lvin
g ra
tio a
nd ra
te to
sol
ve re
al w
orld
pro
blem
s (f
or e
xam
ple,
to
com
pare
the
curr
ency
rate
s be
twee
n th
e U
nite
d St
ates
and
Mex
ico)
.
R
B1:
App
ly th
e co
ncep
t of u
nit r
ate
to s
olve
real
-wor
ld p
robl
ems
invo
lvin
g un
it pr
icin
g.
I can
app
ly u
nit r
ate
to s
olve
real
wor
ld p
robl
ems
with
uni
t pric
ing.
Thi
s m
eans
I w
ill d
eter
min
e th
e un
it ra
te b
y si
mpl
ifyin
g th
e co
st p
er u
nit
ratio
, R
B
2: A
pply
the
conc
ept o
f uni
t rat
e to
sol
ve re
al-w
orld
pro
blem
s in
volv
ing
cons
tant
spe
ed.
I can
app
ly u
nit r
ate
to s
olve
real
wor
ld p
robl
ems
invo
lvin
g co
nsta
nt
spee
d. T
his
mea
ns I
can
dete
rmin
e th
e un
it ra
te o
f spe
ed b
y fin
ding
the
rela
tions
hip
betw
een
the
rate
and
the
spee
d.
K
C1:
Kno
w th
at a
per
cent
is a
ratio
of a
num
ber t
o 10
0
I c
an w
rite
a ra
tio o
f a n
umbe
r to
100
to d
eter
min
e a
perc
ent.
This
m
eans
that
a n
umbe
r com
pare
d to
100
bec
omes
the
num
ber o
f the
pe
rcen
t. K
C2:
Fin
d a
% o
f a n
umbe
r as
a ra
te p
er 1
00.
I can
det
erm
ine
a nu
mbe
r out
of 1
00 b
y th
e %
that
is g
iven
to m
e (f
or
exam
ple,
71%
= 7
1/10
0)
I can
find
the
who
le a
mou
nt o
f a p
ropo
rtion
giv
en it
s pa
rtial
am
ount
and
it
equi
vale
nt p
erce
nt. T
his
mea
ns I
can
corr
ectly
set
up
a pr
opor
tiona
l eq
uatio
n to
sol
ve fo
r the
mis
sing
par
t of a
ratio
. R
C
3: S
olve
real
-wor
ld p
robl
ems
invo
lvin
g fin
ding
the
who
le, g
iven
a p
art
and
a pe
rcen
t.
I can
app
ly p
ropo
rtion
al ra
tios
to s
olve
real
wor
ld m
athe
mat
ical
pr
oble
ms
(for
exa
mpl
e, to
find
the
orig
inal
pric
e of
an
item
giv
en it
s sa
le
pric
e an
d th
e pe
rcen
t val
ue it
was
dis
coun
ted)
K
D1:
App
ly ra
tio re
ason
ing
to c
onve
rt m
easu
rem
ent u
nits
in re
al-w
orld
an
d m
athe
mat
ical
pro
blem
s
I can
cor
rect
ly u
se c
onve
rsio
n ru
les
to s
olve
real
wor
ld m
athe
mat
ical
pr
oble
ms
invo
lvin
g ra
tes
and
ratio
s
R
I can
use
ratio
reas
onin
g to
con
vert
mea
sure
men
t uni
ts in
real
wor
ld
and
mat
hem
atic
al p
robl
ems
(for
exa
mpl
e, 2
ft:10
inch
es =
24
inch
es:1
0 in
ches
) R
D
2: A
pply
ratio
reas
onin
g to
con
vert
mea
sure
men
t uni
ts b
y m
ultip
lyin
g or
div
idin
g in
real
-wor
ld a
nd m
athe
mat
ical
pro
blem
s.
I can
app
ly e
quiv
alen
t rat
ios
to c
onve
rt un
its b
y m
ultip
lyin
g or
div
idin
g (f
or e
xam
ple,
25
diam
onds
:10
emer
alds
= 5
dia
mon
ds:2
em
eral
ds)
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Stat
istic
s an
d Pr
obab
ility
R
ecog
nize
a s
tatis
tical
que
stio
n as
one
that
ant
icip
ates
var
iabi
lity
in th
e da
ta re
late
d to
the
ques
tion
and
acco
unts
for i
t in
the
answ
ers.
For
exa
mpl
e, “
How
old
am
I?”
is n
ot a
stat
istic
al
ques
tion,
but
“H
ow o
ld a
re th
e st
uden
ts in
my
scho
ol?”
is a
stat
istic
al q
uest
ion
beca
use
one
antic
ipat
es v
aria
bilit
y in
stud
ents
’ age
s.
Clu
ster
D
evel
op u
nder
stan
ding
of
stat
istic
al v
aria
bilit
y.
Tar
get
Typ
e St
ate
Tar
get
Stud
ent F
rien
dly
Tar
get
K
R
ecog
nize
that
dat
a ca
n ha
ve v
aria
bilit
y
I can
und
erst
and
that
the
data
I co
llect
can
var
y.
K
Rec
ogni
ze a
sta
tistic
al q
uest
ion
(exa
mpl
es v
ersu
s no
n-ex
ampl
es
I k
now
that
I m
ust a
ntic
ipat
e a
colle
ctio
n of
var
ied
data
for t
he q
uest
ion
to b
e a
stat
istic
al q
uest
ion.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.SP
.1
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Stat
istic
s an
d Pr
obab
ility
U
nder
stan
d th
at a
set
of d
ata
colle
cted
to a
nsw
er a
sta
tistic
al q
uest
ion
has
a di
strib
utio
n w
hich
ca
n be
des
crib
ed b
y its
cen
ter,
spre
ad, a
nd o
vera
ll sh
ape.
Clu
ster
D
evel
op u
nder
stan
ding
of
stat
istic
al v
aria
bilit
y.
Tar
get
Typ
e St
ate
Tar
get
Stud
ent F
rien
dly
Tar
get
K
Kno
w th
at a
set
of d
ata
has
a di
strib
utio
n.
I c
an re
cogn
ize
that
a d
ata
colle
cted
is n
ot g
oing
to b
e al
l the
sam
e.
K
Des
crib
e a
set o
f dat
a by
its
cent
er, e
.g.,
mea
n an
d m
edia
n.
I can
des
crib
e a
set o
f dat
a by
its
cent
er (f
or e
xam
ple,
mea
n, m
edia
n, o
r m
ode)
K
Des
crib
e a
set o
f dat
a by
its
spre
ad a
nd o
vera
ll sh
ape,
e.g
. by
iden
tifyi
ng d
ata
clus
ters
, pea
ks, g
aps
and
sym
met
ry
I can
des
crib
e a
set o
f dat
a by
its
spre
ad a
nd o
vera
ll sh
ape
(for
exa
mpl
e,
iden
tifyi
ng d
ata
clus
ters
, pea
ks, g
aps,
and
sym
met
ry)
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.SP
.2
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Stat
istic
s an
d Pr
obab
ility
R
ecog
nize
that
a m
easu
re o
f cen
ter f
or a
num
eric
al d
ata
set s
umm
ariz
es a
ll of
its
valu
es w
ith a
si
ngle
num
ber,
whi
le a
mea
sure
of v
aria
tion
desc
ribes
how
its
valu
es v
ary
with
a s
ingl
e nu
mbe
r.
C
lust
er
Dev
elop
und
erst
andi
ng o
f st
atis
tical
var
iabi
lity.
T
arge
t T
ype
Stat
e T
arge
t St
uden
t Fri
endl
y T
arge
t
K
Rec
ogni
ze th
ere
are
mea
sure
s of
cen
tral t
ende
ncy
for a
dat
a se
t, e.
g.,
mea
n, m
edia
n, m
ode.
I can
reco
gniz
e di
ffer
ent m
easu
res
of c
entra
l ten
denc
y fo
r a s
et o
f dat
a (f
or e
xam
ple,
mea
n, m
edia
n an
d m
ode)
K
Rec
ogni
ze th
ere
are
mea
sure
s of
var
ianc
es fo
r a d
ata
set,
e.g.
, ran
ge,
inte
rqua
rtile
rang
e, m
ean
abso
lute
dev
iatio
n.
I can
reco
gniz
e di
ffer
ent m
easu
res
of v
aria
nces
for a
dat
a se
t (fo
r ex
ampl
e, ra
nge
and
inte
rqua
rtile
rang
e)
K
Rec
ogni
ze m
easu
res
of c
entra
l ten
denc
y fo
r a d
ata
set s
umm
ariz
es th
e da
ta w
ith a
sin
gle
num
ber.
I can
sum
mar
ize
a se
t of d
ata
with
mea
n, m
edia
n, o
r mod
e.
K
Rec
ogni
ze m
easu
res
of v
aria
tion
for a
dat
a se
t des
crib
es h
ow it
s va
lues
va
ry w
ith a
sin
gle
num
ber.
I can
des
crib
e ho
w a
sin
gle
num
ber c
an c
hang
e a
data
set
(for
exa
mpl
e an
out
lier c
an c
hang
e th
e m
ean)
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.SP
.3
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Stat
istic
s an
d Pr
obab
ility
R
ecog
nize
that
a m
easu
re o
f cen
ter f
or a
num
eric
al d
ata
set s
umm
ariz
es a
ll of
its
valu
es w
ith a
si
ngle
num
ber,
whi
le a
mea
sure
of v
aria
tion
desc
ribes
how
its
valu
es v
ary
with
a s
ingl
e nu
mbe
r.
C
lust
er
Sum
mar
ize
and
desc
ribe
dist
ribut
ions
T
arge
t T
ype
Stat
e T
arge
t St
uden
t Fri
endl
y T
arge
t
K
Iden
tify
the
com
pone
nts
of d
ot p
lots
, his
togr
ams,
and
box
plo
ts
I c
an id
entif
y th
e pa
rts o
f dot
plo
ts, h
isto
gram
s, a
nd b
ox p
lots
.
K
Find
the
med
ian,
qua
rtile
and
inte
rqua
rtile
rang
e of
a s
et o
f dat
a.
I c
an fi
nd th
e m
edia
n, q
uarti
le, a
nd in
terq
uarti
le ra
nge
of a
set
of d
ata.
R
Ana
lyze
a s
et o
f dat
a to
det
erm
ine
its v
aria
nce.
I ca
n us
e m
edia
n, q
uarti
le, a
nd in
terq
uarti
le ra
nge
to a
naly
ze a
set
of
data
.
P C
reat
e a
dot p
lot t
o di
spla
y a
set o
f num
eric
al d
ata.
I c
an c
reat
e a
dot p
lot t
o co
rrec
tly d
ispl
ay d
ata
I hav
e be
en g
iven
.
P C
reat
e a
hist
ogra
m to
dis
play
a s
et o
f num
eric
al d
ata
I can
cre
ate
a hi
stog
ram
to c
orre
ctly
dis
play
dat
a I h
ave
been
giv
en.
P C
reat
e a
box
plot
to d
ispl
ay a
set
of n
umer
ical
dat
a.
I c
an c
reat
e a
box
plot
to c
orre
ctly
dis
play
dat
a I h
ave
been
giv
en.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.SP
.4
K
R
S
P
Mak
e se
nse
of
prob
lem
s and
pe
rsev
ere
in so
lvin
g th
em.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of st
ruct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
D
omai
n St
anda
rd
Stat
istic
s and
Pro
babi
lity
Su
mm
ariz
e nu
mer
ical
dat
a se
ts in
rela
tion
to th
eir c
onte
xt, s
uch
as b
y:
a. R
epor
ting
the
num
ber o
f obs
erva
tions
. b.
Des
crib
ing
the
natu
re o
f the
attr
ibut
e un
der i
nves
tigat
ion,
incl
udin
g ho
w it
was
mea
sure
d an
d its
uni
ts o
f mea
sure
men
t.
c. G
ivin
g qu
antit
ativ
e m
easu
res o
f cen
ter (
med
ian
and/
or m
ean)
and
var
iabi
lity
(inte
rqua
rtile
ra
nge
and
/or m
ean
abso
lute
dev
iatio
n), a
s wel
l as d
escr
ibin
g an
y ov
eral
l pat
tern
and
any
st
rikin
g de
viat
ions
from
the
over
all p
atte
rn w
ith re
fere
nce
to th
e co
ntex
t in
whi
ch th
e da
ta w
ere
gath
ered
. d.
Rel
atin
g th
e ch
oice
of m
easu
res o
f cen
ter a
nd v
aria
bilit
y to
the
shap
e of
the
data
dis
tribu
tion
and
the
cont
ext i
n w
hich
the
data
wer
e ga
ther
ed.
Clu
ster
Su
mm
ariz
e an
d de
scrib
e di
strib
utio
ns
Tar
get
Typ
e St
ate
Tar
get
Stud
ent F
rien
dly
Tar
get
K
Org
aniz
e an
d di
spla
y da
ta in
tabl
es a
nd g
raph
s
I can
org
aniz
e, d
ispl
ay, a
nd in
terp
ret d
ata
by se
tting
the
data
up
in ta
bles
an
d gr
aphs
.
K
Rep
ort t
he n
umbe
r of o
bser
vatio
ns in
a d
ata
set o
r dis
play
I ca
n re
port
the
num
ber o
f obs
erva
tions
in a
dat
a se
t or d
ispl
ay.
K
Des
crib
e th
e da
ta b
eing
col
lect
ed, i
nclu
ding
how
it w
as m
easu
red
and
its u
nits
of m
easu
rem
ent.
I can
des
crib
e th
e ty
pe o
f dat
a th
at w
as c
olle
cted
. I c
an e
xpla
in h
ow th
e da
ta w
as m
easu
red
and
the
unit
of m
easu
re
K
C
alcu
late
qua
ntita
tive
mea
sure
s of c
ente
r, e.
g., m
ean,
med
ian,
mod
e.
I c
an fi
nd th
e m
ean,
med
ian,
and
mod
e.
9 W
eeks
Gra
de.C
onte
nt.S
tand
ard
O
vera
ll St
anda
rd T
ype
1st
2
nd
3
rd
4
th
6.SP
.5
K
R
S
P
Mak
e se
nse
of
prob
lem
s an
d pe
rsev
ere
in s
olvi
ng
them
.
Rea
son
abst
ract
ly
and
quan
titat
ivel
y.
Con
stru
ct v
iabl
e ar
gum
ents
and
cr
itiqu
e th
e re
ason
ing
of o
ther
s.
Mod
el w
ith
mat
hem
atic
s.
Use
app
ropr
iate
tool
s st
rate
gica
lly.
Atte
nd to
pre
cisi
on.
Look
for a
nd m
ake
use
of s
truct
ure.
Lo
ok fo
r and
exp
ress
re
gula
rity
in re
peat
ed
reas
onin
g.
Scott%County%Schools%
Grade%6%
Mathem
atics!
K
Cal
cula
te q
uant
itativ
e m
easu
res
of v
aria
nce,
e.g
., ra
nge,
inte
rqua
rtile
ra
nge,
mea
n ab
solu
te d
evia
tion.
I
can
find
the
rang
e, in
terq
uarti
le ra
nge,
and
mea
n ab
solu
te d
evia
tion.
K
Iden
tify
outli
ers
I can
iden
tify
outli
ers.
P D
eter
min
e th
e ef
fect
of o
utlie
rs o
n qu
antit
ativ
e m
easu
res
of a
set
of
data
, e.g
., m
ean,
med
ian,
mod
e, ra
nge,
inte
rqua
rtile
rang
e, m
ean
abso
lute
dev
iatio
n
I can
iden
tify
the
effe
cts
of o
utlie
rs o
n a
set o
f dat
a (f
or e
xam
ple,
mea
n,
med
ian,
mod
e an
d ra
nge)
. Thi
s m
eans
I ca
n re
cogn
ize
an o
utlie
r in
a se
t of
dat
a an
d ca
lcul
ate
the
cent
ral t
ende
ncy
with
out t
he o
utlie
r to
com
pare
th
e tw
o re
sults
.
P C
hoos
e th
e ap
prop
riate
mea
sure
of c
entra
l ten
denc
y to
repr
esen
t the
da
ta.
I can
det
erm
ine
the
appr
opria
te m
easu
re o
f cen
tral t
ende
ncy
to re
pres
ent
the
data
.
P D
escr
ibe
the
data
bei
ng c
olle
cted
, inc
ludi
ng h
ow it
was
mea
sure
d an
d its
uni
ts o
f mea
sure
men
t.
I can
just
ify th
e ap
prop
riate
mea
sure
of c
entra
l ten
denc
y an
d va
riabi
lity
base
d on
the
shap
e an
d co
ntex
t of d
ata
