6th
Grad
e Co
mmon
Cor
e St
ate
Stan
dard
s
Math
emat
ics
Math
emat
ical P
ract
ices
1. M
ake
sens
e of
pro
blem
s an
d pe
rsev
ere
in s
olvi
ng t
hem
. 2.
Rea
son
abst
ract
ly a
nd q
uant
itat
ivel
y.
3. C
onst
ruct
via
ble
argu
men
ts a
nd c
riti
que
the
reas
onin
g of
oth
ers.
4.
Mod
el w
ith
mat
hem
atic
s.
5. U
se a
ppro
pria
te t
ools
str
ateg
ical
ly.
6. A
tten
d to
pre
cisi
on.
7. L
ook
for
and
mak
e us
e of
str
uctu
re.
8. L
ook
for
and
expr
ess
regu
lari
ty in
rep
eate
d re
ason
ing.
www.amazingclassroom
.blogspo
t.com
Man
y of th
e grap
hics by www.th
istlegirld
esigns.com
6th
Grad
e Co
mmon
Cor
e St
ate
Stan
dard
s
Math
emat
ics
Ratio
s an
d Pr
opor
tiona
l Rela
tions
hips
6.RP
.1. U
nder
stan
d th
e co
ncep
t of
a r
atio
and
use
rat
io la
ngua
ge t
o de
-sc
ribe
a r
atio
rel
atio
nshi
p be
twee
n tw
o qu
anti
ties
. For
exa
mpl
e, “T
he
rati
o of
win
gs t
o be
aks
in t
he b
ird
hous
e at
the
zoo
was
2:1
, bec
ause
fo
r ev
ery
2 wi
ngs
ther
e wa
s 1
beak
.” “F
or e
very
vot
e ca
ndid
ate
A re
-ce
ived
, can
dida
te C
rec
eive
d ne
arly
thr
ee v
otes
.”
6.RP
.2. U
nder
stan
d th
e co
ncep
t of
a u
nit
rate
a/b
ass
ocia
ted
with
a r
a-ti
o a:
b wi
th b
≠ 0
, and
use
rat
e la
ngua
ge in
the
con
text
of
a ra
tio
rela
-ti
onsh
ip. F
or e
xam
ple,
“Thi
s re
cipe
has
a r
atio
of
3 cu
ps o
f fl
our
to 4
cu
ps o
f su
gar,
so
ther
e is
3/4
cup
of
flou
r fo
r ea
ch c
up o
f su
gar.”
“We
paid
$75
for
15
ham
burg
ers,
whi
ch is
a r
ate
of $
5 pe
r ha
mbu
rger
.”
Und
er
stan
d r
atio
con
cep
ts
and
use
rat
io r
eas
onin
g t
o so
lve
pr
oble
ms
- P
art
1
6th
Grad
e Co
mmon
Cor
e St
ate
Stan
dard
s
Math
emat
ics
Ratio
s an
d Pr
opor
tiona
l Rela
tions
hips
6.RP
.3. U
se r
atio
and
rat
e re
ason
ing
to s
olve
rea
l-wor
ld a
nd m
athe
mat
ical
pro
blem
s, e
.g.,
by r
easo
ning
ab
out
tabl
es o
f eq
uiva
lent
rat
ios,
tap
e di
agra
ms,
dou
ble
num
ber
line
diag
ram
s, o
r eq
uati
ons.
M
ake
tabl
es o
f eq
uiva
lent
rat
ios
rela
ting
qua
ntit
ies
with
who
le-n
umbe
r m
easu
rem
ents
, fin
d m
issi
ng
valu
es in
the
tab
les,
and
plo
t th
e pa
irs
of v
alue
s on
the
coo
rdin
ate
plan
e. U
se t
able
s to
com
pare
rat
i-os
.
Solv
e un
it r
ate
prob
lem
s in
clud
ing
thos
e in
volv
ing
unit
pri
cing
and
con
stan
t sp
eed.
For
exa
mpl
e, if
it
took
7 h
ours
to
mow
4 la
wns,
the
n at
tha
t ra
te, h
ow m
any
lawn
s co
uld
be m
owed
in 3
5 ho
urs?
At
what
rat
e we
re la
wns
bein
g m
owed
?
Find
a p
erce
nt o
f a
quan
tity
as
a ra
te p
er 1
00 (e
.g.,
30%
of
a qu
anti
ty m
eans
30/
100
tim
es t
he q
uan-
tity
); so
lve
prob
lem
s in
volv
ing
find
ing
the
whol
e, g
iven
a p
art
and
the
perc
ent.
Use
rat
io r
easo
ning
to
conv
ert
mea
sure
men
t un
its;
man
ipul
ate
and
tran
sfor
m u
nits
app
ropr
iate
ly
when
mul
tipl
ying
or
divi
ding
qua
ntit
ies.
Und
er
stan
d r
atio
con
cep
ts
and
use
rat
io r
eas
onin
g t
o so
lve
pr
oble
ms
- P
art
2
6th
Grad
e Co
mmon
Cor
e St
ate
Stan
dard
s
Math
emat
ics
The
Numbe
r Sy
stem
A
pp
ly a
nd e
xt
end
pr
ev
ious
und
er
stan
din
gs
of m
ult
iplic
atio
n an
d d
ivis
ion
to
div
ide
fr
act
ions
fr
act
ions
by
fr
act
ions
.
6.N
S.1.
Inte
rpre
t an
d co
mpu
te q
uoti
ents
of
frac
tion
s, a
nd s
olve
wor
d pr
oble
ms
invo
lvin
g di
visi
on o
f fr
acti
ons
by f
ract
ions
, e.g
., by
usi
ng v
isua
l fra
ctio
n m
odel
s an
d eq
uati
ons
to r
epre
sent
the
pro
blem
. For
exa
mpl
e, c
reat
e a
stor
y co
ntex
t fo
r (2
/3) ÷
(3/4
) and
use
a v
isua
l fra
ctio
n m
odel
to
show
the
quo
tien
t; u
se t
he
rela
tion
ship
bet
ween
mul
tipl
icat
ion
and
divi
sion
to
expl
ain
that
(2/3
) ÷ (3
/4) =
8/
9 be
caus
e 3/
4 of
8/9
is 2
/3. (
In g
ener
al, (
a/b)
÷ (c
/d) =
ad/
bc.)
How
muc
h ch
ocol
ate
will
each
per
son
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
cup
of y
ogur
t? H
ow w
ide
is a
rec
tan-
gula
r st
rip
of la
nd w
ith
leng
th 3
/4 m
i and
are
a 1/
2 sq
uare
mi?
Com
pute
flu
entl
y wi
th m
ulti
-dig
it n
umbe
rs a
nd f
ind
com
mon
fac
tors
and
mul
tipl
es.
6th
Grad
e Co
mmon
Cor
e St
ate
Stan
dard
s
Math
emat
ics
The
Numbe
r Sy
stem
C
omp
ute
flu
ent
ly w
ith
mul
ti-
dig
it n
umb
er
s an
d f
ind
com
mon
fac
tor
s an
d m
ult
iple
s.
6.N
S.2.
Flu
entl
y di
vide
mul
ti-d
igit
num
bers
usi
ng t
he s
tand
ard
algo
rith
m.
6.N
S.3.
Flu
entl
y ad
d, s
ubtr
act,
mul
tipl
y, a
nd d
ivid
e m
ulti
-dig
it d
ecim
als
usin
g th
e st
anda
rd a
lgor
ithm
for
eac
h op
erat
ion.
6.N
S.4.
Fin
d th
e gr
eate
st c
omm
on f
acto
r of
two
who
le n
umbe
rs le
ss t
han
or
equa
l to
100
and
the
leas
t co
mm
on m
ulti
ple
of t
wo w
hole
num
bers
less
tha
n or
eq
ual t
o 12
. Use
the
dis
trib
utiv
e pr
oper
ty t
o ex
pres
s a
sum
of
two
whol
e nu
m-
bers
1–1
00 w
ith
a co
mm
on f
acto
r as
a m
ulti
ple
of a
sum
of
two
whol
e nu
mbe
rs
with
no
com
mon
fac
tor.
For
exa
mpl
e, e
xpre
ss 3
6 +
8 as
4 (9
+ 2
). Ap
ply
and
ex-
tend
pre
viou
s un
ders
tand
ings
of
num
bers
to
the
syst
em o
f ra
tiona
l num
bers
.
6th
Grad
e Co
mmon
Cor
e St
ate
Stan
dard
s
Math
emat
ics
The
Numbe
r Sy
stem
A
pp
ly a
nd e
xt
end
pr
ev
ious
und
er
stan
din
gs
of n
umb
er
s t
o t
he
sy
ste
m
of r
atio
nal n
umb
er
s -
Par
t 1
6.N
S.5.
Und
erst
and
that
pos
itiv
e an
d ne
gati
ve n
umbe
rs a
re u
sed
toge
ther
to
desc
ribe
qua
ntit
ies
havi
ng o
ppos
ite
dire
c-ti
ons
or v
alue
s (e
.g.,
tem
pera
ture
abo
ve/b
elow
zer
o, e
leva
tion
abo
ve/b
elow
sea
leve
l, cr
edit
s/de
bits
, pos
itiv
e/ne
gati
ve
elec
tric
cha
rge)
; use
pos
itiv
e an
d ne
gati
ve n
umbe
rs t
o re
pres
ent
quan
titi
es in
rea
l-wo
rld
cont
exts
, exp
lain
ing
the
mea
n-in
g of
0 in
eac
h si
tuat
ion.
6.N
S.6.
Und
erst
and
a ra
tion
al n
umbe
r as
a p
oint
on
the
num
ber
line.
Ext
end
num
ber
line
diag
ram
s an
d co
ordi
nate
axe
s fa
mili
ar f
rom
pre
viou
s gr
ades
to
repr
esen
t po
ints
on
the
line
and
in t
he p
lane
wit
h ne
gati
ve n
umbe
r co
ordi
nate
s.
Re
cogn
ize
oppo
site
sig
ns o
f nu
mbe
rs a
s in
dica
ting
loca
tion
s on
opp
osit
e si
des
of 0
on
the
num
ber
line;
rec
ogni
ze t
hat
the
oppo
site
of
the
oppo
site
of
a nu
mbe
r is
the
num
ber
itse
lf, e
.g., –(–3
) = 3
, and
tha
t 0
is it
s ow
n op
posi
te.
U
nder
stan
d si
gns
of n
umbe
rs in
ord
ered
pai
rs a
s in
dica
ting
loca
tion
s in
qua
dran
ts o
f th
e co
ordi
nate
pla
ne; r
ecog
nize
th
at w
hen
two
orde
red
pair
s di
ffer
onl
y by
sig
ns, t
he lo
cati
ons
of t
he p
oint
s ar
e re
late
d by
ref
lect
ions
acr
oss
one
or
both
axe
s.
Fi
nd a
nd p
osit
ion
inte
gers
and
oth
er r
atio
nal n
umbe
rs o
n a
hori
zont
al o
r ve
rtic
al n
umbe
r lin
e di
agra
m; f
ind
and
posi
-ti
on p
airs
of
inte
gers
and
oth
er r
atio
nal n
umbe
rs o
n a
coor
dina
te p
lane
.
6t
h Gr
ade
Common
Cor
e St
ate
Stan
dard
s
Math
emat
ics
The
Numbe
r Sy
stem
A
pp
ly a
nd e
xt
end
pr
ev
ious
und
er
stan
din
gs
of n
umb
er
s t
o t
he
sy
ste
m
of r
atio
nal n
umb
er
s -
Par
t 2
6.N
S.7.
Und
erst
and
orde
ring
and
abs
olut
e va
lue
of r
atio
nal n
umbe
rs.
In
terp
ret
stat
emen
ts o
f in
equa
lity
as s
tate
men
ts a
bout
the
rel
ativ
e po
siti
on o
f tw
o nu
mbe
rs o
n a
num
ber
line
diag
ram
. For
exa
mpl
e, in
terp
ret –3
> –7
as
a st
ate-
men
t th
at –
3 is
loca
ted
to t
he r
ight
of –7
on
a nu
mbe
r lin
e or
ient
ed f
rom
left
to
righ
t.
Wri
te, i
nter
pret
, and
exp
lain
sta
tem
ents
of
orde
r fo
r ra
tion
al n
umbe
rs in
rea
l-wo
rld
cont
exts
. For
exa
mpl
e, w
rite
–3 o C
> –7
o C t
o ex
pres
s th
e fa
ct t
hat –3
o C is
wa
rmer
tha
n –7
o C.
U
nder
stan
d th
e ab
solu
te v
alue
of
a ra
tion
al n
umbe
r as
its
dist
ance
fro
m 0
on
the
num
ber
line;
inte
rpre
t ab
solu
te v
alue
as
mag
nitu
de f
or a
pos
itiv
e or
neg
ativ
e qu
anti
ty in
a r
eal-w
orld
sit
uati
on. F
or e
xam
ple,
for
an
acco
unt
bala
nce
of –
30 d
ol-
lars
, wri
te |–
30| =
30
to d
escr
ibe
the
size
of
the
debt
in d
olla
rs.
6th
Grad
e Co
mmon
Cor
e St
ate
Stan
dard
s
Math
emat
ics
The
Numbe
r Sy
stem
A
pp
ly a
nd e
xt
end
pr
ev
ious
und
er
stan
din
gs
of n
umb
er
s t
o t
he
sy
ste
m
of r
atio
nal n
umb
er
s -
Par
t 3
6.N
S.8.
Sol
ve r
eal-w
orld
and
mat
hem
atic
al p
robl
ems
by g
raph
ing
poin
ts in
all
four
qua
dran
ts o
f th
e co
ordi
nate
pla
ne. I
nclu
de u
se o
f co
ordi
nate
s an
d ab
solu
te v
alue
to
find
dis
tanc
es b
etwe
en p
oint
s wi
th t
he s
ame
firs
t co
ordi
nate
or
the
sam
e se
cond
coo
rdin
ate.
6th
Grad
e Co
mmon
Cor
e St
ate
Stan
dard
s
Math
emat
ics
Expr
essio
ns a
nd E
quat
ions
Ap
ply
and
ex
te
nd p
re
vio
us u
nde
rst
and
ing
s of
ar
ith
me
tic
to
alge
br
aic
ex
pr
ess
ions
. - P
art
1
6.EE
.1. W
rite
and
eva
luat
e nu
mer
ical
exp
ress
ions
invo
lvin
g wh
ole-
num
ber
expo
nent
s.
6.EE
.2. W
rite
, rea
d, a
nd e
valu
ate
expr
essi
ons
in w
hich
lett
ers
stan
d fo
r nu
mbe
rs.
W
rite
exp
ress
ions
tha
t re
cord
ope
rati
ons
with
num
bers
and
wit
h le
tter
s st
andi
ng f
or n
umbe
rs. F
or
exam
ple,
exp
ress
the
cal
cula
tion
“Sub
trac
t y
from
5” a
s 5
– y.
Id
enti
fy p
arts
of
an e
xpre
ssio
n us
ing
mat
hem
atic
al t
erm
s (s
um, t
erm
, pro
duct
, fac
tor,
quo
tien
t, c
o-ef
fici
ent)
; vie
w on
e or
mor
e pa
rts
of a
n ex
pres
sion
as
a si
ngle
ent
ity.
For
exa
mpl
e, d
escr
ibe
the
ex-
pres
sion
2 (8
+ 7
) as
a pr
oduc
t of
two
fac
tors
; vie
w (8
+ 7
) as
both
a s
ingl
e en
tity
and
a s
um o
f tw
o te
rms.
Eval
uate
exp
ress
ions
at
spec
ific
val
ues
of t
heir
var
iabl
es. I
nclu
de e
xpre
ssio
ns t
hat
aris
e fr
om f
or-
mul
as u
sed
in r
eal-w
orld
pro
blem
s. P
erfo
rm a
rith
met
ic o
pera
tion
s, in
clud
ing
thos
e in
volv
ing
whol
e-nu
mbe
r ex
pone
nts,
in t
he c
onve
ntio
nal o
rder
whe
n th
ere
are
no p
aren
thes
es t
o sp
ecif
y a
part
icul
ar
orde
r (O
rder
of
Ope
rati
ons)
. For
exa
mpl
e, u
se t
he f
orm
ulas
V =
s3 a
nd A
= 6
s2 t
o fi
nd t
he v
olum
e an
d su
rfac
e ar
ea o
f a
cube
wit
h si
des
of le
ngth
s =
1/2
.
6th
Grad
e Co
mmon
Cor
e St
ate
Stan
dard
s
Math
emat
ics
Expr
essio
ns a
nd E
quat
ions
Ap
ply
and
ex
te
nd p
re
vio
us u
nde
rst
and
ing
s of
ar
ith
me
tic
to
alge
br
aic
ex
pr
ess
ions
. - P
art
2
6.EE
.3. A
pply
the
pro
pert
ies
of o
pera
tion
s to
gen
erat
e eq
uiva
lent
exp
res-
sion
s. F
or e
xam
ple,
app
ly t
he d
istr
ibut
ive
prop
erty
to
the
expr
essi
on 3
(2
+ x)
to
prod
uce
the
equi
vale
nt e
xpre
ssio
n 6
+ 3x
; app
ly t
he d
istr
ibut
ive
prop
erty
to
the
expr
essi
on 2
4x +
18y
to
prod
uce
the
equi
vale
nt e
xpre
s-si
on 6
(4x
+ 3y
); ap
ply
prop
erti
es o
f op
erat
ions
to
y +
y +
y to
pro
duce
the
eq
uiva
lent
exp
ress
ion
3y.
6.
EE.4
. Ide
ntif
y wh
en t
wo e
xpre
ssio
ns a
re e
quiv
alen
t (i.
e., w
hen
the
two
expr
essi
ons
nam
e th
e sa
me
num
ber
rega
rdle
ss o
f wh
ich
valu
e is
su
bsti
tute
d in
to t
hem
). Fo
r ex
ampl
e, t
he e
xpre
ssio
ns y
+ y
+ y
and
3y
are
equi
vale
nt b
ecau
se t
hey
nam
e th
e sa
me
num
ber
rega
rdle
ss o
f wh
ich
num
ber
y st
ands
for
. Rea
son
abou
t an
d so
lve
one-
vari
able
equ
a-ti
ons
and
ineq
ualit
ies.
6th
Grad
e Co
mmon
Cor
e St
ate
Stan
dard
s
Math
emat
ics
Expr
essio
ns a
nd E
quat
ions
Re
ason
ab
out
and
sol
ve
one
-v
aria
ble
equ
atio
ns a
nd in
equ
alit
ies.
6.EE
.5. U
nder
stan
d so
lvin
g an
equ
atio
n or
ineq
ualit
y as
a p
roce
ss o
f an
swer
ing
a qu
esti
on: w
hich
va
lues
fro
m a
spe
cifi
ed s
et, i
f an
y, m
ake
the
equa
tion
or
ineq
ualit
y tr
ue?
Use
sub
stit
utio
n to
de
term
ine
whet
her
a gi
ven
num
ber
in a
spe
cifi
ed s
et m
akes
an
equa
tion
or
ineq
ualit
y tr
ue.
6.EE
.6. U
se v
aria
bles
to
repr
esen
t nu
mbe
rs a
nd w
rite
exp
ress
ions
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
unk
nown
num
ber,
or,
dep
end-
ing
on t
he p
urpo
se a
t ha
nd, a
ny n
umbe
r in
a s
peci
fied
set
.
6.EE
.7. S
olve
rea
l-wor
ld a
nd m
athe
mat
ical
pro
blem
s by
wri
ting
and
sol
ving
equ
atio
ns o
f th
e fo
rm x
+
p =
q an
d px
= q
for
cas
es in
whi
ch p
, q a
nd x
are
all
nonn
egat
ive
rati
onal
num
bers
.
6.EE
.8. W
rite
an
ineq
ualit
y of
the
for
m x
> c
or x
< c
to r
epre
sent
a c
onst
rain
t or
con
diti
on in
a r
e-al
-wor
ld o
r m
athe
mat
ical
pro
blem
. Rec
ogni
ze t
hat
ineq
ualit
ies
of t
he f
orm
x >
c or
x <
c ha
ve in
fi-
nite
ly m
any
solu
tion
s; r
epre
sent
sol
utio
ns o
f su
ch in
equa
litie
s on
num
ber
line
diag
ram
s.
6th
Grad
e Co
mmon
Cor
e St
ate
Stan
dard
s
Math
emat
ics
Expr
essio
ns a
nd E
quat
ions
Re
pr
ese
nt a
nd a
naly
ze
qua
ntit
ativ
e r
ela
tio
nsh
ips
be
tw
ee
n d
ep
end
ent
and
ind
ep
end
ent
var
iab
les.
.
6.EE
.9.U
se v
aria
bles
to
repr
esen
t tw
o qu
anti
ties
in a
rea
l-wor
ld
prob
lem
tha
t ch
ange
in r
elat
ions
hip
to o
ne a
noth
er; w
rite
an
equa
tion
to
expr
ess
one
quan
tity
, tho
ught
of
as t
he d
epen
dent
va
riab
le, i
n te
rms
of t
he o
ther
qua
ntit
y, t
houg
ht o
f as
the
inde
-pe
nden
t va
riab
le. A
naly
ze t
he r
elat
ions
hip
betw
een
the
depe
nd-
ent
and
inde
pend
ent
vari
able
s us
ing
grap
hs a
nd t
able
s, a
nd r
elat
e th
ese
to t
he e
quat
ion.
For
exa
mpl
e, in
a p
robl
em in
volv
ing
mot
ion
at c
onst
ant
spee
d, li
st a
nd g
raph
ord
ered
pai
rs o
f di
stan
ces
and
tim
es, a
nd w
rite
the
equ
atio
n d
= 65
t to
rep
rese
nt t
he r
elat
ion-
ship
bet
ween
dis
tanc
e an
d ti
me.
6th
Grad
e Co
mmon
Cor
e St
ate
Stan
dard
s
Math
emat
ics
Geom
etry
S
olv
e r
eal
-w
orld
and
mat
he
mat
ical
pr
oble
ms
inv
olv
ing
ar
ea,
sur
-
fac
e a
re
a, a
nd v
olum
e -
Par
t 1
6.G.
1. Fi
nd t
he a
rea
of r
ight
tri
angl
es, o
ther
tri
angl
es, s
peci
al q
uadr
ilate
rals
, and
po
lygo
ns b
y co
mpo
sing
into
rec
tang
les
or d
ecom
posi
ng in
to t
rian
gles
and
oth
er
shap
es; a
pply
the
se t
echn
ique
s in
the
con
text
of
solv
ing
real
-wor
ld a
nd m
athe
-m
atic
al p
robl
ems.
6.G.
2. F
ind
the
volu
me
of a
rig
ht r
ecta
ngul
ar p
rism
wit
h fr
acti
onal
edg
e le
ngth
s by
pac
king
it w
ith
unit
cub
es o
f th
e ap
prop
riat
e un
it f
ract
ion
edge
leng
ths,
and
sh
ow t
hat
the
volu
me
is t
he s
ame
as w
ould
be
foun
d by
mul
tipl
ying
the
edg
e le
ngth
s of
the
pri
sm. A
pply
the
for
mul
as V
= l
w h
and
V =
b h
to f
ind
volu
mes
of
righ
t re
ctan
gula
r pr
ism
s wi
th f
ract
iona
l edg
e le
ngth
s in
the
con
text
of
solv
ing
real
-wor
ld a
nd m
athe
mat
ical
pro
blem
s.
6th
Grad
e Co
mmon
Cor
e St
ate
Stan
dard
s
Math
emat
ics
Geom
etry
S
olv
e r
eal
-w
orld
and
mat
he
mat
ical
pr
oble
ms
inv
olv
ing
ar
ea,
sur
fac
e a
re
a, a
nd v
olum
e -
Par
t 2
6.G.
3. D
raw
poly
gons
in t
he c
oord
inat
e pl
ane
give
n co
ordi
nate
s fo
r th
e ve
rtic
es; u
se c
oord
inat
es t
o fi
nd t
he le
ngth
of
a si
de jo
inin
g po
ints
wit
h th
e sa
me
firs
t co
ordi
nate
or
the
sam
e se
cond
coo
rdin
ate.
App
ly t
hese
te
chni
ques
in t
he c
onte
xt o
f so
lvin
g re
al-w
orld
and
mat
hem
atic
al p
rob-
lem
s.
6.G.
4. R
epre
sent
thr
ee-d
imen
sion
al f
igur
es u
sing
net
s m
ade
up o
f re
ctan
-gl
es a
nd t
rian
gles
, and
use
the
net
s to
fin
d th
e su
rfac
e ar
ea o
f th
ese
figu
res.
App
ly t
hese
tec
hniq
ues
in t
he c
onte
xt o
f so
lvin
g re
al-w
orld
and
m
athe
mat
ical
pro
blem
s.
6th
Grad
e Co
mmon
Cor
e St
ate
Stan
dard
s
Math
emat
ics
Stat
istics
and
Pro
bability
De
ve
lop
und
er
stan
din
g o
f s
tat
ist
ical
var
iab
ility
.
6.SP
.1. R
ecog
nize
a s
tati
stic
al q
uest
ion
as o
ne t
hat
anti
cipa
tes
vari
abili
ty in
the
dat
a re
late
d to
the
que
stio
n an
d ac
coun
ts f
or it
in t
he a
nswe
rs. F
or e
xam
ple,
“How
old
am
I?”
is n
ot a
st
atis
tica
l que
stio
n, b
ut “H
ow o
ld a
re t
he s
tude
nts
in m
y sc
hool
?” is
a s
tati
stic
al q
uest
ion
beca
use
one
anti
cipa
tes
vari
abili
ty in
stu
dent
s’‛ ag
es.
6.SP
.2. U
nder
stan
d th
at a
set
of
data
col
lect
ed t
o an
swer
a s
tati
stic
al q
uest
ion
has
a di
stri
-bu
tion
whi
ch c
an b
e de
scri
bed
by it
s ce
nter
, spr
ead,
and
ove
rall
shap
e.
6.SP
.3. R
ecog
nize
tha
t a
mea
sure
of
cent
er f
or a
num
eric
al d
ata
set
sum
mar
izes
all
of it
s va
lues
wit
h a
sing
le n
umbe
r, w
hile
a m
easu
re o
f va
riat
ion
desc
ribe
s ho
w it
s va
lues
var
y wi
th a
si
ngle
num
ber.
6th
Grad
e Co
mmon
Cor
e St
ate
Stan
dard
s
Math
emat
ics
Stat
istics
and
Pro
bability
Sum
mar
ize
and
de
scr
ibe
dis
tr
ibut
ions
.
6.SP
.4. D
ispl
ay n
umer
ical
dat
a in
plo
ts o
n a
num
ber
line,
incl
udin
g do
t pl
ots,
his
togr
ams,
and
bo
x pl
ots.
6.
SP.5
. Sum
mar
ize
num
eric
al d
ata
sets
in r
elat
ion
to t
heir
con
text
, suc
h as
by:
Re
port
ing
the
num
ber
of o
bser
vati
ons.
Des
crib
ing
the
natu
re o
f th
e at
trib
ute
unde
r in
vest
igat
ion,
incl
udin
g ho
w it
was
mea
sure
d an
d it
s un
its
of m
easu
rem
ent.
·
Givi
ng q
uant
itat
ive
mea
sure
s of
cen
ter
(med
ian
and/
or m
ean)
and
var
iabi
lity
(inte
rqua
rtile
ra
nge
and/
or m
ean
abso
lute
dev
iati
on),
as w
ell a
s de
scri
bing
any
ove
rall
patt
ern
and
any
stri
king
dev
iati
ons
from
the
ove
rall
patt
ern
with
ref
eren
ce t
o th
e co
ntex
t in
whi
ch t
heda
ta
were
gat
here
d.
Re
lati
ng t
he c
hoic
e of
mea
sure
s of
cen
ter
and
vari
abili
ty t
o th
e sh
ape
of t
he d
ata
dist
ri-
buti
on a
nd t
he c
onte
xt in
whi
ch t
he d
ata
were
gat
here
d.
