grade 6 - pearson education...grade 6 prime time factors and multiples instructional time 22 days...
TRANSCRIPT
Grade 6
Grade 6: Suggested Sequence for CMP31 Suggested Instructional Time
Unit 1 Prime Time: Factors and Multiples 22 days
Unit 2 Comparing Bits and Pieces: Ratios, Rational Numbers, and Equivalence
25 days
NYCDOE Fall Benchmark Assessment
Unit 3 Let’s Be Rational: Understanding Fraction Operations
16 days
Unit 4 Covering and Surrounding: Two-Dimensional Measurement
23 days
Unit 5 Decimal Ops: Computing With Decimals and Percents
24 days
NYCDOE Spring Benchmark Assessment
Unit 6 Variables and Patterns: Focus on Algebra 25 days
State Examination
Unit 7 Data About Us: Statistics and Data Analysis 23 days
1This Scope and Sequence represents one way a school may teach the full year’s content and incorporates the state’s pre-post test standards. As the transition to the PARCC assessments progresses, schools may choose to make decisions around the sequence and pacing of Units that address post-test concepts prior to the state examination in consideration of the state’s testing program guidance (see http://www.p12.nysed.gov/assessment/math/math-ei.html).
Scope and Sequence for Grade 6 69
New
Yor
k Ci
ty S
cope
and
Seq
uenc
e fo
r CM
P3
G
rade
6
Pr
ime
Tim
e F
acto
rs a
nd M
ulti
ple
s
Inst
ruct
iona
l Ti
me
22 d
ays
Ess
enti
al Id
eas
• If
a nu
mb
er N
can
be
writ
ten
as a
pro
duc
t o
f tw
o w
hole
num
ber
s,
N =
a ×
b, t
hen
a an
d b
are
fact
ors
of N
. Mul
tiple
s o
f a c
an b
e fo
und
usi
ng
the
exp
ress
ion
a ×
(so
me
who
le n
umb
er),
such
as
2a, 3
a, 4
a et
c.
• W
hen
all f
acto
rs o
f a n
umb
er a
re b
roke
n d
ow
n in
to p
rime
num
ber
s, y
ou
have
a u
niq
ue p
rime
fact
oriz
atio
n. F
ind
ing
the
prim
e fa
cto
rizat
ion
of t
wo
nu
mb
ers
can
be
usef
ul in
find
ing
the
leas
t co
mm
on
mul
tiple
and
gre
ates
t co
mm
on
fact
or
of t
he n
umb
ers.
• W
hen
calc
ulat
ing
the
val
ue o
f an
exp
ress
ion,
the
op
erat
ions
hav
e to
be
per
form
ed in
a c
onv
entio
nal o
rder
, the
ord
er o
f op
erat
ions
.
• So
met
imes
a n
umer
ical
exp
ress
ion
can
be
writ
ten
in d
iffer
ent
way
s b
ut
the
exp
ress
ions
are
eq
uiva
lent
bec
ause
the
val
ue is
the
sam
e.
Go
als
• U
nder
stan
d re
latio
nshi
ps
amo
ng fa
cto
rs, m
ultip
les,
div
iso
rs, a
nd p
rod
ucts
.•
Und
erst
and
why
tw
o e
xpre
ssio
ns a
re e
qui
vale
nt.
Mai
n C
om
mo
n C
ore
Sta
ndar
ds
Com
mon
Cor
e C
onte
nt S
tand
ard
s6.
NS.
B.4
: Fin
d t
he g
reat
est
com
mo
n fa
cto
r o
f tw
o w
hole
num
ber
s le
ss t
han
or
equa
l to
100
and
the
leas
t co
mm
on
mul
tiple
of t
wo
who
le n
umb
ers
less
th
an o
r eq
ual t
o 1
2. U
se t
he d
istr
ibut
ive
pro
per
ty t
o e
xpre
ss a
sum
of t
wo
w
hole
num
ber
s 1–
100
with
a c
om
mo
n fa
cto
r as
a m
ultip
le o
f a s
um o
f tw
o
who
le n
umb
ers
with
no
co
mm
on
fact
or.
6.E
E.A
.1: W
rite
and
eva
luat
e nu
mer
ical
exp
ress
ions
invo
lvin
g w
hole
-num
ber
ex
po
nent
s.
Com
mon
Cor
e St
and
ard
s fo
r M
athe
mat
ical
Pra
ctic
eM
P.1:
Mak
e se
nse
of p
rob
lem
s an
d p
erse
vere
in s
olv
ing
the
m.
MP.
2: R
easo
n ab
stra
ctly
and
qua
ntita
tivel
y.M
P.3:
Co
nstr
uct
viab
le a
rgum
ents
and
crit
ique
the
reas
oni
ng o
f oth
ers.
MP.
4: M
od
el w
ith m
athe
mat
ics.
MP.
5: U
se a
pp
rop
riate
to
ols
str
ateg
ical
ly.
MP.
6: A
tten
d t
o p
reci
sio
n.M
P.7:
Lo
ok
for
and
mak
e us
e o
f str
uctu
re.
MP.
8: L
oo
k fo
r an
d e
xpre
ss re
gul
arity
in re
pea
ted
reas
oni
ng.
Flue
ncy
Go
als*
• D
ivid
e m
ultid
igit
num
ber
s flu
ently
usi
ng t
he s
tand
ard
alg
orit
hm.
• M
ultip
ly m
ulitd
igit
who
le n
umb
ers
usin
g t
he s
tand
ard
alg
orit
hm.*
*
Ass
essm
ents
Uni
t R
ead
ines
sC
heck
Up
1Pa
rtne
r Q
uiz
Che
ck U
p 2
Uni
t Pr
oje
ctSe
lf-A
sses
smen
tU
nit
Test
*CM
P3 d
evel
op
s flu
ency
in p
roce
dur
al s
kills
fro
m a
foun
dat
ion
of c
onc
eptu
al u
nder
stan
din
g, a
n ap
pro
ach
that
lead
s to
long
-ter
m re
tent
ion
of s
kills
and
ab
ility
to
ap
ply
tho
se s
kills
in p
rob
lem
so
lvin
g.
**re
info
rcin
g fl
uenc
y ex
pec
tatio
ns fr
om
pre
vio
us g
rad
es
Teacher Implementation Toolkit70
New
Yor
k Ci
ty S
cope
and
Seq
uenc
e fo
r CM
P3
cont
inued
Gra
de 6
Co
mPa
rin
g B
iTs
an
d P
ieC
es
Rat
ios,
Rat
iona
l Num
ber
s, a
nd E
qui
vale
nce
Inst
ruct
iona
l Ti
me
25 d
ays
Ess
enti
al Id
eas
• R
atio
nal n
umb
ers
can
be
writ
ten
in fr
actio
n o
r d
ecim
al fo
rm a
nd c
an
be
rep
rese
nted
as
po
ints
or
dis
tanc
es o
n a
num
ber
line
. A n
umb
er-li
ne
rep
rese
ntat
ion
is u
sefu
l fo
r o
rder
ing
and
co
mp
arin
g n
umb
ers.
• Fr
actio
ns a
nd d
ecim
als
can
be
rena
med
or
rep
artit
ione
d t
o fi
nd
equi
vale
nt fr
actio
ns o
r dec
imal
s. E
qui
vale
nce
is u
sefu
l for
mov
ing
bet
wee
n fr
actio
n an
d d
ecim
al re
pre
sent
atio
ns a
nd fo
r sol
ving
pro
ble
ms.
• R
atio
s ar
e co
mp
aris
ons
bet
wee
n tw
o n
umb
ers.
Yo
u ca
n sc
ale
ratio
s to
m
ake
equi
vale
nt r
atio
s. P
erce
nts
are
ratio
s w
here
100
par
ts re
pre
sent
s th
e w
hole
.
• A
rat
e is
a p
artic
ular
kin
d o
f rat
io, w
here
the
am
oun
ts c
om
par
ed a
re in
d
iffer
ent
units
. A u
nit
rate
is a
rat
e th
at h
as b
een
scal
ed t
o x
: 1.
Go
als
• U
nder
stan
d fr
actio
ns a
nd d
ecim
als
as n
umb
ers
that
can
be
loca
ted
on
the
num
ber
line
, co
mp
ared
, co
unte
d, p
artit
ione
d, a
nd d
eco
mp
ose
d.
• U
nder
stan
d r
atio
s as
co
mp
aris
ons
of t
wo
num
ber
s.
• U
nder
stan
d e
qui
vale
nce
of f
ract
ions
and
rat
ios,
and
use
eq
uiva
lenc
e to
so
lve
pro
ble
ms.
Mai
n C
om
mo
n C
ore
Sta
ndar
ds
Com
mon
Cor
e C
onte
nt S
tand
ard
s 6.
RP.
A.1
: Und
erst
and
the
co
ncep
t o
f a r
atio
and
use
rat
io la
ngua
ge
to
des
crib
e a
ratio
rela
tions
hip
bet
wee
n tw
o q
uant
ities
.
6.R
P.A
.2: U
nder
stan
d t
he c
onc
ept
of a
uni
t ra
te a
/b a
sso
ciat
ed w
ith a
rat
io
a:b
with
b ≠
0, a
nd u
se r
ate
lang
uag
e in
the
co
ntex
t o
f a r
atio
rela
tions
hip
.
6.R
P.A
.3: U
se r
atio
and
rat
e re
aso
ning
to
so
lve
real
-wo
rld a
nd m
athe
mat
ical
p
rob
lem
s, e
.g.,
by
reas
oni
ng a
bo
ut t
able
s o
f eq
uiva
lent
rat
ios,
tap
e d
iag
ram
s, d
oub
le n
umb
er li
ne d
iag
ram
s, o
r eq
uatio
ns.
6.N
S.C
.5: U
nder
stan
d t
hat
po
sitiv
e an
d n
egat
ive
num
ber
s ar
e us
ed t
og
ethe
r to
des
crib
e q
uant
ities
hav
ing
op
pos
ite d
irect
ions
or v
alue
s (e
.g.,
tem
per
atur
e ab
ove/
bel
ow z
ero,
ele
vatio
n ab
ove/
bel
ow s
ea le
vel,
cred
its/d
ebits
, pos
itive
/ne
gat
ive
elec
tric
cha
rge)
; use
pos
itive
and
neg
ativ
e nu
mb
ers
to re
pre
sent
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.
6.N
S.C
.6: U
nder
stan
d a
rat
iona
l num
ber
as
a p
oin
t o
n th
e nu
mb
er li
ne.
Ext
end
num
ber
line
dia
gra
ms
and
co
ord
inat
e ax
es fa
mili
ar fr
om
pre
vio
us
gra
des
to
rep
rese
nt p
oin
ts o
n th
e lin
e an
d in
the
pla
ne w
ith n
egat
ive
num
ber
co
ord
inat
es.
6.N
S.C
.7: U
nder
stan
d o
rder
ing
and
ab
solu
te v
alue
of r
atio
nal n
umb
ers.
Com
mon
Cor
e St
and
ard
s fo
r M
athe
mat
ical
Pra
ctic
eM
P.1:
Mak
e se
nse
of p
rob
lem
s an
d p
erse
vere
in s
olv
ing
the
m.
MP.
2: R
easo
n ab
stra
ctly
and
qua
ntita
tivel
y.M
P.3:
Co
nstr
uct
viab
le a
rgum
ents
and
crit
ique
the
reas
oni
ng o
f oth
ers.
MP.
4: M
od
el w
ith m
athe
mat
ics.
MP.
5: U
se a
pp
rop
riate
to
ols
str
ateg
ical
ly.
MP.
6: A
tten
d t
o p
reci
sio
n.M
P.7:
Lo
ok
for
and
mak
e us
e o
f str
uctu
re.
MP.
8: L
oo
k fo
r an
d e
xpre
ss re
gul
arity
in re
pea
ted
reas
oni
ng.
Flue
ncy
Go
als*
• D
ivid
e m
ultid
igit
num
ber
s flu
ently
usi
ng t
he s
tand
ard
alg
orit
hm.
• O
per
ate
with
mul
tidig
it d
ecim
als
fluen
tly.
Ass
essm
ents
Uni
t R
ead
ines
sPa
rtne
r Q
uiz
AC
heck
Up
Part
ner
Qui
z B
Self-
Ass
essm
ent
Uni
t Te
st
NY
CD
OE
Fal
l Ben
chm
ark
Ass
essm
ent
*CM
P3 d
evel
op
s flu
ency
in p
roce
dur
al s
kills
fro
m a
foun
dat
ion
of c
onc
eptu
al u
nder
stan
din
g, a
n ap
pro
ach
that
lead
s to
long
-ter
m re
tent
ion
of s
kills
and
ab
ility
to
ap
ply
tho
se s
kills
in p
rob
lem
so
lvin
g.
Scope and Sequence for Grade 6 71
New
Yor
k Ci
ty S
cope
and
Seq
uenc
e fo
r CM
P3
cont
inued
Gra
de 6
LeT’
s B
e r
aTi
on
aL
Und
erst
and
ing
Fra
ctio
n O
per
atio
ns
Inst
ruct
iona
l Ti
me
16 d
ays
Ess
enti
al Id
eas
• E
stim
atio
n is
an
imp
ort
ant
par
t o
f rea
soni
ng q
uant
itativ
ely.
It e
nco
urag
es
mak
ing
sen
se o
f a s
ituat
ion,
allo
ws
you
to re
cog
nize
err
ors
, and
co
mp
lem
ents
oth
er p
rob
lem
so
lvin
g s
kills
.
• Fo
r ea
ch o
per
atio
n, t
here
is a
n ef
ficie
nt, g
ener
al a
lgo
rithm
for
com
put
ing
w
ith fr
actio
ns t
hat
wo
rks
in a
ll ca
ses.
• Va
riab
les
rep
rese
nt u
nkno
wn
valu
es a
nd a
re u
sed
to
writ
e ex
pre
ssio
ns t
hat
help
so
lve
real
-wo
rld p
rob
lem
s.
• So
met
imes
rew
ritin
g a
pro
ble
m u
sing
a d
iffer
ent
op
erat
ion
can
be
help
ful
in fi
ndin
g t
he s
olu
tion.
Go
als
• U
nder
stan
d e
stim
atio
n as
a t
oo
l fo
r a
varie
ty o
f situ
atio
ns a
nd d
evel
op
st
rate
gie
s fo
r es
timat
ing
resu
lts o
f arit
hmet
ic o
per
atio
ns.
• R
evis
it an
d d
evel
op
mea
ning
s fo
r th
e fo
ur a
rithm
etic
op
erat
ions
and
ski
ll at
usi
ng a
lgo
rithm
s fo
r ea
ch.
• U
se v
aria
ble
s to
rep
rese
nt u
nkno
wn
valu
es a
nd e
qua
tions
to
rep
rese
nt
rela
tions
hip
s.
Mai
n C
om
mo
n C
ore
Sta
ndar
ds
Com
mon
Cor
e C
onte
nt S
tand
ard
s 6.
NS.
A.1
: Int
erp
ret
and
co
mp
ute
quo
tient
s o
f fra
ctio
ns, a
nd s
olv
e w
ord
p
rob
lem
s in
volv
ing
div
isio
n o
f fra
ctio
ns b
y fr
actio
ns, e
.g.,
by
usin
g v
isua
l fr
actio
n m
od
els
and
eq
uatio
ns t
o re
pre
sent
the
pro
ble
m.
6.E
E.B
.6: U
se v
aria
ble
s to
rep
rese
nt n
umb
ers
and
writ
e ex
pre
ssio
ns w
hen
solv
ing
a re
al-w
orld
or
mat
hem
atic
al p
rob
lem
; und
erst
and
tha
t a
varia
ble
can
re
pre
sent
an
unkn
ow
n nu
mb
er, o
r, d
epen
din
g o
n th
e p
urp
ose
at
hand
, any
nu
mb
er in
a s
pec
ified
set
.
6.E
E.B
.7: S
olv
e re
al-w
orld
and
mat
hem
atic
al p
rob
lem
s b
y w
ritin
g a
nd s
olv
ing
eq
uatio
ns o
f the
form
x +
p =
q a
nd p
x =
q fo
r ca
ses
in w
hich
p, q
and
x a
re
all n
onn
egat
ive
ratio
nal n
umb
ers.
Com
mon
Cor
e St
and
ard
s fo
r M
athe
mat
ical
Pra
ctic
eM
P.1:
Mak
e se
nse
of p
rob
lem
s an
d p
erse
vere
in s
olv
ing
the
m.
MP.
2: R
easo
n ab
stra
ctly
and
qua
ntita
tivel
y.M
P.3:
Co
nstr
uct
viab
le a
rgum
ents
and
crit
ique
the
reas
oni
ng o
f oth
ers.
MP.
4: M
od
el w
ith m
athe
mat
ics.
MP.
5: U
se a
pp
rop
riate
to
ols
str
ateg
ical
ly.
MP.
6: A
tten
d t
o p
reci
sio
n.M
P.7:
Lo
ok
for
and
mak
e us
e o
f str
uctu
re.
MP.
8: L
oo
k fo
r an
d e
xpre
ss re
gul
arity
in re
pea
ted
reas
oni
ng.
Flue
ncy
Go
als*
• D
ivid
e m
ultid
igit
num
ber
s flu
ently
usi
ng t
he s
tand
ard
alg
orit
hm.
• D
ivid
e fr
actio
ns.
Ass
essm
ents
Uni
t R
ead
ines
sC
heck
Up
1Pa
rtne
r Q
uiz
Che
ck U
p 2
Self-
Ass
essm
ent
Uni
t Te
st
*CM
P3 d
evel
op
s flu
ency
in p
roce
dur
al s
kills
fro
m a
foun
dat
ion
of c
onc
eptu
al u
nder
stan
din
g, a
n ap
pro
ach
that
lead
s to
long
-ter
m re
tent
ion
of s
kills
and
ab
ility
to
ap
ply
tho
se s
kills
in p
rob
lem
so
lvin
g.
Teacher Implementation Toolkit72
New
Yor
k Ci
ty S
cope
and
Seq
uenc
e fo
r CM
P3
cont
inued
Gra
de 6
Co
ve
rin
g a
nd
su
rr
ou
nd
ing
Tw
o-D
imen
sion
al M
easu
rem
ent
Inst
ruct
iona
l Ti
me
23 d
ays
Ess
enti
al Id
eas
• Po
lyg
ons
and
irre
gul
ar fi
gur
es c
an b
e d
eco
mp
ose
d in
to t
riang
les
and
re
ctan
gle
s to
find
the
are
a o
f the
fig
ures
.
• A
fixe
d n
umb
er o
f are
a un
its c
an b
e en
clo
sed
by
man
y d
iffer
ent
per
imet
ers,
and
a fi
xed
num
ber
of p
erim
eter
uni
ts c
an e
nclo
se m
any
diff
eren
t ar
eas.
• Fo
rmul
as fo
r th
e ar
ea a
nd p
erim
eter
of a
rect
ang
le c
an h
elp
yo
u so
lve
pro
ble
ms
by
reas
oni
ng a
bo
ut t
he re
latio
nshi
p b
etw
een
valu
es.
• Th
e vo
lum
e o
f a p
rism
can
be
tho
ught
of a
s m
ultip
lyin
g a
bas
e la
yer
of
unit
cub
es b
y th
e nu
mb
er o
f lay
ers
need
ed t
o fi
ll th
e p
rism
.
• Su
rfac
e ar
eas
of t
hree
-dim
ensi
ona
l so
lids
can
be
foun
d b
y ad
din
g t
he
area
s o
f the
face
s.
Go
als
• U
nder
stan
d w
hat
it m
eans
to
mea
sure
are
a an
d p
erim
eter
.•
Und
erst
and
and
use
the
rela
tions
hip
bet
wee
n fo
rmul
as fo
r ar
ea a
nd
per
imet
er o
f tria
ngle
s an
d p
aral
lelo
gra
ms
and
form
ulas
for
rect
ang
les.
• U
nder
stan
d v
olu
me
as fi
lling
a t
hree
-dim
ensi
ona
l sha
pe
and
dev
elo
p
stra
teg
ies
to fi
nd s
urfa
ce a
rea
by
find
ing
are
a o
f tw
o-d
imen
sio
nal s
hap
es.
Mai
n C
om
mo
n C
ore
Sta
ndar
ds
Com
mon
Cor
e C
onte
nt S
tand
ard
s 6.
EE
.C.9
: Use
var
iab
les
to re
pre
sent
tw
o q
uant
ities
in a
real
-wo
rld p
rob
lem
th
at c
hang
e in
rela
tions
hip
to
one
ano
ther
; writ
e an
eq
uatio
n to
exp
ress
o
ne q
uant
ity, t
houg
ht o
f as
the
dep
end
ent
varia
ble
, in
term
s o
f the
oth
er
qua
ntity
, tho
ught
of a
s th
e in
dep
end
ent
varia
ble
. Ana
lyze
the
rela
tions
hip
b
etw
een
the
dep
end
ent
and
ind
epen
den
t va
riab
les
usin
g g
rap
hs a
nd t
able
s,
and
rela
te t
hese
to
the
eq
uatio
n.
6.G
.A.1
: Fin
d t
he a
rea
of r
ight
tria
ngle
s, o
ther
tria
ngle
s, s
pec
ial
qua
dril
ater
als,
and
po
lyg
ons
by
com
po
sing
into
rect
ang
les
or
dec
om
po
sing
in
to t
riang
les
and
oth
er s
hap
es; a
pp
ly t
hese
tec
hniq
ues
in t
he c
ont
ext
of
solv
ing
real
-wo
rld a
nd m
athe
mat
ical
pro
ble
ms.
6.G
.A.2
: Fin
d t
he v
olu
me
of a
rig
ht re
ctan
gul
ar p
rism
with
frac
tiona
l ed
ge
leng
ths
by
pac
king
it w
ith u
nit
cub
es o
f the
ap
pro
pria
te u
nit
frac
tion
edg
e le
ngth
s, a
nd s
how
tha
t th
e vo
lum
e is
the
sam
e as
wo
uld
be
foun
d b
y m
ultip
lyin
g t
he e
dg
e le
ngth
s o
f the
pris
m. A
pp
ly t
he fo
rmul
as V
= lw
h an
d
V =
bh
to fi
nd v
olu
mes
of r
ight
rect
ang
ular
pris
ms
with
frac
tiona
l ed
ge
leng
ths
in t
he c
ont
ext
of s
olv
ing
real
-wo
rld a
nd m
athe
mat
ical
pro
ble
ms.
Com
mon
Cor
e St
and
ard
s fo
r M
athe
mat
ical
Pra
ctic
eM
P.1:
Mak
e se
nse
of p
rob
lem
s an
d p
erse
vere
in s
olv
ing
the
m.
MP.
2: R
easo
n ab
stra
ctly
and
qua
ntita
tivel
y.M
P.3:
Co
nstr
uct
viab
le a
rgum
ents
and
crit
ique
the
reas
oni
ng o
f oth
ers.
MP.
4: M
od
el w
ith m
athe
mat
ics.
MP.
5: U
se a
pp
rop
riate
to
ols
str
ateg
ical
ly.
MP.
6: A
tten
d t
o p
reci
sio
n.M
P.7:
Lo
ok
for
and
mak
e us
e o
f str
uctu
re.
MP.
8: L
oo
k fo
r an
d e
xpre
ss re
gul
arity
in re
pea
ted
reas
oni
ng.
Flue
ncy
Go
als*
• M
ultip
ly m
ulitd
igit
who
le n
umb
ers
usin
g t
he s
tand
ard
alg
orit
hm.*
*
Ass
essm
ents
Uni
t R
ead
ines
s C
heck
Up
1C
heck
Up
2Pa
rtne
r Q
uiz
Uni
t Pr
oje
ctSe
lf-A
sses
smen
tU
nit
Test
*CM
P3 d
evel
op
s flu
ency
in p
roce
dur
al s
kills
fro
m a
foun
dat
ion
of c
onc
eptu
al u
nder
stan
din
g, a
n ap
pro
ach
that
lead
s to
long
-ter
m re
tent
ion
of s
kills
and
ab
ility
to
ap
ply
tho
se s
kills
in p
rob
lem
so
lvin
g.
**re
info
rcin
g fl
uenc
y ex
pec
tatio
ns fr
om
pre
vio
us g
rad
es
Scope and Sequence for Grade 6 73
*CM
P3 d
evel
op
s flu
ency
in p
roce
dur
al s
kills
fro
m a
foun
dat
ion
of c
onc
eptu
al u
nder
stan
din
g, a
n ap
pro
ach
that
lead
s to
long
-ter
m re
tent
ion
of s
kills
and
ab
ility
to
ap
ply
tho
se s
kills
in p
rob
lem
so
lvin
g.
de
Cim
aL
oP
s C
omp
utin
g w
ith
Dec
imal
s an
d P
erce
nts
Inst
ruct
iona
l Ti
me
24 d
ays
Ess
enti
al Id
eas
• E
stim
atio
n is
an
imp
ort
ant
par
t o
f rea
soni
ng q
uant
itativ
ely.
It h
elp
s yo
u m
ake
sens
e o
f a s
ituat
ion,
allo
ws
you
to re
cog
nize
err
ors
, and
co
mp
lem
ents
oth
er p
rob
lem
so
lvin
g s
kills
.
• Th
e st
and
ard
alg
orit
hm fo
r d
ivid
ing
dec
imal
s is
sup
po
rted
by
the
conn
ectio
ns b
etw
een
frac
tion
and
dec
imal
op
erat
ions
.
• Fl
uenc
y w
ith d
ecim
al o
per
atio
ns a
llow
yo
u to
so
lve
a va
riety
of
pro
ble
ms
invo
lvin
g r
atio
s an
d p
erce
nts.
• In
vers
e o
per
atio
ns c
an b
e us
ed t
o is
ola
te a
var
iab
le w
hen
solv
ing
eq
uatio
ns.
Go
als
• U
nder
stan
d e
stim
atio
n as
a t
oo
l fo
r a
varie
ty o
f situ
atio
ns, i
nclu
din
g
chec
king
ans
wer
s an
d m
akin
g d
ecis
ions
.•
Rev
isit
and
dev
elo
p m
eani
ngs
for
the
four
arit
hmet
ic o
per
atio
ns o
n w
hole
num
ber
s an
d d
ecim
als,
and
ski
ll at
usi
ng a
lgo
rithm
s fo
r ea
ch
dec
imal
op
erat
ion.
• U
se v
aria
ble
s to
rep
rese
nt u
nkno
wn
valu
es a
nd e
qua
tions
to
re
pre
sent
rela
tions
hip
s.•
Dev
elo
p u
nder
stan
din
g o
f var
ious
co
ntex
ts in
whi
ch p
erce
ntag
es a
re
used
, inc
lud
ing
sal
es t
ax, t
ips,
dis
coun
ts, p
erce
nt in
crea
ses.
Mai
n C
om
mo
n C
ore
Sta
ndar
ds
Com
mon
Cor
e C
onte
nt S
tand
ard
s 6.
NS.
B.3
: Flu
ently
ad
d, s
ubtr
act,
mul
tiply
, and
div
ide
mul
ti-d
igit
dec
imal
s us
ing
the
sta
ndar
d a
lgo
rithm
for
each
op
erat
ion.
6.E
E.A
.3: A
pp
ly t
he p
rop
ertie
s o
f op
erat
ions
to
gen
erat
e eq
uiva
lent
ex
pre
ssio
ns.
Com
mon
Cor
e St
and
ard
s fo
r M
athe
mat
ical
Pra
ctic
eM
P.1:
Mak
e se
nse
of p
rob
lem
s an
d p
erse
vere
in s
olv
ing
the
m.
MP.
2: R
easo
n ab
stra
ctly
and
qua
ntita
tivel
y.M
P.3:
Co
nstr
uct
viab
le a
rgum
ents
and
crit
ique
the
reas
oni
ng o
f oth
ers.
MP.
4: M
od
el w
ith m
athe
mat
ics.
MP.
5: U
se a
pp
rop
riate
to
ols
str
ateg
ical
ly.
MP.
6: A
tten
d t
o p
reci
sio
n.M
P.7:
Lo
ok
for
and
mak
e us
e o
f str
uctu
re.
MP.
8: L
oo
k fo
r an
d e
xpre
ss re
gul
arity
in re
pea
ted
reas
oni
ng.
Flue
ncy
Go
als*
• D
ivid
e m
ultid
igit
num
ber
s flu
ently
usi
ng t
he s
tand
ard
alg
orit
hm.
• O
per
ate
with
mul
tidig
it d
ecim
als
fluen
tly.
Ass
essm
ents
Uni
t R
ead
ines
s C
heck
Up
1C
heck
Up
2Pa
rtne
r Q
uiz
Uni
t Pr
oje
ctSe
lf-A
sses
smen
tU
nit
Test
NY
CD
OE
Sp
ring
Ben
chm
ark
Ass
essm
ent
New
Yor
k Ci
ty S
cope
and
Seq
uenc
e fo
r CM
P3
cont
inued
Gra
de 6
Teacher Implementation Toolkit74
va
ria
BLe
s a
nd
Pa
TTe
rn
s In
trod
ucin
g A
lgeb
ra
Inst
ruct
iona
l Ti
me
25 d
ays
Ess
enti
al Id
eas
• In
man
y re
al-w
orld
situ
atio
ns, o
ne v
aria
ble
qua
ntity
dep
end
s o
n an
oth
er. T
able
s, g
rap
hs, a
nd e
qua
tions
are
var
ious
rep
rese
ntat
ions
th
at c
an b
e us
ed t
o b
ette
r un
der
stan
d t
he p
atte
rn o
f cha
nge
bet
wee
n va
riab
le q
uant
ities
.
• N
ot
all r
elat
ions
hip
s ar
e lin
ear.
Line
ar re
latio
nshi
ps
have
a c
ons
tant
rat
e o
f ch
ang
e b
etw
een
varia
ble
s an
d a
re w
ritte
n in
the
form
y =
mx,
y =
b +
x,
and
y =
b +
mx.
• Th
ere
is m
ore
tha
n o
ne w
ay t
o w
rite
an e
xpre
ssio
n to
mo
del
a re
al
wo
rld s
ituat
ion.
Pro
per
ties
of o
per
atio
ns a
llow
yo
u to
gen
erat
e eq
uiva
lent
ex
pre
ssio
ns a
nd c
heck
eq
uiva
lenc
e.
• So
lutio
ns fo
r eq
uatio
ns a
nd in
equa
litie
s ca
n b
e fo
und
by
exam
inin
g t
he
tab
le o
r g
rap
h o
f the
eq
uatio
n o
r b
y re
writ
ing
it a
s a
rela
ted
eq
uatio
n.
Go
als
• D
evel
op
und
erst
and
ing
of v
aria
ble
s an
d h
ow
the
y ar
e re
late
d.
• D
evel
op
und
erst
and
ing
of e
xpre
ssio
ns a
nd e
qua
tions
.
Mai
n C
om
mo
n C
ore
Sta
ndar
ds
Com
mon
Cor
e C
onte
nt S
tand
ard
s 6.
RP.
A.3
: Use
rat
io a
nd r
ate
reas
oni
ng t
o s
olv
e re
al-w
orld
and
mat
hem
atic
al
pro
ble
ms,
e.g
., b
y re
aso
ning
ab
out
tab
les
of e
qui
vale
nt r
atio
s, t
ape
dia
gra
ms,
do
uble
num
ber
line
dia
gra
ms,
or
equa
tions
.
6.N
S.C
.8: S
olv
e re
al-w
orld
and
mat
hem
atic
al p
rob
lem
s b
y g
rap
hing
po
ints
in a
ll fo
ur q
uad
rant
s o
f the
co
ord
inat
e p
lane
. Inc
lud
e us
e o
f co
ord
inat
es
and
ab
solu
te v
alue
to
find
dis
tanc
es b
etw
een
po
ints
with
the
sam
e fir
st
coo
rdin
ate
or
the
sam
e se
cond
co
ord
inat
e.
6.E
E.A
.3: A
pp
ly t
he p
rop
ertie
s o
f op
erat
ions
to
gen
erat
e eq
uiva
lent
exp
ress
ions
.
6.E
E.B
.7: S
olv
e re
al-w
orld
and
mat
hem
atic
al p
rob
lem
s b
y w
ritin
g a
nd s
olv
ing
eq
uatio
ns o
f the
form
x +
p =
q a
nd p
x =
q fo
r ca
ses
in w
hich
p, q
and
x a
re
all n
onn
egat
ive
ratio
nal n
umb
ers.
Com
mon
Cor
e St
and
ard
s fo
r M
athe
mat
ical
Pra
ctic
eM
P.1:
Mak
e se
nse
of p
rob
lem
s an
d p
erse
vere
in s
olv
ing
the
m.
MP.
2: R
easo
n ab
stra
ctly
and
qua
ntita
tivel
y.M
P.3:
Co
nstr
uct
viab
le a
rgum
ents
and
crit
ique
the
reas
oni
ng o
f oth
ers.
MP.
4: M
od
el w
ith m
athe
mat
ics.
MP.
5: U
se a
pp
rop
riate
to
ols
str
ateg
ical
ly.
MP.
6: A
tten
d t
o p
reci
sio
n.M
P.7:
Lo
ok
for
and
mak
e us
e o
f str
uctu
re.
MP.
8: L
oo
k fo
r an
d e
xpre
ss re
gul
arity
in re
pea
ted
reas
oni
ng.
Flue
ncy
Go
als*
• D
ivid
e m
ultid
igit
num
ber
s flu
ently
usi
ng t
he s
tand
ard
alg
orit
hm.
• O
per
ate
with
mul
tidig
it d
ecim
als
fluen
tly.
Ass
essm
ents
Uni
t R
ead
ines
sC
heck
Up
1C
heck
Up
2Pa
rtne
r Q
uiz
Uni
t Te
st
New
Yor
k Ci
ty S
cope
and
Seq
uenc
e fo
r CM
P3
cont
inued
Gra
de 6
*CM
P3 d
evel
op
s flu
ency
in p
roce
dur
al s
kills
fro
m a
foun
dat
ion
of c
onc
eptu
al u
nder
stan
din
g, a
n ap
pro
ach
that
lead
s to
long
-ter
m re
tent
ion
of s
kills
and
ab
ility
to
ap
ply
tho
se s
kills
in p
rob
lem
so
lvin
g.
Scope and Sequence for Grade 6 75
da
Ta a
Bo
uT
us
Stat
isti
cs a
nd D
ata
Ana
lysi
s
Inst
ruct
iona
l Ti
me
23 d
ays
Ess
enti
al Id
eas
• Th
e an
swer
s to
a s
tatis
tical
que
stio
n ar
e ca
lled
dat
a. D
ata
can
be
eith
er
num
eric
al o
r ca
teg
oric
al.
• Th
ere
are
seve
ral w
ays
to t
ry t
o s
ay w
hat
is t
ypic
al o
f a s
et o
f dat
a; in
ea
ch c
ase
a si
ngle
num
ber
, cal
led
a m
easu
re o
f cen
ter,
sum
mar
izes
the
d
ata.
Bec
ause
var
ious
mea
sure
s o
f cen
ter
are
calc
ulat
ed d
iffer
ently
, the
y re
spo
nd d
iffer
ently
to
cha
nges
in t
he d
ata
or
to u
nusu
al d
ata
valu
es.
• Th
e va
riab
ility
of a
set
of d
ata
can
be
mea
sure
d, i
nter
pre
ted
and
co
mp
ared
with
the
var
iab
ility
of o
ther
dat
a se
ts. M
easu
res
of v
aria
bili
ty t
ell
you
how
sp
read
out
the
dat
a ar
e in
rela
tion
to e
ach
oth
er o
r to
the
cen
ter.
• Fi
ndin
g m
easu
res
of c
ente
r o
r va
riab
ility
and
gra
phi
ng d
ata
are
usef
ul fo
r su
mm
ariz
ing
the
info
rmat
ion
in a
var
iab
le d
ata
set.
Vis
ual r
epre
sent
atio
ns
of a
dat
a se
t ca
n he
lp y
ou
to in
terp
ret
the
mea
sure
s o
f cen
ter
and
sp
read
, an
d re
late
thi
s to
the
ove
rall
shap
e o
f the
rep
rese
ntat
ion.
Go
als
• U
nder
stan
d a
nd u
se t
he p
roce
ss o
f sta
tistic
al in
vest
igat
ion:
po
se
que
stio
ns, c
olle
ct a
nd a
naly
ze d
ata,
and
mak
e in
terp
reta
tions
to
an
swer
que
stio
ns.
• U
se m
ultip
le re
pre
sent
atio
ns t
o o
rgan
ize
and
rep
rese
nt d
ata
and
dev
elo
p
und
erst
and
ing
of m
easu
res
of c
ente
r an
d m
easu
res
of v
aria
bili
ty fo
r d
ata
dis
trib
utio
ns.
Mai
n C
om
mo
n C
ore
Sta
ndar
ds
Com
mon
Cor
e C
onte
nt S
tand
ard
s6.
SP.A
.1: R
eco
gni
ze a
sta
tistic
al q
uest
ion
as o
ne t
hat
antic
ipat
es v
aria
bili
ty in
th
e d
ata
rela
ted
to
the
que
stio
n an
d a
cco
unts
for
it in
the
ans
wer
s.
6.SP
.A.2
: Und
erst
and
tha
t a
set
of d
ata
colle
cted
to
ans
wer
a s
tatis
tical
q
uest
ion
has
a d
istr
ibut
ion
whi
ch c
an b
e d
escr
ibed
by
its c
ente
r, sp
read
, and
o
vera
ll sh
ape.
6.SP
.A.3
: Rec
og
nize
tha
t a
mea
sure
of c
ente
r fo
r a
num
eric
al d
ata
set
sum
mar
izes
all
of i
ts v
alue
s w
ith a
sin
gle
num
ber
, whi
le a
mea
sure
of v
aria
tion
des
crib
es h
ow
its
valu
es v
ary
with
a s
ing
le n
umb
er.
6.SP
.B.4
: Dis
pla
y nu
mer
ical
dat
a in
plo
ts o
n a
num
ber
line
, inc
lud
ing
do
t p
lots
, his
tog
ram
s, a
nd b
ox
plo
ts.
6.SP
.B.5
: Sum
mar
ize
num
eric
al d
ata
sets
in re
latio
n to
the
ir co
ntex
t.
Com
mon
Cor
e St
and
ard
s fo
r M
athe
mat
ical
Pra
ctic
eM
P.1:
Mak
e se
nse
of p
rob
lem
s an
d p
erse
vere
in s
olv
ing
the
m.
MP.
2: R
easo
n ab
stra
ctly
and
qua
ntita
tivel
y.M
P.3:
Co
nstr
uct
viab
le a
rgum
ents
and
crit
ique
the
reas
oni
ng o
f oth
ers.
MP.
4: M
od
el w
ith m
athe
mat
ics.
MP.
5: U
se a
pp
rop
riate
to
ols
str
ateg
ical
ly.
MP.
6: A
tten
d t
o p
reci
sio
n.M
P.7:
Lo
ok
for
and
mak
e us
e o
f str
uctu
re.
MP.
8: L
oo
k fo
r an
d e
xpre
ss re
gul
arity
in re
pea
ted
reas
oni
ng.
Flue
ncy
Go
als*
• D
ivid
e m
ultid
igit
num
ber
s flu
ently
usi
ng t
he s
tand
ard
alg
orit
hm.
• O
per
ate
with
mul
tidig
it d
ecim
als
fluen
tly.
Ass
essm
ents
Uni
t R
ead
ines
sC
heck
Up
1Pa
rtne
r Q
uiz
AC
heck
Up
2Pa
rtne
r Q
uiz
BSe
lf-A
sses
smen
tU
nit
Test
New
Yor
k Ci
ty S
cope
and
Seq
uenc
e fo
r CM
P3
cont
inued
Gra
de 6
*CM
P3 d
evel
op
s flu
ency
in p
roce
dur
al s
kills
fro
m a
foun
dat
ion
of c
onc
eptu
al u
nder
stan
din
g, a
n ap
pro
ach
that
lead
s to
long
-ter
m re
tent
ion
of s
kills
and
ab
ility
to
ap
ply
tho
se s
kills
in p
rob
lem
so
lvin
g.
Teacher Implementation Toolkit76