other Bloom’s Cognitive Process Dimensions - Webb’s … · Hess’ Cognitive Rigor Matrix ......
Transcript of other Bloom’s Cognitive Process Dimensions - Webb’s … · Hess’ Cognitive Rigor Matrix ......
Hes
s’ C
ogni
tive
Rig
or M
atrix
& C
urric
ular
Exa
mpl
es: A
pply
ing
Web
b’s
Dep
th-o
f-Kno
wle
dge
Leve
ls to
Blo
om’s
Cog
nitiv
e P
roce
ss D
imen
sion
s - E
LA
©
200
9 K
arin
K. H
ess:
Hes
s’ C
ogni
tive
Rig
or M
atri
x: P
erm
issi
on to
repr
oduc
e is
giv
en w
hen
auth
orsh
ip is
fully
cite
d [k
hess
@nc
iea.
org]
Fo
r ful
l arti
cle,
go
to w
ww
.nci
ea.o
rg
Rev
ised
Blo
om’s
Ta
xono
my
Web
b’s
DO
K L
evel
1
Rec
all &
Rep
rodu
ctio
n W
ebb’
s D
OK
Lev
el 2
Sk
ills
& C
once
pts
Web
b’s
DO
K L
evel
3
Stra
tegi
c Th
inki
ng/ R
easo
ning
W
ebb’
s D
OK
Lev
el 4
Ex
tend
ed T
hink
ing
Rem
embe
r R
etrie
ve k
now
ledg
e fro
m lo
ng-
term
mem
ory,
reco
gniz
e, re
call,
lo
cate
, ide
ntify
o R
ecal
l, re
cogn
ize,
or l
ocat
e ba
sic
fact
s, d
etai
ls, e
vent
s, o
r id
eas
expl
icit
in te
xts
o R
ead
wor
ds o
rally
in c
onne
cted
te
xt w
ith fl
uenc
y &
acc
urac
y
Und
erst
and
Con
stru
ct m
eani
ng, c
larif
y,
para
phra
se, r
epre
sent
, tra
nsla
te,
illus
trate
, giv
e ex
ampl
es,
clas
sify
, cat
egor
ize,
sum
mar
ize,
ge
nera
lize,
infe
r a lo
gica
l co
nclu
sion
), pr
edic
t, co
mpa
re/c
ontra
st, m
atch
like
id
eas,
exp
lain
, con
stru
ct m
odel
s
o Id
entif
y or
des
crib
e lit
erar
y el
emen
ts (c
hara
cter
s, s
ettin
g,
sequ
ence
, etc
.) o
Sel
ect a
ppro
pria
te w
ords
whe
n in
tend
ed m
eani
ng/d
efin
ition
is
clea
rly e
vide
nt
o D
escr
ibe/
expl
ain
who
, wha
t, w
here
, whe
n, o
r how
o
Def
ine/
desc
ribe
fact
s, d
etai
ls,
term
s, p
rinci
ples
o
Writ
e si
mpl
e se
nten
ces
o Sp
ecify
, exp
lain
, sho
w re
latio
nshi
ps;
expl
ain
why
, cau
se-e
ffect
o
Giv
e no
n-ex
ampl
es/e
xam
ples
o
Sum
mar
ize
resu
lts, c
once
pts,
idea
s o
Mak
e ba
sic
infe
renc
es o
r log
ical
pr
edic
tions
from
dat
a or
text
s o
Iden
tify
mai
n id
eas
or a
ccur
ate
gene
raliz
atio
ns o
f tex
ts
o Lo
cate
info
rmat
ion
to s
uppo
rt ex
plic
it-im
plic
it ce
ntra
l ide
as
o E
xpla
in, g
ener
aliz
e, o
r con
nect
id
eas
usin
g su
ppor
ting
evid
ence
(q
uote
, exa
mpl
e, te
xt re
fere
nce)
o
Iden
tify/
mak
e in
fere
nces
abo
ut
expl
icit
or im
plic
it th
emes
o
Des
crib
e ho
w w
ord
choi
ce, p
oint
of
view
, or b
ias
may
affe
ct th
e re
ader
s’
inte
rpre
tatio
n of
a te
xt
o W
rite
mul
ti-pa
ragr
aph
com
posi
tion
for s
peci
fic p
urpo
se, f
ocus
, voi
ce,
tone
, & a
udie
nce
o E
xpla
in h
ow c
once
pts
or id
eas
spec
ifica
lly re
late
to o
ther
con
tent
do
mai
ns o
r con
cept
s o
Dev
elop
gen
eral
izat
ions
of t
he
resu
lts o
btai
ned
or s
trate
gies
us
ed a
nd a
pply
them
to n
ew
prob
lem
situ
atio
ns
App
ly
Car
ry o
ut o
r use
a p
roce
dure
in
a gi
ven
situ
atio
n; c
arry
out
(a
pply
to a
fam
iliar
task
), or
use
(a
pply
) to
an u
nfam
iliar
task
o U
se la
ngua
ge s
truct
ure
(pre
/suf
fix) o
r wor
d re
latio
nshi
ps
(syn
onym
/ant
onym
) to
dete
rmin
e m
eani
ng o
f wor
ds
o A
pply
rule
s or
reso
urce
s to
edi
t sp
ellin
g, g
ram
mar
, pun
ctua
tion,
co
nven
tions
, wor
d us
e o
App
ly b
asic
form
ats
for
docu
men
ting
sour
ces
o U
se c
onte
xt to
iden
tify
the
mea
ning
of
wor
ds/p
hras
es
o O
btai
n an
d in
terp
ret i
nfor
mat
ion
usin
g te
xt fe
atur
es
o D
evel
op a
text
that
may
be
limite
d to
on
e pa
ragr
aph
o A
pply
sim
ple
orga
niza
tiona
l st
ruct
ures
(par
agra
ph, s
ente
nce
type
s) in
writ
ing
o A
pply
a c
once
pt in
a n
ew c
onte
xt
o R
evis
e fin
al d
raft
for m
eani
ng o
r pr
ogre
ssio
n of
idea
s o
App
ly in
tern
al c
onsi
sten
cy o
f tex
t or
gani
zatio
n an
d st
ruct
ure
to
com
posi
ng a
full
com
posi
tion
o A
pply
wor
d ch
oice
, poi
nt o
f vie
w,
styl
e to
impa
ct re
ader
s’ /v
iew
ers’
in
terp
reta
tion
of a
text
o Ill
ustra
te h
ow m
ultip
le th
emes
(h
isto
rical
, geo
grap
hic,
soc
ial)
may
be
inte
rrel
ated
o
Sel
ect o
r dev
ise
an a
ppro
ach
amon
g m
any
alte
rnat
ives
to
rese
arch
a n
ovel
pro
blem
Ana
lyze
B
reak
into
con
stitu
ent p
arts
, de
term
ine
how
par
ts re
late
, di
ffere
ntia
te b
etw
een
rele
vant
-irr
elev
ant,
dist
ingu
ish,
focu
s,
sele
ct, o
rgan
ize,
out
line,
find
co
here
nce,
dec
onst
ruct
(e.g
., fo
r bi
as o
r poi
nt o
f vie
w)
o Id
entif
y w
heth
er s
peci
fic
info
rmat
ion
is c
onta
ined
in
grap
hic
repr
esen
tatio
ns (e
.g.,
map
, cha
rt, ta
ble,
gra
ph, T
-cha
rt,
diag
ram
) or t
ext f
eatu
res
(e.g
., he
adin
gs, s
ubhe
adin
gs, c
aptio
ns)
o D
ecid
e w
hich
text
stru
ctur
e is
ap
prop
riate
to a
udie
nce
and
purp
ose
o C
ateg
oriz
e/co
mpa
re li
tera
ry
elem
ents
, ter
ms,
fact
s/de
tails
, eve
nts
o Id
entif
y us
e of
lite
rary
dev
ices
o
Ana
lyze
form
at, o
rgan
izat
ion,
&
inte
rnal
text
stru
ctur
e (s
igna
l wor
ds,
trans
ition
s, s
eman
tic c
ues)
of
diffe
rent
text
s o
Dis
tingu
ish:
rele
vant
-irre
leva
nt
info
rmat
ion;
fact
/opi
nion
o
Iden
tify
char
acte
ristic
text
feat
ures
; di
stin
guis
h be
twee
n te
xts,
gen
res
o A
naly
ze in
form
atio
n w
ithin
dat
a se
ts
or te
xts
o A
naly
ze in
terr
elat
ions
hips
am
ong
conc
epts
, iss
ues,
pro
blem
s o
Ana
lyze
or i
nter
pret
aut
hor’s
cra
ft (li
tera
ry d
evic
es, v
iew
poin
t, or
po
tent
ial
bias
) to
crea
te o
r crit
ique
a
text
o
Use
reas
onin
g, p
lann
ing,
and
ev
iden
ce to
sup
port
infe
renc
es
o A
naly
ze m
ultip
le s
ourc
es o
f ev
iden
ce, o
r mul
tiple
wor
ks b
y th
e sa
me
auth
or, o
r acr
oss
genr
es, t
ime
perio
ds, t
hem
es
o A
naly
ze c
ompl
ex/a
bstra
ct
them
es, p
ersp
ectiv
es, c
once
pts
o G
athe
r, an
alyz
e, a
nd o
rgan
ize
mul
tiple
info
rmat
ion
sour
ces
o A
naly
ze d
isco
urse
sty
les
Eval
uate
M
ake
judg
men
ts b
ased
on
crite
ria, c
heck
, det
ect
inco
nsis
tenc
ies
or fa
llaci
es,
judg
e, c
ritiq
ue
o C
ite e
vide
nce
and
deve
lop
a lo
gica
l ar
gum
ent f
or c
onje
ctur
es
o D
escr
ibe,
com
pare
, and
con
trast
so
lutio
n m
etho
ds
o Ve
rify
reas
onab
lene
ss o
f res
ults
o
Just
ify o
r crit
ique
con
clus
ions
dra
wn
o E
valu
ate
rele
vanc
y, a
ccur
acy,
&
com
plet
enes
s of
info
rmat
ion
from
m
ultip
le s
ourc
es
o A
pply
und
erst
andi
ng in
a n
ovel
w
ay, p
rovi
de a
rgum
ent o
r ju
stifi
catio
n fo
r the
app
licat
ion
Cre
ate
Reo
rgan
ize
elem
ents
into
new
pa
ttern
s/st
ruct
ures
, gen
erat
e,
hypo
thes
ize,
des
ign,
pla
n,
prod
uce
Bra
inst
orm
idea
s, c
once
pts,
pr
oble
ms,
or p
ersp
ectiv
es re
late
d to
a
topi
c or
con
cept
o G
ener
ate
conj
ectu
res
or h
ypot
hese
s ba
sed
on o
bser
vatio
ns o
r prio
r kn
owle
dge
and
expe
rienc
e
o S
ynth
esiz
e in
form
atio
n w
ithin
one
so
urce
or t
ext
o D
evel
op a
com
plex
mod
el fo
r a
give
n si
tuat
ion
o D
evel
op a
n al
tern
ativ
e so
lutio
n
o S
ynth
esiz
e in
form
atio
n ac
ross
m
ultip
le s
ourc
es o
r tex
ts
o A
rticu
late
a n
ew v
oice
, alte
rnat
e th
eme,
new
kno
wle
dge
or
pers
pect
ive
Hes
s’ C
ogni
tive
Rig
or M
atrix
& C
urric
ular
Exa
mpl
es: A
pply
ing
Web
b’s
Dep
th-o
f-Kno
wle
dge
Leve
ls to
Blo
om’s
Cog
nitiv
e P
roce
ss D
imen
sion
s – M-Sci
© 2
009
Kar
in H
ess p
erm
issi
on to
repr
oduc
e is
giv
en w
hen
auth
orsh
ip is
fully
cite
d k
hess
@nc
iea.
org
Rev
ised
Blo
om’s
Ta
xono
my
Web
b’s
DO
K L
evel
1
Rec
all &
Rep
rodu
ctio
n W
ebb’
s D
OK
Lev
el 2
Sk
ills
& C
once
pts
Web
b’s
DO
K L
evel
3
Stra
tegi
c Th
inki
ng/ R
easo
ning
W
ebb’
s D
OK
Lev
el 4
Ex
tend
ed T
hink
ing
Rem
embe
r R
etrie
ve k
now
ledg
e fro
m
long
-term
mem
ory,
re
cogn
ize,
reca
ll, lo
cate
, id
entif
y
o R
ecal
l, ob
serv
e, &
reco
gniz
e fa
cts,
prin
cipl
es, p
rope
rties
o
Rec
all/
iden
tify
conv
ersi
ons
amon
g re
pres
enta
tions
or
num
bers
(e.g
., cu
stom
ary
and
met
ric m
easu
res)
Und
erst
and
Con
stru
ct m
eani
ng, c
larif
y,
para
phra
se, r
epre
sent
, tra
nsla
te, i
llust
rate
, giv
e ex
ampl
es, c
lass
ify,
cate
goriz
e, s
umm
ariz
e,
gene
raliz
e, in
fer a
logi
cal
conc
lusi
on (s
uch
as fr
om
exam
ples
giv
en),
pred
ict,
com
pare
/con
trast
, mat
ch li
ke
idea
s, e
xpla
in, c
onst
ruct
m
odel
s
o E
valu
ate
an e
xpre
ssio
n o
Loca
te p
oint
s on
a g
rid o
r nu
mbe
r on
num
ber l
ine
o S
olve
a o
ne-s
tep
prob
lem
o
Rep
rese
nt m
ath
rela
tions
hips
in
wor
ds, p
ictu
res,
or s
ymbo
ls
o R
ead,
writ
e, c
ompa
re d
ecim
als
in s
cien
tific
not
atio
n
o Sp
ecify
and
exp
lain
rela
tions
hips
(e
.g.,
non
-exa
mpl
es/e
xam
ples
; ca
use-
effe
ct)
o M
ake
and
reco
rd o
bser
vatio
ns
o E
xpla
in s
teps
follo
wed
o
Sum
mar
ize
resu
lts o
r con
cept
s o
Mak
e ba
sic
infe
renc
es o
r log
ical
pr
edic
tions
from
dat
a/ob
serv
atio
ns
o U
se m
odel
s /d
iagr
ams
to re
pres
ent
or e
xpla
in m
athe
mat
ical
con
cept
s o
Mak
e an
d ex
plai
n es
timat
es
o U
se c
once
pts
to s
olve
non
-rou
tine
prob
lem
s o
Exp
lain
, gen
eral
ize,
or c
onne
ct id
eas
usin
g su
ppor
ting
evid
ence
o
Mak
e an
d ju
stify
con
ject
ures
o
Exp
lain
thin
king
whe
n m
ore
than
one
re
spon
se is
pos
sibl
e o
Exp
lain
phe
nom
ena
in te
rms
of
conc
epts
o R
elat
e m
athe
mat
ical
or s
cien
tific
co
ncep
ts to
oth
er c
onte
nt a
reas
, ot
her d
omai
ns,
or o
ther
co
ncep
ts
o D
evel
op g
ener
aliz
atio
ns o
f the
re
sults
obt
aine
d an
d th
e st
rate
gies
use
d (fr
om
inve
stig
atio
n or
read
ings
) and
ap
ply
them
to n
ew p
robl
em
situ
atio
ns
App
ly
Car
ry o
ut o
r use
a p
roce
dure
in
a g
iven
situ
atio
n; c
arry
out
(a
pply
to a
fam
iliar
task
), or
us
e (a
pply
) to
an u
nfam
iliar
ta
sk
o Fo
llow
sim
ple
proc
edur
es
(rec
ipe-
type
dire
ctio
ns)
o C
alcu
late
, mea
sure
, app
ly a
rule
(e
.g.,
roun
ding
) o
App
ly a
lgor
ithm
or f
orm
ula
(e.g
., ar
ea, p
erim
eter
) o
Sol
ve li
near
equ
atio
ns
o M
ake
conv
ersi
ons
amon
g re
pres
enta
tions
or n
umbe
rs, o
r w
ithin
and
bet
wee
n cu
stom
ary
and
met
ric m
easu
res
o S
elec
t a p
roce
dure
acc
ordi
ng to
cr
iteria
and
per
form
it
o S
olve
rout
ine
prob
lem
app
lyin
g m
ultip
le c
once
pts
or d
ecis
ion
poin
ts
o R
etrie
ve in
form
atio
n fro
m a
tabl
e,
grap
h, o
r fig
ure
and
use
it so
lve
a pr
oble
m re
quiri
ng m
ultip
le s
teps
o
Tran
slat
e be
twee
n ta
bles
, gra
phs,
w
ords
, and
sym
bolic
not
atio
ns (e
.g.,
grap
h da
ta fr
om a
tabl
e)
o C
onst
ruct
mod
els
give
n cr
iteria
o D
esig
n in
vest
igat
ion
for a
spe
cific
pu
rpos
e or
rese
arch
que
stio
n o
Con
duct
a d
esig
ned
inve
stig
atio
n o
Use
con
cept
s to
sol
ve n
on-r
outin
e pr
oble
ms
o U
se &
sho
w re
ason
ing,
pla
nnin
g,
and
evid
ence
o
Tran
slat
e be
twee
n pr
oble
m &
sy
mbo
lic n
otat
ion
whe
n no
t a d
irect
tra
nsla
tion
o S
elec
t or d
evis
e ap
proa
ch
amon
g m
any
alte
rnat
ives
to
solv
e a
prob
lem
o
Con
duct
a p
roje
ct th
at s
peci
fies
a pr
oble
m, i
dent
ifies
sol
utio
n pa
ths,
sol
ves
the
prob
lem
, and
re
ports
resu
lts
Ana
lyze
B
reak
into
con
stitu
ent p
arts
, de
term
ine
how
par
ts re
late
, di
ffere
ntia
te b
etw
een
rele
vant
-irre
leva
nt,
dist
ingu
ish,
focu
s, s
elec
t, or
gani
ze, o
utlin
e, fi
nd
cohe
renc
e, d
econ
stru
ct
o R
etrie
ve in
form
atio
n fro
m a
tabl
e or
gra
ph to
ans
wer
a q
uest
ion
o Id
entif
y w
heth
er s
peci
fic
info
rmat
ion
is c
onta
ined
in
grap
hic
repr
esen
tatio
ns (e
.g.,
tabl
e, g
raph
, T-c
hart,
dia
gram
) o
Iden
tify
a pa
ttern
/tren
d
o C
ateg
oriz
e, c
lass
ify m
ater
ials
, dat
a,
figur
es b
ased
on
char
acte
ristic
s o
Org
aniz
e or
ord
er d
ata
o C
ompa
re/ c
ontra
st fi
gure
s or
dat
a o
Sel
ect a
ppro
pria
te g
raph
and
or
gani
ze &
dis
play
dat
a o
Inte
rpre
t dat
a fro
m a
sim
ple
grap
h o
Ext
end
a pa
ttern
o C
ompa
re in
form
atio
n w
ithin
or
acro
ss d
ata
sets
or t
exts
o
Ana
lyze
and
dra
w c
oncl
usio
ns fr
om
data
, citi
ng e
vide
nce
o G
ener
aliz
e a
patte
rn
o In
terp
ret d
ata
from
com
plex
gra
ph
o A
naly
ze s
imila
ritie
s/di
ffere
nces
be
twee
n pr
oced
ures
or s
olut
ions
o A
naly
ze m
ultip
le s
ourc
es o
f ev
iden
ce
o an
alyz
e co
mpl
ex/a
bstra
ct
them
es
o G
athe
r, an
alyz
e, a
nd e
valu
ate
info
rmat
ion
Eval
uate
M
ake
judg
men
ts b
ased
on
crite
ria, c
heck
, det
ect
inco
nsis
tenc
ies
or fa
llaci
es,
judg
e, c
ritiq
ue
o
Cite
evi
denc
e an
d de
velo
p a
logi
cal
argu
men
t for
con
cept
s or
sol
utio
ns
o D
escr
ibe,
com
pare
, and
con
trast
so
lutio
n m
etho
ds
o Ve
rify
reas
onab
lene
ss o
f res
ults
o G
athe
r, an
alyz
e, &
eva
luat
e in
form
atio
n to
dra
w c
oncl
usio
ns
o A
pply
und
erst
andi
ng in
a n
ovel
w
ay, p
rovi
de a
rgum
ent o
r ju
stifi
catio
n fo
r the
app
licat
ion
Cre
ate
Reo
rgan
ize
elem
ents
into
ne
w p
atte
rns/
stru
ctur
es,
gene
rate
, hyp
othe
size
, de
sign
, pla
n, c
onst
ruct
, pr
oduc
e
o B
rain
stor
m id
eas,
con
cept
s, o
r pe
rspe
ctiv
es re
late
d to
a to
pic
o G
ener
ate
conj
ectu
res
or h
ypot
hese
s ba
sed
on o
bser
vatio
ns o
r prio
r kn
owle
dge
and
expe
rienc
e
o S
ynth
esiz
e in
form
atio
n w
ithin
one
da
ta s
et, s
ourc
e, o
r tex
t o
Form
ulat
e an
orig
inal
pro
blem
giv
en
a si
tuat
ion
o D
evel
op a
sci
entif
ic/m
athe
mat
ical
m
odel
for a
com
plex
situ
atio
n
o S
ynth
esiz
e in
form
atio
n ac
ross
m
ultip
le s
ourc
es o
r tex
ts
o D
esig
n a
mat
hem
atic
al m
odel
to
info
rm a
nd s
olve
a p
ract
ical
or
abs
tract
situ
atio
n
DEPTH OF KNOWLEDGE (DOK) NOTE PAGE
DOK Level 1 DOK Level 2 Recall and Reproduction
Skills and Concepts/Basic Reasoning
DOK Level 3 DOK Level 4 Strategic Thinking and Complex
Reasoning
Extended Thinking
Karen Hess Points to Remember:
• Student instruction should address all DOK levels on a daily/weekly basis
• Planned formative assessment strategies and tools should focus on differing DOK levels
• Assessing only at the highest DOK level will miss opportunities to know how students are progressing in their learning
DOK Question Stems
DOK 1 • Can you recall______? • When did ____ happen? • Who was ____? • How can you recognize____? • What is____? • How can you find the meaning of____? • Can you recall____? • Can you select____? • How would you write___? • What might you include on a list
about___? • Who discovered___? • What is the formula for___? • Can you identify___? • How would you describe___?
DOK 2 • Can you explain how ____ affected ____? • How would you apply what you learned
to develop ____? • How would you compare ____?
Contrast_____? • How would you classify____? • How are____alike? Different? • How would you classify the type of____? • What can you say about____? • How would you summarize____? • How would you summarize___? • What steps are needed to edit___? • When would you use an outline to ___? • How would you estimate___? • How could you organize___? • What would you use to classify___? • What do you notice about___?
DOK 3 • How is ____ related to ____? • What conclusions can you draw _____? • How would you adapt____to create a
different____? • How would you test____? • Can you predict the outcome if____? • What is the best answer? Why? • What conclusion can be drawn from
these three texts? • What is your interpretation of this text?
Support your rationale. • How would you describe the sequence
of____? • What facts would you select to
support____? • Can you elaborate on the reason____? • What would happen if___? • Can you formulate a theory for___? • How would you test___? • Can you elaborate on the reason___?
DOK 4 • Write a thesis, drawing conclusions from
multiple sources. • Design and conduct an experiment.
Gather information to develop alternative explanations for the results of an experiment.
• Write a research paper on a topic. • Apply information from one text to
another text to develop a persuasive argument.
• What information can you gather to support your idea about___?
• DOK 4 would most likely be the writing of a research paper or applying information from one text to another text to develop a persuasive argument.
• DOK 4 requires time for extended thinking.
From Depth of Knowledge – Descriptors, Examples and Question Stems for Increasing Depth of Knowledge in the Classroom Developed by
Dr. Norman Webb and Flip Chart developed by Myra Collins
K-1
2 M
ath
Pra
ctic
e S
tand
ard
s O
VER
ARC
HIN
G H
ABI
TS O
F M
IND
REA
SON
ING
&
EXPL
AIN
ING
M
OD
ELIN
G &
U
SIN
G T
OO
LS
SEEI
NG
STR
UC
TURE
&
GEN
ERA
LIZI
NG
1. M
ake
se
nse
of p
rob
lem
s a
nd p
ers
eve
re in
so
lvin
g th
em
.
6. A
ttend
to p
rec
isio
n.
2. R
ea
son
ab
stra
ctly
and
q
uant
itativ
ely
.
3. C
ons
truc
t via
ble
a
rgum
ent
s a
nd
crit
ique
the
re
aso
ning
of
oth
ers
.
4. M
od
el w
ith
ma
the
ma
tics.
5. U
se a
pp
rop
riate
to
ols
str
ate
gic
ally
.
7. L
oo
k fo
r and
m
ake
use
of
stru
ctu
re.
8. L
oo
k fo
r and
e
xpre
ss re
gul
arit
y in
rep
ea
ted
re
aso
ning
.
Mat
h P
ract
ice
3
Mod
el u
se o
f di
scus
sion
ste
ms
Con
stru
ct
argu
men
ts u
sing
dr
awin
gs, d
iagr
ams,
et
c.
Ask
s cl
arify
ing
ques
tions
Teac
her
Act
ions
S
tude
nt
Act
ions
C
onst
ruct
Arg
umen
ts
Stu
dent
A
ctio
ns
Cri
tique
Rea
soni
ng
Que
stio
n &
pro
mpt
for
just
ifica
tions
: Why
is
that
true
? E
xpla
in
your
thin
king
.
Reh
ears
e ar
gum
ents
List
en a
ctiv
ely
and
rest
ate
Agr
ee &
dis
agre
e po
litel
y
• St
ep
1-
As
a g
rad
e le
vel,
an
aly
ze t
he
DO
K le
vels
of t
ask
s a
nd
/or P
erf
orm
an
ce
Ta
sks
in y
ou
r Tre
asu
res
or M
y M
ath
te
ac
hin
g
ma
teria
ls .
• St
ep
2-
Wh
ich
ta
sks
wo
uld
yo
u u
se, a
nd
w
hy?
• St
ep
3-
Ho
w c
an
ta
sks
be
mo
difi
ed
to
m
ee
t o
ur i
nst
ruc
tion
al n
ee
ds?
De
term
ine
Ac
ce
pta
ble
Ta
sks