DOCUMENT RESUME ED 394 826 SE 058 296 AUTHOR Hill, Peggy TITLE K-4 Mathematics: Manitoba Curriculum Framework of Outcomes and Grade 3 Standards. INSTITUTION Manitoba Dept. of Education and Training, Winnipeg. REPORT NO ISBN-0-7711-1325-0 PUB DATE 95 NOTE 233p.; Includes 20-page insert entitled "Changes to K-4 Mathematics: Goals/Learning Outcomes". AVAILABLE FROM Manitoba Education and Training, School Programs Division, 1970 Ness Avenue, Winnipeg, Manitoba R33 0Y9. PUB TYPE Guides Classroom Use Teaching Guides (For Teacher) (052) EDRS PRICE MFOI/PC10 Plus Postage. DESCRIPTORS *Educational Objectives; Elementary Education; *Elementary School Mathematics; Foreign Countries; Kindergarten; Models; Primary Education; *Standards; *Student Evaluation IDENTIFIERS Manitoba ABSTRACT This document identifies student learning outcomes for kindergarten to grade 4 mathematics and standards of performance for students who are completing grade 3. The document is organized into three parts: overview, student learning outcomes, and standards of student performance. The overview describes the beliefs, goals, and conceptual structure of mathematics instruction and provides the context for the use of student learning outcomes and standards of student performance. The student learning outcomes section provides concise descriptions of the knowledge and skills that K-4 students are expected to learn in mathematics. Outcomes are expressed as general outcomes and specific outcomes. The final section, standards for student performance, provides descriptions of three levels of student performance in relation to general and specific mathematicii outcomes for grade 3. It also contains student samples that illustrate the three different levels of performance for several assessment activities chosen to represent outcomes in each strand of mathematics. (MKR) *********************************************************************** Reproductions supplied by EDRS are the best that can be made from the original document. ***********************************************************************
Transcript
DOCUMENT RESUME
ED 394 826 SE 058 296
AUTHOR Hill, PeggyTITLE K-4 Mathematics: Manitoba Curriculum Framework of
Outcomes and Grade 3 Standards.INSTITUTION Manitoba Dept. of Education and Training,
for kindergarten to grade 4 mathematics and standards of performancefor students who are completing grade 3. The document is organizedinto three parts: overview, student learning outcomes, and standardsof student performance. The overview describes the beliefs, goals,and conceptual structure of mathematics instruction and provides thecontext for the use of student learning outcomes and standards ofstudent performance. The student learning outcomes section providesconcise descriptions of the knowledge and skills that K-4 studentsare expected to learn in mathematics. Outcomes are expressed asgeneral outcomes and specific outcomes. The final section, standardsfor student performance, provides descriptions of three levels ofstudent performance in relation to general and specific mathematiciioutcomes for grade 3. It also contains student samples thatillustrate the three different levels of performance for severalassessment activities chosen to represent outcomes in each strand ofmathematics. (MKR)
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SPE
CIF
ICT
he s
tude
ntPR
-I.
dem
onst
rate
s a
read
ines
s fo
r pa
ttern
ing
PR-I
I.us
es p
atte
rns
to d
escr
ibe
the
wor
ld
uses
pat
tern
s to
det
erm
ine
rela
tions
hips
PR-1
11.
uses
pat
tern
s to
sol
ve p
robl
ems
Iden
tify
and
crea
te p
atte
rns
aris
ing
from
daily
exp
erie
nces
,
sort
s ob
ject
s, u
sing
a s
ingl
e, s
elf-
dete
rmin
ed a
ttrib
ute
(PR
-1.0
.1)
reco
gniz
es, r
epro
duce
s, e
xten
ds, a
ndcr
eate
s pa
ttern
s us
ing
actio
ns a
ndm
anip
ulat
ives
, and
ora
lly d
escr
ibes
them
(PR
-II.
0.1)
*
Iden
tify,
cre
ate,
and
com
pare
pat
tern
sar
isin
g fr
om d
aily
exp
erie
nces
in th
ecl
assr
oom
.
sort
s ob
ject
s, u
sing
a s
ingl
e gi
ven
attr
ibut
e, o
r a
sing
le s
elf-
dete
rmin
ed a
ttrib
ute
(PR
-I.1
.1)
iden
tifie
s, n
ames
, rep
rodu
ces,
exte
nds,
and
cre
ates
pat
tern
s, u
sing
actio
ns, m
anip
ulat
ives
, dia
gram
s,an
d sp
oken
term
s(P
R-I
1.1.
1)
*
begi
ns to
rec
ogni
ze p
atte
rns
in th
een
viro
nmen
t(P
R-I
11.1
.1)
22
23
45
Iden
tify,
cre
ate,
des
crib
e, a
nd tr
ansl
ate
Inve
stig
ate,
est
ablis
h, a
ndIn
vest
igat
e, e
stab
lish,
and
Con
stru
ct, e
xten
d, a
nd s
umm
ariz
e
num
eric
al a
nd n
on-n
umer
ical
pat
tern
sco
mm
unic
ate
rule
s fo
r nu
mer
ical
and
com
mun
icat
e ru
les
for,
and
patte
rns,
incl
udin
g th
ose
foun
d in
aris
ing
from
dai
ly e
xper
ienc
es in
the
non-
num
eric
al p
atte
rns,
incl
udin
gpr
edic
tions
fro
m, n
umer
ical
and
natu
re, u
sing
rul
es, c
hart
s, m
enta
l
scho
ol a
nd o
n th
e pl
aygr
ound
.th
ose
foun
d in
the
hom
e, a
nd u
se th
ese
rule
s to
mak
e pr
edic
tions
.no
n-nu
mer
ical
pat
tern
s, in
clud
ing
thos
e fo
und
in th
e co
mm
unity
.m
athe
mat
ics
and
calc
ulat
ors.
sort
s ob
ject
s an
d sh
apes
, usi
ng o
neor
two
attr
ibut
es, a
nd id
entif
ies
attr
ibut
es a
nd r
ules
in p
re-s
orte
dse
ts(P
R-I
.2.1
)
sort
s, c
oncr
etel
y an
d pi
ctor
ially
,us
ing
two
or m
ore
attr
ibut
es(P
R-I
.3.1
)
ika
iden
tifie
s, c
reat
es, e
xten
ds, d
escr
ibes
uses
obj
ects
and
con
cret
e m
odel
s...
A__
_ co
nstr
ucts
and
exp
ands
pat
tern
sin
and
com
pare
s bo
th n
umer
ical
and
non-
num
eric
al p
atte
rns
(PR
-I1.
2.1)
to e
xpla
in th
e ru
le f
or a
pat
tern
,su
ch a
s th
ose
foun
d on
add
ition
and
mul
tiplic
atio
n ch
arts (P
R-I
I.3.
1)
2 an
d 3
dim
ensi
ons
(con
cret
ely
and
pict
oria
lly),
and
des
crib
esho
w a
pat
tern
gro
ws,
usi
ngev
eryd
ay la
ngua
ge in
spo
ken
and
wri
tten
form
(PR
-II.
5.1)
*id
entif
ies
and
expl
ains
mat
hem
atic
al p
atte
rns
and
rela
tions
hips
usi
ng
deve
lops
cha
rts
to r
ecor
d an
dre
veal
pat
tern
s, a
nd p
redi
cts
and
just
ifie
s pa
ttern
ext
ensi
ons
*ob
ject
s/m
odel
s(P
R-1
1.5.
2)
char
ts/g
rids
Ven
n/C
arro
ll/tr
ee d
iagr
ams
grap
hste
chno
logy
(PR
-I1.
4.2)
tran
slat
es p
atte
rns
from
one
mod
e to
anot
her
incl
udin
g co
ncre
te,
pict
oria
l, ch
arte
d, s
poke
n, w
ritte
n,an
d th
ose
patte
rns
gene
rate
d us
ing
tech
nolo
gy(P
R-1
11.2
.1)
mak
es p
redi
ctio
ns b
ased
on
addi
tion
and
mul
tiplic
atio
npa
ttern
s(P
R-I
11.3
.1)
mak
es a
nd ju
stif
ies
pred
ictio
ns,
usin
g nu
mer
ical
and
non
-nu
mer
ical
pat
tern
s(P
R-I
11.4
.1)
gene
rate
s an
d ex
tend
s nu
mbe
rpa
ttern
s fr
om a
pro
blem
-sol
ving
cont
ext
(PR
-111
.5.1
)
23
0 I)
Patte
rns
and
Rel
atio
ns
63
STU
DE
NT
LE
AR
NIN
GO
UT
CO
ME
SK
(0)
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GE
MIA
LSt
uden
ts w
ill
SPE
CIF
ICT
he s
tude
ntSP
-I.
deve
lops
a p
lan
to a
ddre
ss a
que
stio
n/pr
oble
min
volv
ing
or r
equi
ring
dat
a
com
pose
s qu
estio
ns a
nd c
ateg
orie
s
sele
cts
data
sou
rce(
s)
pred
icts
res
ults
of
the
data
col
lect
ion
proc
ess
SP-I
I.co
llect
s da
ta, a
nd e
valu
ates
the
colle
ctio
n pr
oces
s
impl
emen
ts d
ata
colle
ctio
n ni
etho
d(s)
eval
uate
s da
ta c
olle
ctio
n pr
oces
s
Col
lect
and
org
aniz
e, w
ith a
ssis
tanc
e,da
ta b
ased
on
rust
-han
d in
form
atio
n,
*ch
oose
s, w
ith a
ssis
tanc
e, f
irst
-ban
dso
urce
s fo
r ob
tain
ing
info
rmat
ion
(SP-
I.0.
2)
colle
cts,
with
ass
ista
nce,
fir
st-h
and
info
rmat
ion
(SP-
I1.0
.1)
Col
lect
, org
aniz
e, a
nd d
escr
ibe,
with
guid
ance
, dat
a ba
sed
on f
irst
-han
din
form
atio
n.
*ch
oose
s, w
ith g
uida
nce,
fir
st-h
and
sour
ces
for
obta
inin
g in
form
atio
n(S
P-I.
1.2)
colle
cts
with
gui
danc
e, f
irst
-han
din
form
atio
n by
obse
rvat
ion/
coun
ting
cond
uctin
g su
rvey
sm
easu
ring
perf
orm
ing
sim
ple
expe
rim
ents
(SP-
11.1
.1)
6424
65
23
45
Col
lect
, dis
play
, and
des
crib
e da
ta,
inde
pend
ently
, bas
ed o
n fu
st-h
and
Col
lect
fir
st a
nd s
econ
d-ha
ndin
form
atio
n, d
ispl
ay th
e re
sults
inC
olle
ct f
irst
and
sec
ond-
hand
dat
a,as
sess
and
val
idat
e th
e co
llect
ion
Dev
elop
and
impl
emen
t a p
lan
for
the
colle
ctio
n, d
ispl
ay, a
nd in
terp
reta
tion
info
rmat
ion.
mor
e th
an o
ne w
ay, a
nd in
terp
ret t
heda
ta to
mak
e pr
edic
tions
.pr
oces
s, a
nd g
raph
the
data
.of
dat
a to
ans
wer
a q
uest
ion.
form
ulat
es, i
ndep
ende
ntly
, the
ques
tions
and
cat
egor
ies
for
data
colle
ctio
n(S
P-I.
2.1)
01)
iden
tifie
s a
ques
tion
to g
ener
ate
appr
opri
ate
data
(SP-
I.5.
1)
choo
ses,
inde
pend
ently
, fir
st-h
and
choo
ses
from
fir
st a
nd s
econ
d-se
lect
s a
sam
ple
or p
opul
atio
n, a
nddi
stin
guis
hes
betw
een
a to
tal
sour
ces
of in
form
atio
n (S
P-I.
2.2)
hand
sou
rces
of
info
rmat
ion
orga
nize
s th
e co
llect
ion
of d
ata
popu
latio
n an
d a
sam
ple
of th
at
(SP-
I.3.
2)(S
P-I.
4.2)
popu
latio
n(S
P-I.
5.2)
**
*-
pred
icts
res
ults
(SP-
I.5.
3)
colle
cts,
inde
pend
ently
, fir
st-h
and
colle
cts
data
, usi
ng m
easu
ring
Aus
es a
var
iety
of
met
hods
to
info
rmat
ion,
cho
osin
g an
devi
ces
and
prin
t/tec
hnol
ogy
colle
ct a
nd r
ecor
d da
ta
appr
opri
ate
reco
rdin
g m
etho
d su
chas
tally
mar
ks to
rec
ord
data
(SP-
I1.2
.1)
*
reso
urce
s(S
P-II
.3.1
)
*di
scus
ses
the
proc
ess
by w
hich
the
data
was
col
lect
ed(S
P-II
-4-2
)
(SP4
L5.
1)
disc
usse
s th
e re
ason
able
ness
of
data
and
res
ults
(SP4
I.5h
2)
25
Stat
istic
s an
d Pr
obab
ility
6"
STU
DE
NT
LE
AR
NIN
GO
UT
CO
ME
SK
(0)
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SPE
CIF
IC c
ont'd
SP-I
ll,an
alyz
es a
nd d
ispl
ays
data
anal
yzes
, man
ipul
ates
, and
ope
rate
s on
dat
a
plot
s an
d gr
aphs
dat
a
SP-1
V.
com
mun
icat
es a
nd in
terp
rets
dat
a
disc
usse
s da
ta a
nd p
oses
que
stio
ns
draw
s co
nclu
sion
s an
d m
akes
pre
dict
ions
base
d on
dat
a
cons
truc
ts c
oncr
ete-
obje
ct g
raph
s,w
ith a
ssis
tanc
e, u
sing
1:1
corr
espo
nden
ce(S
P-I1
1.0.
2)
com
pare
s da
ta in
2 c
ateg
orie
s,us
ing
such
wor
ds a
s m
ore,
less
, the
sam
e(S
P-1V
.0.1
)
*
.
*
cons
truc
ts c
oncr
ete-
obje
ct g
raph
san
d pi
ctog
raph
s, w
ith g
uida
nce,
usin
g 1:
1 co
rres
pond
ence (SP-
I11.
1.2)
com
pare
s da
ta, u
sing
app
ropr
iate
lang
uage
, inc
ludi
ng q
uant
itativ
ete
rms
such
as
how
man
y m
ore,
and
pose
s or
al q
uest
ions
inre
latio
n to
the
data
gat
here
d(S
P-IV
1.1)
*
6S26
60
23
45
orga
nize
s da
ta, i
ndep
ende
ntly
,us
ing
such
gra
phic
org
aniz
ers
asus
es r
ank
orde
ring
to o
rgan
ize
data
, and
obt
ains
new
info
rmat
ion
man
ipul
ates
the
data
to c
reat
ein
terv
als
for
both
tabl
es a
ndcr
eate
s cl
assi
fica
tions
and
ran
ges
for
goup
ing
data
(SP-
111.
5.1)
diag
ram
s, c
hart
s, a
nd li
sts
(SP-
I11.
2.1)
by p
erfo
rmin
g ar
ithm
etic
oper
atio
ns o
n th
e da
ta(S
P-I1
1.3.
1)
grap
hs(S
P-I1
1.4.
1)
cons
truc
ts a
nd la
bels
,in
depe
nden
tly, c
oncr
ete-
obje
ctgr
aphs
, pic
togr
aphs
, and
bar
disp
lays
dat
a, u
sing
mor
e th
an o
new
ay to
dis
play
the
sam
e da
ta(S
P-II
I.3.
2)
cons
truc
ts a
bar
gra
ph a
nd a
pict
ogra
ph, u
sing
man
y to
one
corr
espo
nden
ce, a
nd ju
stif
ies
the
disp
lays
dat
a by
han
d or
by
com
pute
r in
a v
arie
ty o
f w
ays,
incl
udin
g
grap
hs(S
P-I1
1.2.
2)ch
oice
of
inte
rval
s an
dco
rres
pond
ence
use
d (S
P-I1
1.4.
2)fr
eque
ncy
diag
ram
slin
e pl
ots
brok
en-l
ine
grap
hs(S
P-I1
1.12
)
disc
usse
s da
ta, a
nd g
ener
ates
new
ques
tions
fro
m d
ispl
ayed
dat
a(S
P-11
.2.1
)
OD
*-
eval
uate
s th
e gr
aphi
c pr
esen
tatio
nof
dat
a to
ens
ure
clea
rre
pres
enta
tion
of th
e re
sults
(SP-
IV.5
.1)
draw
s an
d co
mm
unic
ates
mak
es p
redi
ctio
ns a
nd in
fere
nces
mak
es in
fere
nces
to g
ener
ate
a
appr
opri
ate
conc
lusi
ons
whe
n so
lvin
g si
mila
r pr
oble
ms
./Ig
conc
lusi
on a
bout
the
data
(SP-
IV.2
.2)
(SP-
1V3.
2)(S
P-IV
.5.2
)
7 0
27
Stat
istic
s an
d Pr
obab
ility
1
STU
DE
NT
LE
AR
NIN
GO
UT
CO
ME
SK
(0)
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GE
NE
RA
LSt
uden
ts w
ill
SPE
aFic
The
stu
dent
SP-
Vde
mon
stra
tes
an u
nder
stan
ding
of,
and
use
s th
e
conc
ept o
f, u
ncer
tain
ty
pred
icts
and
com
mun
icat
es c
hanc
e/pr
obab
ility
cond
ucts
sim
ple
prob
abili
ty e
xper
imen
t to
expl
ain
chan
ce/p
roba
bilit
y
repr
esen
ts a
nd c
omm
unic
ates
theo
retic
al
prob
abili
ty
*
Des
crib
e th
e co
ncep
t of
chan
ce a
ndch
ance
eve
nts,
usi
ng o
rdin
ary
lang
uage
.
pred
icts
the
chan
ce o
f an
eve
ntha
ppen
ing,
usi
ng th
e te
rms
neve
r,so
met
imes
, alw
ays
(SP-
V1.
1)
*
28
23
45
Use
sim
ple
expe
rim
ents
, des
igne
d by
othe
rs, t
o ill
ustr
ate
chan
ce.
Use
sim
ple
prob
abili
ty e
xper
imen
ts,
desi
gned
by
othe
rs, t
o ex
plai
nou
tcom
es.
Des
ign
and
use
sim
ple
prob
abili
tyex
peri
nhm
ts to
exp
lain
out
com
es.
Pred
ict o
utco
mes
, con
duct
expe
rim
ents
, and
com
mun
icat
e th
epr
obab
ility
of
sing
le e
vent
s.
desc
ribe
s th
e lik
elih
ood
of a
nou
tcom
e, u
sing
term
s su
ch a
sde
scri
bes
the
likel
ihoo
d of
an
outc
ome,
usi
ng te
rms
such
as
mor
eid
entif
ies
an o
utco
me
as p
ossi
ble,
impo
ssib
le, c
erta
in, u
ncer
tain
, and
desc
ribe
s ev
ents
, usi
ng th
evo
cabu
lary
of
prob
abili
ty:
likel
y, u
nlik
ely,
exp
ect,
prob
ably
likel
y, u
nlik
ely,
equ
al c
hanc
eco
mpa
res
outc
omes
as
equa
llybe
st/w
orst
cha
nce;
(SP-
V2.
1)(S
P-V
3.1)
likel
y, m
ore
likel
y, le
ss li
kely
(SP-
V4.
1)pr
obab
le/im
prob
able
; alw
ays/
mor
elik
ely/
equa
lly li
kely
/less
like
ly/
neve
r(S
P-V
5.1)
mak
es a
pre
dict
ion
base
d on
asi
mpl
e pr
obab
ility
exp
erim
ent
cond
ucts
a p
roba
bilit
y ex
peri
men
t,ch
oose
s an
app
ropr
iate
rec
ordi
ngde
sign
s an
d co
nduc
ts e
xper
imen
tsto
ans
wer
one
's o
wn
ques
tions
cond
ucts
pro
babi
lity
expe
rim
ents
,ex
plai
ns th
e re
sults
usi
ng th
e(S
P-V
2.2)
met
hod,
and
dra
ws
conc
lusi
ons
from
the
resu
lts(S
P-V
.3.2
)(S
P4.4
.2)
*
lang
uage
of
prob
abili
ty, a
ndde
mon
stra
tes
that
res
ults
are
not
infl
uenc
ed b
y ag
e, e
xper
ienc
e, o
rsk
ill o
f pa
rtic
ipan
ts(S
P-V
5.2)
lists
all
poss
ible
out
com
es o
f an
expe
rim
ent i
nvol
ving
a s
ingl
eev
ent
(SP-
V5.
3)
29
Stat
istic
s an
d Pr
obab
ility
75
1th
1ST
UD
EN
T L
EA
RN
ING
OU
TC
OM
ES
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GE
NE
RA
LSt
uden
ts w
ill
SPE
CIF
ICT
he s
tude
ntSS
-I.
dem
onst
rate
s an
und
erst
andi
ng o
f, a
nd u
ses
linea
r m
easu
rem
ent
mea
sure
s an
d co
mm
unic
ates
leng
ths
visu
aliz
es a
nd c
onst
ruct
s le
ngth
s
disc
over
s an
d us
es (
inte
r-)
rela
tions
hips
ss-1
1.de
mon
stra
tes
an u
nder
stan
ding
of,
and
use
sar
ea m
easu
rem
ent
mea
sure
s an
d co
mm
unic
ates
are
a
visu
aliz
es a
nd c
onst
ruct
s ar
ea
Dem
onst
rate
aw
aren
ess
ofm
easu
rem
ent.
clas
sifi
es a
nd d
escr
ibes
line
arat
trib
utes
, (lo
ng, s
hort
) an
dar
rang
es o
bjec
ts in
ord
er o
f si
ze,
by le
ngth
or
heig
ht(S
S-I.
0.1)
cove
rs a
sur
face
with
a v
arie
ty o
fob
ject
s(S
S-I1
.0.1
)
Est
imat
e, m
easu
re, a
nd c
ompa
re,
usin
g w
hole
num
bers
and
non
-st
anda
rd u
nits
of
mea
sure
.
sele
cts
an a
ppro
pria
te n
on-
stan
dard
uni
t, an
d es
timat
es,
mea
sure
s, r
ecor
ds, c
ompa
res,
and
orde
rs o
bjec
ts b
y le
ngth
, hei
ght
and
dist
ance
aro
und
(SS-
I.I.
1)
*
estim
ates
the
num
ber
of u
nifo
rmob
ject
s or
sha
pes,
or
the
num
ber
of ir
regu
lar
shap
es th
at w
ill c
over
a gi
ve a
rea,
and
ver
ifie
s by
cove
ring
and
cou
ntin
g(S
-11.
1.1)
*
30
23
45
Est
imat
e, m
easu
re, a
nd c
ompa
re,
usin
g st
anda
rd u
nits
for
leng
th, a
ndpr
imar
ily n
on-s
tand
ard
units
for
oth
erm
easu
res.
sele
cts
the
mos
t app
ropr
iate
stan
dard
uni
t (cm
, dm
, m),
and
estim
ates
, mea
sure
s, r
ecor
ds,
com
pare
s, a
nd o
rder
s ob
ject
s by
leng
th, h
eigh
t, an
d di
stan
cear
ound
(SS-
I.2.
1)
cons
truc
ts it
ems
of s
peci
fic
leng
ths,
incl
udin
g cm
, dm
, and
m(S
S-I.
2.2)
*
estim
ates
, mea
sure
s, r
ecor
ds, a
ndco
mpa
res
the
area
of
shap
es, u
sing
non-
stan
dard
uni
ts(S
S-II
.2.1
)
conh
truc
ts a
sha
pe, g
iven
asp
ecif
ic a
rea
in n
on-s
tand
ard
units
(SS-
I1.2
.2)
Est
imat
e, m
easu
re, a
nd c
ompa
re u
sing
who
le n
umbe
rs a
nd p
rim
arily
sta
ndar
dun
its o
f m
easu
re.
sele
cts
the
mos
t app
ropr
iate
stan
dard
uni
t, in
clud
ing
kin,
and
estim
ates
, mea
sure
s, r
ecor
ds,
com
pare
s, a
nd o
rder
s ob
ject
s by
leng
th, h
eigh
t, an
d pe
rim
eter
(SS-
I.3.
1)
Ade
scri
bes
the
rela
tions
hip
amon
gcm
, dm
, and
m(S
S-I.
3.3)
sele
cts
an a
ppro
pria
te n
on-
stan
dard
uni
t, an
d es
timat
esm
easu
res,
rec
ords
, com
pare
s, a
ndor
ders
sha
pes
by a
rea
(SS-
II.3
.1)
cons
truc
ts a
var
iety
of
shap
esgi
ven
a sp
ecif
ic a
rea
in n
on-
stan
dard
uni
ts(S
S-11
.3.2
)
Est
imat
e, m
easu
re, a
nd c
ompa
reus
ing
deci
mal
num
bers
and
sta
ndar
dun
its o
f m
easu
re.
sele
cts
the
mos
t app
ropr
iate
stan
dard
uni
t, in
clud
ing
mm
, and
estim
ates
, mea
sure
s, r
ecor
ds,
com
pare
s, a
nd o
rder
s ob
ject
s by
leng
th, h
eigh
t, pe
rim
eter
, and
circ
umfe
renc
e(S
S-I.
4.1)
_ co
nstr
ucts
item
s of
spe
cifi
cle
ngth
s, in
clud
ing
mm
(SS
-I.4
.2)
desc
ribe
s th
e re
latio
nshi
ps a
mon
gm
m, c
m, d
m, m
, and
lcm
, and
rela
tes
the
size
of
a un
it to
the
num
ber
of u
nits
use
d to
mea
sure
leng
th(S
S-L
4.3)
sele
cts
the
mos
t app
ropr
iate
stan
dard
uni
t, an
d es
timat
es,
mea
sure
s, r
ecor
ds, c
ompa
res,
and
orde
rs2sh
apes
by
area
, usi
ng c
m2
and
m(S
S-11
.4.1
)
cons
truc
ts a
num
ber
of s
hape
sgi
ven
a sp
ecif
ic a
rea
(cm
2)(S
S11.
4.2)
Use
mea
sure
men
t con
cept
s,ap
prop
riat
e to
ols,
and
the
resu
lts o
fm
easu
rem
ents
to s
olve
pro
blem
s in
ever
yday
con
text
s.
eval
uate
s th
e ap
prop
riat
enes
s of
uni
tsan
d m
easu
ring
tool
s in
pra
ctic
alco
ntex
ts, e
stim
ates
and
mea
sure
s th
epe
rim
eter
of
irre
gula
r sh
apes
, and
reco
gniz
es a
nd e
xpla
ins
the
mea
ning
of le
ngth
, wid
th, h
eigh
t, de
pth,
thic
knes
s, p
erim
eter
, and
circ
umfe
renc
e(S
S.I.
5.1)
Aes
timat
es a
nd m
easu
res
the
effe
ctof
cha
ngin
g on
e or
mor
edi
men
sion
s of
a r
ecta
ngle
on
itspe
rim
eter
, usi
ng m
anip
ulat
ives
and
diag
ram
s(S
S-1.
5.3)
estim
ates
and
mea
sure
s th
e ar
eaof
irre
gula
r sh
apes
by
divi
ding
them
into
par
ts(S
S-11
.5.1
)
A
3179
Shap
e an
d Sp
ace
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DE
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1 1
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SPE
cwic
SS-
II c
ont'd
disc
over
s an
d us
es (
inte
r-)
rela
tions
hips
..
..
SS-I
II.
dem
onst
rate
s an
und
erst
andi
ng o
f, a
nd u
ses
volu
me/
capa
city
mea
sure
men
t
mea
sure
s an
d co
mm
unic
ates
vol
ume/
capa
city
visu
aliz
es a
nd c
onst
ruct
s vo
lum
e/ca
paci
ty.
..
disc
over
s an
d us
es (
inte
r-)
rela
tions
hips
..
..
SS-I
V.
dem
onst
rate
s an
und
erst
andi
ng o
f, a
nd u
ses
mas
s/w
eigh
t mea
sure
men
ts
mea
sure
s an
d co
mm
unic
ates
mas
s/w
eigh
t.
.
visu
aliz
es a
nd c
onst
ruct
s m
ass/
wei
ght
disc
over
s an
d us
es (
inte
r-)
rela
tions
hips
_
uses
the
wor
ds f
ull,
empt
y, m
ore,
and
less
to ta
lk a
bout
vol
ume
and
capa
city
(SS-
11/.0
.1)
uses
the
wor
ds h
eavi
er o
r lig
hter
tota
lk a
bout
the
mas
s/w
eigh
t of
two
obje
cts
(SS-
IE0.
1)
A
estim
ates
, mea
sure
s, r
ecor
ds, a
ndco
mpa
res
obje
cts
by m
ass/
wei
ght
usin
g no
n-st
anda
rd u
nits (S
S-I1
7.1.
1)
reco
gniz
es ti
rlif
fere
nt o
bjec
tsm
ay h
ave
the
sam
e m
ass (S
S-IV
.1.3
)
32
SO
23
45
estim
ates
, mea
sure
s, r
ecor
ds,
com
pare
s, a
nd o
rder
s co
ntai
ners
,by
cap
acity
/vol
ume
usin
g no
n-st
anda
rd u
nits
(SS-
I11.
2.1)
estim
ates
, mea
sure
s, r
ecor
ds,
com
pare
s, a
nd o
rder
s th
em
ass/
wei
ght o
f ob
ject
s, u
sing
non
-st
anda
rd u
nits
(SS-
IE2.
1)
*re
cogn
izes
that
the
size
and
sha
peof
an
obje
ct d
oes
not n
eces
sari
lyde
term
ine
its m
ass/
wei
ght
(SS-
IE2.
3)
*
sele
cts
an a
ppro
pria
te u
nit,
and
estim
ates
, mea
sure
s, r
ecor
ds,
com
pare
s, a
nd o
rder
s co
ntai
ners
by c
apac
ity, u
sing
non
-sta
ndar
dun
its o
r lit
res
(SS-
I11.
3.1)
*
estim
ates
, mea
sure
s, r
ecor
ds,
com
pare
s, a
nd o
rder
s ob
ject
s by
mas
s/w
eigh
t, us
ing
stan
dard
uni
ts(g
and
kg)
(SS-
IE3.
1)
cons
truc
ts o
bjec
ts to
equ
al a
giv
enm
ass/
wei
ght
(SS-
IE3.
2)
On
rela
tes
the
size
of
a un
it an
d th
enu
mbe
r of
uni
ts n
eede
d to
mea
sure
area
(SS-
11.4
.3)
estim
ates
, mea
sure
s, r
ecor
ds,
com
pare
s, a
nd o
rder
s co
ntai
ners
,by
cap
acity
, usi
ng m
L a
nd L
(SS-
I11.
4.1)
*re
late
s th
e si
ze o
f th
e un
it to
the
num
ber
of u
nits
nee
ded
to m
easu
revo
lum
e ca
paci
ty(S
S-I1
1.4.
3)
solv
es p
robl
ems
invo
lvin
gtn
ass/
wei
ght u
sing
g o
r kg (S
S-IV
.4.1
)
A_
rela
tes
g an
d kg
, and
the
size
of
aun
it to
the
num
ber
of u
nits
use
d to
mea
sure
mas
s(S
S-IE
4.3)
com
pare
s ar
ea to
per
imet
er o
fre
ctan
gles
, and
vic
e ve
rsa,
usi
ngm
anip
ulat
ives
and
dia
gram
s, a
ndde
term
ines
the
effe
ct o
f ch
angi
ngon
e or
mor
e di
men
sion
s of
are
ctan
gle
on it
s ar
ea(S
S-II
.5.3
)
estim
ates
, mea
sure
s, r
ecor
ds, a
ndor
ders
con
tain
ers
by v
olum
e,us
ing
cm3
(SS-
111.
5.1)
- co
nstr
ucts
obj
ects
of
a sp
ecif
icvo
lum
e, e
xpre
ssed
in c
m3
(SS-
I11.
5.2)
rela
tes
cm3
to m
L, u
sing
con
cret
em
ater
ials
(SS-
I11.
5.3)
solv
es p
robl
ems
invo
lvin
g g,
kg,
and
t(S
S-IV
.5.1
)
ita
8233
83
Shap
e an
d Sp
ace
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CIF
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ont'd
SS-
Vde
mon
stra
tes
an u
nder
stan
ding
of,
and
use
s an
gle
mea
sure
men
t
visu
aliz
es a
nd m
easu
res
angl
es
.
SS-V
I.de
mon
stra
tes
an u
nder
stan
ding
of,
and
use
s tim
em
easu
rem
ent
mea
sure
s an
d co
mm
unic
ates
tim
e
sequ
ence
s ev
ents
/tim
e
disc
over
s an
d us
es r
elat
ions
hips
uses
the
term
s lo
ng ti
me
or s
hort
time
to ta
lk a
bout
the
dura
tion
ofev
ents
(SS-
VI.
0.1)
*
estim
ates
and
mea
sure
s th
epa
ssag
e of
tim
e re
late
d to
non
-st
anda
rd u
nits
, and
com
pare
s th
edu
ratio
n of
act
iviti
es (
SS-V
I.1.
1)
desc
ribe
s th
e tim
e of
day
(e.
g.,
mor
ning
), s
eque
nces
eve
nts
with
inon
e da
y an
d ov
er s
ever
al d
ays,
and
nam
es, i
n or
der,
the
days
of
the
wee
k an
d th
e se
ason
s of
the
year
(SS-
VI.
1.2)
1*I
8434
8 5
23
45
sele
cts
the
mos
t app
ropr
iate
stan
dard
uni
t to
mea
sure
a g
iven
time
peri
od, a
nd e
stim
ates
and
mea
sure
s th
e pa
ssag
e of
tim
ere
late
d to
min
utes
and
hou
rs W 2
1)
(SS-
..na
mes
, in
orde
r, th
e m
onth
s of
the
year
, and
rea
ds th
e da
te o
n a
cale
ndar
(SS-
VI.
2.2)
rela
tes
the
num
ber
of d
ays
to a
wee
k, m
onth
s to
a y
ear,
min
utes
toan
hou
r, h
ours
to a
day
(SS-
VI.
2.3)
estim
ates
and
mea
sure
s th
epa
ssag
e of
tim
e, u
sing
sta
ndar
dw
its (
seco
nds,
min
utes
, hou
rs,
days
, wee
ks, m
onth
s, y
ears
), a
ndre
ads
digi
tal c
lock
s an
d w
rite
stim
e to
the
near
est m
inut
e, u
sing
12 h
our
nota
tion
(SS-
VI.
3.1)
read
s an
d w
rite
s th
e da
ys o
f th
ew
eek
and
the
mon
ths
of th
e ye
ar(S
S-V
I.3.
2)
rela
tes
seco
nds
to m
inut
es, d
ays
to
year
s(S
S-V
I.3.
3)
visu
aliz
es a
nd d
escr
ibes
ang
les
ina
vari
ety
of o
rien
tatio
n ac
cord
ing
to w
heth
er th
ey a
re a
rig
ht a
ngle
,si
gnif
ican
tly le
ss th
an a
rig
htan
gle,
or
sign
ific
antly
gre
ater
than
a ri
ght a
ngle
(SS-
V.4
.1)
read
s an
d w
rite
s tim
e us
ing
aman
d pm
, and
rea
ds a
n an
alog
clo
ckto
the
near
est m
inut
e (S
S-V
I.4.
1)
A
rela
tes
year
s to
dec
ades
, dec
ades
toce
ntur
ies,
cen
turi
es to
mill
enni
ums
(SS-
VL
4.3)
*
read
s an
ana
log
cloc
k to
the
near
est m
inut
e, a
nd w
rite
s th
etim
e(S
S-W
.5.1
)
___
read
s an
d w
rite
s SI
not
atio
n fo
rre
cord
ing
date
and
tim
e (SS-
VI.
5.2)
read
s an
d w
rite
s tim
e on
a24
-hou
r cl
ock
(SS-
VI.
5.3)
SG35
87
Shap
e an
d Sp
ace
STU
DE
NT
LE
AR
NIN
GO
UT
CO
ME
SK
(0)
1
ci) W OA cn g:i Z < 14 l:14 4t = C/)
I. CIO
"Fr V r a g. 0 .0 O. a S. 0 I g I
8 g
1 E
4 0
2 A
T 1
1 5 ]
a 6
e 0
0 ...
1 1
ci)
0
«: a 1 E a i X
SPE
CIF
IC c
ont'd
SS-V
I!de
mon
stra
tes
an u
nder
stan
ding
of,
and
use
s m
oney
mea
sure
men
t
reco
gniz
es/c
ount
s m
oney
cons
truc
ts a
mou
nts
of m
oney
disc
over
s an
d us
es r
elat
ions
hips
SS-V
111
dem
onst
rate
s an
und
erst
andi
ng o
f, a
nd u
ses
tem
pera
ture
mea
sure
men
ts
mea
sure
s an
d de
scri
bes
tem
pera
ture
*
exch
ange
s pl
ay m
oney
for
obj
ects
in a
pla
y st
ore
(SS-
VH
.0.2
)
*
uses
wor
ds li
ke h
ot, h
otte
r; c
old,
cold
er; w
arm
, war
mer
, and
coo
l,co
oler
to ta
lk a
bout
tem
pera
ture
(SS-
VI1
1.0.
1)
reco
gniz
es a
nd n
ames
Can
adia
nco
ins
(SS-
VI1
.1.1
)
*st
ates
the
valu
e, in
cen
ts, o
fni
ckel
s an
d cl
inic
s, a
nd c
reat
eseq
uiva
lent
set
s of
coi
ns u
p to
104
:(S
S-V
H.1
.3)
desc
ribe
s an
d co
mpa
res
tem
pera
ture
s, u
sing
the
sens
es(S
S-V
III.
1.1)
8836
89
45
reco
gniz
es a
ll C
anad
ian
coin
s an
dre
cogn
izes
the
valu
e of
bill
s up
toes
timat
es, c
ount
s, a
nd r
ecor
dsA
bills
to $
10, a
nd e
stim
ates
, cou
nts,
and
reco
rds,
usi
ng th
e ce
nt s
ymbo
lon
ly, t
he v
alue
of
colle
ctio
ns o
fco
ins
up to
$1
(SS-
VII
.2.1
)
$100
, and
est
imat
es, c
ount
s, r
eads
,an
d re
cord
s (u
sing
bot
h m
oney
nota
tions
-890
and
$0.
89)
the
valu
e of
col
lect
ions
of
coin
s an
dbi
lls u
p to
$10
(SS-
V11
.3.1
)
colle
ctio
ns o
f co
ins
and
bills
up
to$5
0.
(SS-
VII
.4.1
)
*m
akes
pur
chas
es a
nd c
hang
e up
to$1
0(S
S-V
II.3
.2)
mak
es p
urch
ases
and
cha
nge
up to
$50
(SS-
VH
.4.2
)A
stat
es th
e va
lue,
in c
ents
, of
quar
ters
, a d
olla
r, a
nd b
ills
to $
10,
and
crea
tes
equi
vale
nt s
ets
of c
oins
crea
tes
and
reco
gniz
es th
at a
giv
enva
lue
of m
oney
can
be
repr
esen
ted
in m
any
diff
eren
t way
s
OD
(usi
ng p
enni
es, n
icke
ls, a
nd d
imes
)up
to $
1(S
S-V
II.2
.3)
(SS-
VII
.3.3
)
uses
a th
erm
omet
er to
det
erm
ine
risi
ng a
nd f
allin
g te
mpe
ratu
res
(SS-
VI1
1.2.
1)
estim
ates
, rea
ds, a
nd r
ecor
dste
mpe
ratu
re to
the
near
est
degr
ee C
, and
rel
ates
tem
pera
ture
to e
very
day
situ
atio
ns
A
(SS-
V11
1.3.
4)
37
Ju91
Shap
e an
d Sp
ace
g1
STU
DE
NT
LE
AR
NIN
GO
UT
CO
ME
SK
(0)
1
gi ......
,
W u 4s CA Z g CA
= A 1 as 1 .r:
.o
E0
goA
.2.
IS r
6 g
.4 6 c
11 4
,L
s, 5
i E tJ4) = i
ai ai
i^0 a
Aco
) 0
in. a -c c.
) al A .0 = a 11 41 --,
A 0 0 A
GE
NE
RA
LSt
uden
ts w
ill
SPE
CIF
ICT
he s
tude
ntSS
-1X
.in
vest
igat
es 3
-D o
bjec
ts
iden
tifie
s, c
ompa
res,
and
des
crib
es o
bjec
ts .
..
visu
aliz
es, c
onst
ruct
s, a
nd r
earr
ange
s ob
ject
s
anal
yzes
and
use
s (i
nter
-) r
elat
ions
hips
SS-X
.in
vest
igat
es 2
-D s
hape
s
iden
tifie
s, c
ompa
res,
and
des
crib
es s
hape
s.
. .
Sort
, cla
ssif
y, a
nd b
uild
rea
l-w
orld
obje
cts.
iden
tifie
s, s
orts
, and
cla
ssif
ies
3-D
obje
cts
in th
e en
viro
nmen
t, an
dde
scri
bes,
and
dis
cuss
es o
bjec
ts,
usin
g su
ch w
ords
as
big,
littl
e,ro
und,
like
a b
ox, l
ike
a ca
n(S
S-IX
.0.1
)
build
s 3-
D o
bjec
ts(S
S-IX
.0.2
)
*
Exp
lore
and
cla
ssif
y 3-
D o
bjec
ts a
nd2-
D s
hape
s, a
ccor
ding
to th
eir
prop
ertie
s.
expl
ores
and
des
crib
es 3
-D o
bjec
tsac
cord
ing
to o
ne a
ttrib
ute
(SS-
IX.1
.1)
obse
rves
and
bui
lds
a gi
ven
3-D
obje
ct(S
S-IX
.1.2
)
*
iden
tifie
s, n
ames
, and
des
crib
essp
ecif
ic 2
-13
shap
es a
sci
rcle
str
iang
les
rect
angl
esan
d co
mpa
res,
sor
ts, a
nd c
lass
ifie
s2-
D s
hape
s(S
S-X
././)
9 "
389
9
Nam
e, d
escr
ibe,
and
con
stru
ct a
Des
crib
e, c
lass
ify,
con
stru
ct, a
ndva
riet
y of
3-D
obj
ects
and
2-D
sha
pes.
rela
te 3
-D o
bjec
ts a
nd 2
-D s
hape
s.
iden
tifie
s, n
ames
, cla
ssif
ies,
and
desc
ribe
s 3-
D o
bjec
tscu
bes
sphe
res
cone
scy
linde
rspy
ram
ids
build
s th
e sk
elet
on o
f a
3-D
obj
ect
(SS-
IX.2
.2)
expl
ores
fak
es, v
ertic
es, a
nd e
dges
of 3
-D o
bjec
ts, a
nd d
escr
ibes
how
a sk
elet
on r
elat
es to
a 3
-D o
bjec
t(S
S-IX
.2.3
)
iden
tifie
s an
d co
unts
fac
es,
vert
ices
, and
edg
es o
f 3-
D o
bjec
ts,
and
com
pare
s an
d co
ntra
sts
two
3-D
obj
ects
(SS-
IX.3
.1)
reco
gniz
es c
ongr
uent
(id
entic
al)
3-D
sol
ids
with
rec
tang
ular
fac
es,
and
dem
onst
rate
s th
at a
rect
angu
lar
solid
has
mor
e th
anon
e ne
t(S
S-IX
.3.2
)id
entif
ies
and
nam
es f
aces
of
a3-
D o
bjec
t with
app
ropr
iate
2-D
nam
es, a
nd d
escr
ibes
and
nam
espy
ram
ids
and
pris
ms
by th
e sh
ape
of th
c ba
se(S
S-IX
.3.3
)
Des
crib
e, c
lass
ify,
con
stru
ct, a
ndre
late
3-D
obj
ects
and
2-D
sha
pes,
usin
g m
athe
mat
ical
voc
abul
ary.
com
pare
s an
d co
ntra
sts
pyra
mid
spr
ism
spy
ram
ids
and
pris
ms (S
S-IX
.4.1
)
A*
iden
tifie
s an
d so
rts
spec
ific
quad
rila
tera
ls, i
nclu
ding
squ
ares
,re
ctan
gles
, and
par
alle
logr
ams
(SS-
X.4
.1)
Use
vis
ualiz
atio
n of
3-D
obj
ects
and
2-D
sha
pes
to s
olve
spa
tial p
robl
ems.
build
s, r
epre
sent
s, a
nd d
escr
ibes
geom
etri
c ob
ject
s(S
S-IX
.5.2
)
com
plet
es th
e dr
awin
g of
a 3
-Dob
ject
, on
grid
pap
er, g
iven
the
fron
t fak
e(S
S-IX
.5.3
)
iden
tifie
s an
d cl
assi
fies
quad
rila
tera
ls, i
nclu
ding
trap
ezoi
ds(S
S-X
.5.1
)
39
9
Shap
e an
d Sp
ace
gI
STU
DE
NT
LE
AR
NIN
GO
UT
CO
ME
SK
(0)
1
C2
c4 ;14 ..tt
ti) A Z Cit
Ca A 1 es t .c1. 3' o
0=
A A ..
far
000
C6
gtiz
ps.4 $.
.2
ct ..0
ca41
)
CO
0.)
:8.4
= 4 1 Z 4 E i
'0 a 2
a. co .c cA = A .0 c a i 4.) -, 4 0 C
A A
SPE
CIF
IC S
S-X
con
t'd
visu
aliz
es, c
onst
ruct
s, a
nd r
earr
ange
s sh
apes
anal
yzes
and
use
s (i
nter
-) r
elat
ions
hips
SS-X
/in
vest
igat
es li
nes
and
angl
es
iden
tifie
s, c
ompa
res,
and
des
crib
es li
nes
and
angl
es
and
cons
truc
ts li
nes
and
angl
es
anal
yzes
and
use
s (i
nter
-) r
elat
ions
hips
*
.*v
isua
lizes
4097
23
45
build
s an
d re
arra
nges
a p
atte
rn,
usin
g a
set o
f 2-
13 s
hape
s, a
ndm
atch
es a
nd m
akes
iden
tical
reco
gniz
es c
ongo
ent (
iden
tical
)2-
D s
hape
s(S
S-X
.3.2
)
desi
gns
and
cons
truc
ts n
ets
for
pyra
mid
s an
d pr
ism
s(S
S-X
.4.2
)bu
ilds,
rep
rese
nts,
and
des
crib
essh
apes
, and
cov
ers
a gi
ven
2-D
shap
e w
ith ta
ngra
m p
iece
s
(con
grue
nt)
2-D
sha
pes
(SS-
X.5
.2)
(SS-
X.2
.2)
*re
late
s ne
ts to
3-1
3 ob
ject
s (SS-
X.4
.3)
dete
rmin
es, e
xper
imen
tally
, the
min
imum
info
rmat
ion
need
ed to
draw
a g
iven
2-1
3 sh
ape,
and
iden
tifie
s an
d na
mes
pol
ygon
sac
cord
ing
to th
e nu
mbe
r of
sid
es,
angl
es, a
nd v
ertic
es(S
S-X
.5.3
)
*re
cogn
izes
, fro
m e
very
day
expe
rien
ce, a
nd id
entif
ies
Ola
poin
tlin
ean
gle
para
llel l
ines
inte
rsec
ting
lines
perp
endi
cula
r lin
esve
rtic
al li
nes
hori
zont
al li
nes
(SS-
X1.
4.1)
(see
SS4
.2.2
)01
)de
scri
bes
angl
es in
a v
arie
ty o
for
ient
atio
ns a
kcor
ding
to w
heth
erth
ey a
re a
rig
ht a
ngle
, sig
nifi
cant
lyle
ss th
an a
rig
ht a
ngle
, or
sign
ific
antly
gre
ater
than
a r
ight
angl
e(S
S-X
I.4.
2)
A
*ex
plor
es, c
oncr
etel
y, th
e co
ncep
tsof
per
pend
icul
ar, p
aral
lel,
and
inte
rsec
ting
lines
on
3-13
obj
ects
lk)
*co
nstr
ucts
, ana
lyze
s, a
ndcl
assi
fies
tria
ngle
s ac
cord
ing
toth
e si
de m
easu
res
(SS-
XI.
3.3)
(SS-
XI.
5.3)
9r
41
Shap
e an
d Sp
ace
I Gg
1ST
UD
EN
T L
EA
RN
ING
OU
TC
OM
ES
K (
0)1
cn 4.1
(..) At
Ow
Cn A Z .*t
4.1 a, .tt = ci)
9. *... g s. a 2 ... 4, E C
..) '0 C OS ttir >,
ci c es g 0 t et. ; Z c 4, .0 Z v) g 0 ta g 0 f.
.. 1 L.
GE
NE
RA
LSt
uden
ts w
ill
SPE
CIF
ICT
he s
tude
ntSS
-XI!
.vi
sual
izes
and
use
s sp
atia
l rel
atio
nshi
ps a
ndtr
ansf
orm
atio
ns
loca
tes,
des
crib
es, a
nd u
ses
posi
tion
iden
tifie
s, d
escr
ibes
, and
use
s m
otio
n
anal
yzes
and
use
s (i
nter
-) r
elat
ions
hips
Des
crib
e, o
rally
, the
pos
ition
of
3-D
obje
cts.
desc
ribe
s th
e re
lativ
e po
sitio
n of
3-D
obj
ects
, usi
ng s
uch
wor
ds a
sov
er, u
nder
, bes
ide,
bet
wee
n,in
side
, out
side
(SS-
X11
.0.1
)
*
Des
crib
e, o
rally
, the
rel
ativ
e po
sitio
nof
3-D
obj
ects
and
2-D
sha
pes.
desc
ribe
s th
e re
lativ
e po
sitio
n of
3-D
obj
ects
and
2-D
sha
pes,
usi
ngw
ords
suc
h as
nea
r, f
ar, l
eft,
righ
t(S
S-X
II.1
.1)
- m
atch
es s
ize
and
shap
e of
fig
ures
by s
uper
impo
sing
one
on
top
ofth
e ot
her;
and
des
crib
es r
efle
ctio
nsin
a m
irro
r(S
S-X
II.1
.2)
JOg
42
101
23
45
App
ly p
ositi
onal
lang
uage
, ora
lly a
ndU
se n
umbe
rs a
nd d
irec
tion
wor
ds to
Use
num
bers
and
dir
ectio
n w
ords
toU
se c
oord
inat
es to
des
crib
e th
e
in w
ritin
g, to
com
mun
icat
e m
otio
n.de
scri
be th
e re
lativ
e po
sitio
n of
desc
ribe
the
rela
tive
posi
tion
ofpo
sitio
ns o
f ob
ject
s in
two
obje
cts
in o
ne d
imen
sion
, usi
ngob
ject
s in
two
dim
ensi
ons,
usi
ngdi
men
sion
s an
d de
scri
be m
otio
n in
ever
yday
con
text
s.ev
eryd
ay c
onte
xts.
term
s of
a s
lide,
flip
, or
turn
.
com
mun
icat
es a
nd a
pplie
sco
mm
unic
ates
and
app
lies
term
sco
mm
unic
ates
and
app
lies
term
spl
ots
who
le n
umbe
r or
dere
d pa
irs
posi
tiona
l lan
guag
e in
ora
l,w
ritte
n, o
r nu
mer
ical
for
mof
dir
ectio
n su
ch a
s no
rth
or s
outh
,an
d ea
st o
r w
est,
rela
tes
them
toof
dir
ectio
n su
ch a
s no
rth,
sou
th,
east
, and
wes
t, re
late
s th
em to
in th
e ff
fst q
uadr
ant w
ith in
terv
als
of 1
, 2, 5
, or
10, a
nd id
entif
ies
a
(SS-
XII
.2.1
)m
aps,
and
gra
phs
who
le n
umbe
rm
aps
and
grid
s, a
nd p
lace
s an
poin
t in
the
firs
t qua
dran
t usi
ngpo
ints
on
a ho
rizo
ntal
or
vert
ical
num
ber
line
(SS-
XII
.3.1
)ob
ject
on
a gr
id, u
sing
col
umns
and
row
s(S
S-X
II.4
.1)
orde
red
pair
s(S
S-X
11.5
.1)
crea
tes
sym
met
rica
l 2-D
sha
pes
bytr
aces
a p
ath,
usi
ng o
ral o
r w
ritte
ntr
aces
a p
ath,
usi
ng o
ral o
r w
ritte
nre
cogn
izes
mot
ion
as a
slid
e
fold
ing
and
refl
ectin
gin
stru
ctio
ns(S
S-X
II.3
.2)
inst
ruct
ions
, and
wri
tes
(tra
nsla
tion)
, tur
n (r
otat
ion)
or
(SS-
XII
.2.2
)in
stru
ctio
ns f
or a
giv
en p
ath
(SS-
XII
.4.2
)fl
ip (
refl
ectio
n), c
reat
este
ssel
latio
ns u
sing
reg
ular
poly
gons
, and
cov
ers
a su
rfac
e,us
ing
one
or m
ore
tess
ella
ting
shap
es(S
S-X
II.5
.2)
*cr
eate
s an
d ve
rifi
es s
ymm
etri
cal
2-D
sha
pes
by d
raw
ing
lines
of
sym
met
ry(S
S-X
II.4
.3)
iden
tifie
s pl
anes
of
sym
met
ry b
ycu
tting
3-D
sol
ids,
and
rec
ogni
zes
tess
ella
tions
cre
ated
with
reg
ular
and
irre
gula
r sh
apes
in th
een
viro
nmen
t(S
S-X
II.5
.3)
I 0
)43
103
Shap
e an
d Sp
ace
1g
1ST
UD
EN
T L
EA
RN
ING
OU
TC
OM
ES
K (
0)1
,..Z
....
Cd
44 co Z
4.w
;el
410
,t...
?.-
tu
Gs
-cr
=A
E.r
..S 4
1:3
ata
E6
=0/
C.f
:16.
E °
= N e E i t P
F-1
3 i
4 .4
= =
4.4.
1
..?..
Btin
cn
Is.
t, t., 1 t..) 6. .1 E 2 Z
GE
NE
RA
LSt
uden
ts w
ill
SPE
CIF
ICT
he s
tude
ntN
-1.
dem
onst
rate
s an
d ap
plie
s nu
mbe
r se
nse
for
who
lenu
mbe
rs
unde
rsta
nds
and
uses
cou
ntin
g se
quen
ces
and
estim
atio
n st
rate
gies
read
s an
d w
rite
s nu
mer
als
and
num
ber
wor
ds
reco
gniz
es, b
uild
s, c
ompa
res,
and
ord
ers
sets
Des
crib
e, o
rally
, and
com
pare
quan
titie
s fr
om 0
to 1
0, u
sing
num
ber
wor
ds in
dai
ly e
xpre
ssio
ns.
coun
ts th
e nu
mbe
r of
obj
ects
in a
set (
0-10
)(N
-I.1
).1)
____
exp
lore
s th
e re
pres
enta
tion
ofsi
ngle
dig
it nu
mbe
rs, u
sing
aca
lcul
ator
or
com
pute
r to
rep
rese
ntnu
mer
als
on a
scr
een
(N-I
.0.2
)
build
s, c
ompa
res,
and
ord
ers
two
sets
of
like
obje
cts,
and
des
crib
esre
latio
nshi
ps b
etw
een
them
usi
ngth
e te
rms
mor
e th
an, g
reat
er th
an,
less
than
, the
sam
e as
, equ
al to
(N-1
.0.3
)
Rec
ogni
ze a
nd a
pply
who
le n
umbe
rsfr
om 0
to 1
00, a
nd e
xplo
re h
alve
s in
fam
iliar
set
tings
.
coun
ts o
rally
by
ls, 2
s, 5
5, a
ndlO
s to
100
; and
est
imat
es, t
hen
coun
ts th
e nu
mbe
r of
obj
ects
in a
set (
0-50
), c
ompa
ring
the
estim
ate
with
the
actu
al n
umbe
r (N
-1.1
.1)
read
s an
d w
rite
s nu
mer
als
to 2
0,re
ads
num
ber
wor
ds to
ten,
and
expl
ores
the
repr
esen
tatio
n of
num
eral
s (0
-50)
, usi
ng a
calc
ulat
or o
r co
mpu
ter
(N-1
.1.2
)
reco
gniz
es, b
uild
s, c
ompa
res,
and
orde
rs s
ets
that
con
tain
0 to
50
elem
ents
(N-1
.1.3
)
44
104
105
23
45
Rec
ogni
ze a
nd a
pply
who
le n
umbe
rsD
evel
op a
num
ber
sens
e fo
r w
hole
Dem
onst
rate
a n
umbe
r se
nse
for
Dem
onst
rate
a n
umbe
r se
nse
for
up to
100
0, a
nd e
xplo
re f
ract
ions
num
bers
0 to
100
0, a
nd e
xplo
rew
hole
num
bers
0 to
10
000,
and
who
le n
umbe
rs 0
to 1
00 0
00, a
nd(h
alve
s, th
irds
, and
fou
rths
).fr
actio
ns (
fift
hs a
nd te
nths
).ex
plor
e pr
oper
fra
ctio
ns.
expl
ore
prop
er f
ract
ions
and
dec
imal
s.
coun
ts to
100
0 by
Is,
2s,
5s,
and
coun
ts b
y 2s
, 5s,
10s
, and
100
s to
uses
ski
p co
untin
g (f
orw
ard
and
uses
est
imat
ion
stra
tegi
es f
or10
s, a
nd to
100
by
25s
usin
g10
00, u
sing
ran
dom
sta
rtin
gba
ckw
ard)
to s
uppo
rtde
term
inin
g qu
antit
ies
up to
resp
ectiv
e m
ultip
les
for
star
ting
poin
ts; e
stim
ates
, the
n co
unts
the
poin
ts, c
ount
s by
25s
to 1
000,
usin
g m
ultip
les
of 2
5 as
sta
rtin
gun
ders
tand
ing
of m
ultip
licat
ion
and
divi
sion
; est
imat
es, t
hen
100
000
(N-I
.5.1
)
num
ber
of o
bjec
ts in
a s
et (
0-10
0),
com
pari
ng th
e es
timat
e w
ith th
epo
ints
; ski
p-co
unts
bac
kwar
d by
2s, 5
s, 1
0s, a
nd 1
00s
usin
gco
unts
the
num
ber
of o
bjec
ts in
ase
t (0-
1000
), c
ompa
ring
the
actu
al n
umbe
r; a
nd u
ses
ordi
nal
resp
ectiv
e m
ultip
les
as s
tart
ing
estim
ate
to th
e ac
tual
num
ber;
and
num
bers
to 3
1(N
-I.2
.1)
poin
ts; e
stim
ates
, the
n co
unts
the
num
ber
of o
bjec
ts in
a s
et (
0-us
es o
rdin
al n
umbe
rs to
100
0(N
-I.4
.1)
1000
), c
ompa
ring
the
estim
ate
with
the
actu
al c
ount
; and
use
sor
dina
l num
bers
to 1
00 (
N-1
.3.1
)
read
s an
d w
rite
s nu
mer
als
to 1
00re
ads
and
wri
tes
num
eral
s to
100
0re
ads
and
wri
tes
num
eral
s to
read
s an
d w
rite
s nu
mer
als
and
and
num
ber
wor
ds to
20
and
num
ber
wor
ds to
100
10 0
00 a
nd n
umbe
r w
ords
to 1
000
num
ber
wor
ds to
100
000
(N-I
.2.2
)(N
-I.3
.2)
(N-1
.4.2
)(N
4.5.
2)
reco
gniz
es, b
uild
s, c
ompa
res,
and
orde
rs s
ets
that
con
tain
0 to
100
elem
ents
(N-I
.2.3
)
reco
gniz
es, b
uild
s, c
cmpa
res,
and
orde
rs s
ets
that
con
tain
0 to
100
0el
emen
ts(N
-1.3
.3)
A
106
45
n Ps
)L
I
Num
ber
STU
DE
NT
LE
AR
NIN
GO
UT
CO
ME
SK
(0)
1
Z .....,
Cd
Gz1 02 Z
v,
trl
.?.
. ... .
ji=
13
g::,
..1 =40
g.0
., m a
§ 4
.0 2 0 g
" 3
6 c
jt E *
4*
Ne
Ei g
t=
= 3 3
Z Z 0 0
000.
1
V 1
3a
arn
cfl
B a. i d 1., i 4
SrE
aFic
N-I
con
t'd
repr
esen
ts, e
xpla
ins,
and
use
s pl
ace
valu
eco
ncep
ts
reco
gniz
es, d
escr
ibes
, and
use
s nu
mbe
rch
arac
teri
stic
s
SPE
CIF
ICT
he s
iude
ntN
-II.
dem
onst
rate
s an
d ap
plie
s nu
mbe
r se
nse
for
frac
tions
and
dec
imal
s
repr
esen
ts a
nd d
escr
ibes
fra
ctio
ns a
ndde
cim
als
unde
rsta
nds
and
uses
con
nect
ions
bet
wee
nan
d am
ong
frac
tions
and
dec
imal
s
* *
repr
esen
ts a
nd d
escr
ibes
num
bers
to 5
0 in
a v
arie
ty o
f w
ays (N
-I.1
.4)
*
dem
onst
rate
s, a
nd e
xpla
ins
oral
ly,
an u
nder
stan
ding
of
halv
es a
s pa
rtof
a s
hape
or
solid
(N-I
I.1.
1)
lOs
4610
9
23
45
repr
esen
ts a
nd d
escr
ibes
num
bers
repr
esen
ts a
nd d
escr
ibes
num
bers
repr
esen
ts a
nd d
escr
ibes
num
bers
dem
onst
rate
s, c
oncr
etel
y,
to 1
00 in
a v
arie
ty o
f w
ays;
to 1
000
in a
var
iety
of
way
s;to
10
CO
O in
a v
arie
ty o
f w
ays;
pict
oria
lly, a
nd s
ymbo
lical
ly, a
n
dem
onst
rate
s, c
oncr
etel
y an
dde
mon
stra
tes,
con
cret
ely
and
dem
onst
rate
s co
ncre
tely
,un
ders
tand
ing
of p
lace
val
ue f
rom
pict
oria
lly, p
lace
val
ue c
once
pts
topi
ctor
ially
, pla
ce v
alue
con
cept
s to
pict
oria
lly, a
nd s
ymbo
lical
ly, p
lace
hund
redt
hs, i
nclu
ding
com
pari
ng
give
mea
ning
to n
umbe
rs u
p to
give
mea
ning
to n
umbe
rs u
p to
valu
e co
ncep
ts to
giv
e m
eani
ng to
and
orde
ring
who
le n
umbe
rs
100;
and
rou
nds
num
bers
to th
e10
00; a
nd r
ound
s nu
mbe
rs to
the
num
bers
up
to 1
0 00
0; r
ound
s(N
-I.5
.4)
near
est 1
0(N
-1.2
.4)
near
est 1
00(N
-1.3
.4)
num
bers
to th
e ne
ares
t tho
usan
d;an
d co
mpa
res
and
orde
rs w
hole
num
bers
up
to 1
0 00
0(N
-I.4
.4)
dem
onst
rate
s if
a n
umbe
r fr
omre
cogn
izes
and
exp
lain
s if
aso
rts
num
bers
into
cat
egor
ies
byre
cogn
izes
, mod
els,
and
des
crib
es
1 to
100
is o
dd o
r ev
en (
N-I
.2.5
)nu
mbe
r is
div
isib
le b
y 2,
5, a
nd 1
0(N
-1.3
.5)
one
or m
ore
attr
ibut
es(N
-I.4
.5)
mul
tiple
s, f
acto
rs, c
ompo
site
s,an
d pr
im's
, and
sor
ts n
umbe
rsin
to c
atzg
orie
s by
one
or
mor
eat
trib
utes
(N-I
.5.5
)
illus
trat
es a
nd e
xpla
ins
halv
es,
illus
trat
es a
nd e
xpla
ins
fift
hs a
ndill
ustr
ates
and
exp
lain
s hu
ndre
dths
repr
esen
ts a
nd d
escr
ibes
pro
per
thir
ds, a
nd f
ourt
hs a
s pa
rt o
f a
tent
hs a
s pa
rt o
f a
regi
on o
r se
tas
par
t of
a re
gion
or
set
frac
tions
, and
dec
imal
s to
regi
on o
r se
t(N
-II.
2.1)
(N-1
1.3.
1)(N
-II.
4.1)
hund
redt
hs, c
oncr
etel
y, p
icto
rial
ly,
and
sym
bolic
ally
(N-I
I.5.
1)
*co
nnec
ts p
rope
r fr
actio
ns to
deci
mal
s, (
tent
hs a
nd h
undr
edth
s)us
ing
man
ipul
ativ
es, d
iagr
ams,
and
sym
bols
(N-I
I.4.
2)
repr
esen
ts a
nd d
escr
ibes
equi
vale
nt f
ract
ions
, con
cret
ely,
pict
oria
lly, a
nd s
ymbo
lical
ly(N
-II.
5.2)
47
1 0
liiN
umbe
r
1gi
STU
DE
NT
LE
AR
NIN
GO
UT
CO
ME
SK
(0)
I
is ...... ig 41 go
oi a, c's
0 3
CS
goIC
cyC 0
.42
0 S
IT E
,,,.
cT y
441
.8E
f. 1 ii
0 S
c E
I 2*
= = 7 7
a a
= =
OA
V13
43
a a
CA
CA
2 g 0 U i 2 Z
SPE
CW
ICN
-II
cont
'd
com
pare
s an
d or
ders
fra
ctio
ns a
nd d
ecim
als
..
N-I
II,
dem
onst
rate
s an
d ap
plie
s nu
mbe
r se
nse
for
inte
gers
repr
esen
ts a
nd e
xpla
ins
inte
gers
com
pare
s an
d or
ders
inte
gers
N-I
V.
dem
onst
rate
s an
d ap
plie
s nu
mbe
r se
nse
for
ratio
and
perc
ent
repr
esen
ts a
nd e
xpla
ins
ratio
and
per
cent
..
..
112
48
113
23
45
**
com
pare
s an
d or
ders
pro
per
frac
tions
, and
dec
imal
s to
hund
redt
hs(N
-II.
5.3)
* *
49
1 j
115
Num
ber
iST
UD
EN
T L
EA
RN
ING
OU
TC
OM
ES
K (
0)1
W Z
40 ai..
1 .- 3a
>,
-a
i..2
sic
.a
1A
I*-
--'
u.C
o.9
,...
..
ril
14
A 0
iFi
t,
A e
b.t.
2,
a.
3 c
.1t 1
0..o
IAT
5a
2a
g. i
r. .
..
.....
, = ..
.. 1.D
.
7) 3
f.)
0.
2 ... lg. o 6, 2 E 0 Z
GE
NE
RA
LSt
uden
ts w
ill
SPE
CIF
ICT
he s
tude
ntN
- V
.un
ders
tand
s, p
erfo
rms,
and
ver
ifie
s nu
mbe
rca
lcul
atio
ns
repr
esen
ts, e
xpla
ins,
and
app
lies
addi
tion
and
subt
ract
ion
proc
esse
s
reca
lls f
acts
repr
esen
ts, e
xpla
ins,
and
app
lies
mul
tiplic
atio
nan
d di
visi
on p
roce
sses
reca
lls f
acts
Dem
onst
rate
aw
aren
ess
of a
dditi
onan
d su
btra
ctio
n.
.
repr
esen
ts th
e pr
oces
ses
ofad
ditio
n an
d su
btra
ctio
n th
roug
hro
le p
layi
ng a
nd th
e us
e of
man
ipul
ativ
es(N
-V.0
.1)
App
ly in
form
al m
etho
ds o
f ad
ditio
nan
d su
btra
ctio
n on
who
le n
umbe
rs-
max
imum
sum
of
18.
uses
man
ipul
ativ
es a
nd d
iagr
ams
to d
emon
stra
te a
nd to
des
crib
e th
epr
oces
ses
of a
dditi
onan
dsu
btra
ctio
n of
num
bers
to 1
8(N
-V1.
1)
*
116
5011
7
App
ly a
var
iety
of
addi
tion
and
subt
ract
ion
stra
tegi
es o
n w
hole
num
bers
to 1
00, a
nd u
se th
ese
oper
atio
ns in
sol
ving
giv
en a
ndst
uden
t-cr
eate
d pr
oble
ms.
uses
man
ipul
ativ
es, d
iagr
ams
and
sym
bols
to d
emon
stra
te a
nd to
desc
ribe
mul
tiple
str
ateg
ies
for
dete
rmin
ing
sum
s an
d di
ffer
ence
sof
num
bers
to 1
00, w
ith a
ndw
ithou
t reg
roup
ing
reca
lls a
dditi
on a
nd s
ubtr
actio
nfa
cts
to 1
0(N
-V.2
.1)
App
ly a
n ar
ithm
etic
ope
ratio
n(a
dditi
on, s
ubtr
actio
n, m
ultip
licat
ion,
and
divi
sion
) on
who
le n
umbe
rs, a
ndill
ustr
ate
its u
se in
cre
atin
g an
d
solv
ing
prob
lem
s.
uses
man
ipul
ativ
es, d
iagr
ams,
and
sym
bols
, in
prob
lem
-sol
ving
cont
exts
, to
dem
onst
rate
and
tode
scri
be m
ultip
le s
trat
egie
s fo
rde
term
inin
g su
ms
and
diff
eren
ces
to 1
000
reca
lls a
dditi
on a
nd s
ubtr
actio
nfa
cts
to 1
8(N
-V3.
1)
uses
man
ipul
ativ
es, d
iagr
ams,
and
sym
bols
to d
emon
stra
te a
ndde
scri
be th
e pr
oces
ses
ofm
ultip
licat
ion
and
divi
sion
inpr
oble
m-s
olvi
ng c
onte
xts
(max
imum
pro
duct
s an
ddi
vide
nds
to 5
0)
reca
lls m
ultip
licat
ion
and
divi
sion
s fa
kts
to 4
9 (7
x 7
on
am
ultip
licat
ion
grid
)(N
-V3.
2)
App
ly a
rith
met
ic o
pera
tions
on
who
lenu
mbe
rs, i
llust
rate
thei
r us
e in
crea
ting
and
solv
ing
prob
lem
s, a
ndde
mon
stra
te u
nder
stan
ding
of
addi
tion
and
subt
ract
ion
of d
ecim
als
(ten
ths
and
hund
redt
hs).
uses
man
ipul
ativ
es, d
iagr
ams,
and
sym
bols
, in
prob
lem
-sol
ving
cont
exts
, to
dem
onst
rate
and
tode
scri
be m
ultip
le s
trat
egie
s fo
rde
term
inin
g su
ms
and
diff
eren
ces
to 1
0 00
0, a
nd u
ses
man
ipul
ativ
esan
d di
agra
ms
to a
dd a
nd s
ubtr
act
deci
mal
s (t
enth
s an
d hu
ndre
dths
)(N
-E.4
.1)
uses
man
ipul
ativ
es, d
iagr
ams,
and
sym
bols
to d
emon
stra
te a
ndde
scri
be th
e pr
oces
ses
ofm
ultip
licat
ion
and
divi
sion
inpr
oble
m-s
olvi
ng c
onte
xts
(3 d
igit
by 1
dig
it fo
r m
ultip
licat
ion,
and
2di
git b
y 1
digi
t for
div
isio
n)
reca
lls m
ultip
licat
ion
and
divi
sion
fakt
s to
81
(9 x
9 o
n a
mul
tiplic
atio
n gr
id)
(N-1
1.4.
2)
App
ly a
rith
met
ic o
pera
tions
on
who
lenu
mbe
rs a
nd d
ecim
als,
and
illu
stra
teth
eir
use
in c
reat
ing
and
solv
ing
prob
lem
s.
uses
man
ipul
ativ
es, d
iagr
ams,
and
sym
bols
, in
prob
lem
-sol
ving
cont
exts
, to
dem
onst
rate
and
tode
scri
be th
e ad
ditio
n an
dsu
btra
ctio
n of
who
le n
umbe
rs a
ndof
dec
imal
s to
hun
dred
ths (N
-V.5
.1)
uses
est
imat
ion,
men
tal
calc
ulat
ion,
com
puta
tion,
and
veri
fica
tion
for
who
le n
umbe
r
prod
ucts
(3
digi
t by
2 di
git)
and
quot
ient
s (3
dig
it by
1 d
igit)
, and
uses
man
ipul
ativ
es, d
iagr
ams,
and
sym
bols
to m
ultip
ly a
nd d
ivid
ede
cim
als
to h
undr
edth
s us
ing
sing
le-d
igit,
who
le n
umbe
rm
ultip
liers
and
div
isor
s in
giv
enpr
oble
m-s
olvi
ng c
onte
xts (N
-V.5
.2)
51
l s1
9N
umbe
r
NU
MB
ER
(N)
SIR
AN
)
Num
ber
Ope
ratio
ns:
Stud
ents
will
dem
onst
rate
an
unde
rsta
ndin
g
ofand
prof
icie
ncy
with
calc
ulat
ions
.St
uden
ts
will
deci
de
whi
ch
arith
met
ic
oper
atio
n(s)
can
beusedtosolv
e
prob
lem
s
and
then
solv
e
the
prob
lem
s.
SUB
-
SIR
AN
)
4'tin
giF-
1
aCBgic
V,eD
0..0-
cp=
.
,...00
==0 F5Fi
. c .,n
00
.000
g......
5czi.
cn9
tri
='a
..
..
..
..
..
(....
)ot*
cA1Z0
...
..
.-
..
..
..
'.
..
..
..
..
..
..
..
..
..
..
..
..
..
Z.
ez
..
..
..*
..
..
.
..
..
..
..
..
..
..
..
..
..
..
..
1....
.
.
23
45
Use
an
appr
opri
ate
calc
ulat
ion
Use
and
just
ify
an a
ppro
pria
teU
se a
nd ju
stif
y an
app
ropr
iate
Use
and
just
ify
an a
ppro
pria
test
rate
gy o
r te
chno
logy
to s
olve
calc
ulat
ion
stra
tegy
or
tech
nolo
gy to
calc
ulat
ion
stra
tegy
or
tech
nolo
gy to
calc
ulat
ion
stra
tegy
or
tech
nolo
gy to
prob
lem
s.so
lve
prob
lem
s.so
lve
prob
lem
s.so
lve
prob
lem
s.
uses
a v
arie
ty o
f es
timat
ion
and
just
ifie
s th
e m
etho
d us
ed to
just
ifie
s th
e m
etho
d us
ed to
uses
mul
tiple
ope
ratio
ns; j
ustif
ies
men
tal m
athe
mat
ics
stra
tegi
es f
orso
lvin
g ad
ditio
n an
d su
btra
ctio
nca
lcul
ate
sum
s an
d di
ffer
ence
sch
oosi
ng f
rom
est
imat
ion
calc
ulat
e pr
oduc
ts a
nd q
uotie
nts,
choo
sing
fro
m e
stim
atio
nm
etho
ds u
sed
to s
olve
mul
ti-st
eppr
oble
ms;
and
acc
epts
that
oth
erpr
oble
ms,
and
use
s m
anip
ulat
ives
stra
tegi
es, m
enta
l mat
hem
atic
sst
rate
gies
, men
tal m
athe
mat
ics
met
hods
may
lx 'u
lna
lly v
alid
and
diag
ram
s to
dem
onst
rate
the
proc
esse
s of
mul
tiplic
atio
n an
dst
rate
gies
, man
ipul
ativ
es,
algo
rith
ms,
and
cal
cula
tors
; use
sst
rate
gies
, mar
ripu
lativ
es,
algo
rith
ms,
and
cal
cula
tor,
and
(N-V
I.5.
1)
divi
sion
(N-V
I.2.
1)es
timat
ion,
inve
rse
oper
atio
ns o
rca
lcul
ator
s to
ver
ify
solu
tions
for
prob
lem
s in
volv
ing
addi
tion
and
subt
ract
ion;
and
use
s es
timat
ion
and
men
tal m
athe
mat
ics
stra
tegi
esto
cal
cula
te p
rodu
cts
and
quot
ient
s
uses
est
imat
ion,
inve
rse
oper
atio
ns o
r ca
lcul
ator
s to
ver
ify
solu
tions
for
pro
blem
s in
volv
ing
mul
tiplic
atio
n an
d di
visi
on (N-V
I.4.
I)
(N-V
I.3.
1)
53
123
Num
ber
IV. G
RA
DE
3 S
TA
ND
AR
DS
PU
RP
OS
E
Gra
de 3
Sta
ndar
ds h
as b
een
deve
lope
d by
Man
itoba
Edu
catio
n an
d T
rain
ing
with
the
assi
stan
ce o
f G
rade
3te
ache
rs r
epre
sent
ing
thre
e sc
hool
pro
gram
are
as: E
nglis
hPr
ogra
m, F
ranç
ais
Prog
ram
, and
Fre
nch
Imm
ersi
on P
rogr
am.
Info
rmat
ion
has
been
dra
wn
from
the
Wes
tern
Fra
mew
ork,
exis
ting
Man
itoba
K-4
Mat
hem
atic
s C
urri
cula
, and
Ont
ario
'sC
omm
on C
urri
culu
m, P
rovi
ncia
l Sta
ndar
ds M
athe
mat
ics,
Gra
des
K-9
. Gra
de 3
Sta
ndar
ds r
epre
sent
s th
e be
stkn
owle
dge
and
expe
rien
ce a
vaila
ble
at th
e tim
e of
dra
ftin
g,an
d is
like
ly to
evo
lve
and
impr
ove
as ti
me
pass
es a
nd m
ore
educ
ator
s w
ork
with
and
rea
ct to
it.
Thi
s po
rtio
n of
the
K-4
Mat
hem
atic
sCur
ricu
lum
Fram
ewor
k of
Out
com
es a
nd G
rade
3 S
tand
ards
doc
umen
tw
ill b
e us
ed in
sev
eral
dif
fere
nt w
ays.
(Se
e fi
gure
2 o
n pa
ge55
). T
he G
rade
3 S
tand
ards
will
pri
mar
ily b
e us
ed b
yte
ache
rs f
rom
Kin
derg
arte
n to
Gra
de 3
as
a do
cum
ent w
hich
desc
ribe
s an
d ill
ustr
ates
wha
t stu
dent
s sh
ould
kno
w a
nd b
eab
le to
do
at th
e en
d of
the
firs
t fou
r ye
ars
in a
n E
arly
Yea
rsm
athe
mat
ics
prog
ram
. It i
s ex
pect
ed th
at a
ll te
ache
rs f
rom
Kin
derg
arte
n to
Gra
de 3
, in
each
sch
ool,
will
wor
k to
geth
er to
deve
lop
a m
athe
mat
ics
prog
ram
that
pro
vide
s th
e ex
peri
ence
san
d in
stru
ctio
n ne
cess
ary
for
thei
r st
uden
ts to
per
form
with
inth
e ra
nge
of s
tand
ards
des
crib
ed f
or s
tude
nts
who
are
com
plet
ing
Gra
de 3
. The
doc
umen
t als
o pr
ovid
es in
form
atio
non
a v
arie
ty o
f as
sess
men
t pra
ctis
es th
at c
an b
eus
ed to
prov
ide
data
that
will
ass
ist t
each
ers
in m
akin
g pr
ogra
mm
ing
deci
sion
s.
Gra
de 3
teac
hers
sho
uld
find
the
info
rmat
ion
in G
rade
3St
anda
rds
to b
e of
par
ticul
ar a
ssis
tanc
e in
ass
essi
ng a
ndre
port
ing
prog
ress
. The
y m
ay u
se th
e C
hara
cter
istic
s of
1 2
454
Stud
ent P
erfo
rman
ce, t
oget
her
with
.Per
form
ance
Ind
icat
ors
and
Illu
stra
tive
Exa
mpl
es to
ass
ess
and
eval
uate
stu
dent
wor
k,re
port
on
stud
ent a
chie
vem
ent,
and
to p
lan,
with
the
stud
ent
and
pare
nts,
for
on-
goin
g st
uden
t lea
rnin
g.
Man
itoba
Edu
catio
n an
d T
rain
ingA
sses
smen
t and
Eva
luat
ion
Uni
twill
use
the
Gra
de 3
Sta
ndar
ds a
s th
e ba
sis
for
dete
rmin
ing
stud
ent l
evel
s of
mat
hem
atic
al p
erfo
rman
ceth
roug
hout
the
prov
ince
. It p
rovi
des
the
Ass
essm
ent a
ndE
valu
atio
n U
nit w
ith in
form
atio
n to
gui
de b
oth
the
deve
lopm
ent o
f a
prov
inci
al s
tand
ards
test
for
all
stud
ents
com
plet
ing
thei
r G
rade
3 p
rogr
am, a
nd to
gui
de th
ein
terp
reta
tion
of th
e te
st r
esul
ts. (
Not
e: E
xcep
tiona
l stu
dent
sw
ho h
ave
been
pro
vide
d w
ith I
ndiv
idua
l Edu
catio
nal P
lans
I.E
.P.s
may
be
invo
lved
in S
tand
ards
test
ing
at th
edi
scre
tion
of e
ach
child
's I
.E.P
. tea
m.)
Man
itoba
Edu
catio
nan
d T
rain
ing
will
re-
exam
ine
the
Gra
de 3
Sta
ndar
dses
tabl
ishe
d fo
r th
e en
d of
Gra
de 3
on
an o
n-go
ing
basi
s, a
nd it
is p
ossi
ble
that
som
e ch
ange
s m
ay o
ccur
as
the
Ass
essm
ent
and
Eva
luat
ion
Uni
t ana
lyze
s th
e re
sults
of
stan
dard
s te
stin
g.T
his
on-g
oing
ana
lysi
s al
so m
ay r
esul
t in
curr
icul
ar c
hang
es,
as M
anito
ba E
duca
tion
and
Tra
inin
g se
eks
toim
prov
em
athe
mat
ics
prog
ram
min
g an
d st
uden
t per
form
ance
.
The
Gra
de 3
Sta
ndar
ds a
lso
shou
ld h
elp
teac
hers
at o
ther
grad
e le
vels
, sch
ool a
dmin
istr
ator
s, p
aren
ts, a
nd o
ther
inte
rest
ed c
itize
ns to
dev
elop
a c
lear
and
con
sist
ent p
ictu
re o
fex
pect
ed le
vels
of
stud
ent m
athe
mat
ical
per
form
ance
upo
nco
mpl
etio
n of
Gra
de 3
.
The
re a
re tw
o pa
rts
to th
is p
ortio
n of
the
mat
hem
atic
sfr
amew
ork
docu
men
t. T
he f
irst
par
t dea
ls w
ith a
sses
smen
t as
part
of
the
stru
ctur
e of
mat
hem
atic
s, a
nd in
clud
es d
escr
iptio
nsof
a v
arie
ty o
f as
sess
men
t str
ateg
ies.
The
sec
ond
part
desc
ribe
s th
e st
anda
rds
of s
tude
nt p
erfo
rman
ce f
or s
tude
nts
who
are
com
plet
ing
Gra
de 3
. 19t-
,wt)
figu
re 2
STU
DE
NT
LE
AR
NIN
G
OU
TC
OM
ES
Out
com
es id
entif
y th
ekn
owle
dge
and
skill
sst
uden
ts a
re e
xpec
ted
tole
arn.
The
Wes
tern
Fram
ewor
k an
dK
-4 M
athe
mat
ics:
Man
itoba
Cur
ricu
lum
Fram
ewor
k of
Out
com
es a
nd G
rade
3St
anda
rds
defi
ne th
ekn
owle
dge,
ski
lls, a
ndat
titud
es th
at s
tude
nts
are
expe
cted
tode
velo
p by
the
end
ofG
rade
3.
Usi
ng M
anito
ba O
utco
mes
and
Sta
ndar
ds in
Ass
essi
ng, R
epor
ting,
and
Im
prov
ing
Stud
ent A
chie
vem
entG
rade
3
MA
NIT
OB
A S
TA
ND
AR
DS
OF
STU
DE
NT
PER
FOR
MA
NC
E
Gra
de 3
Sta
ndar
ds s
tate
the
expe
cted
ran
ge o
fst
uden
t per
form
ance
for
each
gen
eral
lear
ning
outc
ome.
Gra
de 3
Sta
ndar
dspr
ovid
e cl
ear
stat
emen
ts d
escr
ibin
gch
arac
teri
stic
s an
din
dica
tors
for
3 le
vels
of s
tude
nt p
erfo
rman
cein
mat
hem
atic
s fo
rst
uden
ts w
ho a
reco
mpl
etin
g G
rade
3.
A
ASS
ESS
ING
ST
UD
EN
T
PER
FOR
MA
NC
E
le*
Stud
ent p
erfo
rman
ce is
asse
ssed
in r
elat
ion
toes
taba
shed
Gra
de 3
Stan
dard
s of
perf
orm
ance
for
eac
hge
nera
l lea
rnin
gou
tcom
e.
Tea
cher
s us
eG
rade
3 S
tand
ards
as th
e ba
sis
for
asse
ssin
g an
dev
alua
ting
stud
ent
perf
orm
ance
inm
athe
mat
ics
at th
e en
dof
Gra
de 3
.
RE
POR
TIN
G S
TU
DE
NT
PER
FOR
MA
NC
E
Stud
ent p
erfo
rman
ce o
fou
tcom
es is
rep
orte
d in
rela
tion
toG
rade
3 S
tand
ards
.
Tea
cher
s re
port
the
leve
l of
stud
ent
perf
orm
ance
for
eac
hle
arni
ng o
utco
me
topa
rent
s or
gua
rdia
ns.
IMPR
OV
ING
PR
OG
RA
MS
AN
D S
TU
DE
NT
PER
FOR
MA
NC
E
The
res
ults
of
asse
ssm
ent a
re u
sed
toim
prov
epr
ogra
ms
and
stud
ent
perf
orm
ance
.
Tea
cher
s pl
anap
prop
riat
e pr
ogra
ms
to e
nabl
e st
uden
ts to
impr
ove
thei
rpe
rfor
man
ce o
f th
est
uden
t lea
rnin
gou
tcom
es.
Man
itoba
Edu
catio
n an
d T
rain
ing
uses
Gra
de 3
Sta
ndar
dsw
hen
desi
gnin
g St
anda
rds
Tes
ts, r
epor
ting
the
prov
inci
al te
stin
g re
sults
, and
revi
sing
or
impl
emen
ting
new
cur
ricu
la.
55
1 9
j
AS
SE
SS
ME
NT
WIT
HIN
TH
E S
TR
UC
TU
RE
OF
MA
TH
EM
AT
ICS
Ass
essm
ent i
s th
e pr
oces
s of
gat
heri
ng e
vide
nce
abou
t ast
uden
t's k
now
ledg
e, s
kills
, and
atti
tude
s. A
sses
smen
t res
ults
are
used
to e
valu
ate
wha
t a s
tude
nt v
alue
s, k
now
s, a
nd c
ando
. Thi
s ev
alua
tion
can
be u
sed
for
mak
ing
inst
ruct
iona
lde
cisi
ons,
mon
itori
ng o
r re
port
ing
stud
ent p
rogr
ess,
and
eval
uatin
g pr
ogra
ms.
,
Mat
hem
atic
s as
sess
men
t tak
es p
lace
with
in a
str
uctu
re o
fim
port
ant c
ompo
nent
s. (
See
figu
re 3
on
page
57.
) T
hest
ruct
ure
prov
ides
the
para
met
ers
with
in w
hich
Gra
de 3
Stan
dard
s w
as d
evel
oped
and
is u
sed.
Gra
de 3
Sta
ndar
ds is
desi
gned
to s
uppo
rt c
onsi
sten
t ass
essm
ent o
f st
uden
tac
hiev
emen
t in
Man
itoba
mat
hem
atic
s cl
assr
oom
s by
prov
idin
g cl
earl
y de
fine
d st
uden
t per
form
ance
exp
ecta
tions
.
128
56
figu
re 3
EST
AB
LIS
HE
D
STA
ND
AR
DS
OF
STU
DE
NT
I.PE
RFO
RM
AN
CE
ASS
ESS
ME
NT
WIT
HIN
TH
E S
TR
UC
TU
RE
OF
MA
TH
EM
AT
ICS
MA
TH
EM
AT
ICA
L S
TR
AN
DS,
with
gen
eral
and
sne
cifi
c le
arni
ng o
utco
mes
stat
ing
the
expe
ctat
ions
for
kno
wle
dge,
ski
lls, a
nd v
alue
s to
be
achi
eved
by
stud
ents
who
are
com
plet
ing
Gra
de 3
.
MB
EN
GL
ISH
K-4
ST
RA
ND
SN
umbe
r
Con
cept
s
Num
ber
Ope
ratio
ns
Patte
rns
and
Mea
sure
men
t
Prob
lem
-Sol
ving
Geo
met
ryD
ata
Man
agem
ent
MB
FR
EN
CH
K-4
ST
RA
ND
SN
umbe
rN
umbe
rPr
oble
m-S
olvi
ng is
Mea
sure
men
t Geo
met
ry
Con
cept
sO
pera
tions
inte
grat
ed in
all
stra
nds
Dat
a M
anag
emen
t(i
nclu
des
Patte
rns)
WE
STE
RN
FRA
ME
WO
RK
STR
AN
DS
NU
MB
ER
PAT
TE
RN
S A
ND
SHA
PE A
ND
SPA
CE
RE
LA
TIO
NS
STA
TIS
TIC
S A
ND
PRO
BA
BIL
ITY
Lev
el 3
perf
orm
ing
abov
eth
e st
anda
rd s
etfo
r th
e gr
ade.
Lev
el 2
perf
orm
ing
with
inth
e ra
nge
set a
sth
e st
anda
rd f
orth
e gr
ade.
a
ASS
ESS
ING
STU
DE
NT
LE
AR
NIN
G
OF
EN
ER
AL
AN
D
OU
TC
ME
S
BIG
ID
EA
SThe
pro
cess
esPr
oble
m-S
olvi
ng, C
omm
unic
atin
g, E
stim
atin
g an
dus
ing
Men
tal M
athe
mat
ics,
Mak
ing
Con
nect
ions
, Rea
soni
ng, U
sing
Tec
hnol
ogy,
and
Vis
ualiz
ing.
3 0
5713
j
A V
AR
IET
Y
OF
ASS
ESS
ME
NT
PRA
CT
ICE
S U
SED
TO
DE
TE
RM
INE
LE
VE
L O
F
STU
DE
NT
PER
FOR
MA
NC
E
AS
SE
SS
ME
NT
ST
RA
TE
GIE
S
Gen
eral
and
spe
cifi
c le
arni
ng o
utco
mes
are
the
obse
rvab
le o
rm
easu
rabl
e kn
owle
dge,
ski
lls, a
nd v
alue
s th
at s
tude
nts
are
expe
cted
to h
ave
acqu
ired
and
dev
elop
ed a
t cer
tain
key
sta
ges
of th
eir
scho
olin
g. T
hey
desc
ribe
wha
t stu
dent
s sh
ould
kno
w,
shou
ld b
e ab
le to
do,
and
sho
uld
valu
e as
a r
esul
t of
thei
rle
arni
ng e
xper
ienc
es.
Mat
hem
atic
al c
ompe
tenc
e in
volv
es c
omm
unic
atin
g, p
robl
em-
solv
ing,
hig
her-
orde
r th
inki
ng, c
reat
ivity
, per
sist
ence
, and
curi
osity
. A v
arie
ty o
f as
sess
men
t str
ateg
ies
shou
ld b
e us
ed to
prov
ide
stud
ents
with
opp
ortu
nitie
s to
dem
onst
rate
thes
ech
arac
teri
stic
s.
Thi
s po
rtio
n of
the
docu
men
t sum
mar
izes
som
e of
the
stra
tegi
es te
ache
rs u
se to
ass
ess
how
stu
dent
s pr
oces
skn
owle
dge,
and
how
wel
l stu
dent
s le
arn.
Inc
lude
d ar
e
obse
rvat
ion
disc
ussi
ons,
con
fere
nces
, and
str
uctu
red
inte
rvie
ws
jour
nal a
nd le
arni
ng-l
og w
ritin
gpe
rfor
man
ce/a
uthe
ntic
task
sin
vest
igat
ions
self
/pee
r as
sess
men
tpa
per-
penc
il qu
izze
s an
d te
sts
The
se a
sses
smen
t str
ateg
ies
inco
rpor
ate
the
follo
win
g
eval
uatin
g pr
oces
s as
wel
l as
prod
uct
eval
uatin
g w
hat s
tude
nts
know
and
how
they
thin
k ab
out
mat
hem
atic
sev
alua
ting
stud
ent p
erfo
rman
ce in
a v
arie
ty o
f m
odes
,in
clud
ing
dem
onst
ratio
n an
d or
al, p
icto
rial
, and
wri
tten/
sym
bolic
rep
rese
ntat
ion
58
13')
usin
g a
broa
d ra
nge
of m
athe
mat
ical
task
s an
d ta
king
aco
nnec
ted
view
of
mat
hem
atic
sus
ing
man
ipul
ativ
esus
ing
calc
ulat
ors
and
com
pute
rsre
cogn
izin
g su
ch a
ttitu
dina
l out
com
es a
s m
otiv
atio
n an
dap
prec
iatio
nge
tting
the
stud
ent i
nvol
ved
in th
e as
sess
men
t pro
cess
A s
hort
des
crip
tion
of e
ach
stra
tegy
is p
rovi
ded
in th
isco
mpo
nent
of
the
Ass
essm
ent F
ram
ewor
k, a
long
with
at l
east
one
(som
etim
es o
nly
part
ial)
sam
ple
stud
ent r
espo
nse.
An
Ass
essm
ent P
ortf
olio
is o
ne m
etho
d of
invo
lvin
gst
uden
ts in
the
asse
ssm
ent a
nd e
valu
atio
n pr
oces
s. S
tude
nts
gath
er s
ampl
es th
at th
ey, a
nd th
eir
teac
her,
thin
k de
mon
stra
teth
eir
deve
lopi
ng k
now
ledg
e an
d sk
ills.
Thi
s in
volv
emen
tbe
com
es a
pow
erfu
l way
of
mot
ivat
ing
self
-res
pons
ibili
ty f
orle
arni
ng. A
bri
ef d
escr
iptio
n of
the
proc
ess
and
the
cont
ents
of
Ass
essm
ent P
ortf
olio
s is
incl
uded
at t
he e
nd o
f th
eA
sses
smen
t Str
ateg
ies
note
s.
133
OB
SE
RV
AT
ION
Obs
erva
tion
is p
roba
bly
the
mos
t fre
quen
tly u
sed
form
of
asse
ssm
ent.
It c
an o
ccur
nat
ural
ly d
urin
g m
athe
mat
ics
clas
ses,
and
can
be
cond
ucte
d w
hen
stud
ents
wor
k al
one
or in
grou
ps. S
yste
mat
ic o
bser
vatio
n ca
n pr
ovid
e in
form
atio
n ab
out
stud
ents
' atti
tude
s to
war
d m
athe
mat
ics,
thei
r fe
elin
gs a
bout
them
selv
es a
s le
arne
rs, t
heir
pre
ferr
ed le
arni
ng s
tyle
s, th
eir
area
s of
inte
rest
, wor
k ha
bits
, and
soc
ial d
evel
opm
ent,
and
thei
r de
velo
pmen
t in
the
abili
ty to
use
mat
hem
atic
al la
ngua
gean
d co
ncep
ts.
It is
impo
rtan
t to
reco
rd th
ese
obse
rvat
ions
. The
y as
sist
in th
ede
velo
pmen
t of
mea
ning
ful p
rogr
ams
for
stud
ents
and
inpr
ovid
ing
usef
ul in
form
atio
n to
par
ents
.
Nal
f/
4f10
141,
1 44
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stel
tdr
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rit
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ST
74f
ALL
Yea
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nt:Is
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siio
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rati
ritui
53o
lutiO
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59B
EST
CO
PY
AV
AIL
AB
LE13
5
DIS
CU
SS
ION
S, C
ON
FE
RE
NC
ES
, AN
DS
TR
UC
TU
RE
D IN
TE
RV
IEW
S
Dis
cuss
ions
and
stu
dent
con
fere
nces
are
opp
ortu
nitie
s fo
r th
ete
ache
r an
d th
e st
uden
t to
shar
e id
eas.
The
y pr
ovid
e a
cont
ext
for
the
expl
orat
ion
of a
stu
dent
's m
athe
mat
ical
rea
soni
ng a
ndfo
r de
term
inin
g ho
w w
ell a
stu
dent
und
erst
ands
a c
once
pt o
r a
proc
edur
e. T
hey
can
be u
sed
to r
evea
l how
wel
l a s
tude
ntex
plai
ns s
olut
ions
or
to p
rovi
de a
n op
port
unity
for
a s
tude
ntto
just
ify
thin
king
and
rea
soni
ng. D
iscu
ssio
ns a
nd s
tude
ntco
nfer
ence
s al
so a
re u
sefu
l for
rev
ealin
g st
uden
t str
engt
hs a
ndpr
efer
ence
s, a
nd f
or d
iscu
ssin
g al
tern
ativ
e st
rate
gies
.
Impo
rtan
t ins
ight
s in
to s
tude
nt k
now
ledg
e, s
kills
, and
val
ues
reve
aled
dur
ing
an in
form
al d
iscu
ssio
n or
con
fere
nce
shou
ldbe
rec
orde
d an
d da
ted.
Stru
ctur
ed in
terv
iew
s pr
ovid
e sp
ecif
ic in
form
atio
n on
ast
uden
t's c
onst
ruct
ion
of m
eani
ng f
or a
ny c
once
pt, p
roce
dure
,re
latio
nshi
p, o
r co
nnec
tion.
Str
uctu
red
inte
rvie
ws
shou
ld b
ebr
ief
and
cond
ucte
d in
a r
elax
ed a
tmos
pher
e. T
he te
ache
rne
eds
to b
e no
n-ju
dgm
enta
l and
to a
void
eng
agin
g in
inst
ruct
ion.
Stru
ctur
ed in
terv
iew
s sh
ould
be
cond
ucte
d pe
riod
ical
ly w
ithal
l stu
dent
s. I
f tim
e be
com
es a
n is
sue,
inte
rvie
ws
may
be
limite
d to
stu
dent
s fo
r w
hom
a c
lear
pic
ture
of
achi
evem
ent
has
not,
been
est
ablis
hed.
The
inte
rvie
w s
crip
t sito
uld
bede
sign
ed to
pro
vide
app
ropr
iate
spa
ce f
or r
ecor
ding
stu
dent
resp
onse
s an
d te
ache
r im
pres
sion
s. T
he r
ecor
ding
she
et c
anbe
sto
red
in th
e te
ache
r's r
ecor
ding
sys
tem
, or
plac
ed in
the
stud
ent's
Ass
essm
ent P
ortf
olio
.
13t;
60
Gra
de 3
Inte
rvie
w S
crip
t / R
ecor
ding
She
etM
easu
rem
ent
Dat
e
.T-
(hol
d up
a d
rinki
ng s
traw
) E
stim
ate
the
leng
th o
f thi
s dr
inki
ag s
traw
in c
entim
etre
s.
5-/6
"C
r11
Nam
e
T. T
ell m
e ho
w y
ou d
ecid
ed e
a yo
ur a
nsw
er.
Aat
tiits
z_ai
,iakk
irow
2 T
. Sup
pose
you
r es
timat
e is
equ
al to
the
actu
al le
ngth
of t
he s
traw
. Abo
ut h
ow m
any
dris
king
str
aws
will
lit c
ad to
end
la th
e le
ngth
of a
met
re?
Z.044
,4 4
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0 e.
t.a 4
t 4 '1
4
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td-
6T
. Tel
l me
how
you
dec
ided
on
your
answ
ert.l
_ges
i±sa
raLl
9/ 0
0.
-30/
or, g
o, 7
c_r_
qo "
3, 7
-Exp
lain
to s
e w
hat "
perim
eter
" m
eans
.
S-
,-m
eaam
ite a
..4.
T-O
ece
spiv
, let
's s
ay y
our
estim
ated
num
ber
of s
traw
s is
the
corr
ect n
umto
At
e %
med
to a
wl i
n *
met
re. A
bout
how
may
drin
king
str
aws
long
Is th
e pe
rimet
er o
f
Ael
emel
acn
cs.r
osst
(in
&A
sia)
S-
a Ln
e.4
%S
in/ 1
.45
T-
Tel
l whe
t you
did
um
iak,
So
arriv
e at
you
r an
swer
?
/11r
iSg
te, 6
'1.4
rylij
A74
Li1
2-2
14d
-mot
e ,c
I,
137
JOU
RN
AL
AN
D L
EA
RN
ING
-LO
G W
RIT
ING
Jour
nal r
espo
nse
to H
ow B
ig is
a F
oot b
y R
olf
My
ler.
Jour
nal w
ritin
g re
pres
ents
an
oppo
rtun
ity f
or s
tude
nts
topr
oduc
e pi
ctur
es a
nd w
ritte
n ex
pres
sion
s of
thou
ghts
and
feel
ings
, v, a
sk q
uest
ions
, and
to c
omm
ent o
n th
eir
lear
ning
expe
rien
ces.
Thi
s st
rate
gy f
or g
athe
ring
ass
essm
ent d
ata
isof
ten
left
uns
truc
ture
d, i.
e., t
he c
onte
nt a
nd th
e fo
rmat
may
be
dete
rmin
ed b
y th
e st
uden
t. Jo
urna
l wri
ting
allo
ws
a st
uden
tto
cla
rify
thin
king
and
to r
efle
ct o
n le
arni
ng, u
sing
the
vari
ous
mod
es o
f m
athe
mat
ical
com
mun
icat
ion.
Jou
rnal
s of
ten
prov
ide
stud
ents
with
a s
afe
foru
m f
or id
entif
ying
str
engt
hs,
wea
knes
ses,
and
inte
rest
s.
Som
e te
ache
rs in
stru
ct th
eir
stud
ents
to k
eep
a m
athe
mat
ics
lear
ning
-log
.It
is s
imila
r to
a w
ritin
g jo
urna
l, bu
t it i
s us
edto
hav
e st
uden
ts r
espo
nd to
spe
cifi
c qu
estio
ns th
at h
ave
been
plan
ned
as a
n in
tegr
al p
art o
f in
stru
ctio
n. Q
uest
ions
may
be
aske
d be
fore
, dur
ing,
or
follo
win
g in
stru
ctio
n. T
he le
arni
ng-
log
is u
sed
to g
ive
stud
ents
an
oppo
rtun
ity to
com
mun
icat
eth
eir
refl
ectio
ns u
sing
gra
phic
s, n
umer
als,
mat
hem
atic
alsy
mbo
ls, a
nd w
ritin
g th
at in
corp
orat
es m
athe
mat
ical
lang
uage
. A le
arni
ng-l
og e
ntry
als
o ca
n re
veal
fee
lings
and
attit
udes
abo
ut le
arni
ng.
Not
ewor
thy
jour
nal a
nd le
arni
ng-l
og e
ntri
es c
an b
eph
otoc
opie
d an
d ad
ded
to a
teac
her's
rec
ordi
ng s
yste
m, o
rpl
aced
in th
e st
uden
t's A
sses
smen
t Por
tfol
io.
138
pirc
aiic
v
I 1<
fow
your
l,i
jo.;I
, by+
I t-
Itin
Ic
o-ic
r .tr
Oye
w p
robl
em. I
+h;
riit
u4se
n }h
e K
irl
resu
red
be4
he d
i1n4
*in
k of
4-1
-e
his
.(ee
iaf
tb;
gger
4-I
--an
you
rs.
Now
,4-
kink
I c
.o.,
561-
you
oo. 0
F,ox
d w
44t
Que
eAs
bed.
44,e
jaile
r 44
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you
+1,
ebe
)A
tnju
sl d
oubl
e
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ree
l. 4-
he W
I SA
4. S
i1f
4d-
w;J
e
cAd
4 ve
lve
S;r<
erel
y. A
XIM
.
Wri
tten
befo
re r
eadi
ng H
ow M
uch
Is a
Mill
ion
by D
avid
Swar
tz.
Aen
iNh
I.ok
s
1001
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;t
t,le
eks
114
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Inno
wfli
Is b
ecoi
6t01
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Vtr
fold
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t
BE
ST
CO
PY
AV
AIL
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LE
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it )M
eta,
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ln.)
5fr
at
139
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se s
oito
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h
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0.44
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. It i
s
PE
RF
OR
MA
NC
E/A
UT
HE
NT
IC T
AS
KS
Thi
s as
sess
men
t str
ateg
y in
volv
es p
rese
ntin
g st
uden
ts w
ithde
sign
ed o
r au
then
tic m
athe
mat
ical
task
s. P
erfo
rman
ce ta
sks
plac
e em
phas
is o
n th
e m
any
mat
hem
atic
al p
roce
sses
cite
dea
rlie
r. S
tude
nts
are
expe
cted
to p
rovi
de a
thor
ough
acc
ount
of th
e st
rate
gies
and
the
reas
onin
g ne
eded
to c
ompl
ete
a ta
sk.
It is
cri
tical
that
sco
ring
rub
rics
be
deve
lope
d an
d sh
ared
with
stud
ents
so
that
stu
dent
s' e
ffor
ts a
re w
ell a
ppra
ised
. Tea
cher
sm
ay w
ant t
o in
clud
e co
nfer
ence
s or
inte
rvie
ws
as p
art o
f th
isas
sess
men
t pro
cess
.
Mea
sure
men
t Per
form
ance
Tas
k: P
erim
eter
Mat
eria
ls: 2
0 co
lour
ed s
quar
e til
es
Wha
t doe
s pe
rim
eter
mea
n?
Part
1: D
irec
tions
Usi
ng 8
tile
s of
any
col
our,
mak
e sh
apes
with
the
peri
met
ers
give
n. T
hetil
es m
ust h
ave
side
s to
uchi
ng, n
ot ju
st c
orne
rs.
1.pe
rim
eter
of
163.
peri
met
er o
f 14
2.pe
rim
eter
of
24.
peri
met
er o
f 18
Part
2: D
irec
tions
Use
10
tiles
to m
ake
shap
es w
ith p
erim
eter
s gi
ven.
Tile
s m
ust h
ave
side
sto
uchi
ng.
1.pe
rim
eter
of
243.
peri
met
er o
f 22
2.pe
rim
eter
of
204.
peri
met
er o
f 18
Part
3: D
irec
tions
Show
you
r fm
ishe
d pa
per
to y
our
teac
her.
Try
to a
nsw
er th
e 2
ques
tions
your
teac
her
will
ask
abo
ut y
our
wor
k.
Peri
met
er S
cori
ng R
ubri
cL
evel
3 (
high
leve
l res
pons
e)kn
ows
the
mea
ning
of
peri
met
erin
depe
nden
tly u
nder
stan
ds th
e ta
skus
es m
ater
ials
eff
ectiv
ely
corr
ectly
com
plet
es P
arts
1 &
2ca
n ex
plai
n w
hy a
per
imet
er o
f 24
is im
poss
ible
show
s so
me
insi
ght i
nto
rela
tions
hips
bet
wee
n le
ngth
of
peri
met
er a
ndsh
ape
whe
n nu
mbe
r of
tile
s (a
rea)
is k
ept c
onst
ant
14 0
62
Lev
el 2
(m
iddl
e le
vel r
espo
nse)
know
s m
eani
ng o
f pe
rim
eter
uses
mat
eria
ls to
und
erst
and
task
corr
ectly
com
plet
es a
ll po
ssib
le s
hape
s in
Par
ts 1
and
2tr
ies
to e
xpla
in w
hy a
per
imet
er o
f 24
is im
poss
ible
Lev
el 1
(lo
w le
vel r
espo
nse)
need
s su
ppor
t to
expl
ain
mea
ning
of
peri
met
erus
es m
ater
ials
corr
ectly
com
plet
es P
art 1
Peri
mie
r;s so
niet
hiv.
+lie
dist
ance
arou
nd
iff,
-;41
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nt14
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eiri
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Mili
nial
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asK
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rsK
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141.
INV
ES
TIG
AT
ION
S
Mat
hem
atic
al in
vest
igat
ions
invo
lve
stud
ents
in e
xten
ded
expl
orat
ions
of
mat
hem
atic
al q
uest
ions
. An
inve
stig
atio
n m
aypr
esen
t stu
dent
s w
ith m
athe
mat
ical
situ
atio
ns th
at in
clud
eth
inki
ng a
bout
and
usi
ng id
eas
rela
ted
to o
ther
sub
ject
are
as.
Mat
hem
atic
al in
vest
igat
ions
som
etim
es s
houl
d gr
ow o
ut o
fin
tere
sts
show
n or
pro
blem
s po
sed
by s
tude
nts.
It m
ay ta
kest
uden
ts d
ays
or w
eeks
to c
ompl
ete
an in
vest
igat
ion.
The
inve
stig
ativ
e w
ork
invo
lved
is in
tend
ed to
pro
vide
info
rmat
ion
abou
t stu
dent
s' a
bilit
ies
to
appl
y an
d le
arn
mat
hem
atic
al c
once
pts
and
skill
sid
entif
y an
d de
fine
a p
robl
emm
ake
and
carr
y ou
t a p
lan
crea
te a
nd in
terp
ret s
trat
egie
sco
llect
and
rec
ord
nece
ssar
y in
form
atio
nor
gani
ze d
ata
and
look
for
pat
tern
spe
rsis
t, lo
okin
g fo
r m
ore
info
rmat
ion
if n
eede
ddi
scus
s, r
evie
w, r
evis
e, a
nd e
xpla
in r
esul
ts
Stud
ents
sho
uld
prod
uce
an a
dequ
ate
reco
rd o
f th
e st
ages
of
deve
lopm
ent,
and
resu
lts a
nd c
oncl
usio
ns u
f in
vest
igat
ions
.A
n ou
tline
of
the
scor
ing
syst
em, t
o be
use
d fo
r ev
alua
ting
the
proc
esse
s us
ed a
nd th
e w
ork
prod
uced
, mus
tbe
giv
en to
the
stud
ents
as
they
beg
in th
e in
vest
igat
ion.
It i
s ad
visa
ble
that
stud
ents
are
invo
lved
in e
valu
atin
g th
eir
inve
stig
ativ
e w
ork.
The
stu
dent
s' r
epor
ts, a
nd p
hoto
grap
hs, c
hart
s, a
udio
or
vide
ota
pes,
etc
., ca
n be
sto
red
in th
eir
Ass
essm
ent
Port
folio
s.
The
fol
low
ing
sam
ples
are
cou
rtes
y of
Gra
de 3
stu
dent
s in
an
elem
enta
ry s
choo
l in
Man
itoba
.
BE
ST C
OPY
AV
AfL
AB
LE
Wha
t is
the
aver
age
num
ber
of p
ets-
for
a gr
ade
thre
e st
uden
t?
Se
e
Lcc:A
r-T:k
1*4
4 F4
1410
51
1
r-
_lqv
$144
41
f-t,t
71
459
dogs
113
ham
ster
s21
rat
s10
0 se
a an
emon
es14
fro
gs83
sna
ils19
sal
aman
ders
2 go
ats
. 4 : , AIM
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NM
i
MU B
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oll I
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i=r2
..7_.
Dear Room 104
Plowmans park
Mississauga Ontario,
We have been comparing your
class with out pet data. We had
the same number of cats but you
have one less dog.
Your class
has
13
more fish than we did
but we both had the same number
of turtles. We have three more
rats than you do.
Your class
had less childern but more
pets.
Or pet data was almost
the same but your class had
nineteen more pets. Thank you
for sending E-mail.
Your friends, Jani and Ashley.
563
cats
1632
fis
h40
6 bi
rds
168
rabb
its48
ger
bils
49 tu
rtle
s61
gui
neap
igs
1cr
ab52
hor
ses
24 li
zard
s32
spi
ders
1sq
uirr
el1
chin
chill
a3
ferr
ets
19 m
ice
3
Tot
al n
umbe
r of
chi
ldre
n in
tbe
surv
ey:
913
Tot
al n
umbe
r of
cla
sses
res
pond
ing:
41
Prov
ince
s re
pres
ente
d:B
.C.,
Man
itoba
, Ont
ario
,N
ova
Scot
ia, P
.E.I
.T
otal
num
ber
of p
ets:
3906
Ave
rage
num
ber
of p
ets
per
stud
entb
etw
een
4 an
d 5
63
SE
LF-
OR
PE
ER
-AS
SE
SS
ME
NT
Self
-ass
essm
ent p
rom
otes
the
abili
ty o
f st
uden
ts to
ref
lect
on
thei
r ow
n ef
fort
s to
use
mat
hem
atic
al th
inki
ng p
roce
sses
, and
thei
r ow
n su
cces
s in
und
erst
andi
ng a
nd a
pply
ing
conc
epts
and
proc
edur
es. O
ppor
tuni
ties
to r
efle
ct o
n th
eir
own
lear
ning
help
stu
dent
s to
take
ow
ners
hip
for
that
lear
ning
and
hel
pth
em to
bec
ome
inde
pend
ent t
hink
ers.
Peer
-ass
essm
ent i
s us
ually
ach
ieve
d w
hen
a sm
all g
roup
look
sba
ck o
n its
elf,
see
king
to u
nder
stan
d gr
oup
dyna
mic
s, a
ndho
w th
ey a
ffec
t gro
up w
ork
and
prod
uctio
n.
Self
- an
d pe
er-a
sses
smen
t can
be
faci
litat
ed b
y m
eans
of
ate
ache
r- o
r st
uden
t-pr
epar
ed q
uest
ionn
aire
, dai
ly jo
urna
lw
ritin
g, a
nd s
tude
nt o
r gr
oup
conf
eren
ces.
Lear
ning
to W
ork
Tog
ethe
r
Fill
in e
ach
happ
y fa
ce to
sho
w b
ow w
ell y
our
are
lear
ning
to w
ork
coop
erat
ivel
y.
1. W
e lis
tene
d to
eac
h ot
hers
' ide
as.
2. W
e ea
ch d
id o
ur f
air
shar
e of
the
wor
k.
3. W
e fi
nish
ed o
ur w
ork
on ti
me.
4. N
ext t
ime
our
grou
p w
ill tr
y to
wor
k fa
ster
114
64
NE
WS
PA
PE
R S
CA
VE
NG
ER
HU
NT
Nam
es o
f you
r te
am m
embe
rs:
ki a
nem
pape
r. fi
nd th
e fo
llow
ing
itern
.s..r
AE
thoc
itesW
Ove
rne
xt to
the
desc
ron.
/
1. T
he p
rice
of s
omet
hing
to e
a79
3g -
110(
k,C
LA
SSIC
CA
ND
Y T
UB
S
99V
2. A
str
eet a
ddre
ss'M
AU
D IN
WIN
NIP
EG
AT
2627
PO
RT
AG
EA
VE
NU
M...
.....,
_3.
A n
umbe
r th
at g
i,,es
a s
ize
4. A
pho
ne n
umbe
r 947-
95.
The
dat
e th
e pa
per
wes
pub
lishe
d
£8vi
nrup
egR
I, la
rest
ytai
day.
Dec
ernb
it 13
. 19N
6. A
num
ber
in a
rec
ipe
7. A
num
ber
that
nam
es a
dis
tanc
e
8. A
num
ber
that
nam
es a
tam
per-
Aur
a
9. A
num
ber
%W
itte
el
10. T
he S
core
of a
gam
e
4
45
PA
PE
R-P
EN
C1L
QU
IZZ
ES
AN
D T
ES
TS
Pape
r-pe
ncil
quiz
zes
and
test
s ar
e an
othe
r w
ay f
or s
tude
nts
tode
mon
stra
te w
hat t
hey
know
and
can
do.
Sev
eral
str
ateg
ies
can
be u
sed
to h
elp
stud
ents
fee
l tha
t tes
ts a
re im
port
ant
oppo
rtun
ities
to le
arn
and
to d
emon
stra
te le
arni
ng. T
hese
stra
tegi
es in
clud
e
prov
idin
g co
ncre
te m
ater
ials
, or
at le
ast a
cces
s to
mat
eria
lsth
at h
ave
been
par
t of
clas
sroo
m in
stru
ctio
n. T
hese
mat
eria
ls h
elp
stud
ents
sol
ve p
robl
ems,
eve
n th
ough
they
may
not
yet
be
capa
ble
of p
rodu
cing
sol
utio
ns in
sym
bolic
form
.pr
ovid
ing
a pi
ctur
e or
dia
gram
as
part
of
the
info
rmat
ion
give
n in
a p
robl
em. T
his
help
s st
uden
ts w
ho e
xper
ienc
edi
ffic
ultie
s w
ith r
eadi
ng o
r in
terp
retin
g pr
int t
o vi
sual
ize
the
info
rmat
ion
and
to s
how
wha
t the
y ha
ve le
arne
d.re
adin
g or
telli
ng th
e co
ntex
t for
som
e pr
oble
ms.
Thi
s is
espe
cial
ly im
port
ant f
or s
tude
nts
in th
e yo
unge
r gr
ades
,an
d fo
r st
uden
ts w
hose
rea
ding
ski
lls p
reve
nt th
em f
rom
dem
onst
ratin
g th
eir
mat
hem
atic
al k
now
ledg
e an
d sk
ills.
prov
idin
g so
me
open
-end
ed q
uest
ions
with
no
pred
eter
min
ed li
mits
on
solu
tions
, pro
cedu
res,
or
proc
esse
s to
be
used
for
fin
ding
sol
utio
ns. T
his
type
of
prob
lem
is e
spec
ially
impo
rtan
t if
test
ing
is to
giv
est
uden
ts o
ppor
tuni
ties
to s
how
the
brea
dth
and
dept
h of
thei
r th
inki
ng a
nd le
arni
ng.
How
man
y di
ffer
ent w
ays
can
you
use
the
D.I
.M.E
. sol
ids
to b
uild
a "
flat
?"
1'11
21 /E
l Eiii
lic
a.- b:T
he d
ots
in th
e di
agra
m a
re 1
uni
tap
art
.W
hat i
s th
e pe
rimet
er o
f the
figur
e? k
3,
Wha
t are
the
dim
ensi
ons
of a
squa
re w
ith th
e sa
me
perim
eter
?
li \i4
4z
'n
... .
2.T
he ta
ble
show
s th
e nu
mbe
r of
boo
kfo
urth
gra
des
durin
g a
thre
e-m
onth
a.In
whi
ch m
onth
wer
e th
egr
eate
st n
umbe
r of
boo
kre
port
s w
ritte
n? m
orel
.
b. W
hich
gra
defe
wer
book
rep
orts
?
repo
rts
writ
ten
by th
e th
ird a
ndpe
riod. BO
OK
RE
PO
RT
S W
RIT
TE
N
Mon
thG
rade
3G
rade
4
Feb
ruar
y11
513
1
Mar
ch
136
117
Apr
il12
310
9
3.T
he n
umbe
rs 1
, 4, a
nd 9
are
cal
led
squa
re n
umbe
rs.
C :1
:; a
.)6
14
9-
ifill
0.20
oot
Po
On.
-,c.
0 4
bS.
Wha
t are
the
next
thre
e sq
uare
num
bers
?
3.4.
The
se a
re 3
diff
eren
t vie
ws
of th
e sa
me
solk
i.
from
IN to
p E
gfr
ont t
he s
ide
A fr
om n
te b
otto
m IL
I
Nam
e th
e so
lid. ,14d
erba
sed
f610
p51
1it-
m;a
r e
l.ca
r, b
ec(
Abe
,:
,4I
dad
4z)
reta
keQ
.
65 BE
ST C
oPv
AV
AIL
AB
LE
AS
SE
SS
ME
NT
PO
RT
FO
LIO
S
Tea
cher
s an
d st
uden
ts w
ho e
ngag
e in
dev
elop
ing
Mat
hem
atic
s Po
rtfo
lios
for
asse
ssin
g pr
ogre
ss a
nd le
arni
ngof
ten
esta
blis
h tw
o po
rtfo
lios:
1. A
Gen
eral
Mat
hem
atic
s Po
rtfo
lioa
gene
ral c
olle
ctio
nof
sam
ples
whi
ch m
ay b
ecom
e ex
ampl
es o
f "b
est"
perf
orm
ance
or
whi
ch d
emon
stra
te s
igni
fica
ntpr
ogre
ss/le
arni
ng f
or a
giv
en u
nit o
f w
ork
or ti
me
fram
e(e
.g.,
2 w
eeks
).2.
An
Ass
essm
ent M
athe
mat
ics
Port
folio
a lim
ited
colle
ctio
n of
sam
ples
, cho
sen
by th
e st
uden
t fro
m th
eG
ener
al M
athe
mat
ics
Port
folio
, to
exem
plif
y th
e le
arni
ngth
at h
as o
ccur
red.
Incl
uded
is a
lette
r fr
om th
e st
uden
tin
dica
ting
the
reas
ons
for
sele
ctin
g th
e pa
rtic
ular
sam
ples
.T
he te
ache
r m
ay p
lace
add
ition
al s
ampl
es, a
necd
otal
note
s, e
tc. i
n th
e st
uden
t's p
ortf
olio
.
An
Ass
essm
ent P
ortf
olio
is in
tend
ed to
pfe
vide
a p
ictu
re o
fth
e st
uden
t's p
erfo
rman
ce a
nd a
chie
vem
ent o
ver
time.
Stud
ent p
ortf
olio
s ca
n pr
ovid
e
evid
ence
of
know
ledg
e ai
ld s
kill
acqu
isiti
onev
iden
ce o
f ap
prop
riat
e us
e of
pro
cess
esop
port
uniti
es f
or th
e st
uden
t to
prac
tice
eval
uatin
g an
dse
lect
ing
"bes
t exa
mpl
es"
of o
ne's
ow
n pe
rfor
man
cean
d le
arni
nga
perm
anen
t rec
ord
of s
tude
nt w
ork
14 6
An
Ass
essm
ent P
ortf
olio
may
incl
ude
the
follo
win
gpe
rson
ally
-cho
sen
and/
or te
ache
r-ch
osen
exa
mpl
es o
f st
uden
tw
ork gr
aphi
c/w
ritte
n de
scri
ptio
ns o
f pr
oble
m-s
olvi
ng,
perf
orm
ance
task
s, in
vest
igat
ions
, etc
.ph
otog
raph
s, v
ideo
and
aud
io ta
pes,
flip
-cha
rts,
etc
. fro
mas
sign
ed o
r se
lf-d
esig
ned
proj
ect w
ork
and
pres
enta
tion
exce
rpts
fro
m th
e st
uden
t's m
athe
mat
ics
jour
nal a
ndm
athe
mat
ics
lear
ning
-log
com
pute
r-ge
nera
ted
exam
ples
of
deve
lopi
ng te
chno
logy
skill
s an
d kn
owle
dge
stud
ent s
elf-
repo
rts
on w
hat h
as b
een
lear
ned,
on
feel
ings
abou
t one
self
as
a le
arne
r, a
nd o
n at
titud
es to
war
dsm
athe
mat
ics
Whe
n yo
u lo
ok a
t my
P-12 '..
-4
rna,
-1-h
?ap
e r
w,4
,I w
ant y
ou to
not
ice
2.gi
rI57
9ho
wA
..oe
1 1
ID
an1
w,-
-t-
yntA
ttipt
y.X
Kno
w.)
....e
... vrn
m f
aths
-to
Hot
,w
__4
,,_ wr
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9
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7
RE
AD
ING
TH
E S
TA
ND
AR
DS
The
fol
low
ing
page
s id
entif
y th
e st
anda
rds
of s
tude
ntpe
rfor
man
ce f
or e
ach
gene
ral l
earn
ing
outc
ome
by th
e en
d of
the
Gra
de 3
. The
re a
re f
our
page
s of
info
rmat
ion
for
each
gen
eral
lear
ning
out
com
e, o
rgan
ized
as
follo
ws:
1. e
ach
gene
ral l
earn
ing
outc
ome,
and
its
corr
espo
ndin
g sp
ecif
icou
tcom
es, i
s lis
ted
on th
e le
ft s
ide
of th
e fi
rst p
age.
3. s
ampl
e as
sess
men
t act
iviti
es a
re p
rovi
ded
on th
e le
ft s
ide
ofth
e th
ird
page
.
"WO
UR
RE
nS
TA
ND
AR
DS
OF
PE
RF
OR
MA
NC
E
LIM
1U
M. 9
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ST
AN
DA
RD
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ER
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LIM
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nt3
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F P
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RM
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CE
MIL
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:tit i
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F P
t IN
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U.4
.tRt-
t.a...
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t.. ...
......
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-
.
2. s
hort
par
agra
hs
desc
ribi
ng th
e ge
nera
l cha
ract
eris
tics
ofst
uden
t per
foan
ce f
or e
ach
of 3
leve
ls (
see
defi
nitio
ns f
orL
evel
s 1
to 3
oi p
age
69),
alo
ng w
ith a
num
ber
ofsa
mpl
e pe
rfor
man
ce in
dica
tors
for
eac
h, a
re f
ound
on
the
rem
aind
er o
f th
e fi
rst a
nd s
econ
d pa
ge. T
his
info
rmat
ion
esta
blis
hes
the
stan
dard
s of
stu
dent
per
form
ance
for
the
gene
ral l
earn
ing
outc
ome
show
n on
the
left
sid
e of
the
firs
tpa
ge.
15;2
4. s
ampl
e re
spon
ses
from
Man
itoba
Gra
de 3
stu
dent
s,ill
ustr
atin
g th
e di
ffer
ence
s in
stu
dent
per
form
ance
at e
ach
ofth
e 3
leve
ls, a
re f
ound
on
the
rem
aind
er o
f th
e th
ird
and
four
thpa
ges.
6 8
1.53
DE
FIN
ING
KE
Y T
ER
MS
Cha
ract
eris
tics
of S
tude
nt P
erfo
rman
ce: h
olis
ticst
atem
ents
sum
mar
izin
g st
uden
t per
form
ance
at e
ach
ofle
vels
1 to
3.
Sam
ple
Perf
orm
ance
Ind
icat
ors:
spe
cifi
c ex
ampl
esw
hich
des
crib
e w
hat s
tude
nts
shou
ld k
now
and
do
toin
dica
te a
chie
vem
ent o
f a
part
icul
ar le
arni
ng 'o
utco
me.
The
sta
tem
ents
are
not
inte
nded
to b
e ex
haus
tive
orre
stri
ctiv
e. T
hey
will
be
help
ful i
n de
term
inin
g bo
th a
leve
l of
stud
ent p
erfo
rman
ce, a
nd th
e qu
ality
of
that
perf
orm
ance
, rel
ativ
e to
the
stan
dard
set
for
the
lear
ning
outc
omes
.
Lev
els
of S
tude
nt P
erfo
rman
ce:
Lev
el 1
:st
uden
t per
form
ance
is li
mite
d (i
.e.,
not y
etw
ithin
the
rang
e se
t as
the
stan
dard
for
the
grad
e).
Lev
el 2
:st
uden
t per
form
ance
is c
ompe
tent
or
prof
icie
nt(i
.e.,
with
in th
e ra
nge
set a
s th
e st
anda
rd f
or th
egr
ade)
.
Lev
el 3
:st
uden
t per
form
ance
is o
utst
andi
ng o
r su
peri
or(i
.e.,
abov
e th
e st
anda
rd s
et f
or th
e gr
ade)
.
69
PR
OB
LEM
-SO
LV1N
G-E
ND
OF
GR
AD
E 3
"Pro
blem
-sol
ving
is th
e fo
cus
of m
athe
mat
ics
at a
ll gr
ade
leve
ls"
(Wes
tern
Fram
ewor
k, p
. 8).
By
the
end
of G
rade
3, s
tude
nts
will
begi
n to
dev
elop
and
app
ly s
trat
egie
s to
sol
ve a
wid
e va
riet
y of
pro
blem
sde
mon
stra
te a
n in
tere
stin
ver
ifyi
ng r
esul
ts w
ith r
espe
ct to
the
orig
inal
prob
lem
begi
n to
use
pro
blem
-sol
ving
app
roac
hes
to in
vest
igat
e an
d un
ders
tand
mat
hem
atic
al c
onte
ntso
met
imes
for
mul
ate
prob
lem
s fr
om e
very
day
and
mat
hem
atic
alsi
tuat
ions
show
a g
row
ing
conf
iden
ce in
abi
lity
to u
se m
athe
mat
ics
mea
ning
fully
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
anso
lve
prob
lem
s w
ith g
row
ing
conf
iden
cetr
y ne
w id
eas
and
purs
ue s
olut
ions
in p
robl
em-s
olvi
ng a
ctiv
ities
deve
lop
and
appl
y si
mpl
e pr
oble
m-s
olvi
ng s
trat
egie
sin
depe
nden
tly v
erif
y re
mits
of
prob
lem
-sol
ving
use
coop
erat
ive
skill
s ia
gyo
up p
robl
em-s
olvi
ng a
ctiv
ities
156
70
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
1
The
stu
dent
can
sol
ve s
impl
e w
ord
prob
lem
s, b
ut r
equi
res
assi
stan
ce to
carr
y th
roug
h pr
oble
m-s
olvi
ng p
roce
sses
for
mul
ti-st
ep a
nd n
on-
trad
ition
al p
robl
ems.
The
stu
dent
doe
s so
me
cont
ribu
ting
to g
roup
prob
lem
-sol
ving
, req
uiri
ng s
uppo
rt a
nd e
ncou
rage
men
t to
pers
ever
ean
d to
bec
ome
a ri
sk-t
aker
.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
ancr
eate
and
sol
ve s
impl
e 1-
step
ari
thm
etic
pro
blem
sso
lve,
with
ass
ista
nce
and
mat
eria
ls, 2
-ste
p pr
oble
ms
and
prob
lem
sin
volv
ing
2- a
nd 3
-dig
it nu
mbe
rsw
ith a
ssis
tanc
e, c
hoos
e a
stra
tegy
, mak
e a
pred
ictio
n or
an
estim
atio
n, a
nd r
ecor
d th
e pr
oces
s us
ed to
sol
ve p
robl
ems
cont
ribu
te to
gro
up p
robl
em-s
olvi
ng b
y co
oper
atin
g, m
akin
ggu
esse
s, u
sing
mat
eria
ls a
nd p
ictu
res,
and
tryi
ng, w
hen
enco
urag
ed,
to e
xpla
in p
roce
sses
and
res
ults
1 :,"
"1
-A. 0
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
2
The
stu
dent
und
erst
ands
the
prob
lem
and
is a
ble
to d
raw
fro
m a
var
iety
of
stra
tegi
es to
sol
ve p
robl
ems.
The
stu
dent
dev
elop
s a
plan
and
car
ries
itou
t in
arri
ving
at t
he s
olut
ion(
s). T
he s
tude
nt s
olve
s th
e pr
oble
m, a
ndve
rifi
es a
nd c
omm
unic
ates
the
solu
tion.
The
stu
dent
wor
ks c
oope
rativ
ely
and
inde
pend
ently
. The
stu
dent
is w
illin
g to
take
ris
ks a
nd p
ursu
es o
ther
optio
ns in
sol
ving
pro
blem
s.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
ande
mon
stra
te a
n un
ders
tand
ing
of th
e pr
oble
m b
y id
entif
ying
key
info
rmat
ion
and
ques
tions
, and
pre
dict
a s
olut
ion(
s)de
velo
p a
plan
and
car
ry it
out
dete
rmin
e an
app
ropr
iate
sol
utio
nve
rify
the
solu
tion
purs
ue o
ther
opt
ions
, with
ass
ista
nce
shar
e an
d co
mm
unic
ate
met
hod(
s) a
nd s
olut
ion(
s)cr
eate
pro
blem
s (1
and
2 s
tep)
fro
m e
very
day
and
mat
hem
atic
alsi
tuat
ions
wor
k co
oper
ativ
ely,
and
mak
e a
sign
ific
ant c
ontr
ibut
ion
to th
e gr
oup
IL,
71
LEV
EL
3
The
stu
dent
inde
pend
ently
iden
tifie
s th
e re
latio
nshi
ps b
etw
een
and
amon
gkn
own
and
unkn
own
info
rmat
ion
in p
robl
em s
ituat
ions
, and
just
ifie
sst
rate
gies
use
d an
d so
lutio
ns f
ound
dur
ing
the
prob
lem
-sol
ving
pro
cess
.T
he s
tude
nt is
sel
f-m
otiv
ated
to id
entif
y pr
oble
ms
of in
tere
st in
rea
l-w
orld
cont
ems,
and
to p
ersi
st u
ntil
satis
fact
ory
solu
tions
are
fou
nd. T
he s
tude
ntis
will
ing
to c
omm
unic
ate
prob
lem
-sol
ving
pro
cess
es a
nd r
esul
ts in
ava
riet
y of
way
s.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
anco
nfid
ently
app
roac
h pr
oble
ms,
taki
ng r
isks
, and
per
seve
ring
unt
ilsa
tisfi
ed w
ith th
e re
sults
use
vari
ous
proc
esse
s (e
.g.,
visu
aliz
atio
n, d
eter
min
e pa
rt-w
hole
num
ber
rela
tions
hips
, etc
.) to
ana
lyze
pro
blem
s an
d ta
sks,
and
tode
term
ine
the
rela
tions
hips
bet
wee
n th
e qu
estio
n or
task
and
the
info
rmat
ion
prov
ided
reco
gniz
e th
at d
iffe
rent
str
ateg
ies
may
be
used
, and
just
ify
the
choi
ce(s
) m
ade
in th
e pr
oble
m-s
olvi
ng p
roce
ssse
ek c
onne
ctio
ns b
etw
een
new
and
pre
viou
s pr
oble
ms
inde
pend
ently
mak
e an
d co
mm
unic
ate
(in
vari
ous
way
s) p
redi
ctio
ns,
met
hods
, opt
ions
, sol
utio
ns, a
nd v
erif
icat
ions
crea
te a
nd s
olve
pro
blem
s fr
om e
very
day
and
mat
hem
atic
al s
ituat
ions
mak
e si
gnif
ican
t con
trib
utio
ns to
gro
up p
robl
em-s
olvi
ng,
dem
onst
ratin
g at
tent
ion
to a
ccur
acy,
thor
ough
ness
, per
sist
ence
, and
crea
tivity
Prob
lem
-Sol
ving
159
PR
OB
LEM
-SO
LVIN
GE
ND
OF
GR
AD
E 3
Sam
pie
Ass
essm
ent A
ctiv
ities
1. R
ules
:B
alan
ce th
e se
esaw
.R
obot
s th
at a
re th
e sa
me
have
the
sam
e w
eigh
t.R
obot
s th
at a
re d
iffer
ent h
ave
diffe
rent
wei
ghts
.A
ll ro
bots
wei
gh m
ore
than
zer
o ki
logr
ams.
Ifon
the
sees
aw w
eigh
s 5
kilo
gram
s, w
hatc
ould
the
othe
r ro
bots
wei
gh?
Giv
e m
ore
than
one
pos
sibi
lity.
Exp
lain
how
you
foun
d yo
ur a
nsw
ers.
2. D
onni
e ha
s to
clim
b 10
ste
ps to
rea
ch h
is b
edro
om d
oCir.
He
clim
bed
up 7
ste
ps a
nd w
ent d
own
3.H
e th
en c
limbe
d 4
mor
e st
eps
and
wen
t dow
n 6.
How
man
y st
eps
mus
t he
now
clim
b to
rea
ch h
is b
edro
omdo
or?,
Show
how
you
fou
nd th
e an
swer
.
3.Lo
olc
at th
e fo
llow
ing
pict
ure
patte
rn.
1.2.
3.4.
1
.. '
..
Wha
t wou
ld y
ou p
redi
ct p
ictu
re 1
to lo
ok li
ke?
Exp
lain
how
you
arr
ived
at t
his
deci
sion
.
72
1. 2. 3.
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
1
kg.
5kg
.
rr;s
TT
S:x
c--4
3 .P
e C
cAW
ve1t17
(9 S
e
onc
e16
(5__
;TP
gs.el
(44
t.2.
3.
1±.1
_J. A
mai
s...
_top
.Jt
4.e
_.1
_ itu
k__1
1,_
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
2LE
VE
L 3
kg.
6kg
.
1 6+
3 +
.3.-
,716
_an
aG
AL
)
.o
he
2.3.
4.
q, 'no
i4P
ontA
ft.
1.0
73
1. 2. 3.
kg.
Ita 3
..
kg.
::=10
2.
I
:
3.4.
IAat
_4_
140
Unl
it ai
teni
ta,
enno
e av
ai ik
aoO
j
163
Prob
lem
-Sol
ving
PA
TT
ER
NS
AN
D R
ELA
TIO
NS
EN
D O
F G
RA
DE
3
"Use
pat
tern
s to
des
crib
e th
e w
orld
and
to s
olve
pro
blem
s."
By
the
end
of G
rade
3, s
tude
nts
will
inve
stig
ate,
est
ablis
h, a
nd c
omm
unic
ate
rule
s fo
r no
n-nu
mer
ical
and
num
eric
al p
atte
rns,
incl
udin
g th
ose
foun
d in
the
hom
e, a
nd u
seth
ese
rule
s to
mak
e pr
edic
tions
Mor
e sp
ecif
ical
ly, s
tude
nts
will
sort
, con
cret
ely
and
pict
oria
lly, u
sing
two
or m
ore
attr
ibut
esus
e ob
ject
s an
d co
ncre
te m
odel
s to
exp
lain
the
rule
for
a p
atte
rn,
such
as
thos
e fo
und
on a
dditi
on a
nd m
ultip
licat
ion
char
tsm
ake
pred
ictio
ns b
ased
on
addi
tion
and
mul
tiplic
atio
n pa
ttern
s
(PR
-1.3
.1 to
PR
-111
.3.1
)
164
74
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
1
The
stu
dent
sor
ts m
ater
ials
, pic
ture
s, a
nd n
umbe
rs b
y on
e an
d tw
oat
trib
utes
. The
stu
dent
rec
ogni
zes,
con
tinue
s, c
reat
es, a
nd d
escr
ibes
repe
atin
g vi
sual
, aud
itory
, and
kin
esth
etic
pat
tern
s. T
he s
tude
ntre
pres
ents
bas
ic n
umbe
r re
latio
nshi
ps u
sing
mat
eria
ls a
nd p
ictu
res.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
anid
entif
y si
mila
ritie
s be
twee
n 2
obje
cts,
pic
ture
s, p
atte
rns,
etc
.so
rt, c
lass
ify,
and
com
pare
str
uctu
red
colle
ctio
ns in
depe
nden
tly, a
ndun
stru
ctur
ed c
olle
ctio
ns w
ith a
ssis
tanc
em
ake
atte
mpt
s to
rec
ord
sort
ing
and
clas
sify
ing,
usi
ng d
iagr
ams
and
grap
hs
reco
gniz
e va
riou
s pa
ttern
s in
the
envi
ronm
ent
desc
ribe
and
tran
slat
e co
ncre
te a
nd p
icto
rial
rep
eatin
g pa
ttern
s in
mor
e th
an o
ne w
ayus
e m
ater
ials
to c
ontin
ue s
impl
e gr
owin
g pa
ttern
s, a
nd d
raw
and
desc
ribe
a g
row
ing
patte
rn, w
ith a
ssis
tanc
esu
pply
mis
sing
num
bers
in p
atte
rns
and
grid
s, u
se m
ater
ials
or
pict
ures
to ju
stif
y th
inki
ng
use
mat
eria
ls to
rep
rese
nt th
e re
latio
nshi
p be
twee
n 2
num
bers
, and
reco
gniz
e sy
mbo
ls th
at d
enot
e m
athe
mat
ical
rel
atio
nshi
ps (
<, ,
=,
>, +
, , a
nd x
)
165
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
2
The
stu
dent
sor
ts a
nd c
lass
ifie
s, u
sing
2 o
r m
ore
attr
ibut
es.
The
stu
dent
iden
tifie
s, c
ompl
etes
, des
crib
es, a
nd c
reat
es n
on-n
umer
ical
and
num
eric
alre
peat
ing
and
grow
ing
patte
rns.
The
stu
dent
use
pat
tern
s an
d ba
sic
num
ber-
fact
rel
atio
nshi
ps to
sol
ve p
robl
ems.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
anid
entif
y si
mila
ritie
s an
d di
ffer
ence
s in
obj
ects
, pic
ture
s, p
atte
rns,
and
num
bers
sort
and
cla
ssif
y st
ruct
ured
and
uns
truc
ture
d m
ater
ials
and
num
ber
colle
ctio
ns, u
sing
ow
n an
d pr
edet
erm
ined
rul
esre
cord
sor
ting
and
clas
sify
ing
usin
g di
agra
ms
and
grap
hs
iden
tify,
sup
ply
mis
sing
ele
men
ts, c
reat
e, d
escr
ibe
in m
ore
than
one
way
, and
cor
rect
err
ors
in c
oacr
ete,
pic
tori
al, a
nd s
ymbo
lic r
epea
ting
patte
rns
( A
BC
, AB
C, A
BC
....)
reco
gniz
e, c
ontin
ue, o
r su
pply
mis
sing
num
bers
in s
kip-
coun
ting
orgr
owin
g pa
ttern
s in
volv
ing
sim
ple
addi
tion,
and
ora
lly d
escr
ibe
the
patte
rn o
r ju
stif
y so
lutio
nsid
entif
y, a
ct o
ut/m
odel
, and
ora
lly d
escr
ibe
patte
rns
visi
ble
on th
ehu
ndre
d, a
dditi
on, a
nd m
ultip
licat
ion
(7 b
y 7)
cha
rts
use
patte
rnin
g as
a s
trat
egy
for
solv
ing
prob
lem
s in
mat
hem
atic
s
reco
gniz
e an
d us
e kn
own
rela
tions
hips
to d
eter
min
e an
unk
now
n fa
ct;
(e.g
., 3
sets
of
7 =
; 2 s
ets
of 7
is 1
4, s
o 3
sets
of
7 is
14
+ 7
or
21)
use,
with
ass
ista
nce,
the
rela
tions
hips
bet
wee
n ad
ditio
n an
dsu
btra
ctio
n, a
nd b
etw
een
mul
tiplic
atio
n an
d di
visi
on w
hen
solv
ing
who
le-n
umbe
r pr
oble
ms
166
75
LEV
EL
3
The
stu
dent
inde
pend
ently
use
s so
rtin
g an
d cl
assi
fyin
g to
org
aniz
ein
form
atio
n. T
he s
tude
nt in
depe
nden
tly d
ispl
ays
a hi
ghly
dev
elop
ed s
ense
for
iden
tifyi
ng a
nd u
sing
pat
tern
s an
d kn
own
rela
tions
hips
to le
arn
abou
tm
athe
mat
ics,
and
to s
olve
pro
blem
s.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
anso
rt a
nd r
e-so
rt, c
lass
ify
and
re-c
lass
ify,
and
com
pare
the
resu
lts f
or th
esa
me
stru
ctur
ed o
r un
stru
ctur
ed c
olle
ctio
n, n
otin
g si
mila
ritie
s an
ddi
ffer
ence
s, e
xcep
tions
, and
exc
lusi
ons,
etc
.de
scri
be a
ttrib
utes
and
cla
ssif
icat
ion
rule
s fo
r ow
n or
pre
-sor
ted
colle
ctio
ns, a
ttem
ptin
g to
use
con
cise
and
pre
cise
lang
uage
just
ify
plac
emen
t of
addi
tiona
l ite
ms
into
exi
stin
g co
llect
ions
reco
rd s
ortin
g an
d cl
assi
fyin
g, u
sing
a v
arie
ty o
f di
agra
ms
and
grap
hs,
and
inte
rpre
t the
rec
ordi
ngs
of o
ther
s
reco
gniz
e, c
ontin
ue, a
nd s
uppl
y m
issi
ng e
lem
ents
in n
on-n
umer
ical
and
num
eric
al g
row
ing
patte
rns,
usi
ng m
ater
ials
, pic
ture
s, a
nd s
ymbo
lsus
e m
ater
ials
, dra
win
gs, a
nd e
very
day
lang
uage
to c
reat
e gr
owin
gpa
ttern
s, a
nd to
just
ify
deci
sion
sse
arch
for
pat
tern
s, a
nd u
se p
atte
rnin
g as
a s
trat
egy
for
solv
ing
prob
lem
s in
oth
er m
athe
mat
ics
stra
nds
or s
ubje
ct a
reas
, and
in r
eal l
ife
reco
gniz
e an
d ap
ply
an u
nder
stan
ding
of
the
rela
tions
hips
bet
wee
nad
ditio
n an
d su
btra
ctio
n, a
dditi
on a
nd m
ultip
licat
ion,
etc
., w
hen
solv
ing
who
le-n
umbe
r pr
oble
ms
Patte
rns
and
Rel
atio
ns
167
PA
TT
ER
NS
AN
D R
ELA
TIO
NS
-EN
D O
F G
RA
DE
3
Sam
ple
Ass
essm
ent A
ctiv
ities
1. T
his
is a
pie
ce c
ut f
rom
a h
undr
ed c
hart
. Fill
in th
e m
issi
ng n
umbe
rs.
66
2. C
ontin
ue th
is p
atte
rn.
Tel
l how
you
dec
ided
wha
t num
bers
topu
t in
each
box
.
Tel
l wha
t you
not
iced
abo
ut th
is p
atte
rn. H
ow d
id th
is h
elp
you
toco
ntin
ue th
e pa
ttern
?
3. C
ompl
ete
the
patte
rn a
nd th
en w
rite
the
next
line
of
the
patte
rn.
Des
crib
e th
e pa
ttern
s yo
u se
e.
1+
3 5+
3 5 7
1s
76
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
1. 2. 3.
LEV
EL
1
(AL
cak
ic-
un-I
- _5
5 +
eiLv
OIL
, e#0
>4
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169
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
2
S57
66
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ontin
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atte
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77
1. 2. 3.
LEV
EL
3
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t hel
ped
you
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ontin
ue th
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atte
rn.
I LO
C k
el c
Jin
At a
xam
pla
,
.a,
Patte
rns
and
Rel
atio
ns
171
ST
AT
IST
ICS
AN
D P
RO
BA
BIL
ITY
(DA
TA
MA
NA
GE
ME
NT
)-E
ND
OF
GR
AD
E 3
"Col
lect
, dis
play
and
ana
lyze
dat
a to
mak
e pr
edic
tions
abo
ut a
popu
latio
n."
By
the
end
of G
rade
3, s
tude
nts
will
colle
ct f
irst
and
sec
ond-
hand
dat
a, b
e ab
le to
dis
play
the
resu
lts in
mor
eth
an o
ne w
ay, a
nd in
terp
ret t
he d
ata
to m
ake
pred
ictio
nsus
e si
mpl
e pr
obab
ility
exp
erim
ents
, des
igne
d by
oth
ers,
to e
xpla
inou
tcom
es
Mor
e sp
ecif
ical
ly, s
tude
nts
will
colle
ct d
ata,
usi
ng p
rint
ed m
ater
ial a
nd m
easu
ring
/tech
nolo
gica
l res
ourc
esdi
spla
y da
ta, u
sing
ran
k or
deri
ngdi
spla
y th
e sa
me
data
in m
ore
than
one
way
mak
e pr
edic
tions
and
infe
renc
es w
hen
solv
ing
prob
lem
sob
tain
new
info
rmat
ion
by p
erfo
rmin
g ar
ithm
etic
ope
ratio
ns o
n th
eda
tade
scri
be th
e lik
elih
ood
of a
n ou
tcom
e, u
sing
suc
h te
rms
as li
kely
, les
slik
ely,
cha
nce
cond
uct a
pro
babi
lity
expe
rim
ent,
choo
se a
n ap
prop
riat
e re
cord
ing
met
hod,
and
dra
w c
oncl
usio
ns f
rom
the
resu
lts
(SP-
I.3.
1 to
SP-
V.3
.2)
78
172
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
1
The
stu
dent
, with
ass
ista
nce,
col
lect
s, o
rgan
izes
, and
dis
play
sin
form
atio
n. T
he s
tude
nt r
eads
tabl
es, e
tc.,
and
the
info
rmat
ion
visi
ble
on c
oncr
ete,
pic
toria
l, an
d ba
r gr
aphs
org
aniz
ed o
n a
1:1
scal
e. T
hest
uden
t use
s ev
eryd
ay la
ngua
ge to
mak
e pr
edic
tions
bas
ed o
n pe
rson
alex
perie
nces
, and
car
ries
out g
iven
pro
babi
lity
expe
rimen
ts.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
anm
ake
a pr
edic
tion
of th
e ou
tcom
eco
llect
and
org
aniz
e m
ater
ials
, and
dis
play
the
resu
lts (
usin
g 1:
1re
latio
nshi
p) o
n co
ncre
te a
nd p
icto
rial
gra
phs,
or
sort
ing
diag
ram
sco
mpl
ete
part
ially
con
stru
cted
tabl
es o
r gr
aphs
(e.g
., fi
ll in
the
freq
uenc
y to
tals
for
a ta
lly c
hart
; lab
el a
gra
ph; e
tc.)
answ
er s
peci
fic
ques
tions
abo
ut th
e in
form
atio
n sh
own
on c
oncr
ete,
pict
oria
l, an
d ba
r gr
aphs
, (1:
1 sc
ale)
and
sor
ting
diag
ram
s
carr
y ou
t, w
ith a
ssis
tanc
e, s
impl
e pr
obab
ility
exp
erim
ents
use
the
ever
yday
lang
uage
of
chan
ce to
mak
e a
pred
ictio
n ba
sed
onpe
rson
al e
xper
ienc
es (
e.g.
, alw
ays,
oft
en, s
omet
imes
, har
dly
ever
, nev
er,
prob
ably
, lik
ely,
unl
ikel
y)
173
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
2
The
stu
dent
col
lect
s, o
rgan
izes
, dis
play
s, a
nd d
escr
ibes
dat
a in
a v
arie
tyof
way
s. T
he s
tude
nt in
terp
rets
the
data
, and
mak
es r
easo
nabl
e pr
edic
tions
and
infe
renc
es b
ased
on
the
data
. The
stu
dent
use
s th
e la
ngua
ge o
f ch
ance
to d
escr
ibe
the
likel
ihoo
d of
eve
nts,
and
car
ries
out
sim
ple
expe
rim
ents
tode
term
ine
outc
omes
.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
anfo
rmul
ate
a qu
estio
n (i
ndep
ende
ntly
/coo
pera
tivel
y)m
ake
a pr
edic
tion
of th
e ou
tcom
ede
term
ine
wha
t dat
a ne
eds
to b
e co
llect
ed, w
here
, and
how
to d
o so
colle
ct d
ata
(ind
epen
dent
ly/c
oope
rativ
ely)
sort
and
cla
ssif
yde
scri
be d
ata
colle
cted
and
tech
niqu
es u
sed
in c
olle
ctin
gdi
spla
y da
ta u
sing
app
ropr
iate
labe
ls a
nd ti
tles
inte
rpre
t rep
rese
ntat
ions
of
data
incl
udin
g gr
aphs
with
1:1
, 1:2
, 1:5
,an
d 1:
10 s
cale
spe
rfor
m a
rith
met
ic o
pera
tions
on
the
data
to c
reat
e ne
w in
form
atio
n,an
d ve
rify
the
calc
ulat
ions
mak
e co
mpa
riso
nsdr
aw a
nd ju
stif
y co
nclu
sion
s
carr
y ou
t pro
babi
lity
expe
rim
ents
reco
rd e
xper
imen
tal r
esul
tsde
scri
be r
esul
ts, u
sing
the
lang
uage
of
prob
abili
ty (
likel
y, u
nlik
ely,
cert
ain,
unc
erta
in, p
roba
ble,
not
pro
babl
e)
79
LEV
EL
3
The
stu
dent
des
igns
and
con
duct
s da
ta m
anag
emen
t act
iviti
es to
fin
dan
swer
s to
cur
ricu
lar
or p
erso
nal q
uest
ions
. The
stu
dent
org
aniz
es a
nddi
spla
ys th
e sa
me
data
in a
var
iety
of
way
s. T
he s
tude
nt d
raw
sco
nclu
sion
s an
d m
akes
pre
dict
ions
bas
ed o
n da
ta, a
nd u
ses
the
lang
uage
of c
hanc
e to
pre
dict
the
outc
omes
of
even
ts.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
anfo
rmul
ate
ques
tions
, and
use
a v
arie
ty o
f m
etho
ds to
col
lect
and
orga
nize
rus
t and
sec
ond-
hand
info
rmat
ion
cons
truc
t and
labe
l cha
rts
and
grap
hs, a
nd e
valu
ate
the
suita
bilit
y of
diff
eren
t cha
rts
and
grap
hs f
or d
ispl
ayin
g th
e sa
me
info
rmat
ion
draw
con
clus
ions
and
mak
e pr
edic
tions
fro
m d
ispl
ayed
info
rmat
ion
appl
y ar
ithm
etic
ope
ratio
ns to
dat
a, a
nd u
se th
e re
sults
to s
uppo
rtpr
edic
tions
or
to f
orm
ulat
e ne
w q
uest
ions
desi
gn g
ames
or
expe
rim
ents
usi
ng c
once
pts
of c
hanc
e, a
nd u
se th
ela
ngua
ge o
f pr
obab
ility
to d
escr
ibe
resu
lts o
r m
ake
pred
ictio
ns
Stat
istic
s an
d Pr
obab
ility
175
ST
AT
IST
ICS
AN
D P
RO
BA
BIL
ITY
(DA
TA
MA
NA
GE
ME
NT
)--E
ND
OF
GR
AD
E 3
Sam
pk A
sses
smen
t Act
iviti
es
1. M
rs. S
mith
has
23
stud
ents
in h
er G
rade
3 c
lass
. Bef
ore
thei
r sw
imm
ing
clas
ses
star
ted
the
stud
ents
wan
ted
to k
now
how
man
y st
uden
ts w
ere
atea
ch s
wim
min
g le
vel.
The
se a
re tb
e da
ta th
ey c
olle
cted
.
yello
wI/
oran
ge.1
44re
dm
aroo
n41
11-
IIbl
ueII
gree
n
Mak
e an
d la
bel a
gra
ph to
dis
play
this
info
rmat
ion.
Rem
embe
r to
incl
ude
all t
he n
eces
sary
par
ts o
f a
grap
h!W
rite
3 q
uest
ions
abo
ut y
our
grap
h th
at y
ou c
ould
ask
a f
rien
d.
441
2. L
ook
at th
e pi
ctur
e be
low
. It s
how
s a
spin
ner
that
mig
ht b
e us
ed in
aga
me.
The
cha
nces
of
land
ing
on R
ED
whe
n us
ing
this
spi
nner
are
2 o
utof
4, o
ri, o
r fi
fty/
fift
y.2
Des
ign
a di
ffer
ent s
pinn
er th
at w
ould
stil
l giv
e R
ED
a f
ifty
/fif
ty c
hanc
e.W
rite
dow
n yo
ur r
easo
ns f
or y
our
desi
gn.
Dis
cuss
you
r so
lutio
n an
d re
ason
s w
ith y
our
part
ner
(gro
up).
If
you
have
time,
des
ign
othe
r sp
inne
rs s
how
ing
diff
eren
t pro
babi
litie
s. L
abel
them
.U
se th
e sp
ace
belo
w to
do
your
wor
k.
80
2.
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
1
8: 6 5 LI 3
Yel
low
Mar
ne"
Orm
v
I Ws.
fcis
7LA
2 O
lich
s's
Nur
nder
?
h:gg
est
3 w
ho/ i
s-t
he g
roph
Abo
ui'?
One
ify
04tg
rire
elee
stgr
f:$oh
-lie
cod
you
shou
ldse
tci
ft
fO
le*
ocre
od
rfr'f
rY()
e'en
,'en
speo
lA;+
goes
.
17 7
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
2LE
VE
L 3
5wnl
nlin
q
I. 9
44,t,
0724
.14,
...0
kto.
3. `
1444
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4k A
ie
"NO
2.hi
ll-$1
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1.3
1.11
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artr
ee-
ery.
s.
qhd
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free
nhec
atig
erA
et-e
art
7470
4771
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14e
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ince
1 'i
S81
1. 2.
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LeV
II
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?,24
44.
Act
*44
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ay?
71."
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mr
4114
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ama
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ow
Sidi
zeo
4771
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444
49 4
44tu
Y45
0) If
ive?
44- P
a' -
offt
v,P
Stty
Asp
.
F D
TI
la I
sle
usec
zt milo
,
fiat
/fir
st L
amm
,' So
t,O
W"c
ed,
Stat
istic
s an
d Pr
obab
ility
179
SH
AP
E A
ND
SP
AC
E (
ME
AS
UR
EM
EN
T)
EN
D O
F G
RA
DE
3
"Des
crib
e an
d co
mpa
re e
very
day
phen
omen
a, u
sing
eith
er d
irect
or
indi
rect
mea
sure
men
t."
By
the
end
of G
rade
3, s
tude
nts
will
estim
ate,
mea
sure
, and
com
pare
, usi
ng w
hole
num
bers
and
pri
mar
ilyst
anda
rd u
nits
of
mea
sure
Mor
e sp
ecif
ical
ly, s
tude
nts
will
estim
ate,
mea
sw".
rec
ord,
com
pare
, and
ord
er o
bjec
ts b
y le
ngth
, hei
ght,
and
peri
met
er u
sing
non
-sta
ndar
d an
d st
anda
rd u
nits
sele
ct th
e m
ost a
ppro
pria
te u
nit,
incl
udin
g km
, to
mea
sure
leng
th, a
ndde
scri
be th
e re
latio
nshi
ps a
mon
g cm
, dm
, and
mse
lect
an
appr
opri
ate
non-
stan
dard
uni
t to
estim
ate,
mea
sure
, rec
ord,
com
pare
, and
ord
er s
hape
s by
are
aco
nstr
uct a
var
iety
of
shap
es g
iven
a s
peci
fic
area
in n
on-s
tand
ard
units
sele
ct a
n ap
prop
riat
e no
n-st
anda
rd u
nit,
or li
tres
, to
estim
ate,
mea
sure
,re
cord
, com
pare
, and
ord
er c
onta
iner
s by
vol
ume/
capa
city
use
non-
stan
dard
and
sta
ndar
d un
its (
g, k
g) to
est
imat
e, m
easu
re, r
ecor
d,co
mpa
re, a
nd o
rder
obj
ects
by
mas
s, a
nd c
onst
ruct
obj
ects
to e
qual
agi
ven
mas
ses
timat
e th
e pa
ssag
e of
tim
e, u
sing
sta
ndar
d un
its (
seco
nds,
min
utes
,ho
urs,
day
s, m
onth
s, y
ears
), a
nd r
elat
e da
ys to
yea
rsre
ad a
nd w
rite
the
days
of
the
wee
k an
d th
e m
onth
s of
the
year
read
dig
ital c
lock
s, a
nd w
rite
tim
e to
the
near
est m
inut
e, u
sing
12-
hour
nota
tion
estim
ate,
rea
d, a
nd r
ecor
d te
mpe
ratu
re to
the
near
est d
egre
e, a
nd r
elat
ete
mpe
ratu
re to
eve
ryda
y si
tuat
ions
estim
ate,
cou
nt, a
nd r
ecor
d co
llect
ions
of
coin
s an
d bi
llsde
term
ine
the
amou
nt o
f ch
ange
fro
m a
pur
chas
e
(SS-
1.3.
1 to
SS-
V11
1.3.
4)
130
82
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL1
The
stu
dent
sel
ects
, som
etim
es in
depe
nden
tly, a
ppro
pria
te n
on-s
tand
ard
and
stan
dard
SI u
nits
to e
stim
ate
and
mea
sure
the
leng
th, m
ass,
or
capa
city
of o
bjec
ts, a
nd u
ses
the
resu
lts to
des
crib
e an
d co
mpa
reob
ject
s. T
he s
tude
nt, w
ith a
ssis
tanc
e, u
ses
conc
rete
ref
eren
ces
toes
timat
e th
e re
sults
of m
easu
rem
ents
, and
com
pare
s es
timat
es w
ithac
tual
mea
sure
men
ts.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
anre
cogn
ize
whi
ch m
easu
rem
ent t
ool(
s) is
use
d fo
r le
ngth
, mas
s,vo
lum
e/ca
paci
ty, t
ime,
and
tem
pera
ture
, and
whi
ch u
nit w
illap
prop
riat
ely
repr
esen
t the
attr
ibut
e th
at is
mea
sure
des
timat
e, m
easu
re, r
ecor
d, c
ompa
re, a
nd o
rder
, with
ass
ista
nce,
linea
r at
trib
utes
, are
a, c
apac
ity, a
nd m
ass
of s
hape
s an
d ob
ject
s in
the
lear
ning
env
iron
men
tco
rrec
tly u
se c
ompa
rativ
e la
ngua
ge (
heav
ier
and
heav
iest
, etc
.)
read
and
wri
te ti
me
to th
e ho
ur a
nd h
alf
hour
(di
gita
l clo
ck)
read
and
rec
ord
tem
pera
ture
on
a C
elsi
us th
erm
omet
er
reco
gniz
e co
ins
and
bills
to $
10, a
nd m
ake
chan
ge to
$1
usin
gva
riou
s co
mbi
natio
ns o
f co
ins
181
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
2T
he s
tude
nt e
stim
ates
in a
ll m
odes
of
mea
sure
men
t (lin
ear,
vol
ume/
capa
city
,m
ass/
wei
ght,
time,
tem
pera
ture
, and
mon
ey)
usin
g no
n-st
anda
rd a
ndst
anda
rd S
I un
its, r
ecog
nizi
ng w
hen
estim
ates
are
app
ropr
iate
. The
stu
dent
perf
orm
s ac
tual
mea
sure
men
ts in
eac
h m
ode,
rec
ordi
ng in
app
ropr
iate
uni
ts.
The
stu
dent
ord
ers,
com
pare
s, a
nd d
escr
ibes
rel
atio
nshi
ps b
etw
een
and
amon
g m
easu
rem
ents
.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
anse
lect
the
mos
t app
ropr
iate
uni
t and
just
ify
the
choi
cees
timat
e an
d m
easu
re, u
sing
non
-sta
ndar
d un
itses
timat
e an
d m
easu
re, i
n st
anda
rd S
I un
its-
linea
r di
stan
ce (
cm, d
m, m
and
km
)-
volu
me/
capa
city
(lit
res)
- m
ass/
wei
ght (
g, k
g)-
tem
pera
ture
(de
gree
s C
elsi
us)
reco
rd, c
ompa
re, a
nd o
rder
mea
sure
men
tsre
cogn
ize
and
desc
ribe
the
rela
tions
hips
bet
wee
n an
d am
ong
the
resp
ectiv
e SI
uni
ts (
e.g.
, urn
= 1
0 dm
; 100
cm
)
cons
truc
t or
draw
- a
vari
ety
of s
hape
s w
ith a
spe
cifi
c ar
ea-
a va
riet
y of
rig
ht a
ngle
sha
pes
with
a s
peci
fic
peri
met
er-
spec
ifie
d le
ngth
s (c
m, d
m)
estim
ate
the
pass
age
of ti
me
in m
inut
es a
nd s
econ
dsre
ad a
nd w
rite
tim
e, u
sing
dig
ital a
nd a
nalo
g (1
2 ho
ur)
cloc
ks (
hour
s an
dha
lf h
ours
, min
utes
pas
t the
hou
r)re
late
hou
rs to
day
s, d
ays
to w
eeks
, wee
ks to
yea
rs, m
onth
s to
yea
rs
read
and
rec
ord
tem
pera
ture
, in
degr
ees
Cel
sius
, usi
ng a
ther
mom
eter
estim
ate,
cou
nt, a
nd r
ecor
d co
llect
ions
of
coin
s an
d bi
lls u
p to
$10
reco
gniz
e bi
lls u
p to
$10
0re
pres
ent a
giv
en v
alue
of
mon
ey in
a v
arie
ty o
f w
ays
(250
= 1
00 +
100
+ 5
0; 2
5 pe
nnie
s; 5
nic
kels
; etc
.)m
ake
chan
ge u
p to
$10
read
and
wri
te b
oth
mon
ey n
otat
ions
($0
.89
and
890)
83
iS
LEV
EL
3T
he s
tude
nt a
pplie
s an
und
erst
andi
ng o
f m
easu
rem
ent s
yste
ms
in a
ll .s
ubje
ctar
eas,
and
in r
eal l
ife.
The
stu
dent
est
imat
es e
ffec
tivel
y, u
ses
rela
tions
hips
amon
g st
anda
rd (
SI)
units
to r
enam
e m
easu
rem
ents
, and
app
lies
obse
rved
patte
rns
to s
impl
ify
the
calc
ulat
ion
of p
erim
eter
, are
a, a
nd v
olum
e.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
anes
timat
e, w
ith a
hig
h de
gree
of
accu
racy
, and
just
ify
mea
sure
men
tex
plai
n an
d ap
ply
the
rela
tions
hips
am
ong
stan
dard
SI
units
, inc
ludi
ngth
e co
nver
sion
of
nun
to m
and
vic
e-ve
rsa,
etc
., an
d re
late
the
met
ric
syst
em to
the
base
10
plac
e-va
lue
syst
em
draw
or
cons
truc
t lin
es a
nd c
onst
ruct
sha
pes
and
pris
ms
acco
rdin
g to
give
n or
sel
f-de
term
ined
mea
sure
men
tsdi
scov
er a
nd u
se r
ules
to f
md
peri
met
er, a
rea,
and
rol
ume
to s
olve
ow
nan
d gi
ven
prob
lem
s
read
dig
ital a
nd a
nalo
g cl
ocks
and
wri
te ti
me
to s
econ
dsIL
- us
e pa
st e
xper
ienc
es to
est
imat
e th
e tim
e ne
eded
for
new
exp
erie
nces
,an
d ap
ply
know
ledg
e of
tim
e re
latio
nshi
ps (
min
utes
to h
ours
, hou
rs to
days
, etc
.) to
sol
ve p
robl
ems
crea
te a
nd s
olve
mul
ti-st
ep p
robl
ems
invo
lvin
g pu
rcha
ses
and
chan
ge u
pto
$10
0
Shap
e an
d Sp
ace
163
SH
AP
E A
ND
SP
AC
E (
ME
AS
UR
EM
EN
T)
EN
D O
F G
RA
DE
3
Sam
ple
Ass
essm
ent A
ctiv
ities
1. E
xpla
in w
hat a
rea
is.
Use
rub
ber
band
s to
mak
e 8
diff
eren
t sha
pes,
eac
h w
ith a
n ar
ea o
f 4
squa
res
on th
e ge
oboa
rd. R
ecor
d al
l the
sha
pes
you
mak
e on
to th
e do
t-pa
per
squa
res
belo
w.
2. I
mag
ine
you
colle
cted
this
mon
ey f
rom
a p
opco
rn s
ale.
Spr
ead
out t
heco
ins
you
find
in y
our
bag.
Tel
l, w
ithou
t cou
ntin
g, a
bout
how
muc
hm
oney
you
thin
k th
ere
is.
Cou
nt th
e m
oney
. The
am
ount
is($
8.20
)D
escr
ibe
how
you
wen
t abo
ut c
ount
ing
the
mon
ey.
The
mon
ey in
the
bag
was
in c
oins
onl
y. H
ow c
ould
you
hav
e th
is s
ame
amou
nt o
f m
oney
usi
ng b
ills
and
as f
ew c
oins
as
need
ed. T
o an
swer
, dra
wan
d la
bel o
r de
scri
be in
wor
ds.
3. T
ell w
hat y
ou k
now
abo
ut h
ow c
entim
etre
s, m
etre
s, a
nd d
ecim
etre
s re
late
or c
onne
ct to
eac
h ot
her. 18
484
1.
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL1
-1;a
e--6
Ote
le-/
- O
ftli&
rova
glis
;
2.44
40_
fe
3.
-91-
4111
14"i
id-1
4114
411.
41,4
118L
r412
14:
-113
41.0
4,..r
dais
id--
;;.-1
7-11
4/21
14.4
.;:tS
-4-1
4/02
1:A
ir-
C3'
czP
17e3
Ora
all
1.44
.tel
lesi
egcl
ih;
0%,
135
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
2
[EP
2.lV
as- 41
0
try
font
*1
AA
P,
and
itet
6:,h
ess*
,,
83.
rntk
re.5
axe
,m
ore,
4.1.
4.4%
.cr
lf\
heY
eal
l are
hies
eri9
Ittl4
6
1.0:
2446
0.1
KM
ct
(24
85
1. 2. 3.
LEV
EL
3
cArr
ze.1
1.4
rME
6.4
INtig
Pik)
--41
S42-
4/ey
oh ib
ij4,0
_,si
, Lj :
si.
onet
L
d11
j4 A
ka-
Jkl
isd
400
4Azi
an
4A
irft
,
gfic
e0
Dot
i04
514
00
OQ
_mm
ext!
.1:I
velh
elPi
stit
woo
rar4
/04
ctnh
q m
ete.
nere
Are
ki)
h a
dm. A
nof
them
cue
q &
hit
ofm
eile
iriiv
.
18 7
Shap
e an
d Sp
ace
SH
AP
E A
ND
SP
AC
E E
ND
OF
GR
AD
E 3
(3-D
, 2-D
, AN
D T
RA
NS
FO
RM
AT
ION
AL
GE
OM
ET
RY
)
"Des
crib
e th
e ch
arac
teris
tics
of 3
-D o
bjec
ts a
nd 2
-D s
hape
s, a
nd a
naly
ze th
ere
latio
ns a
mon
g th
em."
"Per
form
, ana
lyze
and
cre
ate
tran
sfor
mat
ions
."
By
the
end
of G
rade
3, s
tude
nts
will
desc
ribe
, cla
ssif
y, c
onst
ruct
, and
rel
ate
3-D
obj
ects
and
2-D
sha
pes
use
num
bers
and
dir
ectio
n w
ords
to d
escr
ibe
the
rela
tive
posi
tions
ofob
ject
s in
one
dim
ensi
on, u
sing
eve
ryda
y co
ntex
ts
Mor
e sp
ecif
ical
ly, s
tude
nts
will
iden
tify
and
coun
t fac
es, v
ertic
es, a
nd e
dges
of
3-D
obj
ects
iden
tify
and
nam
e fa
ces
of a
3-D
obj
ect w
ith a
ppro
pria
te 2
-D n
ames
desc
ribe
pyr
amid
s an
d pr
ism
s by
the
shap
e of
the
base
dem
onst
rate
that
a r
ecta
ngul
ar s
olid
has
mor
e th
an o
ne n
etco
mpa
re a
nd c
ontr
ast t
wo
3-D
obj
ects
reco
gniz
e co
ngru
ent (
iden
tical
) 3-
D o
bjec
ts a
nd 2
-D s
hape
sex
plor
e, c
oncr
etel
y, th
e co
ncep
ts o
f pe
rpen
dicu
lar,
par
alle
l, an
din
ters
ectin
g lin
es in
3-D
obj
ects
com
mun
icat
e an
d ap
ply
the
term
s of
dir
ectio
n, s
uch
as n
orth
or
sout
h, a
ndre
late
to m
aps
grap
h w
hole
num
ber
poin
ts o
n a
hori
zont
al o
r ve
rtic
al n
umbe
r lin
etr
ace
a pa
th, u
sing
ora
l or
wri
tten
inst
ruct
ions
(SS
-IX
.3.1
to S
S-X
II.3.
2)
iss
86
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
The
stu
dent
use
s ev
eryd
ay la
ngua
ge, a
nd g
eom
etric
lang
uage
with
assi
stan
ce, t
o na
me,
des
crib
e, a
nd c
ompa
re 3
-D o
bjec
ts a
nd 2
-Dsh
apes
. The
stu
dent
use
s co
ncre
te o
bjec
ts a
nd p
aper
to c
onst
ruct
3-D
obje
cts
and
2-D
sha
pes,
and
con
nect
s th
ese
obje
cts
and
shap
es to
rea
l-w
orld
thin
gs.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
anas
soci
ate
3-13
obj
ects
and
2-D
sha
pes
with
geo
met
ric
nam
esin
depe
nden
tly s
ort a
nd c
lass
ify
obje
cts
and
shap
es b
y si
mpl
epr
oper
ties
(col
our,
num
ber
of s
ides
, rol
ls, e
tc.)
and
by
geom
etri
cpr
oper
ties
with
ass
ista
nce
(par
alle
l lin
es, n
umbe
r of
ver
tices
, squ
are
pris
ms,
etc
.)de
scri
be a
nd c
ompa
re 3
-D o
bjec
ts a
nd 2
-13
shap
es u
sing
at l
east
one
proP
enY
use
basi
c 2-
1) s
hape
s an
d 3-
13 o
bjec
ts to
bui
ld r
epea
ting
patte
rns,
and
desc
ribe
the
patte
rnin
g ru
le(s
)
use
mat
eria
ls o
r ne
ts to
sol
ve s
impl
e co
nstr
uctio
n pr
oble
ms
and
puzz
les
use
info
rmal
geo
met
ric
term
s (u
p, d
own,
left
, rig
ht, e
tc.)
and
num
bers
to d
escr
ibe
posi
tions
of
obje
cts
in s
pace
1c9
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
2
The
stu
dent
des
crib
es, c
lass
ifie
s, c
onst
ruct
s, a
nd r
elat
es 3
-D o
bjec
ts a
nd 2
-D
sha
pes,
and
thei
r po
sitio
ning
in s
pace
. The
stu
dent
use
s co
rrec
tte
rmin
olog
y to
des
crib
e th
e pr
oper
ties
and
rela
tions
hips
of
3-D
obj
ects
and
2-D
sha
pes
incl
udin
g co
ncep
ts o
f co
ngru
ence
, par
alle
lism
, per
pend
icul
arity
,an
d sy
mm
etry
.T
he s
tude
nt d
ispl
ays
an a
war
enes
s of
geo
met
ric
idea
s in
his/
her
envi
ronm
ent.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
anid
entif
y, n
ame,
cla
ssif
y, d
escr
ibe,
and
rel
ate
conc
rete
3-D
obj
ects
tosk
elet
ons,
net
s, a
nd p
icto
rial
rep
rese
ntat
ions
com
pare
and
con
tras
t 3-D
obj
ects
and
2-D
usin
g 2
prop
ertie
s(e
xam
ple:
edg
es a
nd f
aces
)
crea
te 2
- an
d 3-
dim
ensi
onal
pat
tern
s us
ing
at le
ast 2
cri
teri
a (e
xam
ple:
shap
e an
d or
ient
atio
n)
build
ske
leto
ns o
f 3-
13 o
bjec
ts a
nd c
onst
ruct
obj
ects
fro
m th
eir
nets
iden
tify,
nam
e, a
nd c
onst
ruct
pol
ygon
s (u
p to
8 s
ides
)sh
ow c
ongr
uenc
y of
obj
ects
and
sha
pes
by s
uper
impo
sing
(cov
erin
g), f
oldi
ng, a
nd m
easu
ring
dem
onst
rate
con
cret
ely,
and
rep
rese
nt p
aral
lel,
perp
endi
cula
r, a
ndin
ters
ectin
g lin
es
desc
ribe
loca
tions
incl
udin
g di
rect
ions
on
a m
ap, g
rid,
or
line
grap
h w
hole
-num
ber
poin
ts o
n a
hori
zont
al o
r ve
rtic
al n
umbe
r lin
e(c
oord
inat
es)
crea
te a
nd f
ollo
w a
pat
h us
ing
oral
and
/or
wri
tten
dire
ctio
n(s)
use
a va
riet
y of
str
atili
es to
sol
ve g
eom
etri
c pr
oble
ms
190
87
LEV
EL
3
The
stu
dent
use
s ac
cura
te g
eom
etri
c la
ngua
ge to
des
crib
e th
e pr
oper
ties
ofre
al-w
orld
obj
ects
and
sha
pes,
and
to e
xpla
in s
hape
and
pos
ition
rela
tions
hips
. The
stu
dent
use
s to
ols
and
tech
nolo
gy to
cre
ate
vari
ous
shap
es a
nd m
aps
with
giv
en o
r se
lf-d
eter
min
ed d
irec
tions
.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
anco
nfid
ently
use
geo
met
ric
lang
uage
ora
lly to
nam
e, d
escr
ibe,
and
rel
ate
the
prop
ertie
s of
obj
ects
and
sha
pes
iden
tify
and
desc
ribe
, with
out p
rom
ptin
g, g
eom
etri
c ob
ject
s an
d sh
apes
with
in o
ther
obj
ects
or
shap
es a
nd n
atur
e
build
com
plex
str
uctu
res
and
shap
es, a
nd p
redi
ct th
e re
sults
of
mak
ing
chan
ges
to c
onst
ruct
ions
use
avai
labl
e te
chno
logy
(ex
ampl
e: L
ogo)
to d
emon
stra
te a
nun
ders
tand
ing
of th
e pr
oper
ties
of s
hape
s, to
cre
ate
figu
res
usin
gco
mbi
natio
ns o
f sh
apes
, and
to g
ive
dire
ctio
ns f
or m
ovin
g th
roug
h sp
ace
draw
mip
s sh
owin
g kn
own
area
s, a
nd p
rovi
de o
ral o
r w
ritte
ndi
rect
ions
for
mov
ing
and
loca
ting
obje
cts
on m
aps
or g
rids
(co
ordi
nate
poin
ts)
with
ass
ista
nce,
exp
lain
a s
trat
egy
for
prov
ing
all p
ossi
ble
solu
tions
for
age
omet
ric
cons
truc
tion
prob
lem
Shap
e an
d Sp
ace
191
NA
PE
AN
D P
A E
EN
D F
RA
DE
3(3
-D, 2
-D, A
ND
TR
AN
SF
OR
MA
TIO
NA
L G
EO
ME
TR
Y)
Sam
pk A
sses
smen
t Act
iviti
es
1. W
hich
two
shap
es a
re th
e sa
me?
Exp
lain
you
r th
inki
ng.
i1
A
2. I
n w
hat 3
way
s ar
e th
ese
obje
cts
the
sam
e? N
ame
3 di
ffer
ence
s be
twee
nth
ese
obje
cts.
3. T
he m
ap s
how
s so
me
of th
e st
reet
s in
a c
ityPe
ter
was
on
the
com
er o
f Se
cond
Ave
nue
and
C S
tree
t. H
e w
alke
d I
bloc
k no
rth,
I b
lock
eas
t, 3
bloc
ks s
outh
, and
2 b
lock
s w
est.
Whe
re is
he
now
?
JLJI
ILJ.
L
2]
Firs
t Ave
nue Can
Seco
nd A
venu
e
MA
MA
it4T
hird
Ave
nue
Four
th A
venu
eM
MM
RM
rm
FP P
w<
88
192
1
1.
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AN
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RD
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F P
ER
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CE
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EL
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ctan
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its
LEV
EL
2
ST
AN
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F P
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RM
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CE
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194
89
LEV
EL
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ays
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s.
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s44
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m o
re is
6.
Seco
nd A
venu
e
N M
M m
ammdirr
On
corn
er0.
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twer
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rici
stre
t 3 5
Shap
e an
d Sp
ace
NU
MB
ER
(C
ON
CE
PT
S)-
EN
D O
F-G
RA
DE
3
"Use
num
bers
to d
escr
ibe
quan
titie
s."
"Rep
rese
nt n
umbe
rs in
mul
tiple
way
s."
By
the
end
of G
rade
3, s
tude
nts
will
deve
lop
a nu
mbe
r se
nse
for
who
le n
umbe
rs 0
to 1
000,
and
exp
lore
frac
tions
(fi
fths
and
tent
hs)
Mor
e sp
ecif
ical
ly, s
tude
nts
will
coun
t for
war
d by
2s,
5s,
10s
, and
100
s to
100
0, u
sing
ran
dom
sta
rtin
gpo
ints
, and
bac
kwar
d by
2s,
5s,
10s
, 25s
, and
100
s us
ing
star
ting
poin
tsth
at a
re m
ultip
les
of th
ese
num
bers
read
and
wri
te n
umer
als
to 1
000,
rea
d an
d w
rite
num
ber
wor
ds to
100
,an
d us
e or
dina
l num
bers
to 1
00re
cogn
ize,
bui
ld, c
ompa
re, a
nd o
rder
set
s co
ntai
ning
0 to
100
0 el
emen
tsre
pres
ent a
nd d
escr
ibe
num
bers
to 1
000
in a
var
iety
of
way
sre
cogn
ize
and
expl
ain
if a
num
ber
is d
ivis
ible
by
2, 5
, cc
10
dem
onst
rate
, con
cret
ely
and
sym
bolic
ally
, pla
ce-v
alue
con
cept
s to
giv
em
eani
ng to
num
bers
to 1
000
roun
d nu
mbe
rs to
the
near
est 1
00es
timat
e, th
en c
ount
the
num
ber
of o
bjec
ts in
a s
et (
0-10
00),
and
com
pare
the
estim
ate
with
the
actu
al c
ount
illus
trat
e an
d ex
plai
n ha
lves
, thi
rds,
fou
rths
, fif
ths,
and
tent
hs a
s pa
rt o
f a
regi
on o
r a
set
(N-I
.3.1
to N
-II.
3.1)
90
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
1
The
stu
dent
cou
nts,
rep
rese
nts,
and
nam
es 2
dig
it nu
mbe
rs, b
ut h
aslim
ited
unde
rsta
ndin
g of
cou
ntin
g an
d pl
ace-
valu
e co
ncep
ts p
ast 1
00.
7he
stud
ent r
ecog
nize
s an
d na
mes
uni
t fra
ctio
ns o
f a
regi
on. (
112,
1/3
,1/
4, 1
/5, a
nd 1
/10)
.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
ande
mon
stra
te a
n un
ders
tand
ing
of c
onse
rvat
ion
of n
umbe
rro
te c
ount
to 1
000,
and
ski
p-co
unt f
orw
ard
and
back
war
d by
2, 5
,an
d 10
to 1
00, u
sing
mul
tiple
s as
sta
rtin
g po
ints
reco
gniz
e, r
ead,
wri
te, a
nd o
rder
num
eral
s to
100
, and
nam
enu
mbe
rs to
100
as
odd
or e
ven
read
and
wri
te n
umbe
r w
ords
to 2
0, a
nd u
se o
rdin
al n
umbe
rs to
31
repr
esen
t and
ren
ame
num
bers
to 1
00, u
sing
dif
fere
nt m
odes
(mat
eria
ls, p
ictu
res,
and
sym
bols
) an
d di
ffer
ent c
ombi
natio
ns(2
5 =
20
+ 5
; 10
+ 1
0 +
5; 1
3 +
12;
etc
.)co
unt,
com
pare
, and
ord
er s
ets
to 1
00us
e sy
mbo
ls to
exp
ress
rel
atio
nshi
ps b
etw
een
num
bers
to 1
00(<
, >, =
,
use
plac
e-va
lue
conc
epts
, with
ass
ista
nce,
to r
enam
e an
d co
mpa
renu
mbe
rs b
eyon
d 10
0
roun
d to
the
near
est m
ultip
le o
f 10
estim
ate
quan
tity
to 1
00 u
sing
a r
efer
ent
reco
gniz
e ha
lves
, thi
rds,
fou
rths
, fif
ths,
and
tent
hs a
nd p
ortio
nsh
apes
to s
how
thes
e fr
actio
ns
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
2LE
VE
L 3
The
stu
dent
rep
rese
nts,
reg
roup
s, a
nd r
enam
es n
umbe
rs. T
he s
tude
ntun
ders
tand
s th
e ch
arac
teri
stic
s of
num
bers
, (od
dlev
en, d
ivis
ibili
ty),
and
uses
pla
ce-v
alue
con
cept
s w
hen
orde
ring
, rep
rese
ntin
g, a
nd r
ound
ing
num
bers
. The
stu
dent
rec
ogni
zes
and
nam
es f
ract
iona
l par
ts o
f re
gion
san
d se
ts. T
he s
tude
nt u
ses
num
ber
conc
epts
in a
var
iety
of
mea
ning
ful
cont
exts
.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
anre
cogn
ize,
cou
nt, r
ead,
wri
te, a
nd o
rder
num
bers
to 1
000
read
and
wri
te n
umbe
r w
ords
to 1
00us
e or
dina
l num
bers
to 1
00sk
ip-c
ount
for
war
d an
d ba
ckw
ard
by 2
, 5, 1
0, a
nd 1
00 f
rom
ran
dom
star
ting
Ant
ssk
ip-c
ount
by
3, 4
, and
25,
usi
ng m
ultip
les
as s
tart
ing
poin
tsre
pres
ent a
nd d
escr
ibe
num
bers
to 1
000
in a
var
iety
of
way
s:-
18=
9+9;
2 x
9 ;1
0+8;
20-
2; 1
4+4;
etc.
- od
d/ev
La
- di
visi
ble
by 2
, 5, o
r 10
- <
, >, =
,
dem
onst
rate
and
use
pla
ce-v
alue
con
cept
s to
rep
rese
nt n
umbe
rsco
ncre
tely
, pic
tori
ally
, and
sym
bolic
ally
(w
ords
and
num
eral
s), u
sing
-ren
amin
g; e
.g.,
320
= 3
2 te
ns; 3
20 o
nes
- ex
pres
sing
num
eral
s in
bot
h st
anda
rd a
ndex
pand
ed f
orm
(e.
g., 3
20 =
300
+ 2
0 +
0 )
H T
0 0
roun
d to
nea
rest
mul
tiple
s of
10
and
100s
estim
ate,
cou
nt, c
ompa
re, a
nd o
rder
set
s of
obj
ects
to 1
000,
usi
ng a
vari
ety
of s
trat
egie
s
reco
gniz
e, n
ame,
and
dem
onst
rate
hal
ves,
thir
ds, f
ourt
hs, f
ifth
s, a
ndte
nths
of
regi
ons
and
sets
19S
91
The
stu
dent
dem
onst
rate
s an
intu
itive
sen
se f
or n
umbe
rs b
eyon
d 10
00.
The
stu
dent
dem
onst
rate
s an
d ap
plie
s an
und
erst
andi
ng o
f pl
ace-
valu
eco
ncep
ts a
nd n
umbe
r re
latio
nshi
ps to
com
pare
, ord
er, e
stim
ate,
and
calc
ulat
e. T
he s
tude
nt r
ecog
nize
s, n
ames
, and
dem
onst
rate
s fr
actio
ns o
fre
gion
s an
d se
ts.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
ande
mon
stra
te a
nd e
xpla
in c
ount
ing
in s
yste
ms
othe
r th
an b
ase
10 (
e.g.
,ba
se 3
, bas
e 4,
etc
.)
dem
onst
rate
and
exp
lain
the
rela
tions
hips
am
ong
coun
ting,
ren
amin
g, a
nd p
lace
-val
ue c
once
pts
appl
y m
ultip
les
of 1
0 to
exp
lain
pla
ce-v
alue
bey
ond
1000
use
num
ber
char
acte
rist
ics,
num
ber
rela
tions
hips
, and
pla
ce-v
alue
conc
epts
to ju
stif
y an
d ex
plai
n es
timat
ion,
rou
ndin
g, a
nd m
enta
lca
lcul
atio
n st
rate
gies
and
sol
utio
ns
nam
e an
d re
pres
ent e
quiv
alen
t fra
ctio
ns o
f a
regi
on
199
Num
ber
NU
MB
ER
(C
ON
CE
PT
S)E
ND
OF
GR
AD
E 3
Sam
ple
Ass
essm
ent A
ctiv
itks
1. S
olve
the
follo
win
g ri
ddle
.I
am g
reat
er th
an 1
5.I
am le
ss th
an 2
2.I
am a
n od
d nu
mbe
r.I
can
be d
ivid
ed e
venl
y by
3.
Wha
t num
ber
am I
?H
ow d
id y
ou g
et y
our
answ
er?
2. I
n Ju
ne, M
arcu
s w
ill p
lay
a te
nnis
gam
e ev
ery
thir
d da
y, b
egin
ning
June
3. H
e w
ill p
lay
a ba
seba
ll ga
me
ever
y ni
nth
day,
beg
inni
ngJu
ne 9
.O
n w
hat d
ates
in J
une
will
be
play
bot
h a
tenn
is g
ame
and
aba
seba
ll ga
me?
3. D
escr
ibe
3 ot
her
num
bers
you
cou
ld s
how
if y
ou tr
ade
tui c
. fla
ts f
or 2
diff
eren
t bas
e te
n bl
ocks
.
I H
0 0
0 0
0
209
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
1
1-
1
iy&
e,c&
wQ
i18
4 3
26
E2
r=1
3.
92
June
q Ll0,
0
201
loL
t
LEV
EL
2
ST
AN
DA
RD
S O
FP
ER
FO
RM
AN
CE
0
2.\,J
efl3
4 y
ttoty
e r)
n(0
61Q
1St
eAl
1.1.
-R3c
)ec
iSe
tic)
0e3C
0
3.
f11
1711
00a1
:30
ELI
202
1.)
2.
3. 93
qtea
r-th,
LEV
EL
3
-f6/
604
hilid
teC
IS ie
nS
04
10
5o
oy)e
s
5-15
OD
OM
000
006-
C P
CIJ
OD
O5-
Mom
-7E
U v
oo 0
,042
,2e.
..
203
Num
ber
NU
MB
ER
PE
RA
TI N
EN
DR
AD
E 3
"Dem
onst
rate
an
unde
rsta
ndin
g of
and
pro
fici
ency
with
cal
cula
tions
.""D
ecid
e w
hich
ari
thm
etic
ope
ratio
n(s)
can
be
used
to s
olve
a pr
oble
m, a
ndth
en s
olve
the
prob
lem
."
By
the
end
of G
rade
3, s
tude
nts
wili
appl
y an
ari
thm
etic
ope
ratio
n (a
dditi
on, s
ubtr
actio
n, m
ultip
licat
ion
ordi
visi
on)
on w
hole
num
bers
, and
illu
stra
te it
sus
e in
cre
atin
g an
d so
lvin
gpr
oble
ms
use
and
just
ify
an a
ppro
pria
te c
alcu
latio
n st
rate
gy o
r de
vice
to s
olve
prob
lem
s
Mor
e sp
ecif
ical
ly, s
tude
nts
will
use
man
ipul
ativ
es, d
iagr
ams,
and
sym
bols
, in
a pr
oble
m-s
olvi
ng c
onte
xt,
to d
emon
stra
te a
nd d
escr
ibe
the
proc
ess
of a
dditi
on a
nd s
ubtr
actio
n to
1000
, and
the
proc
ess
of m
ultip
licat
ion
and
divi
sion
with
pro
duct
s an
ddi
vide
nds
to 5
0re
call
addi
tion
and
subt
ract
ioli
fact
s to
18,
and
mul
tiplic
atio
n an
d di
visi
onfa
cts
to 4
9 (7
x 7
)ve
rify
sol
utio
ns to
add
ition
and
sub
trac
tion
prob
lem
s, u
sing
est
imat
ion,
calc
ulat
ors,
and
inve
rse
oper
atio
nsju
stif
y th
e ch
oice
of
met
hod
for
addi
tion
and
subt
ract
ion
from
amon
ges
timat
ion
or m
enta
l mat
hem
atic
s st
rate
gies
, man
ipul
ativ
es, a
lgor
ithm
s,or
cal
cula
tors
calc
ulat
e pr
oduc
ts a
nd q
uotie
nts,
usi
ng e
stim
atio
nan
,. in
enta
lm
athe
mat
ics
stra
tegi
es
(N-V
.3.1
to N
-V1.
3.1)
204
94
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
1
The
stu
dent
rec
alls
and
app
lies
basi
c ad
ditio
n, s
ubtr
actio
n, a
ndm
ultip
licat
ion
fact
s to
sim
ple
prob
lem
situ
atio
ns. T
he s
tude
nt r
elie
son
visu
al r
epre
sent
atio
ns, a
nd a
ssis
tanc
e, to
app
ly a
dditi
on a
nd s
ubtr
actio
nop
erat
ions
to p
robl
ems
invo
lvin
g 2-
and
3-d
igit
num
bers
.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
anre
call
basi
c ad
ditio
n an
d su
btra
ctio
n fa
cts
to 1
8, a
nd m
ultip
licat
ion
fact
s to
25
use
real
or
conc
rete
mat
eria
ls a
nd p
ictu
res
in c
onju
nctio
n w
ithsy
mbo
ls to
rep
rese
nt a
nd s
olve
pro
blem
s in
volv
ing
addi
tion
and
subt
ract
ion
of 2
- an
d 3-
digi
t num
bers
dem
onst
rate
mul
tiplic
atio
n as
rep
eate
d ad
ditio
n, a
nd d
ivis
ion
asre
peat
ed s
ubtr
actio
n or
as
shar
ing
equa
lly, a
nd m
odel
sol
utio
ns to
prob
lem
s in
volv
ing
thes
e op
erat
ions
estim
ate,
or
calc
ulat
e m
enta
lly, w
ith a
ssis
tanc
e, a
dditi
on a
ndsu
btra
ctio
n of
2-d
igit
num
bers
, usi
ng a
giv
en s
trat
egy
appl
y th
e ap
prop
riat
e op
erat
ion
in a
1-s
tep
prob
lem
, ver
ify
the
solu
tion,
and
just
ify
the
choi
ce o
f op
erat
ion
205
ST
AN
DA
RD
S O
F P
ER
FO
RM
AN
CE
LEV
EL
2
The
stu
dent
cal
cula
tes,
iden
tifie
s an
d ju
stifi
es th
e an
swer
s to
add
ition
,su
btra
ctio
n, m
ultip
licat
ion,
and
div
isio
n qu
estio
ns. T
he s
tude
nt a
pplie
sth
ese
oper
atio
ns in
pro
blem
-sol
ving
situ
atio
ns, v
erify
ing
calc
ulat
ions
and
just
ifyin
g st
rate
gies
.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
anre
call
basi
c ad
ditio
n an
d su
btra
ctio
n fa
cts
to 1
8re
call
mul
tiplic
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n an
d di
visi
on f
acts
to 4
9us
e m
anip
ulat
ives
, dia
gram
s, a
nd s
ymbo
ls in
a p
robl
em-s
olvi
ngco
ntex
t to
dem
onst
rate
and
des
crib
e th
e pr
oces
s of
add
ition
and
subt
ract
ion
to 1
000,
and
mul
tiplic
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n an
d di
visi
on, w
ith a
nd w
ithou
tre
mai
nder
s, to
50
use
and
expl
ain
a va
riet
y of
str
ateg
ies
to a
id in
men
tal a
nd p
aper
-pe
ncil
calc
ulat
ions
(ro
undi
ng o
ff; c
omm
utat
ive
prop
erty
of
addi
tion;
etc.
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ake
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le e
stim
ates
to c
ompu
tatio
nal q
uest
ions
usi
ng a
var
iety
of s
trat
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sap
ply
the
appr
opri
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oper
atio
n(s)
in 1
- or
2-s
tep
prob
lem
s, v
erif
yso
lutio
ns, a
nd ju
stif
y ch
oice
of
oper
atio
n(s)
cons
truc
t and
sol
ve p
robl
ems
that
dem
onst
rate
the
four
bas
icop
erat
ions
reco
gniz
e di
ffer
ent t
ypes
of
prob
lem
s (j
oin,
sep
arat
e, p
art-
part
-who
le,
and
com
pari
sons
) w
hich
req
uire
add
ition
and
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trac
tion
to f
ind
aso
lutio
nse
lect
an
appr
opri
ate
met
hod
of c
alcu
latin
g (c
alcu
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r, p
aper
-pen
cil,
met
al m
athe
mat
ics)
206
95
LEV
EL
3
The
stu
dent
ver
ifies
the
solu
tion(
s) fo
r si
ngle
- or
mul
ti-st
ep p
robl
ems
invo
lvin
g an
y op
erat
ion(
s), a
nd ju
stifi
es th
e so
lutio
n(s)
foun
d or
the
met
hods
app
lied
durin
g th
e pr
oble
m-s
olvi
ng p
roce
ss. T
he s
tude
ntre
cogn
izes
mat
hem
atic
al p
robl
ems
aris
ing
from
rea
l-wor
ld c
onte
xts,
and
purs
ues
thei
r so
lutio
ns.
Mor
e sp
ecif
ical
ly, t
he s
tude
nt c
anus
e pa
rt-w
hole
ana
lysi
s to
des
crib
e nu
mbe
r re
latio
nshi
ps a
nd ju
stif
ych
oice
of
oper
atio
n(s)
to s
olve
dif
fere
nt ty
pes
of p
robl
ems
dem
onst
rate
dif
fere
nt m
odes
(co
ncre
te, p
icto
rial
, sym
bolic
), m
etho
ds(m
ater
ials
, pap
er-p
enci
l, ca
lcul
ator
, men
tal c
alcu
latio
ns),
and
stra
tegi
es (
fron
t-en
d ad
ditio
n, c
ount
ing
on, m
akin
g co
mpa
tible
num
bers
) fo
r so
lvin
g pr
oble
ms
invo
lvin
g ad
ditio
n an
d su
btra
ctio
nof
3-o
r-m
ore-
digi
t num
bers
appl
y m
ultip
licat
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and
divi
sion
fac
ts to
sol
ve p
robl
ems
just
ify
met
hods
use
d to
sol
ve p
robl
ems,
and
use
a v
arie
ty o
f st
rate
gies
(est
imat
ion,
men
tal c
alcu
latio
n, r
elat
ions
hips
am
ong
oper
atio
ns)
toju
dge
the
reas
onib
lene
ss o
f an
swer
sre
cogn
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whe
n an
ope
ratio
n(s)
can
be
used
to a
nsw
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eal-
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ldnu
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r pr
oble
ms,
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ly a
kno
wle
dge
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pera
tions
207
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CHANGES TO K-4 MATHEMATICSGOALS/LEARN1NG OUTCOMES
1995
2 (2
CHANGES TO KINDERGARTEN MATHEMATICSGOALS/LEARNING OUTCOMES
Strand,
1993 Curriculum Goals . 1995 Changes,
Patterns andProblem-Solving
PPS1. Readiness for Patterningidentifies attributes in presortedsets
PPS2. Geometric and Number Patternschanges (translates) a concretepattern to an action patternbegins to recognize patterns inthe environment
PPS3. Uses calculators
PPS4. Problem Solving Strategies
now an outcome in Grade 2
now an outcome in Grade 2
now an outcome in Grade 1
now included in Number Concepts
now incorporated throughout all strands
DataManagement
DMI. Collects Datarepeatedly experiencescollecting data for the purposeof comparing 2 or 3 groups
DM2. Organizes and Displays Dataa graphs (group work) involving
pictographs
DM3. Interprets Datacompares quantities
answers oral questionsexplains answers to questions
change to read: the studentcollects, with assistance, first handinformation (comparing is moved tograde 1)
now an outcome in Grade 1
change to read: the studentI compares 2 categoriesnow an outcome in Grade 1now an outcome in Grade 1
Geometry Gl. 3-D Solids and 2-D Shapes
G2. Position and Spatial RelationshipsPositionchildren describe theirown position and movements
movements along a path
change to read: the studentdescribes the relative position of 3-Dobjects
now an outcome in Grade 3
2
CHANGES TO KINDERGARTEN MATHEMATICS (CONT'D)
Strand, .
.1993 Curriculum Goals i 1995 Changes
Measurement MI. Linear Measurement add this outcome: the studentarranges objects in order of size, bylength, and by height(presently in Grade 1)
M2. Perimeter
M3. Area
M4. Volumeteacher models the language change to read: the student
uses the words full, empty. less, and moreto talk about volume and capacity
MS. Mass/Weight add this outcome: the studentuses the words heavier or lighter to talkabout the mass/weight of two objects(presently in Grades 1&2)
M6. Tune
M7. Money
M8. Temperature add this outcome: the student(not part of the 1993 curriculum) uses words like hot, hotter, cold, colder,
warm, wanner, cool, cooler, to talk abouttemperature (not in present curriculum)
_
2
CHANGES TO KINDERGARTEN MATHEMATICS (CONT'D)
Strand,..1993 Curriculum Coals 1995 Changes
NumberConcepts
NC1. Counting Sequences
NC2. Number Meaning/Number Senseorders up to 3 sets of like objectsaccording to number
NC3. Place Value Concepts
NC4. Fractions
NC5. Decimals
change to read: the studentbuilds, compares, and orders only 2 setsof like objects, based on the number ofobjects in each set, and describes therelationships between them using theterms more than, greater than, fewerthan, less than, the same as and equal to(no written symbols) (presently in Grades1 and 2)
add this outcome: the studentexplores the representation of single digitnumerals using a calculator or computerto represent numerals on a screen(not in present curriculum)
change to read: the studentconstruct: . with guidance, a concreteobject gr ph and a pictograph, using1 to 1 correspondence (symbolic/bargraphs now an outcome in Grade 2).
5
CHANGES TO GRADE I MATHEMATICS (CONT'D)
Strand 1993 Curriculum Goals 1995 Changes
DataManagement
(cont'd)
DM3. Interprets Data
labels data using numbers andwords
describes the data in writing
DM4. Probability
now an outcome in Grade 2
Geometry Gl. 3-D Solids and 2-D Shapes
identifies and describes 3-D solidsusing characteristics such as
number of facesnumber of edgesnumber of verticescurved or straight edgescurved or flat faces
G2. Position and Spatial Relationships
9 i I 1
now an outcome in Grade 2
add these outcomes: the student
identifies, names, and describes specific2-D shapes as
circlestrianglesrectaNgles (not in presentcurriculum)
compares, sorts, and classifies 2-Dshapes (not in present curriculum)
add these outcomes: the student
describes the relative position of 3-Dobjects and 2-D shapes, using suchwords as near, far, left, and rightmatches size and shape of figures bysuperimposing one on top of the otherexplores and describes reflections in amirror (not in present curriculum)
-,
6
CHANGES TO GRADE 1 MATHEMATICS (CONT/D)
Strand 1993 Curriculum Goals 1995 Changes
Measurement M I. Length
M2. Perime ter
M3. Area
M4. Capacity/Volumereadiness activities throughexploration and discussion
MS. Mass/Weightestimates and compares theweight of two objects
M6. lime
M7. Money
M8. Temperature(not in present curriculum)
change to read: the studentestimates, measures, records, andcompares the volume/capacity ofcontainers, using non-standard units(not in present curriculum)
change to read: the studentestimates, measures, records, andcompares the mass of objects, usingnon-standard units
add these outcomes: the studentestimates and measures the passage oftime related to non-standard units(presently in Grade 2)compares the duration of activities (notin present curriculum)names and orders the Jays of the weekand the seasons of the year (presentlyin Grade 2)
add this outcome: the studentdescribes and compares temperatures,using the senses (not in presentcurriculum)
CHANGES TO GRADE 1 MATHEMATICS (CONT'D)
Strand, .I.1993 Curriculum Goals 1995 Changes,,
NumberConcepts
NC1. Counting Sequencesrote counts forward to 50, usingrandom starting points
a oral skip counts by2s to 205s to 50lOs to 100recognizes, builds, and orderssets to 20understands ordinals to 10
NC2. Number Meaning/Number Senserecognizes, builds, and orderssets to 20
NC3. Place-Value Conceptsuses manipulatives to representnumbers to 20reads and writes numerals to 20as shown by manipulatives anddiagrams
NC4. Fractionsunderstands fractions (halvesand fourths with any numerator)
NCS. Decimals
change to read: the studentcounts orally by ls, 2s, 5s, an lOs to100, and estimates, then c9thus thenumber of objects in a set (0 to 50), andcompares the cstimate with the actualnumber
now an outcome in Grade 2 (to 31)
change maximum number from 20 to 50.
change to read: the studentrepresents and describes numbers to 50in a variety of ways, and explores therepresentation of numerals (0 to 50),using a calculator or a computer todisplay numerals
change to read: the studentdemonstrates, and explains orally, anunderstanding of halves as part of ashape or solid
NumberOperations
NO1. Addition
NO2. Subtractionexplores and understandsaddition and subtraction to 10
NO3. Multiplicationconstructs equivalent setsconcretelyintroduce "X" symbol in bothhorizontal and vertical formats
change the maximum numbers to 18 (nomemorization intended) (presently in Grade2)
now an outcome in Grade 3
now an outcome in Grade 3
CHANGES TO GRADE 2 MATHEMATICSGOALS/LEARNING OUTCOMES
Strand..1993 Curriculum Goals 1995 Changes,,
Patterns andProblem-Solving
PPS1. Readiness for Patterning
a sorts/classifies/compares with 1or more attributes
PPS2. Geometric and Number Patternsrecognizes, reproduces,continues, and supplies missingelements in patterns (anddescribes the rule of the pattern)
PPS3. Uses Calculators
PPS4. Problem-Solving Strategies
PPSS. Applies Concepts and Operations
change to read: the studentsorts objects and shapes, using one or twoattributes (more than two is now anoutcome in Grade 3)
"and describes the rule of the pattern" isnow an outcome in Grade 3
now incorporated throughout the Strands
now moved to Number Operations Strand
DataManagement
DM1. Collects Data* Survey questions should be
formulated by the students
DM2. Organizes and Displays Dataorganizes and displayscollections independently
DM3. Interprets DataIII obtains new information by
performing some arithmeticoperations on data
DM4. Probability
change to read: the studentformulates the questions and categoriesfor data collection, and chooses anappropriate recording method, such astally marks, to collect data
change to read: the studentorganizes data, using such graphicorganizers as diagrams, charts and lists
now an outcome in Grade 3
CHANGES TO GRADE 2 MATHEMATICS (CONT'D)
Strand 1993 Curriculum Goals 1995 Changes
Geometry G I. 3-D Solids and 2-D Shapesidentifies and describes 3-Dsolids using characteristics(faces, edges, vertices, etc.)
identifies and describesrectangular solids
observes and reproduces 3-Dsolids using
cubesskeleton models
identifies 3-D solids which arethe same size and shapeidentifies 2-D shapes that are thesame size and shape(introduction to congruence)
G2. Position and Spatial Relationshipsdescribes location of objectsusing positional language
draws and describes a path bothorally and in writing
2 , ,
now an outcome in Grade 3. Change to read:the student
explores faces, vertices and edges of 3-Dobjects
change to readpyramids
change to read: the studentbuilds a skeleton of a 3-D object anddescribes how the skeleton relates to theobject
add this outcome: the studentbuilds and rearranges a pauem, using aset of 2-D shapes
now an outcome in Grade 3
now an outcome in Grade 3
change to read: the studentcommunicates and applies positionallanguage in oral, written, or mimericalform
now an outcome in Grade 3
add this outcome: the studentcreates symmetrical 2-D shapes byfolding and reflecting
10
CHANGES TO GRADE 2 MATHEMATICS (CONT'D)
Strand,
,1993 Curriculum Goals 1995 Changes
Measurement Mi.
M2.
Length
Perimeter
add this outcome: the studentselects the most appropriate standard unit(cm, dm, m) to measure a length(presently in Grade 3)
uses the words perimeter and "perimeter" an outcome in Grade 3 and
circumference "circumference" now an outcome inGrade 4
recognizes that different shapesmay have the same perimeter
now an outcome in Grade 5
M3. Area add this outcome: the studentconstructs a shape given a specific areain non-standard units
M4. Capacity/Volume
M5. Mass/Weight add this outcome: the studentrecognizes that the size and shape of anobject does not necessarily determine itsmass/weight
M6. Timeestimates and uses non-standard change to read: the studentunits to measure the passage of estimates and measures the passage of
time time related to minutes and hours
reads and writes time to the now an outcome in Grade 3
hour- half-hour
add this outcome: the studentselects the most appropriate standard unitto measure a given period of time(presently in Grade 3)
relates add the following24 hours to 1 day days to a week12 months to 1 year minutes to an hour
and reads the date on a calendar
M7. Money
M8. Temperature add this outcome: the studentuses a thermometer to determine risingand falling temperatures (not in presentcurriculum)
1 1
0.
CHANGES TO GRADE 2 MATHEMATICS (CONT'D)
Strand,,1993 Curriculum Goals . 1995 Changes,
NumberConcepts
NC1. Counting Sequencesrote counts 100 (forward/back)using random starting points(oral and written)skip counts using multiples asstarting points (oral and written)
2s to 1005s to 100lOs to 100
NC2. Number Meaning/Number Sense
NC3. Place Value Concepts
NC4. Fractionsunderstands fractions (halves,thirds, and fourths) with anynumerator
NC5. Decimals ,
change maximum from 100 to 1000
change maximum from 100 to 1000add this outcome: the student
counts by 25s to 100
change to read: the studentillustrates and explains halves, thirds, andfourths as part of a region or set
NumberOperations
N01. Addition
NO2. Subtractionbegins to recall basic additionfacts to 18 and subtraction factsto 10
uses mental calculations (tosolve addition and subtractionproblems)
NO3. Multiplication
N04. Divisionunderstands and begins torecall multiplication facts to 25(limit 5 x 5)
2 . ,3
change to read: the studentrecalls addition and subtraction facts to10
change to read: the studentuses a variety of estimation and mentalmathematics strategies to solve additionand subtraction problems
now an outcome in Grade 3
12
CHANGES TO GRADE 3 MATHEMATICSGOALS/LEARNING OUTCOMES
Strand,,,1993 Curriculum Goals 1995 Changes,
Patterns andProblem-Solving
PPSI. Readiness for Patterning
PPS2. Geometric and Number Patterns
PPS3. Uses Calculators
PPS4. Problem-Solving Strategies
PPS5. Applies Concepts and Operations
add this outcome: the studentuses objects and concrete models toexplain the rule for patterns such asthose found on addition andmultiplication charts, and makespredictions based on addition andmultiplication patterns (a summary ofthe present information for PPS2)
.
now incorporated throughout the Strands
now part of Number Operations Strand
DataManagement
DMI. Collects Datacollects measurements, usingstandard units, to use as data
DM2. Organizes and Displays Data
DM3. Interprets Data
DM4. Probabilityconducts experiments using
spinnersprobability sackdie
change to read: the studentcollects data, using measuring devicesand printed/technology resources(presently in Grade 4)
change to read: the studenta conducts a probability experiment,
chooses an appropriate recordingmethod, and draws conclusions fromthe results
CHANGES TO GRADE 3 MATHEMATICS (CONT'D)
Strand .1993 Curriculum Goals . 1995 Changesi
Geometry Gl. 3-D Solids and 2-D Shapes/ change to read: the studentidentifies and counts faces, vertices, andedges of 3-D objects (presently in Grade2), compares and contrasts two 3-13 .
objects, and identifies and namesfaces of a 3-D object with appropriate2-D names
identifies pyramids and prisms change to read: the studentboth in and outside the classroom describes and names pyramids and
prisms by the shape of their base(presently in Grade 4)
add these outcomes: the studentexplores, concretely, the concepts ofperpendicular. parallel, and intersectinglines on 3-D objectsrecognizes congruent (identical) 3-13objects and 2-D shapes (presently inGrade 2)
identifies right angles and angleslarger or smaller than right angles
now an outcome in Grade 4
identifies and describes specificpolygons having up to 8 sides
now an outcome in Grade 5
classifies polygons according to now an outcome in Grade 4 (quadrilaterals)their characteristics and in Grade 5 (triangles)
G2. Position and Spatial Relationshipsdescribes the locations of objectsusing specific directions
add this phrase:... and relates directions to maps(presently in Grade 4)
add these outcomes: the studentgraphs whole number points on ahorizontal and vertical number line (notin present curriculum)traces a path, using oral and writteninstructions (presently in Grades 2and 3)
22 b
i
14
CHANGES TO GRADE 3 MATHEMATICS (CONT'D)
Strand 1993 Curriculum Goals 1995 Changes
Measurement Ml. Lengthrelates 10 centimetres to 1decimetre, and 10 decimetres to1 metre
M2. Perimeter
recognizes that the same shape(arca) may have differentperimeters
M3. Area
estimates, compares, records, and ordersarea by counting the number of squaredecimetres needed to cover a surface
M4. Capacity/Volume
MS. Mass/Weight
M6. Time
selects appropriate unit for measuring(the passage of) timeseconds, minutes,days, months, years
M7. Moneyidentifies 2, 5, 10, and 20 dollar bills
M8. Temperature
change to read: the studentdescribes the relationships among cm,dm and m
add this outcome: the studentestimates, measures, records, compares,and orders objects by...perimeter, usingstandard units (presently in Grade 2)
now an outcome in Grade 5
add these outcomes: the studentselects an appropriate non-standard unitto measure area, (not in presentcurriculum)estimates, measures, records, compares,and orders shapes using non-standardunits, and constructs a variety of shapesgiven a specific area in non-standardunits
now an outcome in Grade 4
add this outcome: the studentreads and writes days of the week andmonths of the year
add these unitshoursweeks
add these bills$50$100
add this outcome: the studentestimates, reads, and records temperatureto the nearest degree C, and relatestemperature to evetyday situations (notin present curriculum)
CHANGES TO GRADE 3 MATHEMATICS (CONT'D)
Strand 1993 Curriculum Goals 1995 Changes
NumberConcepts
NC1. Counting Sequences
relates skip counting to ....multiplication
NC2. Number Meaning/Number Senseidentifies odd and even numbersto 1000
NC3. Place Value Concepts
NC4. Fractionsextend to fifths and tenths
NC5. Decimals
add this outcome: the studentskip counts backward by 2s, 5s, 10s, and100's using respective multiples asstarting points
now an outcome in Grade 4
change to read: the studentrecognizes and explains if a number isdivisible by 2, 5, or 10
change to read: the studentillustrates and explains fifths and tenthsas part of a region or a set
NumberOperations
N01. Addition
NO2. Subtractionunderstands, creates, and solvesaddition problems to 1000 andsubtraction problems to 100uses and discusses variousstrategies (for finding additionand subtraction solutions)
uses mental calculations
NO3. Multiplication
N04. Division
understands and solvesmultiplication questions to 100,and division questions to 50
change so both maximums read ... to 1000
change to read: the studentjustifies the choice of method for additionand subtraction, using
change to read: the studentverifies solutions to addition andsubtraction problems, using
estimationcalculatorsinverse operations
add this outcome: the studentcalculates products and quotients (forproblems involving numbers beyond 50),using estimation strategies and mentalmathematics strategies
2"'4, 116
CHANGES TO GRADE 4 MATHEMATICSGOALS/LEARNING OUTCOMES
Strand 1993 Curriculum Goals 1995 Changes
Patterns andProblem-Solving
PPS1. Readiness for Patterning
PPS2. Number Meanings/Number Patterns
PPS3. Uses Calculators
PPS4. Problem-Solving S trategies
PPSS. Applies Concepts and Operations
add these outcomes: the studentsorts numbers into categories, using oneor more attributesidentifies and explains mathematicalrelationships and patterns, using
Venn/Carroll/tree diagrams
add these outcomes: the studentidentifies and explains mathematicalrelationships and patterns, using
makes and justifies predictions, usingnumerical and non-numerical patterns
now incorporated throughout the strands
now part of Number Operations
DataManagement
DM1. Collects Dataconducts surveys using samplepopulations
DM2. Organizes and Displays Data
DM3. Interprets Data
DM4. Probability
conducts experiments to answerown questions
change to read: the studentselects a sample or population, andorganizes the collection of data
add this outcome: the studentdiscusses the process by which thedata were collected
add this outcome: the studentcompares outcomes as equally likely,more likely, less likely
change to read: the studentdcsigns and conducts experiments toanswer one's own questions
17 0
CHANGES TO GRADE 4 MATHEMATICS (CONT'D)
Strand 1993 Curriculum Goals 1995 Changes
Geometry Gl. 3-D Solids and 2-D Shapesidentifies and describes thecharacteristics of pyramids andprisms
identifies and names specificprisms and pyramids by theshape of the basesearch for a relationshipbetween the number of faces,vertices, and edgesexplores, through construction,the concept of oblique pyramidsand prisms
G2. Position and Spatial Relationshipreads simple map - exploressimple map-making usingdirections
change to read: the studentcompares and contrasts
pyramidsprismspyramids and prisms
now an outcome in Grade 3
now an outcome in Middle years
now an outcome in Middle Years
add these outcomes: the studentidentifies and sorts specificquadrilaterals, including squares,rectangles, and parallelogramsrecognizes, from everyday experience,and identifies
(not in present curriculum)describes angles in a variety oforientations according to whether theyare right, significantly less than right, orsignificantly greater than right
add to this outcome...and grids, and places an object on agrid, using rows and columns(not presently in curriculum)
add this outcome: the studenttraces a path, using oral or writteninstructions, and writes instructions for agiven path (presently in Grade 2)creates and verifies symmetrical 2-Dshapes by drawing lines of symmetry
18
CHANGES TO GRADE 4 MATHEMATICS (CONT'D)
Strandi1
1993 Curriculum Goals . 1995 ChangesI
Measurement Ml. Length
M2. Perimeterrecognizes that shapes with thesame areas may have differentperimeters, and vice versa
M3. Area
M4. CapacityNolume
MS.
constructs dm3 and m3
Mass/Weight
MS. Tunewrites days of the week andmonths of the yearreads and writes time, usingdigital and analog clocks:
to the quarter hourminutes past the hourminutes to Lie hour
relates30 minutes to 1/2 hour15 minutes to 114 hourleap year
recognizes time using 24 hourclockuses metric notation for time
M7. Moneyextend to $50 and $100 bills
MS. Temperature
add this outcome: the studentconstructs items of specific lengths,including mm, and relates the size of theunit to the number of units used tomeasure area (not in present curriculum)
now an outcome in Grade 5
add this outcome: the studentconstructs a number of shapes, given aspecific area (cm2) (presently in MiddleYears)
add this outcome: the studentrelates the size of unit to the number ofunits needal to measure capacity/volume
an outcome in Middle Years
add this outcome: the studentrelates the size of unit to the number ofunits needed to measure mass/weight
now an outcome in Grade 3
change to read: the studentreads an analog clock to the nearest 5minutes, and writes time using am andpm
add these relationshipsyears to decadesdecades to centuriescenturies to millenniums
now an outcome in Middle Years
now an outcome in Middle Years
now an outcome in Grade 3
not in present curriculum
19 2 3 0
CHANGES TO GRADE 4 MATHEMATICS (CONT'D)
Strand 1993 Curriculum Goals 1995 Changes
NumberConcepts
NC1. Counting Sequences
NC2. Number Meanings/Number Senseestimates the number ofobjects (0-9999)uses ordinals to 9999
demonstrates prime andcomposite numbers to 100,using manipulatives, diagrams,and a calculator
NC3. Place Value Concepts
NC4. Fractionsextend to hundredths
NC5. Decimals
add this outcome: the studentuses skip counting (forward andbackward) to support an understandingof multiplication and division
change the maximum to read ...(0 to 1000)
change to read: the studentuses ordinals to 1000
now an outcome in Grade 5
change to read: the studentillustrates and explains hundredths aspart of a region and a set, and connectsproper fractions to decimals (tenths andhundredths) using manipulatives,diagrams, and symbols
NumberOperations
N01. AdditionNO2. Subtraction
NO3. Multiplication
N04. Divisionunderstands and solvesmultiplication questionsinvolving a 2-digit by a 1-digitnumber
add this outcome: the studentdemonstrates an understanding ofaddition and subtraction of decimals(tenths and hundredths) using concreteand pictorial representations
change to read:...3 digit by 1 digit numbers
add this outcome: the studentjustifies the method used to calculateproducts and quotients, choosing fromestimation strategies, mentalmathematics strategies, manipulatives,algorithms, and calculator, and usesestimation, inverse operations, orcalculators to verify solutions forproblems involving multiplication anddivision
