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DOCUMENT RESUME
ED 054 093 SP 007 237
AUTHORTITLEINSTITUTIONPUB DATENOTE
EDRS PRICEDESCRIPTORS
ABSTRACT
Graham, Carolyn; And OthersMathematics Curriculum Guide, K-6.Clark County School District, Las Vegas, Nev.[67]136p.
EDRS Price MF-$0.65 HC-$6.58*Curriculum Guides, *Elementary School Curriculum,*Elementary School Mathematics, *Geometry, Grade 1,Grade 2, Grade 3, Grade 4, Grade 5, Grade 6,Kindergarten, *Mathematics Curriculum
GRADES OR AGES: K-6. SUBJECT MATTER: Mathematics.ORGANIZATION AND PHYSICAL APPEARANCE: The introductory materialdescribes the philosophy behind the guide, its purpose, and the wayit should be used, and also contains a set of graphs which provide aquick ov'rview of the scope and sequence. The main body of the guideis arranged by grade level in five color-coded sections: 1) number,2) numeration, 3) operations, 4) geometry, and 5) measurement. Eachpage is arranged in three columns: content, behavioral objectives,and textbook page coding. The guide is lithographed and spiral boundwith a soft cover. OBJECTIVES AND ACTIVITIES: Both are detailed inthe behavioral objectives column of the guide. INSTRUCTIONALMATERIALS: No instructional materials other than the textbooks arelisted. STUDENT ASSESSMENT: No specific provisions are made forevaluation. (MOM)
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Eaa
,zet
odS
cita
d ?w
awa
Mr.
Geo
rge
W. W
ilkin
son,
Pre
side
ntM
r. G
len
C. T
aylo
r, V
ice
Pre
side
ntM
r. D
ell H
. Rob
ison
, Cle
rkD
r. C
lare
W. W
oodb
ury,
Mem
ber
Mrs
. Hel
en C
. Can
non,
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ber
Mr.
Al i
ck J
. Mac
kie,
Mem
ber
Mr.
C. D
onal
d B
row
n, M
embe
r
/Vee
mei
itia,
zete
c'op
t
Dr.
Jam
es I.
Mas
on,
Sup
erin
tend
ent
Dr.
Clif
ford
J. L
awre
nce,
Ass
ocia
te S
uper
inte
nden
t,D
ivis
ion
of In
stru
ctio
n
Mr.
Rob
ert D
unsh
eath
, Dire
ctor
Cur
ricul
um S
ervi
ces
Dep
artm
ent
Mr.
Pre
ston
T. B
isho
p, C
oord
inat
orC
urric
ulum
Ser
vice
s O
ffice
Mr.
Joh
n P
aul,
Ass
ocia
te S
uper
inte
nden
t,D
ivis
ion
of A
dmin
istr
atio
n
Dr.
Hen
ry C
. Bcz
arth
, Are
a A
dmin
istr
ator
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tern
Zon
e
Mr.
Lya
l Bur
khol
der,
Are
a A
dmin
istr
ator
Cla
rk Z
one
Mr.
Jam
es E
. Em
bree
, Are
a A
dmin
istr
ator
Las
Veg
as a
nd V
alle
y Z
ones
Mr.
Ray
mon
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turm
, Are
a A
dmin
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ator
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Nev
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ente
r an
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dult
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ucat
ion
Mr.
Jam
es W
illia
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a A
dmin
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ator
Ran
cho
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laite
likaP
tee
I0
O
The
cur
ricul
a of
our
scho
ols
l-ave
alw
ays
been
in a
pro
cess
of c
hang
e, b
ut th
e ch
alge
usu
ally
has
not b
een
fund
amen
tal.
Ne:
r co
nten
t was
add
ed; s
ome
old
mat
eria
l was
dis
card
ed. S
ome-
times
who
le c
ours
es d
isap
pear
ed a
nd w
ere
repl
aced
. But
mor
e of
ten
than
not
, the
re..
cour
ses
look
ed m
uch
like
thei
r pr
edec
esso
rs.
The
cur
ricul
um c
hang
e di
d .-
.c: s
eem
to r
efie
c7 th
e ur
-ge
ncy
so e
vide
nt it
the
educ
atio
nal p
robl
ems
and
cont
rove
rsie
s in
our
perio
d of
rap
id s
ocia
l,po
litic
al, a
nd te
chno
logi
cal c
hang
e.S
olvi
ng th
ese
prob
lem
s is
of t
he g
reat
est i
mpo
rtan
ce to
our
loca
l, ou
r na
tiona
l, an
d ou
r w
orld
com
mun
ity.
Itis
in th
is s
ettin
g th
at th
e ne
w m
athe
mat
ics
curr
icul
um g
uide
was
forg
ed.
It ha
s de
part
edfr
om th
e us
ual t
radi
tiona
l, ev
olut
iona
ry c
once
pt a
nd p
rese
nts
a dy
nam
ic n
ew a
ppro
ach
to th
epr
esen
tatio
n of
mat
hem
atic
s in
the
elem
enta
ry s
choo
ls o
f the
Cla
rk C
ount
y S
choo
l Dis
tric
t.It
is to
the
trib
ute
of m
any
that
this
gui
delin
e ha
s be
com
e a
real
ity, a
nd to
eac
h of
tine
dra
ft-er
s an
d pa
rtic
ipan
ts,
Iex
tend
the
high
est c
omm
enda
tion
from
the
Boa
rd o
f Sch
ool T
rust
ees
and
the
adm
inis
trat
ion
for
thei
r ex
celle
nt w
ork.
The
pre
sent
atio
n of
this
cui
ciel
ine
open
s th
e do
or to
a n
ew a
nd e
xciti
ng e
nviro
nmen
t of c
hang
ein
whi
ch w
e se
ek to
de,
elop
the
curr
icul
um in
eac
h of
var
ied
disc
iplin
es to
fir
need
s of
the
lear
ner,
pre
sent
ing
a se
quen
tial p
rogr
am o
f con
tinuo
us g
row
th a
nd d
evel
opm
ent
:in a
Kin
-de
rgar
ten
thro
ugh
twel
fth g
rade
bas
is.
Thi
s ha
s be
en a
sig
nific
ant u
nder
taki
ng In
bot
h tim
ean
d ef
fort
, and
its
resu
lts a
re r
epre
sent
ativ
e of
the
exte
nsiv
e ta
lent
s br
ough
t to
bear
in th
ecr
eatio
n of
this
mat
hem
atic
s cu
rric
ulum
gui
de.
44-P
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Jam
es I
Aos
on
Sup
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ED
0540
93
Man
y di
ffere
nt c
omm
ittee
s an
d in
divi
dual
s ha
ve c
ontr
ibut
ed to
the
deve
lopm
ent o
f the
Cla
rk C
ount
y S
choo
l Dis
tric
t Mat
hem
atic
s
Cur
ricul
um G
uide
.
Ele
men
tary
Mat
hem
atic
s T
extb
ook
Ado
ptio
n C
omm
ittee
Cur
ricul
um T
ask
For
ce
Car
olyn
Gra
ham
, Cha
irman
Will
iam
Orr
Jr.
Hig
hC
arol
yn G
raha
m, C
hairm
anW
illia
m O
rr J
r. H
igh
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, Sec
reta
ryB
asic
Ele
men
tary
Virg
inia
Gilb
ert
Val
ley
Hig
hN
orm
an H
omer
Mar
ion
Cah
lan
Ric
hard
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sH
alle
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etso
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ober
t Hum
eJa
mes
Cas
hman
Jr.
Hig
hT
had
Maj
orV
egas
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des
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e K
aul
Rex
Bel
lM
abel
Sch
oenk
eT
win
Lak
esW
illia
m M
oore
J. T
. McW
illia
ms
Geo
rge
Sta
nger
Tom
Dal
las
Ow
ens
Rub
y T
hom
asLy
nn S
ever
ance
Rex
Bel
l
Her
bert
R. S
teffe
ns, M
athe
mat
ics
Con
sulta
ntS
tate
Dep
artm
ent o
f Edu
catio
n, C
arso
n C
ity, N
evad
a
The
follo
win
g pe
ople
cod
ed th
e te
xtbo
ok p
ages
to th
e M
athe
mat
ics
Cur
ricul
um G
uide
:
Rob
ert D
ietik
erP
atric
ia S
turm
Adr
ian
Boi
Car
olyn
Cre
ekm
ore
Dar
rell
t.',o
rrow
Don
Cre
ekm
ore
John
F. M
iller
Rex
Bel
lB
onan
zaB
onan
zaP
ark
Vill
age
John
F. M
iller
Gra
de 1
Gra
de 2
Gra
de 3
Gra
de 4
Gra
de 5
Gra
de 6
Dur
ing
the
sprin
g of
196
7, a
n in
-ser
vice
cou
rse
(Edu
catio
n 49
9-79
9) w
as c
ondu
cted
in c
oope
ratio
n w
ith N
evad
a S
outh
ern
Uni
vers
ity.
The
par
tic'p
ants
rev
iew
ed th
e w
ork
of th
e C
urric
ulum
Tas
k F
orce
, crit
iciz
ed th
e be
havi
oral
obj
ectiv
es, a
ndsu
gges
ted
chan
ges,
dele
tions
, and
add
ition
s.
Inst
ruct
iona
lS
taff
.M
alco
lG
raha
m, C
hairm
an, M
athe
mat
ics
Dep
artm
en;-
Nev
ada
Sou
ther
n U
nive
rsity
Dr.
Virg
inia
Gilb
ert
Mr.
Her
bert
Ste
ffens
Mr.
Pau
l And
erso
nM
rs. C
arol
yn G
raha
mC
urric
ulum
Ass
ocia
te, M
ath
Mat
hem
atic
s C
onsu
ltant
Per
sonn
el A
ssis
tant
Mat
h C
oord
inat
orV
ci I
ey H
igh
Sta
te D
epar
tmen
t of E
duca
tion
Edu
catio
n C
ente
rW
illia
m O
rr J
r. H
igh
Mr.
Val
Arr
edon
doM
rs. M
abel
Sch
oenk
eM
r. K
enne
th M
cKin
ley
Mrs
. Pau
line
Gile
sM
ath
Dep
t., V
alle
y H
igh
Tw
in L
akes
Ele
men
tary
Par
k V
illag
e E
lem
enta
ryR
uby
Tho
mas
Ele
men
tary
Par
ticip
ants
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rk Z
one
Joyc
e E
. Dae
schn
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asic
Ele
men
tary
John
K. H
illV
egas
Ver
des
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Han
cock
Ann
B. H
ughe
sV
irgin
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ly L
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lwin
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stes
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lder
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n M
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ell
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ricia
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turm
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l
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ray
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oger
M. B
ryan
E. W
. Grif
fith
Lurle
ne H
owar
dC
. V. T
.;A
rthu
r B
. Sad
ler
Ken
neth
E. C
arte
rR
ose
War
ren
Eva
Kat
hryn
How
ell
Bon
anza
Bar
bara
Sch
neid
erT
eddi
e E
. Cen
nam
eR
ose
War
ren
Elm
er E
. Hug
hes
Rut
h F
yfe
Arie
an M
. Sm
ithB
etty
B. C
ooga
n0.
K. A
dcoc
kV
irgin
ia Y
. Kun
zT
win
Lak
esE
idin
e B
. Ste
vens
Car
olyn
Cre
ekm
ore
Bon
anza
Ger
ald
D. M
artin
Pau
l Cul
ley
Jane
t G. T
ank
John
K. D
aile
yC
. V. T
. Gilb
ert
Rob
ert N
. Nor
man
Wes
t Chc
:-;e
s7o-
,G
wen
Tru
scot
tC
arol
yn L
. Dos
sW
est C
harle
ston
Dor
is E
. Oke
lber
ryV
ail P
ittm
anG
lynn
Vas
sar
Pat
ricia
Dw
orza
ckJ.
T. M
cVv'
il I i
ams
Rob
ert O
nken
Pau
l Cul
ley
PPle
iace
PH
ILO
SC
PH
Y.
In o
evel
ooin
g a
cons
iste
ntph
iloso
phy
to g
ive
dire
ctic
n to
mat
hem
atic
s in
stru
ctio
n fo
r al
l stu
dent
s in
the
publ
ic s
choo
ls, i
t
is n
eces
sary
to c
onsi
der
the
follo
win
g qu
estio
ns:
1.W
hy s
houl
d m
athe
mat
ics
beta
ught
?
2.W
hat m
athe
mat
ics
shou
ld b
eta
ught
whe
n an
d to
who
m?
3.H
ow s
houl
d m
athe
mat
ics
be ta
ught
?
It is
obv
ious
that
the
answ
ers
toqu
estio
ns #
2 an
d #3
dep
end
on th
e an
swer
to#1
; and
that
the
seco
nd q
uest
ion
has
to d
o w
ith
the
elec
tion,
sco
pe, a
nd s
eque
nce
of c
onte
nt;
and
that
the
last
que
stio
n de
als
with
met
hodo
logy
.
Que
stio
n #1
is th
e "h
ard"
one
, bec
ause
the
answ
er r
equi
res
that
cer
tain
ass
umpt
ions
abou
t the
nat
ure
of m
an a
ndw
hat
cons
titut
es th
e "g
ood
life"
be
mad
eex
plic
it.F
or e
xam
ple,
if it
is a
ssum
edth
at c
ontr
ol o
f the
env
ironm
ent b
y m
an is
desi
r-
able
, the
n it
logi
cally
follo
ws
that
mat
hem
atic
s sh
ould
be
to_g
ht s
ince
iten
able
s m
an to
des
crib
e an
d pr
edic
tP
hysi
cal
phen
omen
a. O
f cou
rse,
man
exi
sts
at a
poi
ntin
tim
e an
d :p
ace,
so
thes
e as
sum
ptio
nsch
ange
from
tim
e to
tim
e an
d fr
om
plac
e to
pla
ce.
The
com
plet
e de
velo
pmen
t of s
uch
ade
duct
ive
-1E
ySt`
F:'7
is b
eyon
d th
e sc
ope
of th
ese
intr
oduc
tory
rem
arks
. A
sim
ple
stat
emen
t of b
elie
fs m
ust s
uffic
e.
Eve
ry in
divi
dual
sho
uld
be li
mite
d H
ch:H
c.:e
s.
n;au
e se
t of "
orig
inal
" eq
uipm
ent,
such
as
phys
ique
,
inte
llige
nce,
and
hea
lth.
Inso
far
as p
ossi
ble,
he
shc;
;ioe
mas
=er
, not
the
slav
e, o
f the
rou
tines
and
dec
isio
nsw
hich
shap
e hi
s lif
e.E
duca
tion,
incl
udin
g m
athf
.-:m
aric
sed
ucoi
:;m, i
ske
y to
this
mas
tery
.in
an
age
of in
crea
sing
spec
ializ
a-
tion,
the
elem
enta
ry s
choo
l is
beco
min
g th
e la
st fo
rtre
ss c
= g
eTi,r
alea
..:ca
tion.
The
mat
hem
atic
s w
hich
is ta
ught
at
this
leve
l
mus
t be
aim
ed a
t kee
pina
doo
rs o
pen
for
child
ren.
Whe
ther
c:-
-.a
t a s
tude
ntel
ects
mor
e m
athe
mat
ics
in s
econ
dary
scho
ol, h
e
shou
ld le
ave
the
elem
enta
ry s
choo
lw
ith a
:Dow
eriu
! too
lmat
hem
atic
al:it
erac
y--w
ith w
hich
to c
hip
away
his
pie
ceof
the
"goo
d lif
e."
PU
RP
OS
E O
F T
HE
GU
IDE
Thi
s gu
ide
was
writ
ten
to d
efin
e an
inst
ruct
iona
l pro
gram
in m
athe
mat
ics
for
elem
enta
ry s
choo
lst
uden
ts.
Its ,D
urc,
ose
is to
serv
e as
a fr
amew
ork
with
in w
hich
sch
ools
may
des
ign
a m
athe
mat
ics
prog
ram
app
ropr
iate
to th
eir
stud
ents
, sta
ff, a
ndfa
cilit
ies.
Spe
cific
ally
, thi
s cu
rric
ulum
gui
de :s
inte
nded
to:
1.Id
entif
y an
d cl
assi
fy th
e m
ajor
mat
hem
atic
al c
once
pts
and
topi
cs c
onsi
dere
d in
the
elem
enta
ry s
choo
l and
to in
dica
te th
e sc
ope
and
sequ
ence
of c
onte
nt in
gra
des
Kin
derg
arte
n th
roug
h S
ix.
2.P
rovi
de fo
r ar
ticul
atio
n am
ong
ana
with
in th
e el
emen
tary
sch
ools
of t
he D
istr
ict.
3.R
elat
e th
e th
ree
new
ly a
dopt
ed te
xtbo
ok s
erie
s to
the
topi
cs o
utlin
edin
the
guid
e.
4.P
rovi
de fo
r a
smoo
th tr
ansi
tion
from
the
pres
ent m
athe
mat
ics
text
book
sto
the
new
ly a
dopt
ed s
erie
s.
Som
e w
i-;!-
ers
desi
_nat
eas
"cur
ricul
ar"
thos
e co
nsid
eriti
ons
invo
lvin
g w
hat t
heen
ds o
f edu
catio
n sh
ould
be,
and
as "
inst
ruc
tiona
l" th
ose
cons
ider
atio
ns in
volv
ing
the
mea
ns b
y w
hich
thos
e en
ds a
re a
ccom
plis
hed.
Thi
s cu
rric
ulum
aui
ce is
res
tric
ted
to th
e en
ds, r
athe
r th
an th
e m
eans
. How
ever
, the
mos
t crit
ical
pha
se o
f the
entir
e cu
rric
ulum
pla
nnin
g ...
L.re
cess
con
sist
s of
the
teac
her's
ow
n ef
fort
s to
dev
elop
pla
ns to
impl
emen
t the
seob
ject
ives
for
the
pupi
ls h
e te
ache
s.
It is
hop
ed th
at th
is g
uide
will
be
of p
ract
ical
val
ueto
the
teac
her
in te
achi
ng e
lem
enta
ry m
athe
mat
ics
to c
hild
ren
inC
lark
Cou
nty.
US
E 0
TH
E G
UID
E.
The
mea
ning
of c
erta
in te
rms
and
the
orga
niza
tion
of th
e va
rious
sec
tions
mus
tbe
mad
e cl
ear
in o
rder
for
this
cui
de to
achi
eve
its p
urpo
se.
In th
e fo
llow
ing
expo
sitio
n,th
e te
rms,
Str
and,
Beh
avio
ral O
bjec
tive,
and
Tex
tboo
k P
age
Ced
ing,
will
be
disc
usse
d in
som
e de
tail
and
the
over
all o
rgan
izat
ion
of th
e gu
ide
will
be
outli
ned.
Str
ands
A s
tran
d is
a "
big"
topi
c(o
r id
ea, c
once
pt, o
r th
eme)
mat
hem
atic
s w
hich
stu
dent
s st
udy
ever
y ye
arth
at ti
ne,'
are
in e
lem
enta
rysc
hool
, fro
m K
inde
rgar
ten
thro
ugh
Gra
deS
ix.
The
wor
d "s
tran
d" is
use
d be
caus
e it
sugg
ests
that
the
topi
cs w
eave
thro
ugho
utth
e el
emen
tary
gra
des
and
toge
ther
form
the
fabr
ic o
r m
ater
ial o
f the
ele
men
tary
mat
hem
atic
s pr
ogra
m.
The
follo
win
g si
x st
rand
s w
ere
sele
cted
togi
ve fo
rm a
nd c
ontin
uity
to th
iscu
rric
ulum
gui
de:
1.N
umbe
r2.
Num
erat
ion
3. O
pera
tions
4. G
eom
etry
5. M
easu
rem
ent
6.P
robl
em S
olvi
ng(s
ee d
iscu
ssio
n be
low
)
The
se to
pics
are
con
side
red
at e
very
gra
dele
vel c
md,
with
the
exce
ptio
n of
pro
blem
sol
ving
,sp
ecifi
c co
nten
t ite
ms
are
liste
d an
d or
dere
dun
der
each
topi
c.
PR
OB
LEM
SO
LVIN
G
Whi
le p
robl
em s
olvi
ng is
not
mat
hem
atic
al c
onte
ntin
the
sam
e se
nse
as N
UM
BE
R o
rO
PE
RA
TIC
:NS
, it i
s an
impo
rtan
t str
and
in th
e el
emen
tary
mat
hem
atic
s cu
rric
ulum
.T
here
are
two
aspe
cts
of p
robl
em s
oivi
nd:
1.; t
he
deve
lopm
ent o
f a p
robl
em s
olvi
ng fa
cilit
y, a
nd 2
)th
e ap
plic
atio
n of
mat
hem
atic
s.
The
dev
elop
men
t of a
pro
blem
sol
ving
faci
lity
does
not
dep
end
upon
mem
oriz
atio
n of
est&
-.:!i
snec
i aro
czdu
.es
for
solv
ing
all p
robl
ems,
but
rat
her,
upo
nde
velo
ping
a s
trat
egy
for
atta
ckin
g pr
oble
ms.
Suc
cess
in p
r:;:-
;;em
solv
ing
depe
nds
upon
the
stud
ent's
abi
lity
tont
erpr
et th
e si
tuat
ion,
to tr
ansl
ate
it in
to a
mat
hem
atic
alpr
oble
m, a
nd to
inte
rpre
t the
res
ults
Thr
ough
sol
ving
a v
arie
d as
sort
men
t of p
robl
ems,
the
stuc
ent c
an b
e ex
pect
ed to
dev
elop
an
appr
ecia
tion
and
unde
rsta
ndin
g of
the
appl
icab
ility
of m
athe
mat
ics
to th
ere
al w
orld
. The
spe
cific
app
licat
ions
of m
athe
-m
atic
s co
vere
d in
the
text
s ar
e no
t the
mse
lve!
, as
impo
rtan
t as
the
broa
der
conc
ept t
hat m
athe
mat
ic, i
sap
plic
able
to a
larg
e nu
mbe
r an
d w
ide
varie
, y o
f rea
l pro
blem
s ar
isin
g da
ily in
the
pers
onal
and
pro
fess
iona
l
lives
of p
eopl
e.
Thi
s st
rand
is n
ot d
evel
oped
ih th
e gu
ide,
as
are
the
othe
r st
rand
s,be
caus
e of
the
gene
ral n
att.r
e of
the
goal
s.H
owev
er, t
he a
dopt
ed te
xts
cont
ain
abun
dant
pro
blem
s an
d ap
plic
atio
nsth
roug
hout
, and
inde
ed, t
he in
- an
dou
tof-
scho
ol li
ves
of th
e st
uden
ts p
rovi
deric
h op
port
uniti
es fo
r pr
oble
m s
olvi
ng.
Beh
avio
ral
Obj
ectiv
es
Thi
s gu
ide
goes
far
beyo
nd a
mer
e lis
ting
of s
tran
ds c
nd r
elat
ed c
onte
nt it
ems.
For
eac
h co
nten
t ite
m, a
spe
cific
obje
ctiv
e (o
r ob
ject
ives
) ha
s be
en w
ritte
n in
term
s of
obs
erva
ble
stud
ent b
ehav
ior.
The
beh
avio
ral o
bjec
tive
stat
escl
early
wha
t beh
avio
r or
act
ion
is e
xpec
ted
of th
e st
uden
t; un
der
wha
t con
ditio
ns o
rci
rcum
stan
ces
this
c-ic
tion
is
expe
cted
to o
ccur
; and
to w
hat e
xten
t or
degr
ee th
e st
uden
t is
expe
cted
to p
erfo
rmth
e de
sire
d ac
tion.
A s
ampl
ebe
havi
oral
obj
ectiv
e fo
r th
e st
rand
of N
UM
BE
R -
GR
AD
E O
NE
is p
rinte
d be
low
:
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
EA
WS
AB
C
CA
RD
INA
L N
UM
BE
RS
0 -
100
Ord
er r
elat
ions
1.G
iven
two
num
bers
suc
h as
47
and
95, t
he s
tude
nt95
-106
84-1
03
jo
can
orde
r th
e nu
mbe
rs b
y sa
ying
:"4
7 is
less
than
95,
"12
2-14
0<
>an
d by
writ
ing:
47
< 9
5.
The
"gi
ven"
par
t est
ablis
hes
the
circ
umst
ance
s un
der
whi
ch th
e st
uden
t is
expe
cted
tope
rfor
m, a
nd th
e ve
rb p
hras
e
"can
ord
er"
indi
cate
s th
e c-
:tion
.T
his
part
icul
ar b
ehav
iora
l obj
ectiv
e ca
n be
tran
slat
ed in
to s
ever
al te
st it
ems
for
a fir
st g
rade
stu
dent
,ea
ch p
rogr
essi
vely
mor
e di
fficu
lt.F
or e
xam
ple:
1.C
an y
ou te
ll m
e w
hich
is m
ore
(or
less
)-
-i7
or
95?
2.I a
m g
oing
to w
rite
the
nam
esfo
r tw
o nu
mbe
rs o
n th
e bo
ard.
Poi
nt to
the
orea
teri;
esse
r) n
umbe
r
and
read
it.
3.T
he n
umer
al:-
for
two
num
bers
are
on
the
flann
el b
oard
. Cho
ose
one
of th
eor
der
sym
bols
, < o
r
and
plac
e it
_en
the
num
eral
s an
dth
en r
ead
the
num
ber
sent
ence
.
4.P
ut a
rin
g ar
ound
the
corr
ect
sym
bol
,<
j , w
hich
will
mak
e 95
47 a
true
num
ber
sent
ence
.
Sin
ce b
ehav
iora
l obj
ectiv
es h
ave
to e
ow
ith th
e ob
serv
able
act
ions
of c
hild
ren,
wor
dsw
hich
des
crib
e in
tern
al b
ehav
ior,
such
as
"und
erst
and"
and
"kn
ow",
are
not
used
.T
he q
uest
ion
is: W
hat d
oes
a ch
ild d
o w
ho "
unde
rsta
nds"
plac
e va
lue?
The
act
ion
wor
ds th
at a
re m
ost f
requ
ently
used
in th
is g
uide
are
iden
tify,
dist
ingu
ish,
nam
e, c
onst
ruct
, ord
er, d
escr
ibe,
stat
e, a
nd d
emon
stra
te. T
he m
eani
ngof
thes
e w
ords
is c
lear
to m
ost
teac
hers
with
the
exce
ptio
n of
"na
me"
. To
nam
e
mea
ns to
sup
ply
the
corr
ect n
ame
oral
ly o
r in
writ
ing
for
a cl
ass
of o
bjec
ts o
r se
ts.
For
exa
mpl
e:
"Nam
e th
e su
m o
f 27
and
48."
The
stu
dent
is e
xpec
ted
to d
eter
min
e th
e su
mby
com
putin
g, a
nd to
say
or
writ
e:75
.
The
beh
avio
ral o
bjec
tives
wer
e w
ritte
nw
ith th
e ty
pica
l or
aver
age
stud
ent i
n m
ind.
The
refo
re, i
t is
felt
that
from
75%
to 8
0% o
f the
chi
ldre
n in
a ty
pica
lcl
ass
shou
ld b
e ab
le to
acc
ompl
ish
all t
he o
bjec
tives
for
thei
r pa
rtic
ular
gra
de
leve
l. S
ome
stud
ents
can
und
oubt
edly
acco
mpl
ish
muc
h m
ore.
How
ever
, onl
y ad
equa
te tr
ial a
nd te
stin
g w
illes
tabl
ish
the
leve
l of p
erfo
rman
ce p
ossi
ble.
Beh
avio
ral o
bjec
tives
are
not
a p
anac
ea fo
red
ucat
iona
l pro
blem
s.T
hey
are
usef
ul to
the
exte
nt th
at th
ey p
oint
out
the
dest
inat
ion
so th
at te
ache
rs c
an -
-,on
cern
them
selv
es w
ith s
elec
ting
and
plan
ning
the
mos
tef
ficie
nt r
oute
s.
Textbook
Pane
Codin
Pag
es o
f the
thre
e ne
wly
ado
pted
text
book
ser
ies
whi
ch r
elat
e to
the
cont
ent a
nd b
ehav
iora
lob
ject
ives
are
list
ed o
n
the
right
sid
e of
eac
h pa
ge u
nder
the
initi
als,
AW
, S, a
nd A
BC
(se
e th
e sa
mpl
e be
havi
oral
obje
ctiv
e ab
ove
for
illus
tra-
tion)
.A
W r
efer
s to
the
Add
ison
-Wes
ley
text
s,S
to th
e L.
W. S
inge
r se
ries,
and
AbC
toth
e A
mer
ican
Boo
k C
ompa
ny
serie
s.
Tea
cher
s ar
e ur
ged
to e
xplo
re a
ll th
ree
serie
s fo
r id
eas
an p
rese
ntat
ions
and
app
licat
ions
reg
ardl
ess
of w
hich
text
s ar
e av
aila
ble
to s
tude
nts.
Org
aniz
atio
n
A s
et o
f gra
phs
imm
edia
tely
follo
ws
thes
e in
trod
ucta
ry r
emar
ks.
A g
raph
has
bee
n pr
epar
edfo
r ea
ch s
tran
dto
pro
vide
a qu
ick
over
view
of t
he s
cope
and
sequ
ence
of c
onte
nt fr
om K
inde
rgar
ten
thro
ugh
Gra
de S
ix.
TI 2
gra
phs
are
colo
rco
ded
by s
tran
d in
ard
eras
follo
ws:
1.N
umbe
rr:
',"R
On
2.N
umer
atio
nP
ink
3.O
pera
tions
Yel
low
4.G
eom
etry
Blu
e5.
Mea
sure
men
t-
Buf
f
The
sec
tion
on c
onte
nt, b
ehav
iora
l obj
ectiv
es, a
nd te
xtbo
okpa
ge c
odin
g fa
llow
s th
e gr
aphs
and
form
s th
e bu
lk o
f the
guid
e.T
his
part
of t
he g
uide
isor
gani
zed
by g
rade
leve
l mer
ely
as a
mat
ter
of c
onve
nien
ce. E
very
teac
her
real
izes
that
a p
artic
ular
gra
de le
vel
desi
gnat
ion
may
hav
eve
ry li
ttle
mea
ning
for
a pa
rtic
ular
stud
ent.
For
this
rea
son,
the
stra
nds
are
also
col
or c
oded
by
pape
r co
lor,
so
that
it is
pos
sibl
eto
qui
ckly
ref
er to
a s
tran
don
any
gra
de le
vel.
For
exam
ple:
a th
ird g
rade
teac
her
may
wis
h to
exa
min
e th
e ob
ject
ives
for
the
stra
nd O
PE
RA
TIO
NS
for
Gra
des
Tw
o an
dF
our.
Sin
ce a
ll of
the
OP
ER
AT
ION
Sst
rand
is o
n ye
llow
pape
r, s
he c
an s
impl
y fli
p to
the
yello
wse
ctio
ns w
hich
pre
cede
and
follo
w th
e th
ird g
rade
yel
low
sect
ion.
Thi
s ty
pe o
f org
aniz
atio
n ha
sth
e ad
vant
age
of m
akin
gsp
iralin
g ex
plic
it.S
pira
ling
mea
ns th
ata
topi
c is
can
side
red
man
ytim
es d
urin
g th
e el
emen
tary
scho
ol y
ears
.Id
eally
, diff
eren
t app
roac
hes
to a
nd a
pplic
atio
ns o
f a to
pic
are
pres
ente
dse
vera
l tim
es d
urin
ga
scho
ol y
ear
and,
as
the
year
s go
by
and
the
stud
ents
mat
ure,
the
leve
l of r
igor
is g
radu
ally
incr
ease
d.
Thi
s cu
rric
ulum
gui
de is
not n
ow, a
nd n
ever
will
be,
"fin
ishe
d". A
cur
ricul
umsh
ould
be
a vi
able
thin
g, c
onst
antly
refle
ctin
g th
e ch
angi
ng n
eeds
and
valu
es o
f the
soc
iety
whi
ch c
reat
es it
.T
hose
of u
s w
ho w
orke
don
the
guid
e si
ncer
ely
hope
that
it w
ill b
e us
eful
to te
ache
rs a
nd th
at it
will
bec
ome
a ke
rnel
for
addi
tiona
l stu
dy a
nd w
ork
in m
athe
mat
ics
educ
atio
n in
Cla
rk C
ount
y.
1\111.6ER
SETS
Collections, one-to-one correspondence, equivalentand non-equivalent sets, empty set, and subsets
Finite and infinite sets
WHOLE NUMBERS (CARDINALS)
Abstracting the concept of whole number fromequivalent sets
0 10
0 100
0 1,000
0 10,000
0 1,000,000
0 1,000,000,000
0 infinity
Order relations
Even and odd numbers
Prime and composite numbers
RATIONAL NUMBERS
Abstracting the concept of rational number frommodels and from sets of equivalent fractions
One-half, one-third, one-fourth
Halves, thirds, fourths (i.e. 3/4)
a (denominators of 2 - 12)
a (denominators of 1, 2, 3, 4 ..
Order relations
.)
K 1 2 3 5 6
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INTEGERS
IRRATIONAL NUMBERS ( Tr )
ORDINAL NUMBERS
First third
tenth
twentieth
beyond
111111 Intuitive Development
Standard Grade Level Content
MMM Maintain Concepts and Skills
000 Optional
14
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6
6
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NUMERATION
A NUMBER HAS MANY NAMES
WHOLE NUMBERS
Numerals for numbers 0 9
0 99
0 999
0 - 9,999
0 - 999,999
0 - 999,999,999
0 beyondPlace value (positional value of digits andexpanded numeral form)
through
Prime factorization
Roman numerals
through
Non-decimal numeration
99
999
9,999
99,999
999,999,999
beyond
XV ( 15 )
L ( 50 )
C ( 100 )
M ( 1000 )
K 1 2 3 4 5 6
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RATIONAL NUMBERS
1/2, 1/3, 1/4
Halves, thirds, fourths (I. e. 3/4 )
a
b
a
b
(denominators of 2 - 12)
[RATION
(denominators of 1, 2, 3, 4 ...)
Equivalent fractions
Improper fractions and mixed numerals
Decimal notation through - thousandths
hundred thousandths
Percent notation
INTEGERS (NOTATION)
IRRATIONAL NUMBERS ( )
OTHER NOTATION
Rounding
Exponential notation
Scientific notation
11111 Intuitive Development
Standard Grade Level Content
MMM Maintain Concepts and Skills
000 Optional
1 ij
MM
OPERATIONS
WHOLE NUMBERS
Addition and Subtraction
Definition
Inverse relationship
Basic facts
Discovery through sums of 18
Immediate recall through sums of 10
Immediate recall through sums of 18
Properties
Commutative property of addition
Associative property of addition
Identity element for addition ( 0 )
Algorithms
Column addition and subtraction without regrouping
Column addition and subtraction with regrouping(numbers appropriate to grade level)
Multiplication and Division
Definition
Inverse relationship
Basic facts
Discovery through products of 81
Immediate recall through products of 45
Immediate recall through products of 81
1/
K 4 5 6
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MM
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-2- OPERATIONS
Properti?s
Commutative Hluporty of multiplication
Associative property of multiplication
Identity element for multiplication ( 1 )
Multiplicative property of 0
Distributive property of multiplication over addition
Algorithms
Factors of 10, 100...
One-digit factors and divisors
Two or more digit factors or divisors
Other Operations
Averaging
Greatest common factor
Least common multiple
Exponentiation
RATIONAL NUMBERS
Addition and Subtraction
Definition
Inverse relationship
Properties
Commutative property of addition
Associative property of addition
Identity element for addition ( 0 )
1 ts
2 3 4
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Algorithms
Fraction Notation
Like denominators
Unlike denominators
Mixed numerals
Decimal Notation
OPERATIONS
Multiplication and Division
Definition
Inverse relationship
Properties
Commutative property of multiplication
Associative property of multiplication
Identity element for multiplication ( 1 )
Multiplicative inverses (reciprocals)
Distributive property of multiplication over addition
Algorithms
Fraction Notation
Multiplication - common fractions
Multiplication mixed numerals
Division - common fractions and mixed numerals
Decimal Notation (whole number divisors)
Percent Notation
1 2 3 4 5 6
mill
111111
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-4-
INTEGERS
Addition and Subtraction
Definition
OPIIIATIONS
111111 Intuitive Development
MStandard Grade Level Content
MMM Maintain Concepts and Skills
000 Optional
GEOMIETRY
GEOMETRIC FIGURES
Identifying and Naming Plan( Figures
As sets of points
Point
Path (curve)
Line (including number line)
Line segment
Ray
Angle
Polygon
Triangle
Quadrilateral
Parallelogram
Square
Rectangle
Rhombus
Pentagon, hexagon, octagon
Circle
21
K 1 2 3 4 5 6
11111
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0.=
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K 1 2 3 4 5
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-2- GEOMETRY
Identifying and Naming Space Figures
As sets of points
Point
None
Polyhedron
Prism
Pyramid
Sphere
Cylinder
Cone
PROPERTIES
Length
Perimeter
Area
Volume
Paro!lel lines
Pependicular lines
Congruence
Symmetry
22
1 5 6
MM i\AMNI
M
CONSTRUCTIONS
-3-
Line segment
Circle
Triangle
Angle
Line segment bisector
Angle bisector
Perpendicular lines
Parallel I ines
GEOMETRY
11111 Intuitive Development
Standard Grade Level Content
MMM Maintain Concepts and Skills
000 Optional
3 4 5
MM
flEASUREMENT
CONCEPTS OF MEASUREMENT
Process of measuring
Arbitrary selection of unit
Approximate nature of measurement(precision)
MEASUREME 'T OF PHYSICAL PROPERTIES(standard units)
Length
Perimeter
Circumference
Area
Volume
Liquid measure
Time
Weight
Temperature
Money
Angle
Speed
RENAMING MEASURES
Comparison of units (e.g., 1 inch ( 1 foot)
Conversion of units (e .9 ., 6 quarts = 1 1/2 gallons)
COMPUTATIONS WITH MEASURES
(appropriate to the grade level)
11111 Intuitive Development
Standard Grade Level Content
MMM Maintain Concepts and Skills
000 Optional
3 4
I?' i=fie=Av=la%smi=Ar Ar
K 2 3 4 5 6
1111111
111111
MMMMM
Ar
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M MM
MM
MMN,
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1 2 3 4 5 6
CO
NT
EN
T
SE
TS C
olle
ctio
ns
One
-to-
one
corr
espo
nden
ce
Equ
ival
ent a
ndno
n-eq
uiva
lent
sets
NU
MB
ER
- K
IND
ER
GA
RT
EN
BE
HA
VIO
RA
L O
BJE
CT
IVE
ST
EX
TB
OO
K P
AG
ES
AW
SA
BC
1. G
iven
a v
erba
l des
crip
tion
of a
set
, the
stu
dent
can
dis
tingu
ish
1-
9C
hart
s i,
betw
een
mem
bers
of t
he s
et a
nd th
ings
whi
ch a
re n
ot m
embe
rs.
i )41
2, 3
, 4, 5
42 -
71
2. G
iven
two
equi
vale
nt s
ets
(obj
ects
or
pict
ures
), th
e st
uden
t can
17-1
9,21
-24,
26de
mon
stra
te a
one
-to-
one
mat
chin
g be
twee
n m
embe
rs o
f the
set
sby
con
stru
ctin
g lin
es o
r by
phy
sica
lly a
ssoc
iatin
g th
e ob
ject
s.
3. T
he s
tude
nt c
an d
istin
guis
h be
twee
n pa
irs o
f set
s w
hose
mem
bers
27-3
0,39
,43,
Cha
rt 1
2ca
n be
mat
ched
one
-to-
one
and
pairs
of s
ets
who
sem
embe
rs c
anno
t49
,53,
59,6
3be
mat
ched
one
-to-
one.
4. G
iven
two
non-
equi
vale
nt s
ets,
the
stud
ent i
s ab
le to
iden
tify
13-1
5,23
,24
the
set w
hich
has
mor
e m
embe
rs a
nd th
e se
t whi
ch h
as fe
wer
mem
bers
.
One
-mor
e pa
ttern
--5.
Giv
en te
n no
n-eq
uiva
lent
set
s, th
e st
uden
t can
arr
ange
the
sets
in32
,36,
39,4
3,se
ts w
ith c
ardi
nal
orde
r.F
or e
xam
ple:
49,5
3,59
,63,
num
bers
of 1
- 10
X69
XX XX
X, e
tc.
Em
pty
set
6. T
he s
tude
nt c
an d
escr
ibe
verb
ally
a s
et w
hich
has
no
mem
bers
, suc
h 35
as th
e se
t of a
ll liv
e tig
ers
in th
e cl
assr
oom
!
CA
RD
INA
L N
UM
BE
RS
10
-;".
The
stu
dent
can
cou
nt th
e m
embe
rs o
f a s
et b
y si
mul
tane
ousl
y sa
ying
40,
44,5
0,58
,th
e nu
mbe
r na
mes
one
to te
n) in
ord
er a
nd m
atch
ing
each
num
ber
60,6
4-66
,68,
nam
e to
a u
niqu
e m
embe
r of
the
set.
70,7
2
7212
;8C
hart
s 12
,13
, 14
NU
MB
ER
- K
IND
ER
GA
RT
EN
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
AW
SA
BC
8. G
iven
a s
et w
ith z
ero
to te
n m
embe
rs, t
he s
tude
nt c
an n
ame
33,3
4,36
-39,
42-7
1C
hart
s 8,
9,
how
man
y ob
ject
s ar
ein
the
set b
y sa
ying
the
num
ber
nam
e41
-43,
45,4
6,10
, 11
or b
y se
lect
ing
the
corr
ect
num
eral
.48
,49,
51-5
3,55
,56,
58,5
9,61
-63,
65,6
6,68
,70,
72
Ord
er r
elat
ions
betw
een
num
bers
9. G
iven
two
num
bers
(ve
rbol
or
writ
ten
num
eral
s) s
uch
asse
ven
and
thre
e, th
e st
uden
t can
ord
erth
em b
y sa
ying
:
17C
hart
12
0 -1
0"S
even
is g
reat
er th
an th
ree"
or
"Thr
ee is
less
than
sev
en."
OR
DIN
AL
NU
MB
ER
S
Firs
t thr
ough
third
10. G
iven
a s
eque
nce
of o
bjec
ts, p
eopl
e, e
tc.,
the
stud
ent c
anid
entif
y th
e se
cond
obj
ect i
n th
e se
quen
ce.
2,9-
12C
hart
15
141.
,
CO
NT
EN
T
WH
OLE
NU
MB
ER
S0
- 9
NU
ME
RA
TIO
NK
IND
ER
GA
RT
EN
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
1. G
iven
a s
et o
f obj
ects
or
pict
ures
, the
stu
dent
can
iden
tify
32-3
4,36
-39,
and
nam
e or
ally
the
num
eral
for
the
card
inal
num
ber
of th
ese
t. 41
-43,
45,4
6,48
-49,
51-5
3,55
,56,
58,5
9,61
-63,
65,6
6,68
,70,
72
2. G
iven
a v
erba
l or
writ
ten
num
eral
suc
has
7, t
he s
tude
nt c
an27
-32,
35,3
6,co
nstr
uct a
nd id
entif
y se
ts c
onta
inin
g 7
mem
bers
.40
,44,
50,5
4,60
,64,
69,7
1
CO
NT
EN
T
WH
OLE
NU
MB
ER
S
Add
ition
and
Sub
trac
tion
Def
initi
on o
f add
ition
(thr
ough
sum
s of
10)
1, 2.
Def
initi
on o
f sub
trac
tion
(thr
ough
sum
s of
10)
3. 4.
OP
ER
AT
ION
S -
KIN
DE
RG
AR
TE
N
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
Giv
en tw
o di
sjoi
nt s
ets
of p
hysi
cal o
bjec
ts, t
he s
tude
nt c
anun
ite th
e se
ts a
nd n
ame
the
card
inal
num
ber
of th
e ne
w s
etth
us fo
rmed
.
Giv
en tw
o nu
mbe
rs s
uch
as 3
and
2, t
he s
tude
nt c
an d
esig
na
sim
ple
expe
rimen
t inv
olvi
ng th
e un
ion
of tw
o di
sjoi
nt s
ets
to d
eter
min
e an
d na
me
the
sum
of t
he n
umbe
rs,
Giv
en a
set
of 7
obj
ects
, the
stu
dent
can
iden
tify
and
re-
mov
e a
subs
et w
ith 3
mem
bers
and
nam
e th
e ca
rdin
alnu
mbe
rof
the
rem
aini
ng s
ubse
t
Giv
en a
set
of 5
obj
ects
, the
stu
dent
can
con
stru
ct a
set
of
9 ob
ject
s an
d na
me
how
man
y m
ore
obje
cts
wer
e ne
eded
toco
nstr
uct t
he s
econ
d se
t,
39, 4
1-43
,45
, 46,
49,
51-5
3, 5
5,56
, 59,
61-6
3, 6
5,66
, 70,
72
71
TE
XT
BO
OK
PA
GE
S
SA
BC
Not
e: P
ages
are
not l
ist-
edfo
r S
inge
r an
dA
mer
ican
Boc
kbe
caus
e cf
revi
sion
s an
dtim
e.
CO
NT
EN
T
GE
OM
ET
RIC
FIG
UR
ES
Pla
ne fi
gure
sC
ircle
Squ
are
Rec
tang
leT
riang
le
GE
OM
ET
RY
- K
IND
ER
GA
RT
EN
BE
HA
VIO
RA
L O
BJE
CT
IVE
ST
EX
TB
OO
K P
AG
ES
AW
SA
BC
1. G
iven
mod
els
of c
ircle
s,sq
uare
s, r
ecta
ngle
s, a
nd tr
iang
les
2,12
,14
- 1
6,(w
ire, p
aper
or
flann
el c
utou
ts, p
enci
lor
cha
lk o
utlin
es),
21,
22,
24,
34,
the
stud
ent c
an id
entif
y,na
me
oral
ly, a
nd d
istin
guis
ham
ong
tiese
37,
46,
50,
52,
plan
e ge
omet
ric fi
gure
s.54
,56
,58
,60
,62
CO
NT
EN
T
CO
NC
EP
TS
OF
ME
AS
UR
EM
EN
T
ME
AS
UR
EM
EN
T -
KIN
DE
RG
AR
TE
N
BE
HA
VIO
RA
L O
BJE
CT
IVE
ST
EX
TB
OO
K P
AG
ES
Leng
th1.
Giv
en a
set
of o
bjec
ts o
r pi
ctur
es o
f obj
ects
, the
stu
dent
Com
paris
onca
n co
mpa
re th
em a
nd id
entif
y an
d na
me
the
long
est,
shor
test
, tal
lest
, and
wid
est.
C.;
3-6
AB
C
CO
NT
EN
T
SE
TS C
olle
ctio
ns
One
-to-
one
corr
espo
nden
ce
Equ
ival
ent a
nd n
on-
equi
vale
nt s
ets
One
-mor
e pa
ttern
NU
MB
ER
- G
RA
DE
ON
E
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
1. G
iven
a v
erba
l des
crip
tion
of a
set
, the
stu
dent
can
dis
-tin
guis
h be
twee
n m
embe
rs o
f the
set
and
thin
gs w
hich
are
not m
embe
rs.
1-13
2. G
iven
two
equi
vale
nt s
ets
(obj
ects
or
pict
ures
), th
e st
uden
t3-
13ca
n de
mon
stra
te a
one
-to-
one
mat
chin
g be
twee
n m
embe
rsof
the
sets
by
cons
truc
ting
lines
or
by p
hysi
cally
ass
ocia
ting
the
obje
cts.
3. G
iven
two
sets
(ob
ject
s, p
ictu
res,
ver
bal d
escr
iptio
n), t
hest
uden
t can
iden
tify
them
as
equi
vale
nt o
r no
n-eq
uiva
lent
,an
d if
non-
equi
vale
nt, t
ell w
hich
!.et
has
mor
e an
d w
hich
has
few
er m
embe
rs.
4. G
iven
ten
non-
equi
vale
nt s
ets,
the
stud
ent
sets
in o
rder
.F
or e
xam
ple:
X XX XX
X, e
tc.
AW
1-5
S
1, 2
, 9-1
2, 9
56-
11, 3
0-32
,96
73
can
arra
nge
the
14, 3
6, 4
0
AB
C
iii, v
iii, x
i,xi
i, 2,
19,
37,
48, 5
5
vi, v
ii, x
iii,
xiv,
3, 5
, 24,
25, 3
0, 5
7
24, 2
7
Em
pty
set
Sub
sets
5. T
he s
tude
nt c
an d
escr
ibe
verb
ally
a s
et w
hich
has
no
mem
bers
, 37,
such
cs
the
of a
ll gr
andf
athe
rs in
the
clas
sroo
m!
6. G
iven
a s
et, s
uch
as a
ll st
uden
ts in
the
clas
sroo
m, t
he s
tude
nt 2
3,ca
n id
entif
y a
subs
et, s
uch
as th
e bo
ys w
ith b
row
n ey
es.
33,
39-4
2
25, 2
7, 3
1,10
9, 1
1041
,11
6
42,
69,
1, 3
6, 5
7,81
, 179
CA
RD
INA
L N
UM
BE
RS
- 10
07.
Giv
en a
set
, the
stu
dent
can
cou
nt (
see
Kin
derg
arte
n --
obj
et-
15-3
5, 3
8-44
,tiv
e #7
) th
e m
embe
rs a
nd n
ame
how
man
y th
ings
are
in th
e se
t. 47
-51,
53-
64,
71-7
4, 7
7, 7
8,95
, 96,
107
-11"
24-2
9, 3
3-42
,46
-52,
58,
59,
68, 6
9, 7
1, 7
2,94
, 95,
i45,
151
iv, v
, ix,
xiv
,xi
, xvi
, 1, 7
,11
, 13,
15-1
8, 2
4, 2
7,42
, 50,
57,
.5E
,62
, 82,
83,
115
NU
MB
ER
- G
RA
DE
ON
E
CO
NT
EN
T
Ord
er r
elat
ions
<3
RA
TIO
NA
L N
UM
BE
RS
One
-hal
fO
ne-t
hird
One
-fou
rth
OR
DIN
AL
NU
MB
ER
SF
irst t
hrou
gh te
nth
BE
HA
ViO
RA
L
8. G
iven
two
num
bers
suc
h as
47
and
them
by
sayi
ng: "
47 is
less
than
95,
"
9. G
iven
app
ropr
iate
mat
eria
ls (
pape
ret
c.)
the
stud
ent c
an id
entif
y an
don
e-th
ird, a
nd o
ne-f
ourt
h.F
or e
xam
ple:
1/2
10. G
iven
a s
eque
nce
of o
bjec
ts, e
vent
s,id
entif
y th
e po
sitio
n in
spcc
e or
tim
e
OB
JEC
TIV
ES
AW
95, t
he s
tude
nt c
an o
rder
95-1
06, 1
74an
d by
writ
ing
47.<
95.
192,
210
, 230
,24
0, 2
87, 2
88,
289
regi
ons,
Cui
sena
ire r
ods,
303-
306
cons
truc
t mod
els
for
one-
half,
224,
138,
231
S
225
139,
230,
AB
C
29, 7
3, 7
9, 9
7,10
3, 1
15, 1
23,
126
138,
139
, 197
viii,
x, 2
, 19,
37, 4
2, 8
5et
c.,
of a
par
ticul
arth
e st
uden
t can
1, 2
obje
ct o
rev
ent b
y sa
ying
:T
his
(obj
ect)
is fo
urth
" or
"T
his
(eve
nt)
happ
ened
sec
ond.
"
NU
ME
RA
TIO
NG
RA
DE
ON
E
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
AV
SA
BC
NA
ME
S F
OR
NU
MB
ER
S1.
The
stu
dent
can
iden
tify
and
nam
edi
ffere
nt n
umer
als
for
151,
163,
165,
161-
171,
240,
58,7
3,78
,104
,
the
sam
e nu
mbe
r. F
or e
xam
ple:
183,
186,
195,
241,
254-
263,
105,
131,
142,
5 =
4 +
1 =
3 4
-2 =
7 -
2, e
tc.
204,
213,
219,
267
172,
188
220,
222,
233,
249
-25'
t,26
1-26
7
WH
OLE
NU
MB
ER
S0
- 99
2. T
he s
tude
nt c
an id
entif
y, n
ame,
rea
d, a
nd w
rite
num
eral
s43
-52,
61-6
5,39
-42,
46-5
9,v,
ix,4
,5,1
1,fo
r w
hole
num
bers
.67
,69,
71-7
5,71
,72,
94,9
5,13
-18,
24,2
5,77
-79,
85,8
6,15
0,21
2,21
327
,30-
33,3
9,88
-92
42,4
8,50
,52,
57-5
9,73
,84,
103,
114,
123,
133,
140,
169,
198
CZ
'3.
The
stu
dent
can
rea
d an
d w
rite
num
ber
wor
ds o
neth
roug
h te
n.53
116-
118
,220
-ix
,11,
13,1
4,22
262
,82,
101,
103,
114,
123,
195,
198
Pla
ce v
alue
- -
two
-dig
it nu
mer
als
4. G
iven
a n
umer
al s
uch
as 7
3, th
e st
uden
t can
iden
tify,
nam
e,an
d di
stin
guis
h th
e nu
mer
als
that
are
in th
e on
es a
nd te
ns59
-70,
93,9
4,10
0-10
2,25
5-14
5-14
9,15
2,18
0,23
312
7- 1
30,1
32-
135,
143,
144,
plac
es,
258
146,
147,
149,
162,
163,
165,
169-
171,
189,
192,
193
Exp
ande
d no
tatio
n5.
Giv
en a
num
eral
suc
h as
54,
the
stud
ent c
anw
rite
the
expa
nded
num
era
I(
50 +
4 )
.59
-70,
93,9
4,_
145-
149,
152,
127-
130
,132
-10
0-10
2,18
0,23
313
5,14
3,14
4,25
5 -2
5814
6,14
7,14
9,16
2,16
3,16
5,16
9-17
1,18
9,19
2,19
3
CO
NT
EN
T
RA
TIO
NA
L N
UM
BE
RS
12,
1/3
, 1/4
NU
ME
RA
TIO
N -
GR
AD
E O
NE
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
6. G
iven
a m
odel
of o
ne-t
hird
, the
stu
dent
can
iden
tify
and
303-
306
nam
e a
num
eral
(fr
actio
n)fo
r th
e ra
tiona
l num
ber
asso
ciat
edw
ith th
e m
odel
.F
or e
xam
ple:
1/3
224-
255
138,
139
OP
ER
AT
ION
S -
GR
AD
E O
NE
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
A1
114-
118,
149,
80-8
2,84
,A
BC
9,10
,12,
16,
WH
OLE
NU
MB
ER
S16
3,17
9,18
0,85
,91-
93,
20,2
4,26
,28,
197,
198,
201,
100-
115,
30-3
2,34
,35,
Add
ition
Sub
trac
tion
202,
215,
216,
123,
126,
38,4
3-47
,58,
219,
220
140,
141,
63,6
5-67
,92,
Def
initi
on o
f add
ition
1. G
iven
an
addi
tion
prob
lem
suc
h as
5 +
7 =
,th
e st
uden
t14
3,15
7,93
,95,
104,
can
desi
gn a
sim
ple
expe
rimen
t inv
olvi
ng th
e un
ion
of tw
o16
8-17
0,10
5,10
8,11
1di
sjoi
nt s
ets
to d
eter
min
e an
d na
me
the
sum
of t
he n
umbe
rs.
209
Def
initi
on o
f suL
trac
tion
2. G
iven
a s
ubtr
actio
n pr
oble
m s
uch
as 1
4 -
8 --
the
stud
ent
133-
136,
140
196-
201,
8-10
,12,
15,
can
cons
truc
t a s
et o
f 14
obje
cts,
rem
ove
a su
bset
with
815
5,15
6,16
9,20
4-20
7,26
,28,
30,3
1,m
embe
rs, a
n(' n
ome
the
card
inal
num
ber
of th
e re
mai
ning
sub
set.
170,
187,
188,
210,
252,
34,3
5,43
-45,
205,
206,
225,
253
53,6
0,65
,68-
70,
3. G
iven
a p
robl
em s
uch
as 6
= 1
5, th
e st
uden
t can
226
109,
111
cons
truc
t a s
et o
f 15
obje
cts,
rem
ove
a su
bset
with
6 m
embe
rs,
125,
1 7,
145
;an
d na
me
the
card
inal
num
ber
of th
e re
mai
ning
sub
set.
165,
183,
201,
202
Inve
rse
rela
tions
hip
4. T
he s
tude
nt c
an d
emon
stra
te b
y us
ing
sets
or
a nu
mbe
r lin
e th
atsu
btra
ctin
g 2
from
9 "
undo
es"
addi
ng 2
to 7
.16
1,16
2,17
5,43
,51,
87,1
10,
176,
194,
211,
118,
136,
137,
DO
0000
000
007
+ 2
= 9
212,
231,
232,
153,
159,
172,
275-
277
;74
UN
DO
0000
000
(.,
009
2 =
7
7
CO
NT
EN
T
Bas
k fa
cts
Thr
ough
sum
s of
10
Thr
ough
sum
s of
18
esigirkl
OP
ER
AT
ION
S -
GR
AD
E O
NE
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
5. G
iven
an
addi
tion
or s
ubtr
actio
n co
mbi
natio
nsu
ch a
s 4
+ 6
or
9 -
5, th
e st
uden
t can
imm
edia
tely
*nam
e th
e su
m o
r di
ffere
nce
and
use
sets
or
a nu
mbe
r lin
e to
pro
ve h
is r
esul
t.
6.G
iven
an
addi
tion
or s
ubtr
actio
n co
mbi
natio
n su
ch a
s 7
+ 8
or
16 -
9, t
he s
tude
nt c
an u
se s
ets
or a
num
ber
line
to d
eter
--..t
ean
d na
me
the
sum
or
diffe
renc
e.
7.T
he s
tude
nt c
an id
entif
y an
d na
me
sum
s, d
iffer
ence
s, a
nd m
issi
ngad
dend
s in
pro
blem
s w
ritte
n in
bot
h ho
rizon
tal a
nd v
ertic
alno
tatio
n.F
or e
xam
ple:
1416
- 8
=8
- 6
= 4
- 8
+
4 +
7 =
103+
=12
8, G
iven
a p
robl
em s
uch
as 1
46
= 8
, the
stu
dent
can
iden
tify
and
nam
e th
e m
issi
ng o
pera
tiona
l sig
n,
Pro
pert
ies
Com
mut
ativ
e pr
oper
ty9.
The
stu
dent
can
dem
onst
rate
by
usin
g se
ts o
r a
num
ber
line
that
of a
dditi
on7
+ 4
= 1
1an
d4
+ 7
= 1
1.
Ass
ocia
tive
prop
erty
10.
The
stu
dent
can
dem
onst
rate
by
usin
g se
ts o
r a
num
ber
line
that
:
of a
dditi
on(7
+ 2
) +
8 =
9 +
8 =
17
and
7 +
(2
+ 8
) =
+ 1
0 =
17,
AW
119-
124,
13/-
139,
141,
142,
147,
148,
150,
152-
154,
157-
159,
161,
164,
166-
168,
171-
173
,175
-17
8,18
9 -1
91,
207-
209,
227-
229
259-
264,
275,
277,
279,
243-
286
126,
128,
143-
146,
148,
151-
154,
160,
162,
165-
168,
183-
185,
201,
203,
221,
229,
.251
-254
,25
9-28
2
290
235-
239
241-
248,
259,
260
83,9
8,99
119-
122,
129,
131,
159,
180,
202,
203,
208,
211,
215,
234,
239,
244,
267
127,
128,
132-
134,
136,
137,
158,
160,
181,
209,
210,
238,
242,
243,
245-
251,
285,
287
130
AB
C69
,71,
72,7
4,76
,79
,80,
87,9
0,95
,97
,99-
102,
106
-11
1,12
. -12
6,14
4,15
3,16
1,16
6,17
1,17
7,18
6,18
7,19
4,20
0-20
6
129,
134,
135,
172-
176,
181,
184,
185
40,4
1,53
,55,
75-7
7,86
,91,
97,9
8,12
1,14
2,
164,
184,
185,
189-
191,
197,
200,
231,
203,
204
145
83,9
9,12
0, 3
4,43
,46,
66,
122,
135
67,7
2,87
,90,
153,
158
116,
117
''3
malt
'*N
NR
4.01
w-0
14
*Im
med
iate
ly is
def
ined
as
5 se
cond
s or
less
.
CO
NT
EN
T
OP
ER
AT
ION
SG
RA
DE
ON
E
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
W
Iden
tity
elem
ent f
or11
.G
iven
pro
blem
s su
ch a
s 0
+14
=
addi
tion
7 -
7 =
; 9=
9;25
7
; and
32
+=
32;
the
stud
ent c
an n
ame
the
sum
s, d
iffer
ence
s, a
nd m
issi
ng a
dden
ds a
nd u
se s
ets
ora
num
ber
line
to p
rove
his
resu
lts.
SA
BC
Alg
orith
ms
Col
umn
addi
tion
and
12.
The
stu
dent
can
nam
e th
e su
ms
and
diffe
renc
esfo
r pr
oble
ms
1`3-
156,
subt
ract
ion
(tw
o-di
git
such
as
2an
d37
.16
0,18
1,
num
eral
s) w
ithou
t61
-13
235-
237
regr
oupi
ng+
14
CO
NT
EN
T
GE
OM
ET
RIC
FIG
UR
ES
GE
OM
ET
RY
- G
RA
DE
ON
E
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
A C
Pla
ne fi
gure
sC
ircle
Squ
are
Rec
tang
leT
riang
le
Line
seg
men
t
Line
(num
ber
line)
PR
OP
ER
TIE
S
Leng
th
CO
NS
TR
UC
TIO
NS
Circ
leS
quar
eR
ecta
ngle
Tria
ngle
1. G
iver
, mod
els
of c
ircle
s,sq
uare
s, r
ecta
ngle
s, tr
iang
les,
line
segm
ents
, and
a n
umbe
r lin
e (w
ire, p
aper
or
flann
el c
utou
ts,
penc
il or
cha
lk o
utlin
es),
the
stud
ent c
an id
entif
y, n
ame,
and
dist
ingu
ish
amon
g th
ese
plan
e ge
omet
ric fi
gure
s.
2. G
iven
mod
els
of li
ne s
egm
ents
of d
iffer
ent l
engt
hs, t
hest
uden
t can
iden
tify
the
long
est a
nd s
hort
est.
3. G
; ,en
a p
egbo
ard
and
rubb
er b
ands
, the
stu
dent
can
con
stru
cta
squa
re, r
ecta
ngle
, and
tria
ngle
.
4. T
he s
tude
nt c
an m
ake
roug
h pe
ncil
and/
or c
halk
dra
win
gs (
outli
nes)
of c
ircle
s,sq
uare
s, r
ecta
ngle
s, a
nd tr
iang
les.
2,8,
21,2
6,38
,42,
108,
118,
125,
136,
169.
180,
187,
205,
225,
250
285,
286
2,8,
38
268,
269
272,
273,
275,
276,
278-
280,
282,
283,
276,
277,
281,
284
138,
197
NO
111"
...
CO
NT
EN
T
CO
NC
EP
TS
OF
ME
AS
UR
EM
EN
T
Pro
cess
of m
easu
ring:
leng
th Sel
ectio
n of
uni
t(a
rbitr
ary)
Cou
ntin
g
ME
AS
UR
EM
EN
T -
GR
AD
E O
NE
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
1. G
iven
an
obje
ct w
ith th
e pr
oper
ty o
f len
gth,
suc
h as
ape
ncil,
and
a v
arie
d se
t of o
bjec
ts w
ith w
hich
to m
easu
reth
e pe
ncil,
the
stud
ent c
an s
elec
t a s
uita
ble
unit
of le
ngth
and
mea
sure
the
penc
il by
cou
ntin
g th
e nu
mbe
r of
uni
tsne
eded
to m
atch
the
leng
th o
f the
pen
cil.
ME
AS
UR
EM
EN
T O
F P
HY
SIC
AL
PR
OP
ER
TIE
S
Leng
thR
uler In
chC
entim
eter
Vol
ume
Liqu
id m
easu
reC
upP
int
Qua
rt
Tim
e Clo
ck Hou
rC
alen
dar
Day
Wee
kM
onth
Wei
ght
AW
307-
.308
2. T
he s
tude
nt c
an m
easu
re s
mal
l obj
ects
or
pict
ures
of o
bjec
ts 3
07-3
10to
the
near
est w
hole
uni
t usi
ng b
oth
arbi
trar
y un
its a
nd a
rule
r.
3. B
ased
on
expe
rienc
es w
ith c
ups,
pin
ts, a
nd q
uart
s, th
est
uden
t can
com
pare
and
ord
er th
ese
liqui
d m
easu
res.
For
exa
mpl
e: 3
cup
s is
(m
ore,
less
) th
an 1
pint
.
4. G
iven
a c
lock
, or
cloc
k fa
ce, t
he s
tude
nt c
an te
ll tim
eon
the
hour
.
5. G
iven
a s
et o
f obj
ects
, the
stu
dent
can
com
pare
them
and
iden
tify
and
nam
e th
e he
avie
st a
nd li
ghte
st.
311,
312
S
226-
228,
266,
274,
275
223
172-
175,
217-
219,
266
AB
C
94 94 94,1
41,1
43,
148,
178,
185,
196
94
CO
NT
EN
T
ME
AS
UR
EM
EN
T -
GR
AD
E O
NE
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
Tem
pera
ture
6. B
ased
on
expe
rienc
es w
ith r
eadi
ng s
cale
s on
ath
erm
omet
er,
The
rmom
eter
the
stud
ent c
an r
ecor
d te
mpe
ratu
res
insi
de a
nd o
utsi
deth
e
Deg
ree
(F.)
clas
sroo
m a
nd a
nsw
er q
uest
ions
suc
h as
:
Is it
war
mer
insi
de o
r ou
tsid
e th
e cl
assr
oom
?
Mon
ey7.
The
stu
dent
can
iden
tify
and
nam
e pe
nnie
s,ni
ckel
s, a
nd29
1-30
217
6-17
992
,93,
95,
Pen
nydi
mes
and
sta
te th
e va
lue,
in c
ents
, of e
ach
coin
.12
2-12
9
Nic
kel
Dim
e8.
Giv
en a
set
of p
enni
es a
nd/o
r ni
ckel
s, th
e st
uden
t can
dete
rmin
e an
d na
me
the
tota
l val
ue, i
n ce
nts,
oft
he c
oins
.
CO
NT
EN
T
SE
TS
NU
MB
ER
- G
RA
DE
TW
O
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
Col
lect
ions
1. G
iven
a v
erba
l des
crip
tion
of a
set
, the
stu
dent
can
1-10
1-13
, 161
-171
,2,
26,
28-
33,
dist
ingu
ish
betw
een
mem
bers
of t
he s
et a
nd th
ings
whi
ch21
-, 2
29, 2
51,
33, 7
8-82
are
not m
embe
rs.
2._1
1, 2
63-2
65,
275
One
-to-
one
2. G
iven
two
equi
vale
nt s
ets
(obj
ects
or
pict
ures
), th
e1-
44
-726
, 28-
29co
rres
pond
ence
stud
ent c
an d
emon
stra
te a
one
-to-
one
mat
chin
g be
twee
nm
embe
rs o
f the
set
s by
con
stru
ctin
g lin
es o
rby
phy
sica
llyas
soci
atin
g th
e ob
ject
s.
One
to-m
any
3. T
he s
tude
nt c
an d
escr
ibe
fam
iliar
phy
sica
l situ
atio
ns in
corr
espo
nden
cew
hich
a o
ne-t
o-m
any
mat
chin
g oc
curs
.F
or e
xam
ple:
one
hand
to fi
ve fi
nger
s or
two
whe
els
to o
ne b
icyc
le.
Equ
ival
ent a
nd n
on-
equi
vale
nt s
ets
Em
pty
set
Sub
sets
275-
276
4. G
iven
two
sets
(ob
ject
s, p
ictu
res,
ver
bal d
escr
iptio
n),
1-4,
53-
54,
1-13
the
stud
ent c
an id
entif
y th
em a
s eq
uiva
lent
or
non-
251-
260,
equi
vale
nt, a
nd if
non
-equ
ival
ent,
tell
whi
ch s
et h
as26
9-27
0m
ore
and
whi
ch h
as fe
wer
mem
bers
.
5. T
he s
tude
nt c
an d
escr
ibe
verb
ally
a s
et w
hich
has
no
1-13
29, 3
2, 7
5m
embe
rs, s
uch
as th
e se
t of c
hild
ren
in th
e cl
assr
oom
with
gree
n ha
ir!
6. G
iven
a s
et, s
uch
as a
ll st
uden
ts in
the
clas
sroo
m, t
hest
uden
t can
iden
tify
a su
bset
: suc
h as
the
girls
with
blon
d ha
ir.
124-
136
2, 2
4, 3
3,41
, 99,
135
,,3
4
CO
NT
EN
T
CA
RD
INA
L N
UM
BE
RS
NU
MB
ER
GR
AD
E T
WO
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
0 -
1000
7. T
he s
tude
nt c
an g
roup
the
mem
bers
of a
giv
en s
et b
yon
es, t
wos
, fiv
es, a
nd te
ns a
nd d
eter
min
e by
cou
ntin
gho
w m
any
mem
bers
are
in th
e se
t.
11-1
4, 1
6-17
,22
, 26,
53-
54,
175,
251
-260
,
14-1
9,48
-49
22-4
1,26
,83
,30
, 49,
128,
i 30
Ord
er r
elat
ions
< >
= )1\
23 RA
TIO
NA
L N
UM
BE
RS
Hal
ves
Thi
rds
Fou
rths
OR
DIN
AL
NU
MB
ER
S
Firs
t thr
ough
twen
tieth
8. G
iven
a m
athe
mat
ical
sen
tenc
e su
ch a
s 15
+ 1
2th
e st
uden
t can
writ
e th
:pis
sing
rel
atio
n sy
mbo
l.
9. G
iven
mod
els
of 1
/3, 2
/3, 3
/3, e
tc.,
the
stud
ent
can
iden
tify
and
nam
e th
e ra
tiona
l num
bers
asso
ciat
ed w
ith th
e m
odel
s.
1/3
EIM
M:1
11 3
/L'
10. G
iven
a s
eque
nce
of o
bjec
ts, e
vent
s, e
tc.,
the
stud
ent
can
iden
tify
the
posi
tion
in s
pace
or
time
of a
par
ticul
arob
ject
or
even
t by
sayi
ng: "
Thi
s (o
bjec
t) is
four
th"
or"T
his
(eve
nt)
happ
ened
sec
ond.
"
ININ
IMII
MI
OMNI
OM
Oums
ammo
1111
1110
10
263-
264,
269-
270,
274
,27
7-27
8
15, 2
2-24
,96
, 140
-155
89, 9
1, 9
5,33
-35,
188
,14
2, 1
83, 1
96,
194,
197
-198
,20
3, 2
1921
5-21
7, 2
84
289-
306
190-
200,
126,
128
,21
5-21
6, 2
30,
152-
153,
171
,25
3, 2
8819
9-20
1, 2
03,
257
118-
119
,31
, 177
,21
.!
NU
ME
RA
TIO
N -
GR
AD
E T
WO
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
AW
SA
3C
NA
ME
S F
OR
NU
MB
ER
S1.
The
stu
dent
can
iden
tify,
nam
e, r
ead,
and
writ
e m
any
dif-
i5,7
9,89
-97,
37,1
44,1
57,
fere
nt n
ames
for
the
sam
e nu
mbe
r.F
or e
xam
ple:
145-
148,
153-
162,
175,
179-
123
= 1
00 +
20
+ 3
= 9
0 +
20
+ 1
3 =
1?0
7, e
tc.
155,
159,
165,
181,
202,
208-
169,
183,
185,
189,
201,
203-
209
204,
219
-223
,22
5-22
7W
HO
LE N
UM
BE
RS
099
92.
The
stu
dent
can
iden
tify,
nam
e, r
ead,
and
writ
e nu
mer
als
2-11
,18-
21,2
5,14
-21,
67,7
8-88
,7-
8,10
,12,
25,
for
who
le n
umbe
rs.
27-2
8,36
,60,
181,
97,1
12,1
17,1
8930
,34-
35,3
7,24
1-25
046
,78-
82,9
2,11
0,11
3,11
9-12
0,13
2 -1
33,
168,
3. T
he s
tude
nt c
an r
ead
and
writ
e nu
mbe
r w
ords
thro
ugh
twen
ty.
1-20
68-7
0,75
,12
,22-
24,3
5,78
-88,
9945
,97,
110,
132-
133,
179
Pla
ce v
alue
- -
thre
e -d
igit
num
eral
s4.
Giv
en a
num
eral
suc
h as
307
, the
stu
dent
can
iden
tify,
nam
e,an
d di
stin
guis
h th
e nu
mer
als
that
are
in th
e on
es, t
ens,
and
19-2
0,29
-32,
177,
182
42-4
6,73
,100
,1'
3-11
4,13
8,11
-12,
34-3
5,37
,45-
46,5
4,hu
ndre
ds p
lace
s.20
2-20
8,77
,97,
111,
219-
223
113-
116,
120,
163,
179-
180,
198,
208
CO
NT
EN
T
Exp
ande
d no
tatio
n
RA
TIO
NA
L N
UM
BE
RS
1'2,
1.'3
,1,
4,
2/2
2/3,
2/4,
3/3
3/4,
4/4
NU
ME
RA
TIO
N -
GR
AD
E T
WO
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
5. G
iven
a n
umer
al s
uch
as 5
86, t
he s
tude
nt c
an w
rite
the
expa
nded
num
eral
( 5
00 +
80
+ 6
).
6. G
iven
a m
odel
of t
hree
-fou
rths
, the
stu
dent
can
iden
tify,
nam
e, r
ead,
and
writ
e a
num
eral
(fr
actio
n) fo
r th
e ra
tiona
lnu
mbe
r as
soci
ated
with
the
mod
el.
For
exa
mpl
e:
3,/4
AW
79,8
9- 9
7,14
:11,
-14
8,15
3- 1
55,1
59,
163,
169,
183,
185,
189,
201,
203-
204,
219-
223,
2;5-
227
299-
306
SA
BC
34,3
7,11
1,11
3,18
1
190-
200,
215-
126,
128,
152-
216,
230,
253,
153,
171,
199-
288
201,
203,
207
CO
NT
EN
T
WH
OLE
NU
MB
ER
S
Add
ition
and
Sub
trac
tion
Def
initi
on
Inve
rse
rela
tions
hip
Bas
ic fa
cts
Thr
ough
sum
s of
18
OP
ER
AT
ION
S -
GR
AD
E T
WO
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
I. G
iven
an
addi
tion
or s
ubtr
actio
n pr
oble
m s
uch
ac 5
+ 7
=or
14 -
8 =
,th
e st
uden
t can
des
ign
a si
mpl
e ex
perim
ent i
nvol
ving
sets
or
a nu
mbe
r lin
e to
det
erm
ine
and
rime
the
sum
or
diffe
renc
e of
the
num
bers
.
2. G
iven
two
sets
, the
stu
dent
can
com
pare
the
sets
by
mat
chin
g th
em
embe
rs a
nd w
rite
a su
btra
ctio
n eq
uatio
n to
exp
ress
the
diffe
renc
ebe
twee
n th
e ca
rdin
al n
umbe
rs o
f the
set
s.F
or e
xam
ple:
1200
000C
_)00
I14
. 1 I
8X
X X
X AI;
X A
Adi
ffere
nce
12 -
8 =
4
o. G
iven
a s
et m
odel
, the
stu
dent
can
writ
e tw
o ad
ditio
n an
d tw
osu
btra
ctio
nto
des
crib
e th
e ph
ysic
al s
ituat
ion.
F--
exa
mpl
e:
0 0
0 0
0
DO
67
= 1
3U
ND
O13
7 =
6
XX
X X
X X
X
7 +
6 =
13
13 -
6 =
7
4. G
iven
an
addi
tion
or s
ubtr
actio
n co
mbi
nai i
on s
uch
as 7
+ 8
or
16 -
9,
the
stud
ent c
an H
med
iate
lyna
me
the
sum
or
diffe
renc
e an
d us
e se
tsor a number in
to p
rove
his
res
ult.
* Im
med
iate
ly is
dcH
ned
as 5
sec
onds
or
less
.
AW
SA
BC
09-5
2,55
-57,
22-4
1,2-13,14-23,
59-6
0,62
-64,
50-6
6,73
,83-
88,
98-
74-9
1,38-4S, 51,58,
1C3,
103
-116
,99
-101
,68-70,84-85,
118,
120,
122,
104-
111,
100,107-109,
124,
126-
130,
132,
134,
136-
187-
188
112
137
53-5
454
-61
5882 2-
10,1
4,23
,27
,33,
36,
38-4
8,51
,58,
39-5
2,67
-68,
22-4
1,68
-70,
77-7
9,70
,72,
83 -
84,
50-6
6,84
-85,
95-9
6,86
,98-
100,
74-9
1,98
,100
,107
-10
3-11
6...1
8,99
-101
,10
9,11
2,12
1-12
0,12
2,12
4,10
4-11
1,-.
25,1
39,1
47,
126-
130,
132,
187-
188
149-
151,
16.9
-13
6-13
7,3T3=g9'195,
OP
ER
AT
ON
S -
GR
AD
E T
WO
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
5. T
he s
tude
nt c
an id
entif
y an
d na
me
sum
s, d
iffer
ence
s, m
issi
ng
AW
39-5
9,62
-68,
S
224L
AB
C
2- 1
0,14
, ?3,
adde
nd.,
and
mis
sing
ope
ratio
nal s
igns
in p
robl
ems
writ
ten
inbo
th h
oriz
onta
l and
ver
tical
not
atio
r.F
or e
xam
ple:
70-7
3,80
,83-
84,8
6-88
,98-
5C-L
o,74
-91,
27,3
3,36
,38
-48,
51,5
8,R
AT
iOt-
149
16 -
8 =
8-
6=
410
0,10
3-11
6,11
8,12
0,12
2,99
-101
,10
4-11
1,68
-70,
74-7
5,77
-79,
84-8
5,1
2,
-8
712
4,12
6-13
0,13
2,13
4,13
6-18
7-18
895
-96,
98,1
00,
107-
109
,121
-10
4 +
7 =
3+=
1213
8,17
312
5,13
9,14
4,16
9-17
1,21
0-22
214
6 =
89
3 =
12
Pro
pert
ies
Com
mut
ativ
e pr
oper
ty6.
Giv
en a
set
mod
el, t
he s
tude
nt c
an w
rite
two
fiddi
tion
equa
tions
of a
dditi
onto
des
crib
e th
e ph
ysic
al s
ituat
ion.
For
exa
mpl
e:
0000
0SX
XX
3 =
83
+ 5
= 8
7. T
he s
ruae
nt c
an s
olve
equ
atio
ns s
uch
as 2
+ 6
= 6
+rin
d
4+=
+4.
Ass
ocia
tive
prop
erty
8. G
iven
a s
et m
odel
, the
stu
dent
can
writ
e an
add
ition
equ
atio
nus
ing
pare
nthe
ses
to d
escr
ibe
the
;-.)
1lys
ical
situ
atio
n.F
or e
xam
ple
of a
dditi
on
17,..
05E
AT
S
and
--,
( 3
+ 2
) +
4 =
9
74 77-
78,1
45-
146
Cr;
(7)
0 0
3 +
( 2
+4
) =
9
119,
The
stu
dent
can
sol
ve e
quat
ions
such
as
( 2
+ 3
)4
=+
4 =
;77-
78,8
0,13
8-14
2,14
5-14
6(
7 +
4 )
+ 2
=+
( 4
+ 2
);
and
3 +
(+
l ) =
cV*9
vulv
a,
80-E
1
CO
NT
EN
T
Iden
tity
elem
ent
for
addi
tion
'Alg
orith
ms
Col
umn
addi
tion
and
subt
ract
ion
(thr
ee-
digi
t num
eral
s) w
ithou
tre
grou
ping
.0,,.
.
Col
umn
addi
tion
and
..,
subt
ract
ion
(tw
o-di
git n
umer
als)
with
regr
oupi
ng
OP
ER
AT
ION
SG
RA
DE
TW
O
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
10. T
he s
tude
nt c
an d
emon
stra
te h
is u
nder
stan
ding
of t
he g
roup
ing
prin
cipl
e of
add
ition
by
solv
ing
equa
tions
suc
h as
7-7
7 +
8 =
10
+
AW
89-
97,1
45-
147
S47
,C
11. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as 0
+ 1
4 =
;o
9;66
-68,
70,7
2,11
1-11
2,11
826
,3z-
-11,
78-8
97
7 =
; 32+
=32
; 27+
= 2
7; a
nd! 2
+ 0
) +
9 =
12. T
he s
tude
nt c
an n
ame
the
sum
s, d
iffer
ence
s, a
nd m
issi
ng17
6-17
8,11
4-11
6,12
:, IL
-'3,
digi
ts fo
r pr
oble
ms
such
as:
180,
183-
138,
159
2r..)
2,2j
914
124
72
J 7
5 6
E18
6,19
0-22
123
+ 1
5 E
l-
21
I:,19
3,19
6+
413
09 8
1"C
7
13. T
he s
tude
nt c
an n
ame
the
sum
s an
d di
ffere
nces
for
prob
lem
s su
ch34
52
+ 5
835
as:
156,
174,
200-
206,
208,
210,
236-
214,
218-
227,
231,
252,
111,
115-
11.::
, 12'
D,
17::-
-, 1
9,.'-
,,
214,
218-
262,
289,
(Not
e: A
ny o
f the
follo
win
g al
gorit
hms
may
be
used
:)1
44 1
-44,
J,34
3434
)37
/5,-
+ 5
8+
58
+ 5
835
3552 35
228,
230,
232,
234,
236,
238,
240
315-
318
1292
9217
1717
80 92
30 +
450
+ 8
80 +
12 =
90
+ 2
92
50 +
2 =
40 +
12
( '3
0 +
5 )
= -
( 3
0)
107
-7-
17
WH
OL
Add
iti
CO
NT
EN
T
Mul
tiplic
atio
n an
d D
ivis
ioi.
Def
initi
on o
f mul
tipli
-ca
tion
(one
- d
igit
fact
ors)
Def
initi
on o
f div
isio
ndi
git f
acto
rs)
Bas
ic fa
cts
Thr
ough
pro
.--
,ts o
f 45
(one
- d
igit
ract
ors)
Pro
pert
ies
Com
mut
ativ
e pr
oper
tyof
mul
tipl i
catio
n
MN
ME
lidM
O
OP
ER
AT
ION
S -
GR
AD
E T
WO
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
W
14. G
iven
sev
eral
equ
ival
ent d
isjo
int s
ets,
the
stud
ent c
anun
iteth
e se
ts a
n- n
ame
the
card
inal
num
ber
of th
e ne
w s
et th
us fo
rmed
.
15. G
iven
a m
ultip
licat
ion
prob
lem
suc
h as
4 x
3 =
,th
e st
uden
t
can
desi
gn a
sim
ple
expe
rimen
t inv
olvi
ng th
e un
ion
of 4
equ
i-va
lent
dis
join
t set
s ea
ch w
ith 3
mem
bers
to d
eter
min
e an
d na
me
the
prod
uct o
f the
num
bers
.F
or e
xam
ple:
16. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as 2
x 3
=+
3 a
nd
5 +
5 +
5 +
5 =
x 5
ucid
use
set
s to
pro
ve h
isre
sults
.
17. G
iven
a s
et o
f 15
obje
cts,
the
stud
ent c
an p
artit
ion
the
set i
nto
equi
vale
nt d
isjo
int s
ubse
ts e
ach
havi
ng 3
mem
bers
and
nam
eho
w
man
y su
.ch
subs
ets
can
be fo
rmed
.
251-
256
255-
256
261-
262,
265-
266,
287
18. G
iven
a m
ultip
licat
ion
com
bina
tion
such
as
3 x
2, th
e st
uden
t can
255
-260
,us
e se
ts o
r a
num
ber
line
to d
eter
min
e an
d na
me
the
prod
uct
22
272,
285-
287
For
exa
mpl
e:2
3
3 x
2 =
6
19. T
he s
tude
nt c
an d
emon
stra
te b
y us
ing
sets
or
a nu
mbe
r lin
eti-
Ict
25.7
-258
,27
3-27
4,
mem
3 x
4 =
12
and
4 x
3 =
12.
S
263-
269,
274
270-
271,
273
AB
C
278-
283
134-
13::
CO
NT
EN
T
OP
ER
AT
ION
S -
GR
AD
E T
WO
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
Iden
tity
elem
ent f
or20
. The
stu
dent
can
dem
onst
rate
by
usin
g se
ts o
r a
num
ber
ine
that
258
-259
,27
1,27
3-28
0
mul
tiplic
atio
n1
x 6=
6 a
nd 6
x 1
= 6
.F
or e
xam
ple:
266-
268,
272,
283,
`,_>
<X
XX
X X
286
6 se
ts o
f 16
x 1
= 6
1 se
t of 6
1 x
6 =
6
6i
II
45
67
Mul
tiplic
ativ
e21
. The
stu
dent
can
sol
ve e
quat
ions
suc
h as
5 x
0 =
and
prop
erty
of 0
0 x
7 =
260,
274,
275-
277
283
(der
add
Alg
ori
Col
sub
nun
reg
CO
NT
EN
T
GE
OM
ET
RIC
FIG
UR
ES
Pla
ne fi
gure
sC
ircle
Squ
are
Rec
tang
leT
riang
le
Line
seg
men
t
Line
(num
ber
line)
Spa
ce fi
gure
sC
ylin
der
Con
e
PR
OP
ER
TIE
S
Sim
ple
dose
d pl
ane
figur
es
GE
OM
ET
RY
GR
AD
E T
WO
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
1. G
iven
mod
els
of c
ircle
s, s
quar
es, r
ecta
ngle
s, tr
iang
les,
line
segm
ents
, and
a n
umbe
r lin
e (w
ire, p
aper
or
flann
el c
utou
ts,
penc
il or
cha
lk o
utlin
es),
the
stud
ent c
an id
entif
y, n
ame,
and
dist
ingu
ish
amon
g th
ese
plan
e ge
omet
ric fi
gure
s.
2. G
iven
mod
els
of c
ylin
ders
and
con
es (
woo
d or
pla
stic
sol
ids,
rolle
d pa
per,
etc
.), t
he s
tude
nt c
an id
entif
y, n
ame,
and
dist
ingu
ish
betw
een
thes
e sp
ace
figur
es.
3. G
iven
a s
et o
f pla
ne fi
gure
s, th
e st
uden
t can
dis
tingu
ish
the
sim
ple
dose
d fig
ures
and
iden
tify
the
insi
de a
nd o
utsi
de r
egio
ns.
For
exa
mpl
e:
4. T
he s
tude
nt c
an d
emon
stra
te h
is u
nder
stan
ding
of t
he c
once
pt o
f!e
ngth
by
draw
ing
a lin
e se
gmen
t of g
iven
leng
th (
who
le u
nits
).
AW
SA
BC
3-4
161-
162,
60-6
116
4,17
417
9,25
4
180-
184,
256
258
61,6
3
CO
NT
EN
T
CO
NS
TR
UC
TIO
NS
Circ
leS
quar
eR
ecta
ngle
Tria
ngle
Line
Seg
men
t
Num
ber
line
moo
MO
Bis
mPi
ma
GE
OM
ET
RY
GR
AD
E T
WO
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
5. G
iven
a p
egbo
ard
and
rubb
er b
ands
, the
stu
dent
can
con
stru
cta
squa
re,
rect
angl
e, tr
iang
le, a
nd li
ne s
egm
ent.
6. T
he s
tude
nt c
an m
ake
roug
h pe
ncil
and/
or c
halk
draw
ings
(out
lines
)of
circ
les,
squ
ares
, rec
tang
les,
tria
ngle
s, a
nd li
ne s
egm
ents
.
7. U
sing
a s
trai
ghte
dge,
the
stud
ent c
an d
raw
a "
reco
gniz
able
" sq
uare
,re
ctan
gle,
and
tria
ngle
.
8. U
sing
a r
uler
, the
stu
dent
can
con
stru
ct a
line
seg
men
t of g
iven
leng
th.
For
exa
mpl
e$
Dra
w a
line
seg
men
t 5 in
ches
long
.
Usi
ng a
rul
er, t
he s
tude
nt c
an c
onst
ruct
a n
umbe
r lin
e an
d la
bel
the
poin
ts w
ith th
e w
hole
num
bers
.
AW
S
175-
179,
257-
258
175-
179,
257-
258
AB
CC
C
CO
NC
Pro
cess
leng
th Sel
(
Cot
.
ME
AS
I
Leng
thR
ule
Vol
um,
L iq
Tim
e Clc
Cal
We
igh
CO
NT
EN
T
CO
NC
EP
TS
OF
ME
AS
UR
EM
EN
T
Pro
cess
of m
easu
ring:
leng
th Sel
ectio
n of
uni
t(a
rbitr
ary)
Cou
ntin
g
ME
AS
UR
EM
EN
TG
RA
DE
TW
O
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
1. G
iven
an
obje
ct w
ith th
e pr
oper
ty o
f len
gth,
the
stud
ent
can
307
sele
ct a
sui
tabl
e un
it cf
leng
th a
nd m
easu
re th
e ob
ject
by
coun
ting
the
num
ber
of u
nits
nee
ded
to m
atch
the
leng
th o
fth
e ob
ject
.
ME
AS
UR
EM
EN
T O
F P
HY
SIC
AL
PR
OP
ER
TIE
S
Leng
thR
uler In
ch, f
oot
Cen
timet
er
Vol
ume
Liqu
id m
easu
reC
up, p
int,
quar
t,ga
llon
Tim
e Clo
ck Hou
r, h
alf-
hour
Cal
enda
rD
ay, w
eek,
mon
th
Wei
ght
Bal
ance
Sca
les
Pou
nd
2.
The
stu
dent
can
mea
sure
a g
iven
line
sea
men
tor
obj
ect t
oth
e ne
ares
t who
le u
nit.
AW
2c-.
0-2(
2'5
307-310
-309
3.
Usi
ng a
mea
surin
g cu
p, th
e st
uden
tca
n m
easu
re th
e ca
paci
ty311
of a
giv
en c
onta
iner
to th
e ne
ares
t who
le u
nit.
.U
sing
a c
lock
, the
stu
dent
can
tell
time
on th
e ho
ur a
ndH
alf-
hour
.
5. G
iven
two
obje
cts
and
usin
g a
sim
ple
bala
nce,
the
stud
ent
can
dete
rmin
e an
d na
me
whi
ch is
hea
vier
and
whi
ch is
I ipn
ter.
AS
C
137-138
12c
31,159-1Q1,1L7,
177
90
6. U
sing
sim
ple
scal
es, t
he s
tude
ntca
n de
term
ine
and
nam
e90,128
t;-:e
wei
ght o
f a g
iven
obj
ect t
o th
ene
ares
t pou
nd.
CO
NT
EN
T
Tem
pera
ture
The
rmom
eter
Deg
ree
(F.)
Mon
ey Pen
nyN
icke
lD
ime
Qua
rter
Hal
f dol
lar
RE
NA
MIN
G M
EA
SU
RE
S
Com
paris
on o
f uni
tsC
onve
rsio
n of
uni
ts
ME
AS
UR
EM
EN
T-
GR
AD
E T
WO
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
7. B
ased
on
expe
rienc
es w
ith r
eadi
ng s
cale
s on
a th
erm
omet
er,
the
stud
ent c
an r
ecor
d te
mpe
ratu
res
insi
de a
nd o
utsi
de th
ecl
assr
oom
and
ans
wer
que
stio
ns s
uch
as:
Is it
coo
ler
(col
der)
or
war
mer
(ho
tter)
toda
y th
an y
este
rday
?
8. T
he s
tude
nt c
an id
entif
y an
d na
me
pe;In
ies,
nic
kels
, dim
es,
quar
ters
, and
hal
f dol
lars
and
sta
te th
e va
lue,
in c
ents
,of
eac
h co
in.
AW
289-
298
9. G
iven
a s
et o
f coi
ns (
penn
ies,
dim
es, q
uart
ers,
etc
.), t
he s
tude
ntca
n de
term
ine
and
nam
e th
e to
tal v
alue
of t
he c
oins
in b
oth
cent
nota
tion
and
deci
mal
not
atio
n (e
.g.,
97 a
nd $
.97)
.
10, T
he s
tude
nt c
an e
xpre
ss th
e re
latio
nshi
ps b
etw
een
units
of
mea
sure
app
ropr
iate
to th
e gr
ade
leve
l and
can
ren
ame
am
easi
re
in o
ther
uni
ts.
For
exa
mpl
e:
1 fo
ot is
(lo
nger
, sho
rter
) th
an 1
inch
.
1 qu
art =
pint
s.
1 ha
lf do
llar
=di
mes
.
ISM
ME
gAR
SOO
W 1
4w
ittsi
m10
-.-.
7...
311
S
249
AB
C
92-9
3,31
0-31
171
-75,
85,8
8,15
6-15
7
79,8
2-83
,85
-88,
306,
308-
309
126,
137-
138
SE
TS C
ali
One
corr
e
One
-co
rre
Equ
iveq
uiv
Em
pt
Sub
s
CO
NT
EN
T
SE
TS
NU
MB
ER
- G
RA
DE
TH
RE
E
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
NA
/S
AB
C
Col
lect
ions
1G
iven
a d
escr
iptio
n of
a s
et, t
he s
tude
nt c
an d
istin
guis
h26
- 3
0,be
twee
n m
embe
rs o
f the
set
and
thin
gs w
hich
are
not
mem
bers
.2,
430
, 32,
33,
CA
RD
II`0
One
-to-
one
502.
Giv
en tw
o eq
uiva
lent
set
s (o
bjec
ts o
r pi
ctur
es),
the
stud
ent
94,
34, 3
8, 3
9,
corr
espo
nden
ceca
n de
mon
stra
te a
one
-to-
one
mat
chin
g be
twee
n m
embe
rsof
the
sets
by
cons
truc
ting
lines
or
by p
hysi
cally
ass
ocia
ting
200
201,
157
- 15
9
the
obje
cts.
202
One
-to-
man
yco
rres
pond
ence
3. T
he s
tude
nt c
an d
escr
ibe
fam
iliar
phy
sica
l situ
atio
ns in
whi
ch a
one
-to-
man
y m
atch
ing
occu
rs.
For
exa
mpl
e:O
rd.
one
foot
to fi
ve to
es o
r on
e co
at to
two
sle,
.es.
C.5
1E
quiv
alen
t and
4. G
iven
two
sets
(ob
ject
s, p
ictu
res,
ver
bal d
escr
iptio
n), t
heno
n-eq
uiva
lent
sets
stud
ent c
an id
entif
y th
em a
s eq
uiva
lent
or
non-
equi
vale
nt,
and
if no
n-eq
uiva
lent
, tel
l whi
ch s
et h
as m
ore
and
whi
cL.
RA
TIO
!
Hal
\ha
s fe
wer
mem
bers
.T
hir
Em
pty
set
5. T
he s
tude
nt c
an d
escr
ibe
verb
ally
a s
et w
hich
has
no
mem
bers
,su
ch a
s th
e se
t of a
ll na
tive
Mar
tians
in th
e cl
assr
oom
!F
our
Sub
sets
6. G
iven
a s
et, s
uch
as a
ll st
uden
ts in
the
clas
sroo
m, t
hest
uden
t can
iden
tify
a su
bset
, suc
h as
the
stud
ents
wea
ring
tenn
is s
hoes
.
OR
DIN
Firs twe
CA
RD
INA
L N
UM
BE
RS
0 -
10,0
007.
The
stu
dent
can
det
erm
ine
the
card
inal
num
ber
of a
giv
en s
et.
175,
189
10, 1
1, 6
6, 7
4,38
-4C
.),
134-
135,
137
-91
-92,
138,
159
-160
130,
224
8. G
iven
a n
umbe
r, th
e st
uden
t can
iden
tify
the
num
bers
whi
ch17
444
, 61,
95,
11, 7
-9, 4
4,pr
eced
e an
d fo
llow
it.
172,
2)7
, 211
,11
2, 1
11P
, 2.5
9,28
628
7
CO
NT
EN
T
Ord
er r
elat
ions
NU
MB
ER
- G
RA
DE
TH
RE
E
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
9. G
iven
a s
et o
f who
le n
umbe
rs, t
he s
tude
nt c
an w
rite
them
in
AW
33,7
4,16
6,20
7,2,
10
AB
C
112,
125,
orde
r fr
om le
ast t
o 3r
eate
st a
nd v
ice
vers
a.17
414
7,28
7
10. T
he s
tude
nt c
an w
rite
the
sym
bols
<,
=,
to e
xpre
ss th
e96
,97,
121,
258,
6,94
,202
-206
,9,
70,7
7,12
6,re
latio
nshi
p be
twee
n tw
o gi
ven
num
bers
.26
220
8-21
0,21
5,27
4,28
7,29
521
7,22
0,22
2-22
3,24
4,29
1,29
8,30
7
RA
TIO
NA
L N
UM
BE
RS
Den
omin
ator
s of
11. T
he s
tude
nt c
an c
onst
ruct
and
iden
tify
mod
els
for
ratio
nal
298-
305
103-
107,
111,
48,5
4,73
,288
2 -
12nu
mbe
rs.
114,
116,
118,
12. G
iven
a s
et o
f 12
obje
cts,
the
stud
ent c
an c
onst
ruct
a m
odel
298-
303,
for
7/12
by
grou
ping
the
mem
bers
of t
he s
et in
to s
ubse
ts.
305
C71
For
exa
mpl
e:o(b0000
o o 0 olo 0
Ord
er r
elat
ions
13. G
iven
mod
els
of tw
o ra
tiona
l num
bers
nam
ed w
ith fr
actio
nsha
ving
the
sam
e nu
mer
ator
s or
the
sam
e de
nom
inat
ors,
the
stud
ent c
an w
rite
the
sym
bol.;
=,/ t
oex
pres
sth
e
305
50-5
4,56
,62
rela
tions
hip
betw
een
them
.F
or e
xam
ple:
02/
54/
5i
4/5
> 2
/5an
d
03/
41
1
ommi
sone
ONM,
POD;
pftlum,
>
3/7
Ill i
tit
3/7
< 3
/4
CO
NT
EN
T
OR
DIN
AL
NU
MB
ER
SB
eyon
d tw
entie
th
(51
NU
MB
ER
- G
RA
DE
TH
RE
E
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
14. G
iven
a s
eque
nce
of o
bjec
ts, e
vent
s, e
tc.,
the
stud
ent c
anid
entif
y th
e po
sitio
n in
spa
ce o
r tim
e of
a p
artic
ular
obj
ect
or e
vent
by
sayi
ng: "
Thi
s (o
bjec
t) is
four
th"
or "
Thi
s (e
vent
)ha
ppen
ed s
econ
d."
AW
SA
BC
Ex
RA
TIO
,1
CO
NT
EN
T
NU
ME
RA
TIO
N -
GR
AD
E T
HR
EE
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
NA
ME
S F
OR
NU
MB
ER
S1.
The
stu
dent
can
iden
tify,
nam
e, r
ead,
and
writ
e m
any
2866
,74,
75,7
6,16
,152
,209
diffe
rent
nam
es fo
r th
e sa
me
num
ber.
For
exa
mpl
e:82
-84,
87,
14 =
10
+ 4
= X
IV =
2 x
7 -
= 2
06,
etc
.15
9-16
3
WH
OLE
NU
MB
ER
S0
9,99
92.
The
stu
dent
can
iden
tify,
nam
e, r
ead,
and
\vrit
e nu
mer
als
for
who
le n
umbe
rs.
27-2
8,13
411
,18,
180-
181
3. T
he s
tude
nt c
an r
ead
and
writ
e nu
mbe
r w
ords
thro
ugh
nine
hund
red
nine
ty-n
ine.
190-
191
Pla
ce v
alue
--4.
Giv
en a
num
eral
suc
h as
807
3, th
e st
uden
t can
iden
tify,
31,3
4,37
-38,
286
6,11
,13,
108,
C'7
, fou
r-di
git n
umer
als
nam
e, a
nd d
istin
guis
h th
e nu
mer
als
that
are
in th
e on
es,
44-4
5,19
712
5-12
6,te
ns, h
undr
eds,
and
thou
sand
s pl
aces
.15
2-15
3,17
3,19
8,23
6,25
9,28
7
5. G
iven
a n
umer
al, t
he s
tude
nt c
an n
ame
the
plac
e va
lue
for
each
dig
it.19
7,27
913
Exp
ande
d no
tatio
n6.
Giv
en a
num
eral
suc
h as
444
4, th
e st
uden
t can
writ
e th
e26
-27,
31,3
3,67
,82-
84,8
7,15
3ex
pand
ed n
umer
al (
400
0 +
400
+ 4
0 +
4 ).
39-4
1,14
7,15
9-16
3,30
619
7,.2
79
Rom
an n
umer
als
thro
ugh
XV
7, G
iven
a n
umer
al s
uch
as 1
2, th
e st
uden
t can
writ
e th
e R
oman
num
eral
XII.
188
150-
151,
173
8. G
iven
a R
oman
num
eral
suc
h as
XIV
, 4-h
e st
uden
t can
writ
e th
e18
8,22
415
0-15
1,17
3A
rabi
c nu
mer
al 1
4.
WH
OL
Add
iti
Def
init
inve
rs
Bas
k Th
CO
NT
EN
T
RA
TIO
NA
L N
UM
BE
RS
Den
omin
ator
sof
2 -
12
NU
ME
RA
TIO
N -
GR
AD
E T
HR
EE
BE
HA
VIO
RA
L O
BJE
CT
IVE
SAW
SABC
9. G
iven
a m
odel
of
thre
e-ei
ghth
s,th
e st
uden
t can
iden
tify,
nam
e, r
ead,
and
writ
e a
num
eral
(fr
actio
n) fo
r th
era
tiona
l
num
ber
asso
ciat
ed w
ith th
e m
odel
.F
or e
xam
ple:
eNta
mM
gtM
IN N
Mni
sei
tem
3/8
298-303
102-107,111,113,
48-54,56,5'3
114,116,118
CO
NT
EN
T
WH
OLE
NU
MB
ER
S
Add
ition
and
Sub
trac
tion
OP
ER
AT
ION
SG
RA
DE
TH
RE
E
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
Def
initi
on1.
Giv
en a
n ad
ditio
n or
sub
trac
tion
prob
lem
suc
h as
5 4
- 7
=or
48-4
913
-15,
10
148
=,
the
stud
ent c
an d
esig
n a
sim
ple
expe
rimen
t inv
olvi
ng22
-27,
sets
or
a nu
mbe
r lin
e to
det
erm
ine
and
nam
e th
e su
m o
r di
ffere
nce
of th
e nu
mbe
rs.
212-
214
Inve
rse
rela
tions
hip
2. G
iven
an
addi
tion
equa
tion
such
as
1324
= 3
7, th
e st
uden
t can
writ
e th
e tw
o re
late
d su
btra
ctio
n eq
uatio
ns, 3
724
= 1
3 an
d92
31, 1
:1:-
.)
37 -
13
= 2
4.
3. G
iven
an
addi
tion
equa
tion
with
a m
issi
ng a
dden
d su
ch a
s52
,56,
65,
20,(
,4,9
4,3
3 -3
4,16
3,÷
61
= 1
57, t
he s
tude
nt c
an w
rite
the
rela
ted
subt
ract
ion
68,7
4,85
,12
4-13
1,28
8,29
4eq
uatio
n, 1
57 -
61
=10
2,31
2,13
522
4
Bas
ic fa
cts
4. T
he s
tude
nt c
an c
heck
sub
trac
tion
prob
lem
s by
add
ition
,
54-5
5,57
-58,
19,2
6,27
,4-
5, 1
2, 1
7-1P
.,T
hrou
gh s
ums
of 1
85.
Giv
en a
ny s
ingl
e-di
git a
dditi
on o
r su
btra
ctio
n co
mbi
natio
n, th
e66
,71,
73,7
5,31
,34-
35,
'2.4
-28
,3 0
,
stud
ent c
an im
med
iate
ry*n
ame
the
sum
or
diffe
renc
e10
9,16
362
,94
40-4
1,44
-47,
100,
1D',
,12
9,P
rope
rtie
s21
2,21
3C
omm
utat
ive
prop
erty
6. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as 1
7 +
= 3
2 +
17
and
of a
dditi
on+
16
= 1
6 +
60,6
3,66
,21
7,22
2,22
,42,
163,
180,
186,
223
255
Ass
ocia
tive
prop
erty
of a
dditi
on7.
Giv
en a
pro
blem
suc
h as
3 +
49
T 1
=,
the
stud
ent c
an in
dica
te30
8th
e gr
oupi
ng o
f adc
lnds
whi
ch w
ill m
ake
the
addi
tion
easi
est b
y en
-cl
osin
g th
e 49
and
1in
par
enth
eses
,F
or e
xam
ple:
61,6
2,65
,22
6-23
042
,163
8 +
( 4
9 +
1)
= 5
8.13
4,18
4,18
6
*Im
rned
iate
ly is
cie
finc,
-' as
5 s
econ
ds o
r! 2
55.
CO
NT
EN
T
iden
tity
elem
ent
for
addi
tion
OP
ER
AT
ION
S -
GR
AD
E T
HR
EE
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
8. G
iven
a p
robl
emsu
ch a
s 5
+ 7
+ 2
+ 3
=,
the
stud
ent c
an
dem
onst
rate
how
to fi
nd th
e su
min
the
easi
est w
ay b
y re
arra
rjing
the
adde
nds.
9. T
he s
tude
nt c
an s
olve
equa
tions
suc
h as
41
+=
41;
37 -
L=
37
-;
17=
0 ;
and
53=
53.
Alg
orith
ms
Col
umn
addi
tion
and
10. T
he s
tude
nt c
an n
ame
the
sum
s,
subt
ract
ion
(fou
r -
digi
ts fo
r pr
oble
ms
such
as
:
digi
t num
eral
s) w
ithou
tre
grou
ping
2405 71
Col
umn
addi
tion
and
subt
ract
ion
(thr
ee -
digi
t num
eral
s) w
ithre
grou
ping
Oth
er n
otat
ion
301
4012
5673
-40
52
diffe
renc
es, a
nd m
issi
ng
706
-0 3
42
60
11. T
he s
tude
nt c
an n
ame
the
sum
san
d di
ffere
nces
for
prob
lem
ssu
ch a
s:
453
694
570
803
+ 4
39+
19
- 14
722
7
12. T
he s
tude
nt c
an id
entif
yan
d na
me
sum
s, d
iffer
ence
s,m
issi
ng
adde
nds,
and
mis
sing
ope
ratio
nal
sign
s in
pro
blem
s w
ritte
n in
both
hor
izon
tal a
nd v
ertic
al n
otat
ion.
AW
62,3
08
83,8
8,91
,.97
,146
,292
,31
1
99,104,108,
11,),135,14:
147,167,12z,
180,184,219,
232,313-321,
S
163
130
84-8,88-93,
93,95,101,
123,133,17,
172,198,223,
298,37,3:)9
AB
C
12-14,40-41,
1.)4,198-1?9,
22;)
, 231
, 244
,2
132-132,13E,
147-148,
15z-U5,
168-174,
18.J-1E:1,184,
256-25., 277,
29C),298-299,
OP
ER
AT
ION
S -
GR
AD
E T
HR
EE
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
Mul
tiplic
atio
n an
d D
ivis
ion
AW
AB
C
Def
initi
on o
fm
ultip
licat
ion
13. G
iven
a m
ultip
licat
ion
prob
lem
suc
h as
4 x
7 =
114,
122,
124,
148
36-3
7,56
15,2
9,36
-38,
87,8
9,19
0,th
e st
uden
t can
des
ign
a si
mpl
e ex
perim
ent i
nvol
ving
the
unio
n of
4 e
quiv
alen
t dis
join
t set
s ea
ch w
ith 7
mem
bers
to d
eter
min
e an
d na
me
the
prod
uct o
f the
num
bers
.
221,
239
14, T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as 3
7 =
7 +
114,
115,
120,
38-4
3,88
,90-
91,
and
8 +
8 +
8 +
8 +
8 =
x 8
and
use
sets
or
skip
cou
nt12
2,12
8,12
9,50
-51,
221-
222
to p
rove
his
res
ults
.14
814
9
Def
initi
on o
f div
isio
n15
, Giv
en a
set
of 2
1 ob
ject
s, th
e st
uden
t can
par
titio
nth
e13
4-13
5,92
, 224
set i
nto
equi
vale
nt d
isjo
int s
ubse
ts e
ach
havi
ng3
mem
bers
and
nam
e ho
w m
any
such
sub
sets
can
be
form
ed.
137-
138
I, 0_
-0);
(00
61(
101)
0" 0
(0\
0 0
)107
00)
rrO
l _C
)
16. G
iven
a s
et o
f 21
obje
cts,
the
stud
ent c
an p
ertit
ion
the
set i
nto
3 eq
uiva
lent
dis
join
t sub
sets
and
nam
eho
w m
any
mem
bers
are
in e
ach
subs
et.
281
(0 0
o0
0 0
0 h
:16-
6-60
00-0
4-6-
0 0
-76-
6-;
17. G
iven
a d
ivis
ion
prob
lem
suc
h as
36
7. 9
=,
the
stud
ent
can
desi
gn a
sim
ple
expe
rimen
t inv
olvi
ng s
et p
artit
ion
(see
obje
ctiv
es#
15an
d #1
6 ab
ove)
to d
eter
min
e an
d na
me
the
quot
ient
,
OP
ER
AT
ION
SG
RA
DE
TH
RE
E
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
18. T
he s
tude
nt c
an r
epea
tedl
ysu
btra
ct 6
from
18
until
ther
e is
a re
mai
nder
of 0
, nam
e ho
w m
any
times
the
6 ca
nbe
sub
trac
ted,
and
writ
e th
e re
late
d di
visi
on e
quat
ion.
For
exa
mpl
e:
1812
6
6 P
-6
f -6
12
6 ca
n be
sub
trac
ted
from
18
3 tim
es
6J0
18 =
6 =
3
Inve
rse
rela
tions
hip
19. T
he s
tude
nt c
an d
emon
stra
te b
y us
ing
sets
or
anu
mbe
r lin
e
that
div
idin
g 15
by
3 "u
ndoe
s"m
ultip
lyin
g 5
by 3
.1
DO
X00
00
0 0
0 0
00
0 0
0 0
05
x 3
= 1
5
OU
ND
O0
0 0
!0
0 0
0'/0
0 0
5 0
0 0
c0 0
0 (
0 0
00
0 0
c000
(000
15:
3= 5
Bas
ic fa
cts
Thr
ough
pro
duct
s of
20. G
iven
a m
ultip
licat
ion
or d
ivis
ion
com
bina
tion
such
as
4 x
8 or
45 (
one-
digi
t fac
tors
)24
= 6
, the
stu
dent
can
imm
edia
tely
" na
me
the
prod
uct o
r qu
otie
nt
and
use
sets
or
a nu
mbe
r lin
e to
pro
vehi
s re
sult.
Thr
ough
pro
duct
s of
81 (
one-
digi
t fac
tors
)21
. Giv
en a
mul
tiplic
atio
n or
div
isio
nco
mbi
natio
n su
ch a
s 7
x 7
or
729,
the
srl;r
4ent
can
use
set
s or
a n
umbe
rlin
e to
det
erm
ine
and
nam
e th
e pr
oduc
t or
quot
ient
.
22. T
he s
tude
nt c
an id
entif
y an
d na
me
prod
ucts
,qu
otie
nts,
mis
sing
fact
ors,
and
mis
sing
ope
ratio
nal s
igns
inpr
oble
ms
writ
ten
in
both
hor
izon
tal a
nd v
ertic
al n
otat
ion.
Pro
pert
ies
Com
mut
ativ
e pr
oper
ty23
. The
stu
dent
can
dem
onst
rate
by
usin
g se
ts o
r a
num
ber
line
of m
ultip
licat
ion
that
6 x
4 =
24
and
4 x
6 =
24.
*Im
med
iate
ly is
def
ined
as
5 se
cond
s or
less
:
AW
156,
157,
162,
163,
247-
248,
250,
251
S
160,
161,
163,
140-
142
171,
176,
232
116,
120,
129,
137,
138,
145,
149,
158-
161,
165,
172,
175-
176,
196,
233,
255,
278,
288,
292,
322-
323
137,
140,
172,
175
44,4
9,57
,65
,122
,14
3,14
6,14
8,15
2,15
4
AB
C
92,1
57-1
59,
215,
297
204
96-9
8,10
3 -1
0110
4-10
5,11
311
1,14
2 -1
4o,
156,
165-
136,
182,
188-
190,
193,
203,
206,
217,
261
188,
190,
218,
240-
242,
244,
2) 0
1
CO
NT
EN
T
OP
ER
AT
ION
S -
GR
AD
E T
HR
EE
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
24. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as 7
x2
=x
7 an
d
x 8
= d
X.
Ass
ocia
tive
prop
erty
25.
The
stu
dent
can
sol
ve e
quat
ions
such
as
( 2
x 3
) x
4 =
x 4
=__
of m
ultip
licat
ion
(x
2 )
x 3
=x
( 2
x 3
); a
nd 8
x(
1 x
3 )
=
Iden
tity
elem
ent f
or26
. The
stu
dent
can
sol
ve e
quat
ions
suc
h as
1 x
18
mul
tipl '
catio
n
Mul
tipl i
cativ
epr
oper
ty o
f 0
4 x
= 4
;12
12 =
;14
1 =
;an
d
3 x
= 3
27. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as 1
5 x
0 =
x 52
= 0
; and
13
x0
x 7
=
Dis
trib
utiv
e pr
oper
ty 2
8. T
he s
tude
nt c
an d
emon
stra
teby
usi
ng s
ets
that
:
of m
ultip
licat
ion
over
add
ition
3 x(
2 4
)z--
(3 x
2 )
+(3
x 4
)=
6 +
12=
18
117,
123,
129,
142,
181,
187
218-
219,
222-
223,
298
185,
187
231-
236,
175,207,240,
238,
298
255,259
128,
132,
136
48-4
9,13
7
156
133,
136,
164
46-4
7
194
277-
282
(3x6
)
(4x6
)
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0
(3x2
) 0
00
010
29. G
iven
a m
ultip
licat
ion
can
use
the
dist
ribut
ive
to d
eter
min
e an
d na
me
7 se
ts o
f 6 m
ay b
e th
ough
t
7 x
6 =
( 3
x 6
) +
( 4
0 0
0 0
0 0
0 0
(3x4
)0
0 0
com
bina
tion
such
as
7 x
6, th
e st
uden
tpr
oper
ty o
f mul
tiplic
atio
n ov
er a
dditi
onth
e pr
oduc
t.
of a
s 3
sets
of 6
and
4 s
ets
of 6
.
x 6
)18
+ 2
4 =
42
121,
129,
190-
.264
-274
,19
3,19
5,19
8- 2
77-2
8219
9,20
4,20
8,21
0,23
4,23
5
165,207,264-
266,289,304
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
(Not
e: S
ee il
lust
ratio
n in
mar
gin.
)
CO
NT
EN
T
Alg
orith
ms
Fac
tors
of 1
0, 1
00,
an.;
mul
tiple
s of
10 a
nd 1
00
Mul
tiplic
atio
n- -
vert
ical
not
atio
n(t
hree
-dig
it fa
ctor
by o
ne-d
igit
fact
or)
with
and
with
out
regr
oupi
ng
Long
div
isio
n(t
hree
-dig
it di
vide
ndby
one
-dig
it di
viso
r)w
ithou
t rem
aind
er
OP
ER
AT
ION
SG
RA
DE
TH
RE
E
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
30. T
he s
tude
nt c
an n
ame
the
prod
ucts
and
quo
tient
s fo
rpr
oble
ms
such
as:
7x1
=7x
4=36
00 -
;1
=36
00=
9=
7x 1
0=7x
40=
3600
= 1
0=36
00=
90=
7 x
100
=I
7 x
400
=36
00 +
100
=36
00 =
900
=
31. T
he s
tude
nt c
an n
ame
the
prod
ucts
for
prob
lem
s su
ch a
s:
132
217
132
704
x3x4
x7x6
(Not
e: A
ny o
f the
follo
win
g al
gorit
hms
may
be
used
:)12
i
100
+ 3
0+
213
213
213
2
x7
x7x7
x770
0+
210
+ 1
4=
924
1492
4
210
924
700
924
32. T
he s
tude
nt c
an n
ame
the
quot
ient
s fo
r pr
oble
ms
such
as:
8 )
240
9 T
TR
)7)
308
5 )
625
NU
MM
I&aM
eeel
tlan
AW
AB
C
202-
203,
237,
239-
153,
228,
232,
204-
207,
231,
240
,242
,24
3,29
0,30
324
1,24
4,24
5, 2
84-2
8524
6,24
9,25
8,26
2,29
3-29
5,32
4
212-
214,
216,
241
,272
-22
0,22
2 -2
24,
283,
287,
226,
231,
234,
311
278,
286,
325,
326
258-
261,
264,
284
,285
266-
274,
283,
285,
289,
327
233,
234,
265-
271,
278
272-
276,
290
CO
NT
EN
T
32. (
cont
inue
d)(N
ote:
Any
OP
ER
AT
ION
S -
GR
AD
E T
HR
EE
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
of th
e fo
llow
ing
algo
rithm
s m
ay b
e us
ed:)
AW
SA
BC
237
284,
285
272-
276,
290
258-
261,
264,
266-
274,
283,
5 )
625
5-
125
285,
289,
500
100
20'(
125
5)62
5
125
100J
500
100
205
)62
512
5
2550
010
0
255
125
25
012
510
025
250
250
RA
TIO
NA
L N
UM
BE
RS
Add
ition
Def
initi
on o
f add
ition
(fra
ctio
ns w
ith th
esa
me
deno
min
ator
s)
33. G
iven
a m
odel
(re
gion
or
num
ber
line)
for
the
addi
tion
oftw
o ra
tiona
l num
bers
, the
stu
dent
can
dete
rmin
e an
d na
me
the
sum
.F
or e
xam
ple:
33
3
2+
1=
3 3
119-
122,
56-5
7,16
017
3,24
5,31
1
CO
NT
EN
T
GE
OM
ET
RIC
FIG
UR
ES
GE
OM
ET
RY
- G
RA
DE
TH
RE
E
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
Pla
ne fi
gure
s1
Giv
en a
ver
bal d
escr
iptio
n of
a p
reci
se lo
catio
n in
the
clas
sroo
m,
46,4
7,76
,77
100,
176,
49,1
14P
oint
the
stud
ent c
an lo
cate
and
iden
tify
the
poin
t.24
6Li
neLi
ne s
egm
ent
Ray
For
exa
mpl
e: W
here
is th
e pl
ace
whe
re th
e flo
or a
nd th
ese
two
wal
ls m
eet?
4-8
Pat
h (c
urve
d lin
e)2.
Giv
en m
odel
s of
the
plan
e ge
omet
ric fi
gure
s na
med
on
the
left
178
49,9
9,11
6,A
ngle Rig
ht a
ngle
(wire
, pap
er o
r fla
nnel
cut
outs
, pen
cil o
r ch
alk
outli
nes)
,th
e st
uden
t can
iden
tify,
nam
e, a
nd d
istin
guis
h am
ong
them
.12
1,12
3
200,
236-
237
32-3
:3,6
3, 9
6-Q
uadr
ilate
ral
97,1
03,1
05,
Squ
are
Rec
tang
le13
2,17
1,17
9,24
7-24
9,25
5,25
7,26
2T
riang
le16
-18,
150-
32,3
3,63
,96-
114
151,
178-
97,1
32,1
71,
Circ
le17
9,20
0-20
117
9,24
7-24
9,C
ente
r25
5,25
8,26
0,26
2R
adiu
sD
iam
eter
46,4
7,76
,77,
105,
106,
249,
Cho
rd11
2,11
325
5,25
9,26
0,26
2S
pace
figu
res
3. G
iven
mod
els
of c
ubes
, sph
eres
, cyl
inde
rs, a
nd c
ones
(w
ood
orC
ube
plas
tic s
olid
s, r
olle
d pa
per,
etc
.), t
he s
tude
nt c
an id
entif
y,2-
5,20
-21,
33,6
3,13
2,17
112
2-S
pher
ena
me,
and
dis
tingu
ish
amon
g th
ese
spac
e fig
ures
.25
123
Cyl
inde
rC
one
Sim
ple
clos
ed p
lane
figur
es
Are
a
CO
NS
TR
UC
TIO
NS
GE
OM
ET
RY
- G
RA
DE
TH
RE
E
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
AW
SA
BC
PR
OP
ER
TIE
S
Leng
th4.
The
stu
dent
can
dem
onst
rate
his
unde
rsta
ndin
g of
the
conc
ept
6,13
of le
ngth
by
draw
ing
a lin
e se
gmen
tof
giv
en le
ngth
.
5. G
iven
a s
et o
f pla
ne fi
gure
s,th
e st
uden
t can
dis
tingu
ish
the
sim
ple
clos
ed fi
gure
s an
d id
entif
yth
e in
side
and
out
side
regi
ons.
6. T
he s
tude
nt c
an d
emon
stra
tehi
s un
ders
tand
ing
of th
e co
ncep
t1-
5,16
-19,
52-5
5,14
4-23
0
of a
rea
by c
over
ing
an in
terio
r(in
side
) re
gion
with
uni
t25
,194
147,
184-
185,
regi
ons
(are
as).
283
150
251-
255,
117-
118
257,
309
Pla
ne g
eom
etric
figu
res
7. T
he s
tude
nt c
an m
ake
roug
hpe
ncil
and/
or c
halk
dra
win
gs (
outli
nes)
100,
251
of th
e pl
ane
figur
es n
amed
und
erG
EO
ME
TR
IC F
IGU
RE
S
on th
e pr
evio
us p
age.
Line
8. U
sing
a s
trai
ghte
dge,
the
stud
ent c
anco
nstr
uct m
odel
s fo
r lin
es,
150-
151
100,
246-
248,
113
-117
,
line
segm
ents
, ray
s, a
nd a
ngle
s an
dla
bel t
hem
in th
e fo
llow
ing
250,
254,
261,
1:9-
121
Ray
way
:30
9Li
ne s
egm
ent
Ang
les
B'
AB
AB
'BC
Rig
ht a
ngle
,9.
Usi
ng a
str
aigh
tedg
e an
d fo
lded
pap
er,
the
stud
ent c
an c
onst
ruct
a
Circ
le Cen
ter
Rad
ius
1 0
,G
iven
the
cent
er a
nd r
adiu
s an
dus
ing
a co
mpa
ss, t
he s
tude
nt c
an76
-77,
cons
truc
t a c
ircle
,11
2-11
3,17
9
178-
179,
120
right
ang
le.
200,
236-
237
*WN
Wor
MIN
NM
wan
ge.
......
.
ME
AS
UR
EM
EN
T -
GR
AD
E T
HR
EE
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
CO
NC
EP
TS
OF
ME
AS
UR
EM
Et :
T
AW
SA
BC
Pro
cess
of m
easu
ring:
1. G
iven
an
obje
ct o
r pi
ctur
e of
an
obje
ctw
ith th
e pr
oper
ty
leng
th, a
rea,
vol
ume
of le
ngth
, are
a, o
r vo
lum
e an
d a
set o
f uni
t len
gths
, are
as,
117
464
-65
Sel
ectio
n of
uni
tan
d vo
lum
es, t
he s
tude
nt c
an s
elec
t asu
itabl
e un
it an
d
(arb
itrar
y)co
unt t
o m
easu
re th
e pr
oper
ty o
fth
e ob
ject
.
Cou
ntin
g
ME
AS
UR
EM
EN
T O
F P
HY
SIC
AL
PR
OP
ER
TIE
S
Leng
th2.
The
stu
dent
can
mea
sure
a g
iven
line
seg
men
t or
obje
ct to
1,5,
7-15
176-
178
66-6
8,70
,196
Rul
er, y
ards
tick
the
near
est h
alf-
unit.
Inch
, foo
t, ya
rd, m
ileC
entim
eter
Are
a3.
The
stu
dent
can
det
erm
ine
and
nam
eth
e ar
ea o
f a g
iven
1,16
-19,
52-5
5,14
4,
Squ
are
units
rect
angu
lar
regi
on b
y co
untin
g th
enu
mbe
r of
are
a un
its(s
quar
e re
gion
s) n
eede
d to
cov
erth
e re
gion
.25
145,
147,
184,
185,
283
Vol
ume
4. T
he s
tude
nt c
an d
eter
min
e an
d na
me
the
volu
me
of a
giv
en5,
20-2
1,25
Cub
ic u
nits
right
rec
tang
ular
spa
ce f:
gure
by
coun
ting
the
num
ber
ofvo
lum
e un
its (
cube
s) n
eede
d to
fill
the
spac
e.
Liqu
id m
easu
re5.
The
stu
dent
can
mea
sure
the
capa
city
of a
giv
en c
onta
iner
22,2
379
,80
Oun
ce, c
up, p
int,
to th
e ne
ares
t who
le u
nit.
quar
t, ga
llon
Tim
e6.
Usi
ng a
clo
ck, t
he s
tude
nt c
an te
ll tim
e to
the
near
est
217
186-
188
71-7
5,81
,82,
85,
Clo
ckm
inut
e.12
1,16
1,28
7,29
5
Hou
r, h
alf-
hour
,qu
arte
r-ho
ur, m
inut
e
CO
NT
EN
T
Wei
ght
Sca
les
Oun
ce, p
ound
Tem
pera
ture
The
rmom
eter
Deg
ree
(F.)
Mon
ey Uni
ted
Sta
tes
coin
sU
nite
d S
tate
s bi
lls
RE
NA
MIN
G M
EA
SU
RE
S
Com
paris
on o
f uni
tsC
onve
rsio
n of
uni
ts
ME
AS
UR
EM
EN
T -
GR
AD
E T
HR
EE
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
7. U
sing
sim
ple
scal
es, t
he s
tude
nt c
ande
term
ine
and
nam
e
the
wei
ght o
f a g
iven
obj
ect t
o th
e ne
ares
t oun
ce.
100
8. T
he s
tude
nt c
an r
ecor
d te
mpe
ratu
res
insi
de a
nd o
utsi
de th
e94
clas
sroo
m a
nd id
entif
y an
d na
me
the
tem
pera
ture
at
whi
ch w
ater
free
zes
(fre
ezin
g po
int)
.
9. T
he s
tude
nt c
an id
entif
y, n
ame,
and
stat
e th
e va
lue
of a
llU
nite
d S
tate
s co
ins
and
bills
.
10. G
iven
pic
ture
s of
coi
ns a
nd b
ills
ofdi
ffere
nt d
enom
inat
ions
,th
e st
uden
t can
det
erm
ine
and
nam
e th
e to
tal
valu
e in
deci
mal
not
atio
n.
11. T
he s
tude
nt c
an e
xpre
ss th
e re
latio
nshi
psbe
twee
n un
its o
f
mea
sure
app
ropr
iate
toth
e gr
ade
leve
l and
rena
me
a
mea
sure
in o
ther
uni
ts.
For
exa
mpl
e:
1 po
und
wei
ghs
(mor
e, le
ss)
than
8 o
unce
s.14
feet
=ya
rds
and
feet
.
CO
MP
UT
AT
ION
S W
ITH
ME
AS
UR
ES
Add
ition
and
sub
trac
tion
12. T
he s
tude
nt c
an c
ompu
te w
ith m
easu
res
appr
opria
te to
the
grad
e le
vel,
assi
gnth
epr
oper
unit
to th
e re
sult,
and
rena
me
if ne
cess
ary.
For
exa
mpl
e:
3 qu
arts
+ 5
qua
rts
= 8
qua
rts
= 2
gal
lons
.
50 c
ents
38 c
ents
= 1
2 ce
nts
= $
.12
AW
78-8
0,10
8,11
7,20
4
227,
276
215,
230
SA
BC
194
77,7
8
8083
59,9
1-93
,1-
4,16
7,16
9,16
6-17
017
1,19
8-19
9,20
8-21
1,26
7
175,
177,
178,
76,7
9-80
,99,
192-
195,
286,
287,
295
310
179
69,7
7-80
,84,
85,9
9
CO
NT
EN
T
SE
TS
(R
evie
w a
nd m
aint
ain
conc
epts
and
ski
lls.)
Col
lect
ions
NU
MB
ER
- G
RA
DE
FO
UR
1-E
HA
VIO
RA
L O
BJE
CT
IVE
SA
ir:S
AB
C
1. G
iven
a d
escr
iptio
n of
a s
et, t
he s
tude
nt c
an d
istin
guis
hbe
twee
n m
embe
rs o
f the
set
and
thin
gs w
hich
are
not
mem
bers
.
One
-to-
one
2. G
iven
two
equi
vale
nt s
ets
(obj
ects
or
pict
ures
), th
e st
uden
tco
rres
pond
ence
can
dem
onst
rate
a o
ne-t
o-on
e m
atch
ing
betw
een
mem
bers
of th
e se
ts b
y co
nstr
uctin
g lin
es o
r by
phy
sica
lly a
ssoc
iatin
gth
e ob
ject
s.
One
-to-
man
yco
rres
pond
ence
Equ
ival
ent a
ndno
n-eq
uiva
lent
sets
Em
pty
set
3. T
he s
tude
nt c
an d
escr
ibe
fam
iliar
phy
sica
l situ
atio
ns in
whi
ch a
one
-to-
man
y m
atch
ing
occu
rs.
For
exa
mpl
e:on
e no
tebo
ok to
thre
e rin
gs o
r on
e ca
t to
four
paw
s!
4. G
iven
two
sets
(ob
ject
s, p
ictu
res,
des
crip
tions
), th
e st
uden
tca
n id
entif
y th
em a
s eq
uiva
lent
or
non-
equi
vale
nt.
5. T
he s
tude
nt c
an id
entif
y an
d de
scrib
e se
ts w
hich
hav
e no
mem
bers
.F
or e
xam
ple:
The
set
of a
ll liv
ing
peop
le 2
00 y
ears
old
or
olde
rha
s no
mem
bers
.
18 -
19
1
Sub
sets
6. G
iven
a s
et, t
he s
tude
nt c
an id
entif
y an
d de
scrib
e a
subs
et.
17, 7
7-79
,F
or e
xam
ple;
For
ds a
re a
sub
set o
f the
set
of a
ll au
tom
obile
s.81
, 321
WH
OLE
NU
MB
ER
S0
1,00
0,00
07.
The
stu
dent
can
det
erm
ine
the
card
inal
num
ber
of a
giv
en s
et.
26-2
8, 3
0, 3
2,5,
60,
67,
4-15
, 45,
7, 2
,40
-41
154-
155,
300
178-
179
CO
NT
EN
T
Ord
er r
elat
ions
RA
TIO
NA
L N
UM
BE
RS
Den
omin
ator
s of
1, 2
, 3, 4
...
Ord
er r
elat
ions
OR
DIN
AL
NU
MB
ER
SB
eyon
d tw
entie
th
NU
MB
ER
- G
RA
DE
FO
UR
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
VM
/
8. G
iven
a n
umbe
r, tn
e st
uden
t can
iden
tify
the
num
bers
whi
ch70
-71
prec
ede
and
follo
w it
.
9. T
he s
tude
nt c
an id
entif
y an
d na
me
odd
and
even
num
bers
.22
0-22
1
10. G
iven
a s
et o
f who
le n
umbe
rs, t
he s
tude
nt c
an w
rite
them
in29
4
orde
r fr
om le
ast t
o gr
eate
st a
nd v
ice
vers
a.
11. T
he s
tude
nt c
an w
rite
the
sym
bols
K, >
,to
exp
ress
the
33,8
6-89
,260
,re
latio
nshi
p be
twee
n tw
o gi
ven
num
bers
.21
4
12. T
he s
tude
nt c
an c
onst
ruct
and
iden
tify
mod
els
for
ratio
nal
num
bers
.
13. G
iven
a s
et o
f 12
obje
cts,
the
stud
ent c
an c
onst
ruct
a m
odel
for
5/6
by g
roup
ing
the
mem
bers
into
sub
sets
.F
or e
xam
ple:
(00
0 0
0
oo o
cIfo
o
240-
255,
262
-26
3, 2
65, 2
68,
278,
282
-289
,29
6-29
9
248
-249
,-25
1, 2
53
14. G
iven
two
ratio
nal n
umbe
rs s
uch
as 3
/5 a
nd 4
/7, t
he s
tude
nt29
6, 3
04,
can
nam
e th
em w
ith li
ke fr
actio
ns a
ndw
rite
the
sym
bols
(,
311,
328
=,/
to e
xpre
ss th
e re
latio
nshi
p be
twee
n th
em.
15. G
iven
a s
ituat
ion
invo
lvin
g a
num
ber,
the
stud
ent c
an id
entif
yth
e nu
mbe
r as
car
dina
l or
ordi
nal (
or n
eith
er).
For
exa
mpl
e:I a
m fi
fth in
line
.(O
rdin
al)
I hav
e fiv
e ca
ts.
(Car
dina
l)I d
rive
a F
ord
Gal
axie
500
. (N
eith
er C
ardi
nal
nor
Ord
inal
)
S
61, 6
4, 6
9, 7
5,11
4, 1
63, 2
28
300
2-3,
19,
21,
44-4
5, 7
5, 9
910
3-10
5, 1
15,
129,
148
, 162
,17
8, 2
37, 2
43,
278,
293
, 301
,32
3
AB
C
159
34-3
5, 5
3, 6
8,86
, 90-
91, 1
18,
268,
325
76-8
6, 8
8 -
90,
171-
172,
192-
194
174-
187
77-7
9, 8
183
-85,
192
86, 1
93, 1
9521
1, 2
36
186-
187
36-3
7
CO
NT
EN
T
NU
ME
RA
TIO
N -
GR
AD
E F
OU
R
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WA
BC
NA
ME
S F
OR
NU
MB
ER
S
WH
OLE
NU
MB
ER
S
1. T
he s
tude
nt c
an id
entif
y, n
ame,
rea
d, a
nd w
rite
man
ydi
ffere
ntna
mes
for
the
sam
e nu
mbe
r.F
or e
xam
ple:
12 =
7 +
5 =
27
- 15
= 3
x 4
= 4
8 ".
4 =
11
+ 1
/2+
1/2
.
7-9,
55,1
17,
219-
221,
224-
225,
226,
^')Q
0 -
999,
999
2. T
he s
tude
nt c
an id
entif
y, n
ame,
rea
d, a
nd w
rite
num
eral
s26
-45,
72,
12-2
3,29
,1-
20,2
4-33
,52,
for
who
le n
umbe
rs.
204
38-3
9,54
,81,
89,1
17,
154-
157,
169,
229-
232,
159-
161
268,
270
3. G
iven
a n
umer
al s
uch
as 4
67,3
04, t
he s
tude
nt c
an w
rite
the
28,3
0,36
,38
154,
157,
16-1
7,49
-50,
tiw
ords
: fou
r hu
ndre
d si
xty-
seve
n th
ousa
nd, t
hree
hun
dred
four
.15
9 16
189
,325
Pla
ce v
alue
- -
six
-dig
it nu
mer
als
4. G
iven
a b
ase
ten
(dec
imal
) nu
mer
al, t
he s
tude
nt c
an id
entif
yan
d na
me
the
plac
e va
lue
for
each
dig
it.28
,30,
204
154,
156,
159-
160
14,1
9-20
,53,
117
Exp
ande
d no
tatio
n5.
Giv
en a
num
eral
suc
h as
473
,245
, the
stu
dent
can
writ
eth
e27
,29,
31,3
3,59
,152
,155
,24
-25,
27-2
8,ex
pand
ed n
umer
al in
the
follo
win
g w
ay:
74,8
2,31
215
6,15
9,21
7,75
,87
473,
245
= (
4 x
100
,000
) +
( 7
x 1
0,00
0 )
+x
1000
)22
2,26
5+
( 2
x 10
0 )+
(4 x
10
)+(5
x 1
).
Rom
an n
umer
als
thro
ugh
L
6. G
iven
a n
umer
al s
uch
as 5
2, th
e st
uden
t can
writ
e th
eR
oman
num
eral
LII.
7. G
iven
a R
oman
num
eral
suc
h as
LV
I , th
e st
uden
t can
writ
eth
e A
rabi
c nu
mer
al 5
6.
168
51
CO
NT
EN
T
RA
TIO
NA
L N
UM
BE
RS
Den
omin
ator
s of
1, 2
, 3, 4
,...
Equ
ival
ent f
ract
ions
Impr
oper
frac
tions
and
mix
ed n
umer
als
NU
ME
RA
TIO
N -
GR
AD
E F
OU
R
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
8. G
iven
a m
odel
of t
hree
- n
inth
s, th
e st
uden
t can
iden
tify,
nam
e, r
ead,
and
writ
e a
num
eral
(fr
actio
n) fo
r th
e ra
tiona
lnu
mbe
r as
soci
ated
with
the
mod
el.
9. G
iven
a fr
actio
n su
ch a
s 3/
5, th
e st
uden
t can
iden
tify,
nam
e,an
d di
stin
guis
h th
e nu
mer
ator
and
the
deno
min
ator
.
10. G
iven
a fr
actio
n su
ch a
s 7/
8, th
e st
uden
t can
writ
e a
set o
ffr
actio
ns w
hich
are
equ
ival
ent t
o 7/
8.F
or e
xam
ple:
7/8
= 1
4/16
= 2
1/24
= 2
8/32
= e
tc.
11.
The
stu
dent
can
ren
ame
a gi
ven
frac
tion
in s
impl
est f
orm
.F
or e
xam
ple:
12/
32 =
3/8
.
12. G
iven
a m
odel
suc
h as
17,,
4,
the
stud
ent
can
iden
tify,
nam
e, r
ead,
and
writ
e th
e fr
actio
n 7/
4 an
d/or
the
mix
ed n
umer
al 1
3/4
for
the
ratio
nal n
umbe
r as
soci
ated
with
the
mod
el.
OT
HE
R N
OT
AT
ION
Rou
ndin
g to
the
near
est 1
3. G
iven
a n
umer
al s
uch
as 4
651,
the
stud
ent c
an r
ound
it to
ten,
hun
dred
, tho
usan
d46
50 to
the
near
est t
en, t
o 47
00 to
the
near
est h
undr
ed,
and
to 5
000
to th
e ne
ares
t tho
usan
d.
AV
.'
240-
259
,262
-26
3,26
5,26
8,27
8,28
2-29
3,29
6-29
9,30
7,31
0
S
76-8
1,83
-85,
86-9
0,20
4,20
6,
258-
259,
262,
84-8
529
9
252-
257,
259,
264,
266-
271,
278-
279,
284
-28
6,28
9-29
3,29
7,30
2
251,
272-
275
263,
304
42-4
3
87,1
92-1
94,
199,
200-
201
206-
207
AB
C
171-
172,
174-
179,
182-
187
,
192-
193
1 7
3 -
1 7
4,
2 0
1
183-
191,
201-
203,
226-
227
204
192-
193
CO
NT
EN
T
WH
OLE
NU
MB
ER
S
Add
ition
and
Sub
trac
tion
OP
ER
AT
ION
S -
GR
AD
E F
OU
R
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
AA
/S
AB
C
Inve
rse
rela
tions
hip
1. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as:
50,5
2,88
7,74
,152
,22
,67,
73-7
416
2,23
789
,92,
165,
207
+=
896
150
-=
9832
5
+27
= 4
068
- 21
46=
976
3
2. T
he s
tude
nt c
an c
heck
sub
trac
tion
prob
lem
s by
add
ition
."P
icl
Bas
ic fa
cts
Thr
ough
sum
s of
18
3. G
iven
any
sin
gle
digi
t add
ition
or
subt
ract
ion
com
bina
tion,
49-5
1,31
36-
9,11
-13,
22,4
0-41
,48,
the
stud
ent c
an im
med
iate
ly*n
ame
the
sum
or
diffe
renc
e.18
-19,
21,
53,5
7,7"
,.)-6
1,74
64-6
7P
rope
rtie
sC
omm
utat
ive
and
asso
ciat
ive
prop
ertie
sof
add
ition
4. G
iven
an
addi
tion
prob
lem
with
thre
e to
six
add
ends
, the
stud
ent c
an d
emon
stra
te h
ow to
find
the
sum
in th
e ea
sies
tw
ay b
y re
nam
ing
and
rear
rang
ing
the
adde
nds.
56-6
1,14
4,26
,95-
102,
314-
315
115,
237,
315
44,5-r;-5",.
92
Iden
tity
elem
ent
for
addi
tion
5. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as 4
09 +
= 4
09;
6, 1
8-19
116-
= 1
16 ±
- 34
12 =
0; a
nd-
0 =
23,
809.
Alg
orith
ms
Col
umn
addi
tion
and
subt
ract
ion
(fiv
e-di
git n
umer
als)
with
and
with
out r
enam
ing
6. T
h,)
stud
ent c
an n
ame
the
sum
s an
d di
ffere
nces
for
prob
lem
s su
ch a
s:
72,0
4840
;001
+ 1
9,96
9-
28,9
73
62-6
6,75
,24
- 33
,35
-36,
77-7
8,83
-'8
- 40
,42,
59,
84,8
6,88
-93
,114
,143
,89
,98,
126
157,
159,
163,
69-7
0,76
,82,
84,8
6-87
,93,
92,1
18,1
65,
170,
223,
228,
158,
180,
204;
211,
278,
315,
230,232,237,
214,260,27t,323
241,257-259,
294,308,315-
269,306,326
* im
med
iate
ly is
def
ined
as
5 se
cond
s or
less
.317,319,220
CO
NT
EN
T
OP
ER
AT
ION
S-
GR
AD
E F
OU
R
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
Oth
er n
otat
ior.
7. T
he s
tude
nt c
an id
entif
y an
d na
me
sum
s, d
iffer
ence
s, m
issi
ngad
dend
s, a
nd m
issi
ng o
pera
tiona
l sig
ns in
pro
blem
s w
ritte
nin
bot
h ho
rizon
tal a
nd v
ertic
al n
otat
ion.
49-5
07
42,6
2
Mul
tiplic
atio
n an
d D
ivis
ion
Def
initi
on8.
Giv
en a
mul
tiplic
atio
n or
div
isio
n pr
oble
m s
uch
as 7
x 9
=92
-93
6712
1-12
2,or
54
:.- 6
=,
the
stud
ent c
an d
esig
n a
sim
ple
expe
rimen
t12
5in
volv
ing
sets
or
a nu
mbe
r lin
e to
det
erm
ine
and
nam
e th
epr
oduc
t or
quot
ient
.
9. G
iven
a m
ultip
licat
ion
or d
ivis
ion
prob
lem
suc
h as
7 x
9 =
94-9
563
,63
121-
122,
126,
or 5
46
=,
the
stud
ent c
an d
emon
stra
te h
ow to
find
the
130,
214
prod
uct o
r qu
otie
nt b
y re
peat
ed a
dditi
on o
r su
btra
ctio
n.
Inve
rse
rela
tions
hip
10. G
iven
a s
et m
odel
(re
ctan
gula
r ar
ray)
, the
stu
dent
can
writ
etw
o m
ultip
licat
ion
and
two
divi
sion
equ
atio
ns to
des
crib
e th
e96
70,1
1912
7,13
1,14
8
phys
ical
situ
atio
n.F
or e
xam
ple:
00
00
00
00
00
00
00
00
00
00
00
00
DO
4 x
6 =
246
x 4
=24
UN
DO
24 -
; 6 =
424
;14
=6
OP
ER
AT
ION
S-
GR
AD
E F
OU
R
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
AW
SA
BC
103-
196,
61,6
4-65
,68-
124-
1:7,
Bas
ic fa
cts
111-
113,
73,7
4,93
,114
,129
-13
:,T
hrou
gh p
rodu
cts
of11
. Giv
en a
mul
tiplic
atio
n or
div
isio
n co
mbi
natio
n su
ch a
s 9
x 7
115,
128,
132,
144-
145,
139-
14-J
,
81 (
one-
digi
t fac
tors
)or
42
6, th
e st
uden
t can
imm
edia
tely
nam
e th
e pr
oduc
t or
186,
153,
210,
237,
147,
153,
quot
ient
and
use
set
s or
a n
umbe
r lin
e to
pro
ve h
is r
esul
t,32
1-32
227
9,?.
2415
5-15
-3,
159,
251,
12. T
he s
tude
nt c
an id
entif
y an
d na
me
prod
ucts
, quo
tient
s, m
issi
ngfa
ctor
s, a
nd m
issi
ng o
pera
tiona
l sig
ns in
pro
blem
s w
ritte
n in
325
both
hor
izon
tal a
nd v
ertic
al n
otat
ion.
92-9
3,13
4-13
5,12
7,25
211
1,18
865
,144
Pro
pert
ies
Com
mut
ativ
e pr
oper
tyof
mul
tiplic
atio
n13
. The
stu
dent
can
dem
onst
rate
by
usin
g se
ts o
r a
num
ber
line
that
9 x
6 =
6 x
9.
100,
132-
135
63,7
5,11
5,31
512
4,13
9
14. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as 2
7 x
= 3
x 2
7 an
d10
0144
253,
313
443
x=
x 44
3.
Ass
ocia
tive
prop
erty
of m
ultip
licat
ion
15. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as:
140
109-
111,
281,
284
247-
248
300
x 27
= (
3 x
) x
27 =
3 x
(x
27 )
= 3
xE1=
L.
16. G
iven
a p
robl
em s
uch
as 7
x 5
x 8
=,
the
stud
ent c
an in
dica
teth
e1o
3,32
419
1,1'
34,
1421
53,
grou
ping
of f
acto
rs w
hich
will
mak
e th
e m
ultip
licat
ion
easi
est b
y13
9,23
7,30
8-en
clos
ing
the
5 an
d 8
in p
aren
thes
es.
For
exa
mpl
e:11
0-11
1,3.
7)9,
315
126
7 x
( 5
x 8
) =
280
.
Iden
tity
elem
ent
17. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as 1
x 4
53 =
102,
114,
Jul
128,
212-
21:
for
mul
tiplic
atio
n32
x=
32;
27
7, 2
7 =
;19
1 =
; and
144
317
45=
45
x
* Im
med
iate
ly is
def
ined
as
5 se
cond
s cr
less
.
CO
NT
EN
T
Mul
tiplic
ativ
epr
oper
ty o
f 0
Dis
trib
utiv
epr
oper
ty o
f mul
ti-pl
icat
ion
over
addi
tion
Alg
orith
ms
Fac
tors
of 1
0,10
0,an
d m
ultip
les
of10
and
100
OP
ER
AT
ION
S -
GR
AD
E F
OU
R
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
18. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as 7
320
x 0
0=x
700;
07
=-
;0
x 1
=; a
nd
=
A
102,
114
,14
4
101,
142
arra
ys)
that
:
01
=
19. T
he s
tude
nt c
an d
emon
stra
te b
y us
ing
sets
(re
ctan
gula
r
9x 7
=(5
x 7
)-1
-( 4
x 7
) an
d 9x
7 =
( 9x
3)+
(9
x 4)
=35
+28
=27
+36
63=
63
20. T
he s
tude
nt c
an d
emon
stra
te b
y us
ing
sets
(re
ctan
gula
r ar
rays
) th
at:
132,
162-
163
3x 1
23 =
( 3
x 1
00 )
+ (
3 x
20
) +
( 3
x 3
)=
330
+60
+9
369
21. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as:
143-
144,
169
72 x
147
8 =
1478
) +
(:\
x 14
78)
and
( 40
x 7
62 )
( 8
x 76
2 )
=x
762.
22. T
he s
tude
nt
1 x
23 =
10 x
23
=
100
x 23
=
can
nam
e th
e pr
oduc
ts a
nd q
uotie
nts
for
prob
lem
s
3 x
23 =
1490
0;1
30 x
23
=
300
x 23
=
4900
10 =
--
4900
= 1
00 =
such
as:
132
-13
6,14
1,14
5,49
00 =
7 =
158,
168-
169,
174-
4900
70 =
175,
180,
192,
197,
4900
; 70
0 =
200,
202,
206,
208,
236,
322-
323
SA
BC
6012
8
127-
131,
154
133,
278
141-
143,
240,
306,
252-
253
136
144
108,
116-
133-
134,
120,
123-
136,
246,
124,
179,
248,
250-
218,
223,
251,
262
280-
282,
284-
285
CO
NT
EN
T
Mul
tiplic
atio
n- -
vert
ical
not
atio
n(f
our-
digi
t fac
tor
by tw
o-di
git f
acto
r)w
ith a
nd w
ithou
tre
grou
ping
Long
div
isio
n(f
our-
digi
t div
iden
dby
two-
digi
t div
isor
)w
ith a
nd w
ithou
tre
mai
nder
ti R
AT
ION
AL
NU
MB
ER
S
Add
ition
and
Sub
trac
tion
Def
initi
on(f
ract
ions
v it
h th
esa
me
deno
min
ator
s)
OP
ER
AT
ION
S -
GR
AD
E F
OU
R
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
23. T
he s
tude
nt c
an n
ame
the
prod
ucts
for
prob
lem
ssu
ch a
s:
2129
7640
05x3
4x2
4x4
8
AW
170,
174-
176,
178,
182,
204,
236,
260,
276,
294,
308
137-
142,
253,
265,
314,
322
ABC
144,148,160,
163,166,170,
237,241,244,
259,269-270,
306,326
24. T
he s
tude
nt c
an n
ame
the
quot
ient
s an
d re
mai
nder
s fo
rpr
oble
ms
such
as:
189-
191
,193
-19
7,20
1,20
2,22
0,22
4-24
6,28
3,146,148,150,
162-163,166,
207-
208,
211,
213,
216,
236,
286-
290,
292,
325
170,237,243,
245,255,257,
9 )
585
14)
1008
98 )
467
321
) 66
58
(Not
e: S
ee o
bjec
tive
# 32
for
Gra
de T
hree
for
exam
ples
260,
276,
294,
308,
326-
328
259,261,263,
265- 266,269-
of a
lgor
ithm
s.270,306,326
25. G
iven
a m
odel
(re
gion
or
num
ber
line)
for
the
addi
tion
orsu
btra
ctio
n of
two
ratio
nal n
umbe
rs, t
he s
tude
nt c
an d
eter
min
ean
d na
me
the
sum
or
diffe
renc
e.(S
ee o
bjec
tive
# 33
for
Gra
de
300-
302,
328
88-8
9,90
-91,
93,1
96,
194-
198
Thr
ee fo
r ex
ampl
es o
f mod
els.
)20
3,20
4,25
0-25
1,
26. G
iven
an
addi
tion
or s
ubtr
actio
n pr
oble
m s
uch
as 3
/8 +
7/8
=
30:',
306,
311,
323
253
207,
251
199-
200,
235,
269-
270
or 5
/9 -
2/9
=,
the
stud
ent c
an n
ame
the
sum
or
diffe
renc
eas
a p
rope
r or
impr
oper
frac
tion
in lo
wes
t ter
ms,
or
as a
mix
ednu
mer
al, a
nd u
se r
egio
ns o
r a
num
ber
line
to p
rove
his
res
ult.
CO
NT
EN
T
OP
ER
AT
ION
S -
GR
AD
E F
OU
R
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
A'
SA
BC
Alg
orith
ms
Dec
imal
not
atio
n27
. The
stu
dent
can
nam
e th
e su
ms
and
diffe
renc
es fo
r pr
oble
ms
such
as:
68,3
08,3
18, 3
5,37
,41,
78-7
9,84
,
(mon
ey)
320
7 53
,1
7086
,165
,249
,l';
'1,2
29,
259
S8.
76S
1001
.00
252
349.
06-
998.
9923
.55
GE
OM
ET
RY
- G
RA
DE
FO
UR
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
AW
SA
BC
GE
OM
ET
RIC
FIG
UR
ES
Pla
ne fi
gure
s1.
The
stu
dent
can
dra
w a
nd n
ame
a se
t of p
oint
s sa
tisfy
ing
46-4
746
-47
,56
94-9
7,10
1-(a
s se
ts o
f poi
nts)
give
n co
nditi
ons.
For
exa
mpl
e:18
1,18
4,10
3,10
9-P
oint
254,
258
,11
4,11
9-P
ath
(cur
ve)
The
set
of a
i! po
ints
one
inch
from
a g
iven
poi
nt is
322
120,
164
,1cS
Line
a (n
)(circle)
'769
,287
Line
seg
men
tR
ayT
he s
et o
f all
poin
ts c
'nta
ined
in tw
o ra
ys w
ith a
com
mon
end
poin
t is
a (n
)(a
ngle
)
Ang
le Rig
ht a
ngle
2. G
iven
mod
els
of th
e pl
ane
geom
etri
figur
es n
amed
nn
the
146,
147
255-257
115,118
left
(wire
, pap
er o
r fla
nnel
cut
outs
, pen
cil o
r ch
alk
outli
nes)
,th
e st
uden
t can
iden
tify,
nam
e, a
nd d
istin
guis
h am
ong
them
.23
8, 2
39
Pol
ygo
n13
0, 1
3143
,48-
49,
272-
285,
Tria
ngle
146,
147
52-5
3,57
- 30
2-30
::R
ight
tria
ngle
160,
161
58,9
2,11
5,Q
uadr
ilate
ral
(dia
gona
l)16
2,18
7,18
9,22
8,25
7,P
aral
lelo
gram
259-
260,
297,
Squ
are
314,
323,
325
Rec
tang
le
Circ
le23
8, 2
8018
0, 1
82,
286-
288
Cen
ter
183,
186
,R
adiu
s18
9D
iam
eter
Cho
rd
CO
NT
EN
T
Spa
ce fi
gure
sR
ight
rec
tang
ular
pris
mC
ube
Sph
ere
Cyl
inde
rC
one
Pyr
amid
PR
OP
ER
TIE
S
Par
alle
l lin
es
Inte
rsec
ting
lines
Sim
ple
clos
edcu
rves
Per
imet
er
GE
OM
ET
RY
- G
RA
DE
FO
UR
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
3G
iven
mod
els
of th
esp
ace
figur
es n
amed
on
the
left
(ood
or p
last
ic s
olid
s, p
aper
mod
els,
ske
tche
s, e
tc.)
, the
stu
dent
can
iden
tify,
nam
e, a
nd d
istin
guis
ham
ong
them
.
4. T
he s
tude
nt c
an s
ketc
h an
d de
scrib
epa
ralle
l lin
es.
For
exam
ple:
Par
alle
l lin
esar
e lin
es in
the
sam
e pl
ane
that
nev
er m
eet.
5. T
he s
tude
nt c
an s
ketc
h an
d de
scrib
ein
ters
ectin
g lin
es.
For
exam
ple:
Inte
rsec
ting
lines
are
lines
that
hav
e on
e po
int i
nco
mm
on.
6. G
iven
a s
et o
f pla
ne fi
gure
s,th
e st
uden
tca
n di
stin
guis
h th
esi
mpl
e cl
osed
cur
ves
and
iden
tify
the
inte
rior
and
exte
rior
regi
ons.
7. G
iven
a m
odel
of
a po
lygo
n an
d us
ing
a ru
ler,
the
stud
ent c
ande
term
ine
and
nam
e th
e pe
rimet
er (
leng
th o
f the
clo
sed
poly
gona
lpa
th)
of th
e po
lygo
n.
A'A
"S
184-
185,
92,
218-
219
261-
264
46,
90 -
91,
130
14-1
7,73
99,3
08
46-4
7,16
2,21
0
AB
C
297-
302,
305
284-
285
53-5
6,27
1-27
3,17
9,18
2,96
,26
530
2-30
3
50-5
1,10
5,28
0-19
1,27
928
2,32
428
9-29
1
GE
OM
ET
RY
- G
RA
DE
FO
UR
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
AW
SA
BC
Are
a8.
Giv
en a
mod
el o
f a s
impl
e cl
osed
cur
ve, t
he s
tude
nt c
an c
ount
1-2,
8-11
,72
-73,
202-
296,
(est
imat
e if
nece
ssar
y) th
e nu
mbe
r of
uni
t squ
ares
nee
ded
to24
-25,
73,
191,
279,
3O
cove
r th
e in
terio
r re
gion
.99
,126
,166
,32
4
204,
214,
308
Vol
ume
9. T
he s
tude
nt c
an d
emon
stra
te h
is u
nder
stan
ding
of t
he c
once
pt o
f12
-13,
21,
106-
107,
volu
me
by fi
lling
the
inte
rior
spac
e of
a r
ight
rec
tang
ular
pris
m25
,73,
171,
191,
279
(i.e.
,cha
lkbo
x, s
hoeb
ox, e
tc.)
with
uni
t cub
es.
294
CO
NS
TR
UC
TIO
NS
130-
131
,160
-46
,48,
182-
101
-102
,:P
lane
geo
met
ric fi
gure
s10
. Usi
ng a
str
aigh
tedg
e, th
e st
uden
t can
con
stru
ct m
odel
s fo
r lin
es,
161,
218,
238
183,
185-
104,
110-
line
segm
ents
, ray
s, a
ngle
s, a
nd q
uadr
ilate
rals
and
labe
l the
m.
188,
190,
111,
114,
254,
322
116,
120,
164,
277-
279,
282,
284-
285,
303
Rig
ht tr
iang
le11
, Usi
ng a
str
aigh
tedg
e an
d fo
lded
pap
er, t
he s
tude
nt c
an c
onst
ruct
146-
147,
a rig
ht tr
iang
le.
281
Tria
ngle
12, G
iven
the
thre
e si
des
of a
tria
ngle
and
usi
ng a
str
aigh
tedg
e an
d13
0-13
1,48
,187
-188
,27
5
com
pass
,th
e st
uden
t can
con
stru
ct th
e tr
iang
le,
280
190,
259-
260,
322
Circ
le13
. Giv
en th
e ce
nter
and
rad
ius
and
usin
g a
strin
g or
a c
ompa
ss, t
he23
8,28
118
0-18
428
6-28
7,C
ente
rst
uden
t can
con
stru
ct a
circ
le.
302
Rad
ius
CO
NT
EN
T
CO
NC
EP
TS
OF
ME
AS
UR
EM
EN
T
Pro
cess
of m
easu
ling
Arb
itrar
y se
lect
ion
of u
nit
ME
AS
UR
EM
EN
TG
RA
DE
FO
UR
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
1. G
iven
a m
easu
rabl
e ph
ysic
al p
rope
rly s
uch
as le
ngth
, are
a,w
eigh
t, te
mpe
ratu
re, e
tc.,
the
stud
ent
can
sele
ct a
sui
tabl
eun
it an
d/fo
r m
easu
ring
devi
ce a
nd m
easu
re th
e pr
oper
ty.
For
exa
mpl
e:
Wei
ght c
an b
e m
easu
red
by u
sing
a(n
)
2. T
he s
tude
nt c
anna
me
at le
ast t
wo
units
sui
tabl
e fo
r na
min
gth
e m
easu
re o
;.- a
giv
en p
hysi
cal p
rope
rty.
For
exa
mpl
e:
The
are
a of
a fl
oor
can
be e
xpre
ssed
Hsq
uare
feet
, in
squa
re y
ards
, or
in s
quar
e vi
nyl t
iles
( 9"
x 9
" ).
App
roxi
mat
e na
ture
of
3. T
he s
tude
nt c
an d
emon
stra
te h
is u
nder
stan
ding
of t
heap
prox
i-m
easu
rem
ent
mat
e na
ture
of m
easu
rem
ent b
y st
atin
g th
e pr
ecis
ion
of th
e m
easu
re.
For
exa
mpl
e:
The
dis
tanc
e be
twee
n La
s V
egas
and
Bou
lder
City
is30
mile
s co
rrec
t to
the
near
est 5
mile
s.
ME
AS
UR
EM
EN
T O
F P
HY
SIC
AL
PR
OP
ER
TIE
S
Leng
th4.
The
stu
dent
can
use
vario
us m
easu
ring
devi
ces
(rul
er, y
ards
tick,
Inch
, foo
t, ya
rd, m
ilem
eter
stic
k) to
mea
sure
leng
th in
who
le a
nd fr
actio
nal p
arts
Cen
timet
er, m
eter
of u
nits
.
AW
3,23
-25,
203
4-5
6 2-7,
23-2
4,72
,204
,276
,2'
24,3
05,3
11
S
106,
1T!,
173-
174,
176,
247
51,1
76,2
ABC
106-
108,
296
67 00,1
03 -
'.0:0
;,119
-12C
,
2:2,3-284,287
CO
NT
EN
T
Per
imet
er
Are
a--s
quar
e un
itsre
late
d to
uni
ts o
fle
ngth Rec
tang
le
Vol
ume-
-cub
ic u
nits
rela
ted
to u
nits
of
leng
th Liqu
id m
easu
reO
unce
, cup
, pin
t,qu
art,
gallo
n
Tim
e Sec
ond,
min
ute,
hou
r
V;e
ight
Oun
ce, p
ound
,to
n
Tem
pera
ture
cahr
enhe
it de
gree
sC
entig
rade
deg
rees
ME
AS
UR
EM
EN
T-
GR
AD
E F
OU
R
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
5. T
he s
tude
nt c
on d
eter
min
e an
d na
me
the
perim
eter
of
a
give
n po
lygo
n by
add
ing
the
mea
sure
s of
the
side
s.(N
ote:
See
obj
ectiv
e #
7 fo
r G
EO
ME
TR
Y-
GR
AD
E F
OU
R.)
6. G
iven
the
mea
sure
of t
he b
ase
and
altit
ude
ofa
rect
angu
lar
regi
on in
who
le u
nits
, the
stu
dent
can
dete
rmin
e ar
ia n
ame
the
area
of t
he r
eaio
n by
mul
tiplic
atio
n (a
s th
ene
cess
ary
mul
tiplic
atio
n fa
cts
and
algo
rithm
sar
e le
arne
d).
(Not
e: S
ee o
bjec
tive
# 8
for
GE
OM
ET
RY
GR
AD
E F
OU
R.)
7. G
iven
a s
ketc
h of
a r
ight
rec
tang
ular
spoc
e fig
ure,
the
stud
ent c
an d
eter
min
e an
d na
me
the
volu
me
of th
e fig
ure
by c
ount
ing
the
num
ber
of v
olum
e un
its (
cube
s;zf
ecie
dto
fill
the
spac
e.(N
ote:
See
obj
ectiv
e n
9 fo
r G
EO
ME
TR
YG
RA
DE
FO
UR
.)
8. T
he s
tude
nt c
an n
ame
the
stan
dard
Eng
lish
units
liqui
dm
easu
re a
nd m
easu
re th
e ca
paci
ty o
f a g
iver
, :-.
.ont
--J:
ner
to th
e ne
ares
t who
le u
nit.
9. U
sing
o c
lock
, Ti-)
euc
et
cc.r
wr-
ce ti
me
-ne
near
est s
econ
d an
d :-
..dic
ate
A.M
. or
P.M
,
10. U
sing
c s
ca,e
,-d
oecc
ngi
ven
cble
ct in
.v.,7
cie
and
frac
tiona
l cat
':i t
r';7!
.(N
ote:
Stu
dent
sca
n na
me
the
ton
as a
uni
t of w
eigh
tbu
t are
not
exp
ecte
d to
wei
gh o
I:jec
ts th
at h
eavy
!)
11. U
sing
c tn
err-
.orn
eter
cal
ibra
ted
in e
ithei
Cen
tigra
de d
egre
es, t
he s
tude
nt c
an r
ecc.
; .T
he te
..oer
dtur
eto
t: -
e ne
e: s
' des
lree.
AW
SA
BC
14-1
7,25
,73,
50-5
1,19
1,23
0- 2
82,2
89-
99,3
008
279,
324
291,
302,
304,
326
1-2,
8- 1
1,18
-21
,25,
73,9
9,12
6,16
6,20
4,21
4,29
4,30
8
1-2,
12-1
3,21
,25,
73,
171,
294
22
63,7
2-73
,12
1,12
7,12
6-12
8,19
129
2-29
6,29
8,27
9,32
430
2,30
5,32
6
106-
107,
191,
279
174-
175,
167
215,
230-
235,
164-
167,
292
168
261
277
203
171-
172
247
CO
NT
EN
T
ME
AS
UR
EM
EN
T -
GR
AD
E F
OU
R
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
RE
NA
MIN
G M
EA
SU
RE
S
Com
paris
on o
f uni
ts12
. The
stu
dent
can
exp
ress
the
rela
tions
hips
bet
wee
n un
its o
f5,
22-2
4,72
,16
5,17
1,17
3-10
7-10
8,11
8,C
onve
rsio
n of
uni
tsm
easu
re a
ppro
pria
te to
the
grad
e le
vel a
nd c
an r
enam
e a
212,
261,
277,
176,
208,
229,
120,
164,
mea
sure
in o
ther
uni
ts.
For
exa
mpl
e:30
8,36
923
6,30
3,32
4,16
7-16
8,17
037
0
1 m
eter
is (
long
er, s
hort
er)
than
1 y
ard,
3000
pou
nds
=to
ns.
CO
MP
UT
AT
ION
S W
ITH
ME
AS
UR
ES
13. T
he s
tude
nt c
an c
ompu
te w
ith m
easu
res
appr
opria
te to
the
grad
e le
vel,
assi
gn th
e pr
oper
uni
t to
the
resu
lt, a
ndre
nam
e if
nece
ssar
y,F
or e
xam
ple:
1 3
ft.8
in, =
12
ft. 2
0 in
.-
5 ft.
11
in. =
5 ft.
11
in.
7 ft.
9 in
.
NU
MB
ER
- G
RA
DE
FIV
E
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
AW
SE
TS Fin
ite1.
The
stu
dent
can
con
stru
ct a
Ven
n di
agra
m to
sho
w th
e re
latio
nshi
p66
,67
Infin
iteof
who
le n
umbe
rs to
rat
iona
l num
bers
.E
mpt
y
S
314-
321
AB
C
109
2. T
he s
tude
nt c
an c
lass
ify a
giv
en s
et a
s:31
259
Fin
ite--
-has
a d
efin
ite n
umbe
r of
mem
bers
Infin
iteha
s an
unl
imite
d nu
mbe
r of
mem
bers
Em
pty-
--ha
s no
mem
bers
WH
OLE
NU
MB
ER
S0-
1,00
0,00
0,00
03.
The
stu
dent
can
det
erm
ine
the
card
inal
num
ber
of a
giv
en s
et.
.;)
4. G
iven
a n
umbe
r, th
e st
uden
t can
iden
tify
the
num
bers
whi
chpr
eced
e an
d fo
llow
it.
5. T
he s
tude
nt c
an id
entif
y an
d na
me
odd
and
even
num
bers
.
7,55
170-
173
42,4
3,62
6. G
iven
a n
umbe
r gr
eate
r th
an 1
000,
the
stud
ent c
an v
erba
lize
his
5-8
170-
175
42-4
5no
tion
of th
e qu
antit
y in
volv
ed.
For
exa
mpl
e: "
A m
illio
n do
llars
is h
avin
g a
thou
sand
dol
lars
in e
ach
of a
thou
sand
ban
ks!"
Prim
e an
d co
mpo
site
7. G
iven
a w
hole
num
ber
grea
ter
than
1 a
nd le
ss th
an 1
00, t
he s
tude
nt17
0-17
341
-43
num
bers
can
clas
sify
the
num
ber
as:
Prim
e--h
as e
xact
ly tw
o fa
ctor
sC
ompo
site
--ha
s m
ore
than
two
fact
ors
Ord
er r
elat
ions
8. G
iven
a s
et o
f who
le n
umbe
rs, t
he s
tude
nt c
an w
rite
them
in o
rder
8,9,
from
leas
t to
grea
test
and
vic
e ve
rsa.
226-
229,
235
,
9. T
he s
tude
nt c
an w
rite
the
sym
bois
<,s
,)>
I,
=/ t
oex
pres
s th
ere
latio
nshi
p be
twee
n nu
mbe
rs.
74-7
660
,61,
113,
133
NU
MB
ER
- G
RA
DE
FIV
E
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
AV
VA
BC
RA
TIO
NA
L N
UM
BE
RS
10. T
he s
tude
nt c
an id
entif
y a
ratio
nal n
umbe
ras
one
whi
ch c
an b
eex
pres
sed
as th
e ra
tio o
f tw
o w
hole
num
bers
a/b
whe
n b/
0.
220-
229
72-7
610
9,11
1,11
3
11. T
he s
tude
nt c
an d
emon
stra
te th
at a
ll w
hole
num
bers
are
als
o22
8,22
9,78
,79
117,
125,
126
ratio
nal n
umbe
rs.
For
exa
mpl
e:24
0,24
12
= 4
/2 =
14/
7 =
100
/50,
etc
.
12. G
iven
a s
ituat
ion
invo
lvin
g a
ratio
nal n
umbe
r, th
e st
uden
tca
nid
entif
y a/
b as
a r
atio
, as
a fr
actio
n, o
r as
an in
dica
ted
divi
sion
.30
078
,79
113
INT
EG
ER
S13
. The
stu
dent
can
nam
e th
e nu
mbe
rs a
ssoc
iate
d w
ith p
oint
s op
posi
teth
e po
ints
for
who
le n
umbe
rs o
n th
e nu
mbe
r lin
e.16
718
4-18
9
NU
ME
RA
TIO
NG
RA
DE
FIV
E
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
NA
ME
S F
OR
NU
MB
ER
S
WH
OLE
NU
MB
ER
S0
- 99
9,99
9,99
9
Pla
ce v
alue
-ni
ne -
digi
t num
eral
s
Exp
ande
d no
tatio
n- -
nine
-di
git n
umer
als
1. T
he s
tude
nt c
an id
entif
y, n
ame,
rea
d, a
nd w
rite
man
ydi
ffere
nt n
ames
for
the
sam
e nu
mbe
r.F
or e
xam
ple:
6 7/
10 =
6 +
7/1
0 =
6,7
= 6
7/10
= 2
+ 4
+ .7
= e
tc.
2. T
he s
tude
nt c
an id
entif
y, n
ame,
rea
d, a
nd w
rite
num
eral
sfo
r w
hole
num
bers
.
3. G
iven
a n
umer
al s
uch
as 4
67,3
04, t
he s
tude
nt c
an w
rite
the
wor
ds: f
our
hund
red
sixt
y-se
ven
thou
sand
, thr
ee h
undr
ed fo
ur.
4. G
iven
a v
erba
l phr
ase
nam
ing
a nu
mbe
r, th
e st
uden
t can
writ
e th
e nu
mbe
r w
ords
and
/or
the
Ara
bic
num
eral
.
5. G
iven
a b
ase
ten
(dec
imal
) nu
mer
al, t
he s
tude
nt c
an id
entif
yan
d na
me
the
plac
e va
lue
for
each
dig
it.
6, G
iven
a n
ine-
digi
t num
eral
the
stud
ent c
an id
entif
y an
dna
me
the
perio
d va
lue
for
each
gro
up o
f thr
ee d
igits
.F
or e
xam
ple:
473
1201
1(7
15)
mill
ions
hoiC
2!cI
nd;\
(One
s)
7. G
iven
a n
umer
al s
uch
as 4
73,2
31,7
15, t
he s
tude
nt c
an w
rite
the
expa
nded
num
eral
in th
e fo
llow
ing
way
: 473
,231
,715
=(
4 x
100,
000,
000
)(
7 x
10,0
00,0
00 )
( 3
x 1,
000,
000
)+
( 2
x 10
0,00
0 )
+ (
3 x
10,0
00 )
(1
x 1,
000
) +
(x
100
)+
(1
x 10
) +
( 5
x 1
).
8. G
iven
a n
umer
al s
uch
as 2
73,4
01,7
15, t
he s
tude
nt c
an w
rite
the
expa
nded
num
eral
illu
stra
ting
perio
d (r
athe
r th
an p
lace
)va
lue
in th
e fo
llow
ing
way
:
AW
45,2
22-2
24
5A
BC
35,7
5,81
7,47
171
42-4
4
4717
142
-44
171
38-4
0,42
,45
1-7
170,
256
38-4
0,42
,43
717
038
-40,
43
271
174,
175
47-4
9
6,17
174
38-4
9
273,
401,
715
= (
273
x 1
,000
,000
) +
( 4
01 x
1,0
00 )
+ (
715
x 1
).
NU
ME
RA
TIO
N -
GR
AD
E F
IVE
CO
NT
EN
T
Prim
e fa
ctor
izat
ion
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
9. G
iven
a n
umer
al fo
r a
com
posi
te n
umbe
r, th
e st
uden
t can
writ
e a
num
eral
whi
ch n
ames
the
num
ber
as th
e pr
oduc
t of
prim
e nu
mbe
rs.
For
exa
mpl
e: 6
0 =
2 x
2 x
3 x
5.
169,
170,
172,
173
41 -
43
AB
C
Rom
an n
umer
als
thro
ugh
C10
. Giv
en a
num
eral
suc
h as
104
, the
stu
dent
can
writ
e th
eR
oman
num
eral
CIV
.
1416
935
-37
11. G
iven
a R
oman
num
eral
suc
h as
CII,
the
stud
ent c
an w
rite
the
1416
935
-37
Ara
bic
num
eral
102
.
12. G
iven
the
num
eral
s X
XX
and
333
, the
stu
dent
can
des
crib
eth
e di
ffere
nce
betw
een
them
by
sayi
ng:
In th
e R
oman
num
eral
the
"X"
alw
ays
has
the
valu
e of
ten,
but
in th
e de
cim
alnu
mer
al th
e va
lue
of th
e "3
" de
pend
s up
on it
s pl
ace
in th
e
1416
935
-37
num
eral
.T
here
fore
, XX
X =
10
+ 1
0 +
10, b
ut33
3 =
300
+ 3
0 +
3.
Non
-dec
imal
num
era-
tion-
-bas
e tw
o, fo
ur,
five
13. G
iven
a s
et w
ith fr
om 1
to 1
00 m
embe
rs, t
he s
tude
nt c
angr
oup
the
mem
bers
and
writ
e a
base
five
num
eral
for
the
card
inal
num
ber
of th
e se
t.
10-1
317
9-18
153
-58
RA
TIO
NA
L N
UM
BE
RS
Com
mon
frac
tions
a:13
14. T
he s
tude
nt c
an id
entif
y, n
ame,
rea
d, a
nd w
rite
frac
tions
for
ratio
nal n
umbe
rs.
186-
217
70-7
952
,53,
110
15. G
iven
a fr
actio
n su
ch a
s 3/
5, th
e st
uden
t can
iden
tify,
nam
e,an
d di
stin
guis
h th
e nu
mer
ator
and
the
deno
min
ator
.19
0,19
170
,71
111-
172
Equ
ival
ent f
ract
ions
16. G
iven
a fr
actio
n su
ch a
s 7/
8, th
e st
uden
t can
writ
e a
set o
f19
6-20
5,13
7-13
9,10
9-12
7
frac
tions
whi
ch a
re e
quiv
alen
t to
7, "
8.F
or e
xam
ple:
7,/8
=21
0-21
2,14
8-15
0,14
'16
= 2
1/24
= 2
8/32
= e
tc.
240-
242,
236,
254,
255
254-
256
CO
NT
EN
T
NU
ME
RA
TIO
N -
GR
AD
E F
IVE
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
17. T
he s
tude
nt c
an r
enam
e a
give
nfr
actio
n in
sim
ples
t for
m.
For
exa
mpl
e: 1
2/32
= 3
/8.
196-
205,
210-
212,
240-
242
254,
255
137-
139,
148-
150,
236,
254-
256
109-
127
18. G
iven
a m
athe
mat
ical
sen
tenc
esu
ch a
s 4/
9 =
?/1
8 =
32/
?,th
e st
uden
t can
nam
e th
e m
issi
ng n
umer
ator
or
deno
min
ator
.24
0-24
274
121-
124
Impr
oper
frac
tions
and
19.
The
stu
dent
can
ren
ame
an im
prop
er fr
actio
n as
am
ixed
mix
ed n
umer
als
num
eral
and
vic
e ve
rsa.
For
exa
mpl
e:
240-
242
74,7
8,79
,13
512
5,17
8
25/7
= 3
4/7
and
16
2/3
= 5
0/3.
Dec
imal
frac
tions
- -
tent
hshu
ndre
dths
20. T
he s
tude
nt c
an id
entif
y, n
ame,
rea
d,an
d w
rite
deci
mal
num
eral
s fo
r ra
tiona
l num
bers
nam
ed w
ith c
omm
onfr
actio
ns
havi
ng d
enom
inat
ors
of 1
0, 1
00,
1000
.F
or e
xam
ple:
270-
274
256
50-5
2,26
5-26
7
thou
sand
ths
7 14
/100
=7.
14.
21. G
iven
a n
umer
al s
uch
as 2
3,74
,th
e st
uden
t can
writ
e th
eex
pand
ed n
umer
al in
the
follo
win
g w
ay:
23.7
4 =
( 2
x '0
) +
272-
273
256
263,
264
( 3
x 1
) +
( 7
x 1
/10
) +
( 4
x 1
/100
).
22. G
iven
a s
et o
f Num
eral
s su
ch a
s 1,
/3, 2
1/2
, .23
,th
e st
uden
t
can
clas
sify
them
as
com
mon
frac
tions
,de
cim
al fr
actio
ns, o
rm
ixed
num
eral
s.
241,
270,
273
254,
255
125,
142-
143
OT
HE
R N
OT
AT
ION
Rou
ndin
g to
the
near
est o
ne, t
en,
hund
red,
thou
sand
,te
nth,
hun
dred
th,
thou
sand
th
23. G
iven
a n
umer
al s
uch
as 1
4.36
, the
stu
dent
can
roun
d it
to74
-81,
10 to
the
near
est t
en, t
o 14
to th
e ne
ares
t one
(who
le n
umbe
r), 1
06-1
08,
and
to 1
4.4
to th
e ne
ares
t ten
th,
116-
118,
126-
128
176
77,9
8,10
2,21
1,23
3,23
9,28
8
CO
NT
EN
T
WH
OLE
NU
MB
ER
S
Add
ition
and
Sub
trac
tion
Inve
rse
rela
tions
hip
Bas
ic fa
cts
Thr
ough
sum
s of
18
Pro
pert
ies
Com
mut
ativ
e an
das
soci
ativ
e pr
oper
ties
of a
dditi
on
Iden
tity
elem
ent
for
addi
tion
Alg
orith
ms
Col
umn
addi
tion
and
subt
ract
ion
(nin
e-di
git n
umer
als)
Oth
er n
otat
ion
OP
ER
AT
ION
SG
RA
DE
FIV
E
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
1. T
he s
tude
nt c
an s
olve
add
ition
or
subt
ract
ion
prob
lem
s w
ithm
issi
ng s
ums,
diff
eren
ces,
or
adde
nds.
For
exa
mpl
e:
+ 4
687
= 1
0,00
0an
d-
23,4
59 =
146
1
2. T
he s
tude
nt c
an c
heck
sub
trac
tion
prob
lem
s by
add
ition
.
3. G
iven
any
sin
gle-
digi
t add
ition
or
subt
ract
ion
com
bina
tion,
the
stud
ent c
an im
med
iate
ly*n
ame
the
sum
or
diffe
renc
e.
4. G
iven
an
addi
tion
prob
lem
with
thre
t or
mor
e ad
dend
s, th
est
uden
t can
dem
onst
rate
how
to fi
nd th
e su
m in
the
easi
est
way
by
rena
min
g an
d re
arra
ngin
g th
e ad
dend
s.
5. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as 3
905
+=
390
5;54
77 -
--=
547
7+;
0 --
=-
380,
3p7;
Gild
8,77
7,30
0 =
0.
6. T
he s
tude
nt c
an n
ame
the
sum
s an
d di
ffere
nces
for
prob
lem
ssu
ch a
s47
8,30
5,07
760
0,70
3,20
0+
23,
989,
196
5,87
6,99
9
7. T
he s
tude
nt c
an id
entif
y an
d na
me
sum
s, d
iffer
ence
s, m
issi
ngad
dend
s, m
issi
ng d
igits
, and
mis
sing
ope
ratio
nal s
igns
inpr
oble
ms
writ
ten
in b
oth
horiz
onta
l and
ver
tical
nat
atio
n.
' im
med
iate
k. is
def
ined
as
.5 s
econ
ds o
r :e
ss.
AW 28
,30,
31,
45,4
E
20-2
330
-31,
540O
c,c-
-, D
20-2
3,30
,314
S
21,2
9,54
,14
,19
86,8
7,31
4,30
315,
319
21,2
6,87
,88
.25
8
K-2
330
-31
sb 31
4
31
AB
C
79,8
0
78,8
021
0, 2
13
73 26,7
7
28,3
083
18,1
9,73
-33
17?
14-1
9
OP
ER
AT
ION
S -
GR
AD
E F
IVE
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
Mul
tiplic
atio
n an
d D
ivis
ion
AW
20,3
4
S 46
AB
C
91-9
5in
vers
e re
latio
nshi
p8.
Giv
en a
mul
tiplic
atio
n eq
uatio
n su
ch a
s 5
x 34
= 1
70,
the
stud
ent c
an w
rite
the
two
rela
ted
divi
sion
equ
atio
ns,
170
; 34
= 5
and
170
; 5
= 3
4.
9. G
iven
a m
ultip
licat
ion
prob
lem
with
a m
issi
ng fa
ctor
suc
h as
3446
94,9
5,';9
,x
17 =
391
, the
stu
dent
can
writ
e th
e re
late
d di
visi
on11
;'_)
equa
tion,
391
-; 1
7 =
10. T
he s
tude
nt c
an c
heck
div
isio
n pr
oble
ms
by m
ultip
licat
ion.
20 -
23
48, 1
01,
91-9
5,99
,34
,62,
6310
910
0,10
2,10
4,10
7,22
2
Bas
ic fa
cts
Thr
ough
pro
duct
s of
81
11. G
iven
any
sin
gle-
digi
t mul
tiplic
atio
n or
div
isio
n co
mbi
natio
n,th
e st
uden
t can
imm
edia
tely
*nam
e th
e pr
oduc
t or
quot
ient
and
24 -
2920
,22
94
use
sets
or
a nu
mbe
r lin
e to
pro
ve h
is r
esul
t.
Pro
pert
ies
Com
mut
ativ
e pr
oper
ty12
. Giv
en a
mu'
tiplic
atio
n pr
oble
m s
uch
as 4
68 x
100
3 =
the
26 -
27
20-2
087
, 89
of m
ultip
licat
ion
stud
ent c
an s
elec
t the
ver
tical
alg
orith
m w
hich
will
mak
e th
e52
- 5
3m
ultip
licat
ion
easi
est.
For
exa
mpl
e:96
-1
JO
468
inst
ead
of10
03
x 10
03x
468
13 T
he s
tude
nt c
an c
heck
mul
tiplic
atio
n pr
oble
ms
by r
ever
sing
the
orde
r of
the
fact
ors
and
mul
tiply
ing
agai
n.26
20,2
187
,89
Imm
edia
tely
is d
efin
ed a
sse
cond
s or
less
.
CO
NT
EN
T
Ass
ocia
tive
prop
erty
of m
ultip
licat
ion
OP
ER
AT
ION
S -
GR
AD
E F
IVE
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
14. G
iven
a p
robl
em s
uch
as 6
7 x
25 x
4 =
,th
e st
uden
t can
indi
cate
the
grou
ping
of f
acto
rs w
hich
will
mak
e th
e m
ultip
licat
ion
easi
est b
y en
clos
ing
the
25 a
nd 4
in p
aren
thes
es.
For
exa
mpl
e:
67 x
( 2
5 x
4 )
= 6
700.
AW
26 -
27
52 -
53
290
S 20-3
0
ALI
C
87, 8
9
15. G
iven
a m
ultip
licat
ion
prob
lem
suc
h as
400
0 x
500
=,
the
stud
ent
can
nam
e th
e :r
oduc
t.56
-59
92-9
395
,`31
iden
tity
elem
ent
16. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as 1
x 8
967
=fo
r m
ultip
licat
ion
555
x=
555
; 89,
453
2; 8
9,45
3 =
;34
9=
349
;an
d 87
0=
870
x
Mul
tiplic
ativ
e pr
oper
ty 1
7. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as 7
320
x 0
=of
00
=x
4900
; 0; 6
85 =
;0
x 1
=;
and
01
=
18. G
iven
a d
ivis
ion
prob
lem
suc
h as
70
=,
the
stud
ent c
ande
mon
stra
te th
at th
e pr
oble
m h
as n
o so
luti7
n7y
usin
g re
peat
edsu
btra
ctio
n an
d/or
the
inve
rse
rela
tions
hip.
.
RE
PE
AT
ED
SU
BT
RA
CT
ION
INV
ER
SE
RE
LAT
ION
SH
IP
0
- 0
1
7
- 0
3
7-
025
7et
c.et
c.et
c.
no n
umbe
r
beca
use
no n
umbe
r x
0 =
7
2629
,30,
95
95
96 -
100
55-5
9
36,1
17,
137
20,9
595
, 231
,23
3,24
4
95
CO
NT
EN
T
Dis
trib
utiv
e pr
oper
tyof
mul
tiplic
atio
n ov
erad
ditio
n
Alg
orith
ms
Mul
tiplic
atio
n-ve
rtic
al n
otat
ion
(fou
r-di
git f
acto
rby
thre
e-di
git f
octo
r)
Long
div
isio
n(f
ive-
digi
t div
iden
dby
two-
digi
t div
isor
)w
ith a
nd w
ithou
tre
mai
nder
Sho
rt d
ivis
ion
(fiv
e-di
git d
ivid
end
by o
ne-d
igit
divi
sor)
with
and
with
out
rem
air
Jer
OP
ER
AT
ION
SG
RA
DE
FIV
E
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
19. T
he s
tude
nt c
an n
ame
the
mis
sing
num
bers
in p
robl
ems
such
as:
6754
x34
2
2701
60 =
2 x
6754
x 67
5420
2620
0 =
300
x x 67
54
20. T
he s
tude
nt c
an n
ame
the
prod
ucts
for
prob
lem
s su
ch a
s:
9607
7956
x 17
3x
798
21. T
he s
tude
nt c
an n
ame
the
quot
ient
s an
d re
mai
nder
s fo
rpr
oble
ms
such
as:
47)
43,5
9675
) 10
,000
(Not
e: S
ee o
bjec
tive
# 32
for
Gra
de T
hree
for
exam
ples
of a
lgor
ithm
s.)
22. T
he s
tude
nt c
an u
se th
e sh
ort a
lgor
ithm
(sh
ort
divi
sion
form
) to
det
erm
ine
and
nam
e th
e qu
otie
nts
and
rem
aind
ers
for
prc,
I.Jle
ms
such
as:
9) 4
203
5 )
37,4
16
SA
BC
26,2
7,52
,24
-27,
3088
,89,
96,9
7,53
232
56-6
1,17
3
96-1
00
106-
109,
96-9
8,11
2-11
5,10
0,10
1,11
7-12
0,10
4-10
612
6-13
1,13
4-13
6
134-
136
48-5
4
97,2
15,2
16,
219,
223,
231-
234
101
-10L
,21
8,22
1,22
2,22
5-23
0,23
7-24
1
221,
222
OP
ER
AT
ION
S -
GR
AD
E F
IVE
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
AW
A3C
Oth
er n
otat
ion
23,.
The
stu
dent
can
iden
tify
and
nam
e pr
oduc
ts, q
uotie
nts,
mis
sing
fact
ors,
and
mis
sing
ope
ratio
nal s
igns
in p
robl
ems
writ
ten
in b
oth
horiz
onta
l and
ver
tical
not
atio
n.
34,3
5,37
,56
,59-
63,
71,9
6-98
,
32-3
9,46
-55
E7-
1 04
,13
8
100,
112,
113,
Oth
er O
pera
tions
116-
120
,126
-13
1,13
4 -1
37
Ave
ragi
ng24
. Giv
en a
set
of n
umbe
rs s
uch
as 9
8, 7
5, 8
3, 1
00, a
nd79
, the
stu
dent
can
nam
e th
e av
erag
e (a
rithm
etic
mea
n)
of th
e nu
mbe
rs.
110,
111,
143,
325
108-
111
Gre
ates
t com
mon
fact
or25
. Giv
en a
set
of n
umbe
rs s
uch
as 8
, 12,
20,
and
32,
the
(gre
ates
t com
mon
div
isor
)st
uden
t can
nam
e th
e gr
eate
st c
omm
on fa
ctor
of t
henu
mbe
rs.
176,
177,
207,
212
148-
150
123,
124
Leas
t com
mon
mul
tiple
26. G
iven
a s
et o
f num
bers
suc
h as
8, 1
2, 2
0, a
nd 3
2, th
e st
uden
t(le
ast c
omm
on d
enom
inat
or)
can
nam
e th
e le
ast c
omm
onm
ultip
le o
f the
num
bers
.17
8,17
9,25
4,25
514
0-14
613
6-13
9
RA
TIO
NA
L N
UM
BE
RS
Add
ition
and
Sub
trac
tion
Def
initi
on27
. Giv
en a
mod
el (
regi
on o
r nu
mbe
r lin
e) fo
r th
e ad
ditio
n or
(fra
ctio
ns w
ith li
kesu
btra
ctio
n of
rat
iona
l num
bers
, the
stu
dent
can
det
erm
ine
cnd
unlik
e de
nom
inat
ors)
and
nam
e th
e su
m o
r di
ffere
nce.
inve
rse
rela
tions
hip
28. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as:
254-
258,
266
258,
260
145-
147
82,8
3
127-
135
134,
135
3/4
+=
7,/8
2 2/
3=
5/6
+ 3
/5 =
1 2/
7=
1 1
/2
OP
ER
AT
ION
S -
GR
AD
E F
IVE
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
AW
SA
3C
29. T
he s
tude
nt c
an c
heck
sub
trac
tion
prob
lem
s by
add
ition
.82
,83
134,
135
Pro
pert
ies
Com
mut
ativ
e pr
oper
tyof
add
ition
30. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as:
258,
259
,29
0
133,
134
1/2+
= 1
/3 +
1/2
3/8
++
3/8
Ass
ocia
tive
prop
erty
of a
dditi
on31
. The
stu
dent
can
sol
ve e
quat
ions
suc
h as
:25
8,25
912
8
( 1/
2 +
1/3
)2/
5 =
1,/2
+ (
+2/
5
32. G
iven
an
addi
tion
prob
lem
with
thre
e ad
dend
s,th
e st
uden
tca
n in
dica
te th
e gr
oupi
ngof
add
ends
whi
ch w
ill m
ake
the
addi
tion
easi
est b
y in
sert
ing
pare
nthe
ses.
For
exa
mpl
e:
14/3
3 +
( 2
1/35
+ 1
4/35
) =
1 1
4/33
258,
259
Iden
tity
elem
ent f
or33
. The
stu
dent
can
sol
ve e
quat
ions
suc
h as
1/2
+=
258
addi
tion
4/7
-=
0; 0
/7 +
0/1
0 =
; and
- 0/
2 =
7/1
5.(
0 =
0/1
= 0
/2 =
0/3
)
Alg
orith
ms
Fra
ctio
n no
tatio
nLi
ke d
enom
inat
ors.
134,138,
139
34. T
he s
tude
nt c
an n
ame
the
sum
s an
d di
ffere
nces
(as
frac
tions
81,8
2,23
8-77
- 8
612
7-13
0
in lo
wes
t ter
ms
and/
or a
s m
ixed
num
eral
s) fo
r pr
oble
ms
such
as:
251,
256,
137
- 13
925
7,25
9,14
0 -
152
7/11
+ 3
.11
=8/
12 -
5/1
2 =
264
OP
ER
AT
ION
S -
GR
AD
E F
IVE
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
Unl
ike
deno
min
ator
s35
. The
stu
dent
can
nam
e th
e su
ms
and
diffe
renc
es (
as fr
actio
ns(r
enam
ing
with
com
mon
in lo
wes
t ter
ms
and/
or a
s m
ixed
num
eral
s) fo
r pr
oble
ms
such
as:
deno
min
ator
)3/
7 +
Q/9
+ 1
3/18
=5/
9 -
1/4
=
Mix
ed n
umer
als
(ren
amin
g an
dre
grou
ping
)
36. T
he s
tude
nt c
an n
ame
the
sum
s an
d di
ffere
nces
(as
frac
tions
inlo
wes
t ter
ms
and/
or a
s m
ixed
num
eral
s) fo
r pr
oble
ms
such
as:
7 1/
4 =
73/
12+
4 2
/3 =
4 8
/12
11 1
1/12
7 1/
4 =
7 3
/12
= 6
15/
12-
4 2/
3 =
4 8
/12
= 4
8/1
22
7/12
Dec
imal
not
atio
n37
. The
stu
dent
can
nam
e th
e su
ms
and
diffe
renc
es fo
r pr
oble
ms
(incl
udin
g m
oney
)su
ch a
s:
5.26
+ 3
9.1
+ .8
32 =
78.0
2 -
13.7
41 =
Mul
tiplic
atio
n an
d D
ivis
ion
Def
initi
on o
f mul
tipli-
38. G
iven
a m
odel
(re
gion
or
num
ber
line)
for
the
mul
tiplic
atio
nca
tion
of tw
o ra
tiona
l num
bers
, the
stu
dent
can
det
erm
ine
and
nam
e th
e
prod
uct.
For
exa
mpl
e:
..=41
1111
1111
1111
4
3x 1
/4 =
AW
SA
BC
254-
256
236
- 24
513
1-13
5,14
2,14
313
9,14
1,25
9
258-
261
239-
242
131-
135,
139-
141
274-
278,
110,
111,
142
- 14
728
225
7-26
115
1
286-
289
8717
1 -
184
246
- 24
7
CO
NT
EN
T
OP
ER
AT
ION
SG
RA
DE
FIV
E
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
Def
initi
on o
f div
isio
n(in
vers
e re
latio
nshi
p)39
. Giv
en a
div
isio
n eq
uatio
n su
chas
5/1
2 i 1
/4 =
,th
e29
4-29
589
,24
9-25
118
5-19
0,19
2-19
3,st
uden
t can
writ
e an
d so
lve
the
rela
ted
mul
tiplic
atio
neq
uatio
n,x
1/4
= 5
/12.
197
Alg
orith
ms
Fra
ctio
n no
tatio
nM
ultip
licat
ion
40. T
he s
tude
nt c
an n
ame
the
prod
ucts
(as
frac
tions
in lo
wes
tte
rms)
for
prob
lem
s su
ch a
s 3/
4 x
2/5
=
Dec
imal
not
atio
n41
. The
stu
dent
can
nam
e th
e pr
oduc
ts a
nd q
uotie
nts
for
prob
lem
s su
ch a
s:13
8-13
926
113
2,21
5,21
6,22
9(m
oney
)
5 2.
5345
) 5
41.
85x
27
GE
OM
ET
RY
- G
RA
DE
FIV
E
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
AW
SA
BC
GE
OM
ET
RIC
FIG
UR
ES
Pla
ne fi
gure
s1.
The
stu
dent
can
des
crib
e a
plan
e ge
omet
ric fi
gure
as
a se
t14
6-14
710
-12,
1-7
(as
sets
of p
oint
s)of
poi
nts.
For
exa
mpl
e:56
-57
Poi
ntP
ath
(cur
ve)
A c
ircle
is th
e se
t of a
ll po
ints
in a
pla
ne a
fixe
dLi
nea
dist
ance
from
a g
iven
poi
nt.
Line
seg
men
tA
BR
ay76
An
angl
e is
the
set o
f all
poin
ts c
onta
ined
in th
e un
ion
of tw
o ra
ys w
ith a
com
mon
end
poin
t.A
ngle
(ve
rtex
) L
AB
CR
ight
ang
le2.
Giv
en m
odel
s of
the
plan
e ge
omet
ric fi
gure
s na
med
on
the
146-
163
56-6
8,3-
8,14
,15,
left
(wire
, pap
er o
r fla
nnel
cut
outs
, pen
cil o
r ch
alk
outli
nes,
266-
275
18-2
0,
Pol
ygon
(ve
rtic
es)
etc.
), th
e st
uden
t can
iden
tify,
nam
e, a
nd d
istin
guis
h am
ong
them
.22
-25,
28
Tria
ngle
A A
BC
Rig
ht tr
iang
le3.
The
stu
dent
can
rea
d an
d w
rite
stan
dard
not
atio
n fo
r th
e pl
ane
146-
153
56,5
88
Qua
drila
tera
l ,P
7AB
CD
figur
es n
amed
on
the
left.
For
exa
mpl
e:P
aral
lelo
gram
Squ
are
Rec
tang
leis
den
oted
by
L. Z
AP
Rho
mbu
s
Pen
tago
nis
den
oted
by
HO
Hex
agon
Oct
agon
Circ
le Cen
ter
Rad
ius
Dia
met
erC
hord
Circ
umfe
renc
e
0(N
ote:
See
illu
stra
tion
of n
otat
ion
besi
de n
ames
on
the
left.
)
CO
NT
EN
T
Spa
ce fi
gure
sP
lane
Pris
m
Sph
ere
Hem
isph
ere
Cyl
inde
rC
one
*Pyr
amid
PR
OP
ER
TIE
S
Par
alle
lI i
nes
Inte
rsec
ting
lines
Per
pend
icul
ar li
nes
GE
OM
ET
RY
- G
RA
DE
FIV
E
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
4. G
iven
mod
els
of th
e sp
ace
figur
es n
amed
on
the
left
(woo
d or
pla
stic
sol
ids,
pap
er m
odel
s, s
ketc
hes,
etc
.),
the
stud
ent c
an id
entif
y, n
ame,
and
dis
tingu
ish
amon
g th
em.
5. T
he s
tude
nt c
an s
ketc
h, d
escr
ibe,
and
giv
e ex
ampl
es o
fpa
ralle
l lin
es.
For
exa
mpl
e: P
aral
lel l
ines
are
line
sin
the
sam
e pl
ane
that
nev
er in
ters
ect.
The
opp
osite
edge
s of
the
tabl
e ar
e pa
ralle
l .
6. T
he s
tude
nt c
an s
ketc
h, d
escr
ibe,
and
giv
e ex
ampl
es o
fin
ters
ectin
g lin
es.
For
exa
mpl
e: In
ters
ectin
g lin
es a
relin
es th
at h
ave
one
poin
t in
com
mon
. Mar
ylan
d P
arkw
ayin
ters
ects
Des
ert I
nn R
oad.
The
cro
ss h
airs
on
my
rifle
sigh
t int
erse
ct.
7. T
he s
tude
nt c
an s
ketc
h, d
escr
ibe,
and
giv
e ex
ampl
es o
fpe
rpen
dicu
lar
lines
.F
or e
xam
ple:
Per
pend
icul
ar li
nes
are
inte
rsec
ting
lines
that
form
rig
ht a
ngle
s. T
he to
p ed
gean
d si
de e
dge
of th
e w
indo
w a
re p
erpe
ndic
ular
to e
ach
othe
r.
8. U
sing
a r
uler
, str
ing,
pap
er c
utou
ts, e
tc.,
the
stud
ent c
ande
mon
stra
te h
ow to
det
erm
ine
the
perim
eter
of a
giv
en s
impl
e
r."'
"","
.
clos
ed c
urve
.E
xam
ples
:
CO
NT
EN
T
GE
OM
ET
RY
- G
RA
DE
FIV
E
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
9. T
he s
tude
nt c
an s
tate
and
app
ly a
rul
e fo
r de
term
inin
g th
epe
rimet
er o
f any
pol
ygon
.F
or e
xam
ple:
The
per
imet
er o
fa
poly
gon
is e
qual
to th
e su
m o
f the
leng
ths
of it
s si
des.
AW
50-5
1
S
129,
273
A3C
26
Are
a10
. Usi
ng a
grid
of s
quar
e un
its (
regi
ons)
, the
stu
dent
can
101,
129
29,
dem
onst
rate
how
to d
eter
min
e th
e ar
ea o
f a g
iven
sim
ple
72-7
3,16
2-16
5cl
osed
cur
ve.
84-8
5
11. T
he s
tude
nt c
an s
tate
and
app
ly a
rul
e fo
r de
term
inin
g th
e72
-73
129
29,
area
of a
ny p
aral
lelo
gram
.F
or e
xam
ple:
The
are
a of
apa
ralle
logr
am is
equ
al to
the
leng
th o
f the
bas
e m
ultip
lied
by (
the
leng
th o
f) th
e al
titud
e.
162-
165
Vol
ume
12. G
iven
a h
ollo
w r
ight
rec
tang
ular
pris
m, t
he s
tude
nt c
anco
unt (
estim
ate
if ne
cess
ary)
the
num
ber
of u
nit c
ubes
need
ed to
fill
the
inte
rior
spac
e.
144-
145
163
Con
grue
nce
13. G
iven
a p
air
of li
ne s
egm
ents
, ang
les,
tria
ngle
s, o
r ot
her
150
- 15
157
- 5
99
-po
lygo
ns, t
he s
tude
nt c
an id
entif
y th
e pa
irs a
s co
ngru
ent
154,
155
_
or n
ot c
ongr
uent
b.;,
mat
chin
g th
e fig
ures
in s
ome
man
ner
158
(tra
ce a
nd o
verla
y, c
utou
ts, e
tc.)
.
CO
NS
TR
UC
TIO
NS
50,5
1,57
-59
20,2
2,23
,P
lane
geo
met
ric fi
gure
s14
. Usi
ng a
str
aigh
tedg
e, th
e st
uden
t can
con
stru
ct m
odel
s fo
r15
0, 1
60,
28lin
es, l
ine
segm
ents
, ray
s, a
ngle
s, a
nd p
olyg
ons
and
labe
l the
m.
161
CO
NT
EN
T
Cop
y: Line
seg
men
tA
ngle
Tria
ngle
GE
OM
ET
RY
- G
RA
DE
FIV
E
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
15. U
sing
a s
trai
ghte
dge
and
com
pass
, the
stu
dent
can
con
stru
cta
plan
e fig
ure
cong
ruen
t to
a gi
ven
line
segm
ent,
angl
e, o
rtr
iang
le.
For
exa
mpl
e:
GIV
EN
CO
NS
TR
UC
TE
D
Line
seg
men
t bis
ecto
r16
. Usi
ng a
str
aigh
tedg
e an
dco
mpa
ss,
the
stud
ent c
an b
isec
tA
ngle
bis
ecto
r(s
epar
ate
into
two
cong
ruen
t fig
ures
) a
give
n lin
e se
gmen
tan
d a
give
n an
gle.
For
exa
mpl
e:
Ci,.--
1,
...y A
lii--
----
----
--'
.e7
-C
ircle
17. U
sing
aco
mpa
ss, t
he s
tude
nt c
an c
onst
ruct
a c
ircle
with
agi
ven
cent
er a
nd r
adiu
s (o
r di
amet
er).
AW
SA
BC
151,
57,
12,1
7,15
6-15
762
-68,
158-
160
160-
161
266-
277
156-
157
6516
0
186
273-
276
154-
159
ME
AS
UR
EM
EN
TG
RA
DE
FIV
E
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
CO
NC
EP
TS
OF
ME
AS
UR
EM
EN
T
Pro
cess
of m
easu
ring
1. G
iven
a m
easu
rabl
e ph
ysic
al p
rope
rty
such
as
leng
th, a
rea,
wei
ght,
tem
pera
ture
, etc
., th
e st
uden
t can
sel
ect a
sui
tabl
eun
it an
d/or
mea
surin
g de
vice
and
mea
sure
the
prop
erty
.F
or e
xam
ple:
Tim
e ca
n be
mea
sure
d by
usi
ng a
(n)
AW
18-1
9
18-1
9
18-1
9,26
8-26
9
18-1
9,26
8-26
9
S
114-
115
114-
115
127-
128
127-
128
AB
C
314
Arb
itrar
y se
lect
ion
2. T
he s
tude
nt c
an n
ame
at le
ast t
wo
units
sui
tabl
e fo
r na
min
gof
uni
tth
e m
easu
re o
f a g
iver
s ph
ysic
al p
rope
rty.
For
exa
mpl
e:
The
roo
m te
mpe
ratu
re c
an b
e ex
pres
sed
in d
egre
esF
ahre
nhei
t or
Cen
tigra
de.
App
roxi
mat
e na
ture
of
3. T
he s
tude
nt c
an d
emon
stra
te h
is u
nder
stan
ding
of t
he a
ppro
xi-
mea
sure
men
tm
ate
natu
re o
f mea
sure
men
t by
stat
ing
the
prec
isio
nof
the
mea
sure
.F
or e
xam
ple:
The
vol
ume
of a
bot
tle is
14
ounc
es c
orre
ct to
the
near
est o
unce
.
ME
AS
UR
EM
EN
T O
F P
HY
SIC
AL
PR
OP
ER
TIE
S
Leng
th4.
The
stu
dent
can
use
var
ious
mea
surin
g de
vice
s (r
uler
, yar
dstic
k,In
ch, f
oot,
yard
, mile
met
er s
tick)
to m
easu
re le
ngth
in w
hole
and
frac
tiona
l par
tsM
illim
eter
, cen
timet
er,
of u
nits
.m
eter
CO
NT
EN
T
ME
AS
UR
EM
EN
TG
RA
DE
FIV
E
BE
HA
VIO
RA
L O
BJE
CT
IVE
SS
AB
C
Per
imet
er5.
Giv
en th
e m
easu
res
of th
e si
des
of a
poly
gon,
the
stud
ent
50,5
112
9-13
026
-28,
126
can
com
pute
the
perim
eter
.(N
ote:
See
obj
ectiv
e #
9 fo
r G
EO
ME
TR
Y -
GR
AD
EF
IVE
.)
Are
a --
squ
are
units
6. U
sing
pap
er fi
gure
s an
d sc
isso
rs, t
he s
tude
nt c
ande
mon
-72
-73
129-
130
28
rela
ted
to u
nits
of
stra
te th
at th
e ar
eaF
of a
par
alle
logr
am a
nd a
rect
angl
e
leng
thha
ving
the
sam
e ba
se a
nd a
ltitu
de m
easu
res
are
equa
l.
Rec
tang
leF
or e
xam
ple:
Par
alle
logr
am8"
8"
3"
311
7. G
iven
the
mea
sure
s of
the
base
and
alti
tude
of a
rec
tang
le72
-73,
84-
85,
129-
130
28-2
9,
or p
aral
lelo
gram
,th
e st
uden
t can
com
pute
the
area
.10
112
6-16
3,
(Not
e: S
ee o
bjec
tive
# 11
for
GE
OM
ET
RY
GR
AD
E F
IVE
.)16
5
Vol
ume-
-cu
bic
units
8. G
iven
a s
ketc
h of
a r
ight
rec
tang
ular
spa
cefig
u-e,
the
101, 144-145
163
rela
ted
to u
nits
of
stud
ent c
an d
eter
min
e an
d na
me
the
volu
me
of th
e fig
ure
leng
thby
cou
ntin
g th
e nu
mbe
r of
vol
ume
units
(cub
es)
netd
edto
fill
the
spac
e,(N
ote:
See
obj
ectiv
e #
12 fo
r G
EO
ME
TR
YG
RA
DE
FIV
E.)
Liqu
id m
easu
re9.
The
stu
dent
can
nam
e th
e st
anda
rd E
nglis
h un
itsof
liqu
id14
5,2:
=6-
237
119
Oun
ce, c
up, p
int,
mea
sure
and
mea
sure
the
capa
city
of a
giv
en c
onta
iner
quar
t,; g
allo
nto
the
near
est w
hole
uni
t.Li
ter
Tim
e10
. Giv
en th
at th
e tim
e is
9:0
0 A
.M. i
nLa
s V
egas
, the
stu
dent
116,
123-
124
Sec
ond,
min
ute,
hou
rca
n na
me
the
time
inD
enve
r, C
hica
go, a
nd N
ew Y
ork.
Yea
r, d
ecad
e, c
entu
ryT
ime
zone
s
CO
NT
EN
T
Wei
ght
Oun
ce, p
ound
, ton
Gro
m
Tem
pera
ture
Fah
renh
eit d
egre
esC
entig
rade
deg
rees
Ang
le Deg
ree
RE
NA
MIN
G M
E/,S
UR
ES
Com
poris
on o
f uni
tsC
onve
rsio
n of
uni
ts
ME
AS
UR
EM
EN
T -
GR
AD
E F
IVE
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
11. T
he s
tuoe
nt c
an n
ame
the
cent
ury
for
a gi
ven
date
.F
or e
xam
ple:
1492
was
in th
e 15
th c
entu
ry.
Usi
ng a
sca
le, t
he s
tude
nt c
an m
easu
re th
e w
eigh
t of
a gi
ver
obje
ct in
who
le a
nd fr
actio
nal p
arts
of u
nits
.
13. U
sing
a th
erm
omet
er c
alib
rate
d in
eith
er F
ahre
nhei
t or
Cen
tigra
de a
egre
es, t
he s
tude
nt c
an r
ead
the
tem
pera
ture
to th
e ne
ares
t deg
ree
and
nam
e th
e fr
eezi
ng a
nd b
oilin
gpo
ints
of w
ater
.
14. U
sing
a p
rotr
acto
r, th
e st
uden
t can
mea
sure
an
angl
e to
the
near
est d
egre
e.
15. T
he s
tude
nt c
an e
xpre
ss th
e re
latio
nshi
ps b
etw
een
units
of
mea
sure
app
ropr
iate
to th
e gr
ade
leve
l and
can
ren
ame
am
easu
re in
oth
er u
nits
.F
or e
xam
ple:
248
hour
s =
10
doys
, 8 h
ours
-=
1 w
eek,
3 da
ys, 8
hou
rs.
AW
253
218-
219
236-
237,
284-
285
If1
inch
=--
2.5
4 ce
ntim
eter
s, th
en 7
inch
es =
cent
imet
ers.
S
117
120
118
118
114-
117,
119-
122,
125-
126
AB
C
11-1
2,15
8-15
9,25
8
ME
AS
UR
EM
EN
T -
GR
AD
E F
IVE
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
AW
SA
BC
CO
MP
UT
AT
ION
S W
ITH
ME
AS
UR
ES
16. T
he s
tude
nt c
an c
ompu
te w
ith m
easu
res
appr
opria
te to
the
236-
237
315
grad
e le
vel,
assi
gn th
e pr
oper
uni
t to
the
resu
lt, a
ndre
nam
e if
nece
ssar
y.F
or e
xam
ple:
2 ft.
5 in
.x
6
12 ft
. 30
in. =
14
ft. 6
in. =
14
1,/2
ft, =
4yd
. 2 ft
. 6 in
.
CO
NT
EN
T
SE
TS
NU
MB
ER
- G
RA
DE
SIX
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
1. G
iven
a li
st o
f fin
ite a
nd in
finite
set
s, th
e st
uden
t can
iden
tify
92,9
91-
2,3-
5,th
ose
whi
ch a
re fi
nite
(th
e se
t of s
tude
nts
in th
e 6t
h gr
ade)
and
6-7
thos
e w
hich
are
infin
ite (
the
set o
f cou
ntin
g nu
mbe
rs).
WH
OLE
NU
MB
ER
S0
- in
finity
2. T
he s
tude
nt c
an d
eter
min
e th
e ca
rdin
alnu
mbe
r of
a g
iven
set
.30
25
3. G
iven
a n
umbe
r, th
e st
uden
t can
iden
tify
the
num
bers
whi
chpr
eced
e an
d fo
llow
it.
4. T
he s
tude
nt c
an id
entif
y an
d na
me
odd
and
even
num
bers
.
5. G
iven
a n
umbe
r gr
eate
r th
an 1
000,
the
stud
ent c
anve
rbal
ize
his
notio
n of
the
quan
tity
invo
lved
.F
or e
xam
ple:
"A
mill
ion
dolla
rsis
hav
ing
a th
ousa
nd d
olla
rs in
eac
h of
a th
ousa
ndba
nks!
"
Prim
e an
d co
mpo
site
6. G
iven
a s
et o
f who
le n
umbe
rs, t
he s
tude
nt c
an c
lass
ify th
em a
s87
,91,
59,6
614
6-14
7,22
5
num
bers
prim
e or
com
posi
te.
98-9
9
7. T
he s
tude
nt c
an e
xpre
ss a
com
posi
te n
umbe
r as
the
prod
uct o
f89
-91,
66-6
814
6-14
7,
prim
e nu
mbe
rs.
For
exa
mpl
e: 2
8 =
2 x
2 x
7.
98-9
917
9-18
0,22
5
Ord
er r
elat
ions
8. G
iven
a s
et o
f who
le n
umbe
rs, t
he s
tude
nt c
an w
rite
them
in o
rder
25-2
6,fr
om le
ast t
o gr
eate
st a
nd v
ice
vers
a.29
8-29
9
9. T
he s
tude
nt c
an w
rite
the
sym
bols
<",
rela
tions
hip
betw
een
num
bers
.
=/ t
oex
pres
sth
e
NU
MB
ER
- G
RA
DE
SIX
CO
NT
EN
T
RA
TIO
NA
L N
UM
BE
RS
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
Rat
io10
. The
stu
dent
can
writ
e th
e ra
tio o
f thr
ee p
enni
es to
four
nic
kels
as
218-
221,
28,1
22,2
6315
8-15
9,3:
20 a
nd/o
r 3/
20, a
nd g
iven
the
sym
bol 4
/9, t
he s
tude
nt c
anex
pres
s it
in w
ords
as
"the
rat
io o
f 4 to
9."
223,
225
267-
275,
289
Indi
cate
d di
visi
on11
. Giv
en a
num
eral
suc
h as
25/
4, th
e st
uden
t dem
onst
rate
s hi
s un
der-
232,
254,
30,1
17_1
2021
3-21
4st
andi
ng o
f the
sym
bol a
s an
indi
cate
d di
visi
on b
y re
nam
ing
it as
260
61/
4 an
d as
6.2
5.
Ord
er r
elat
ions
12. G
iven
a s
et o
f rat
iona
l num
bers
suc
h as
1/8
, .33
2/3,
1/4
,50
,111
,28
,30,
33,
25-2
6,29
,109
,.5
, 7/4
, 5/6
, .75
, and
4/3
, the
stu
dent
can
arr
ange
them
in o
rder
113,
115,
35,3
8,75
,16
0-16
1,25
7-fr
om le
ast t
o gr
eate
st a
nd v
ice
vers
a.17
911
4-11
5,25
8,26
0,30
0-12
1,12
3,19
230
1
INT
EG
ER
SD
irect
ed n
umbe
rs13
. Giv
en th
e nu
mbe
rs +
3, -
3, +
4, -
2, 0
, the
stu
dent
can
gra
ph th
em28
4-28
7,88
-89
308-
310
on th
e nu
mbe
r lin
e,29
5
IRR
AT
ION
AL
NU
MB
ER
S14
. Ask
ed to
def
ine
If th
e st
uden
t sta
tes
that
it is
app
roxi
mat
ely
equa
lto
22/
7 or
3.1
4 ro
unde
d to
the
near
est h
undr
eth.
283
253
94-9
5
NU
ME
RA
TIO
N -
GR
AD
E S
IX
CO
NT
EN
T
NA
ME
S F
OR
NU
MB
ER
S
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
W
1. T
he s
tude
nt c
an id
entif
y, n
ame,
rea
d, a
nd w
rite
man
ydi
ffere
nt n
ames
for
the
sane
num
ber.
For
exa
mpl
e:8
= 8
/1 =
32/
4 =
8.0
0 =
2=
V I
II =
13
= e
tc.
five
S
65
AB
C
WH
OLE
NU
MB
ER
S0
- in
finity
2. T
he s
tude
nt c
an id
entif
y, n
ame,
rea
d, a
nd w
rite
num
eral
s6-
7,26
0fo
r w
hole
num
bers
.U
O1-
2,19
,109
3. G
iven
a fi
fteen
-dig
it nu
mer
al, t
he s
tude
nt c
an r
ead
itan
d w
rite
it in
wor
ds.
120
18-1
9
4. G
iven
a v
erba
l phr
ase
nam
ing
a nu
mbe
r, th
e st
uden
t can
6
writ
e th
e nu
mbe
r w
ords
and
/or
the
Ara
bic
num
eral
.
120
3-4,
19,1
09
Pla
ce v
alue
--pe
rlfif
teen
-dig
it nu
mer
als
5. G
iven
a b
ase
ten
(dec
imal
) nu
mer
al, t
he s
tude
nt c
an1-
7,19
iden
tify
and
nam
e th
e pe
riod
valu
e fo
r ea
ch g
roup
of
120-
121
3-6
thre
e di
gits
and
the
plac
e va
lue
for
each
dig
it.
Exp
ande
d no
tatio
n6.
Giv
en a
num
eral
suc
h as
473
,245
, the
stu
dent
can
writ
e th
e12
153,
225
5-7,
15-1
7,ex
pand
ed n
umer
al in
the
follo
win
g w
ay:
54,2
8547
3,24
5 =
( 4
x 1
00,0
00 )
+ (
7 x
10,
000
) +
( 3
x 1
000
) +
(2x
100
)+(4
x 1
0 )±
(5 x
1).
7. G
iven
a n
umer
al s
uch
as 8
1,43
7, th
e st
uden
t can
writ
e10
-12,
56
the
expa
nded
num
eral
usi
ng e
xpon
entia
l not
atio
n.F
or80
exam
ple:
225
15-1
7,10
5,1-
J9
81,4
37 T
c (
8 x
104
) +
(1
x10
3)
+ (
4 x
102
)=
( 3
x.
101
( 7
x 10
0).
Prim
e fa
ctor
izat
ion
8. G
iven
a n
umer
al fo
r a
com
posi
te n
umbe
r, th
e st
uden
t can
writ
e 89
-91,
9959
,66-
68,
146-
147,
a nu
mer
al w
hich
nam
es th
e nu
mbe
r as
the
prod
uct o
f prim
enu
mbe
rs.
For
exa
mpl
e: 6
0 =
2 x
2 x
3 x
5.
329
179-
180,
225
NU
ME
RA
TIO
N -
GR
AD
E S
IX
CO
NT
EN
T
Rom
an n
umer
als
thro
ugh
M
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
V/
9. G
iven
a n
umer
al s
uch
as 1
,151
, the
stu
dent
can
writ
eth
e
Rom
an n
umer
al M
CLI
.
S
232
AB
C
28,1
48
10. G
iven
a R
oman
num
eral
suc
h as
MC
CX
LV, t
he s
tude
nt c
an w
rite
the
Ara
bic
num
er-7
! 1,2
45.
232
28,1
48
11. G
iven
the
num
eral
s X
XX
and
333
, the
stu
dent
can
des
crib
eth
e di
ffere
nce
betw
een
them
by
sayi
ng:
In th
e R
oman
num
eral
the
"X"
alw
ays
has
the
valu
e of
ten,
but
in th
e de
cim
al n
um-
eral
the
valu
e of
the
"3"
depe
nds
upon
its
plac
e in
the
num
er-
al.
The
refo
re, X
XX
= 1
0 +
10
+ 1
0, b
ut 3
33 =
300
+ 3
0 +
3.
12. G
iven
the
num
eral
CD
LX, t
he s
tude
nt c
an w
rite
the
num
eral
3623
228
,36,
109,
( 50
0 -
100
) +
5r)
+ 1
0.14
8,19
3,34
3
Non
-dec
imal
13. G
iven
a s
et w
ith fr
om 1
to 1
00 m
embe
rs, t
he s
tude
nt c
an g
roup
num
erat
ion-
-ba
se tw
o, fo
ur, f
ive
the
mem
bers
and
writ
e a
base
five
num
eral
for
the
card
inal
14-1
9
num
ber
of th
e se
t.22
8-22
97-
11
14. G
iven
a n
umer
al s
uch
as 1
0110
two,
the
stud
ent c
an w
rite
14-1
9th
e ex
pand
ed n
umer
al in
the
follo
win
g w
ay:
228-
230
8
1011
0tw
o =
(1
x 1
)(
0 x
E3
+ (
1 x
4 )2
+ (
1 x
2 )
+ (
0 x
1 )
and
/or
1011
0tw
o=(1
x2
)+(0
x2
)+(
1 x
2 )+
(1x2
1)+
(0x
2°).
RA
TIO
NA
L N
UM
BE
RS
Com
mon
frac
tions
a/b
15. G
iven
a m
odel
of f
ive-
seve
nths
, the
stu
dent
can
iden
tify,
nam
e,re
ad, a
nd w
rite
a nu
mer
al (
frac
tion)
for
the
ratio
nal n
umbe
r10
2-10
3as
soci
ated
with
the
mod
el,
16. G
iven
a fr
actio
n su
ch a
s 7/
3, th
e st
uden
t can
iden
tify,
nam
e,an
d di
stin
guis
h th
e nu
mer
ator
and
the
deno
min
ator
.
28-3
015
8-16
1
Equ
ival
ent f
ract
ions
17. G
iven
a fr
actio
n su
ch a
s 7
'8, t
he s
tude
nt c
an w
rite
a se
t of
104-
110
29,3
4-38
,16
0-16
1,16
3,
frac
tions
whi
ch a
re e
quiv
alen
t to
7/8.
165-
166,
170-
172,
225
.111
.
CO
NT
EN
T
NU
ME
RA
TIO
N -
GR
AD
E S
IX
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
18. T
he s
tude
nt c
an r
enam
e a
give
n fr
actio
n in
sim
ples
t for
m.
For
exa
mpl
e:12
/32
= 3
/8.
19. G
iven
a m
athe
mat
ical
sen
tenc
e su
ch a
s 4/
9 =
?/1
8 =
32/
?,th
e st
uden
t can
nam
e th
e m
issi
ng n
umer
ator
or
deno
min
ator
.
AN
N
104-
110
S
29,3
4-38
,40
75,7
7
AB
C
160-
161,
163
165-
166,
170-
172,
225
20. G
iven
a s
et o
f fra
ctio
ns s
uch
as 3
/4, 3
/5, 6
/8, 1
8/24
,10
4-10
6,29
,34-
38,
160-
163,
165-
18/3
0, 6
/10,
75/
100,
15/
25, 6
0/10
0, th
e st
uden
tca
n11
5,25
840
-41,
75,
166,
192,
250-
iden
tify
and
nam
e th
e fr
actio
ns w
hich
are
equ
ival
ent.
77,1
2225
1,27
8,28
9,34
0,34
3
Impr
oper
frac
tions
112,
115,
128,
29-3
0,15
9-16
3,16
5,
eiL
1,77
721
. Giv
en a
mod
el s
uch
asLI
1.I
1,
the
stud
ent
and
mix
ed n
umer
als
can
iden
tify,
nam
e, r
ead,
and
writ
e th
e fr
actio
n 7/
4 an
d/or
138-
139,
143,
71-7
2,13
9th
e m
ixed
num
eral
13/
4 fo
r th
e ra
tiona
l num
ber
asso
ciat
edw
ith th
e m
odel
.16
5
22. T
he s
tude
nt c
an r
enam
e an
impr
oper
frac
tion
as a
mix
ednu
mer
al a
nd v
ice
vers
a.F
or e
xam
ple:
25/7
= 3
4/7
and
16
2/3
= 5
0/3.
Dec
imal
frac
tions
- -
23. T
he s
tude
nt c
an id
entif
y, n
ame,
rea
d, a
nd w
rite
deci
mal
228-
233
114-
116
20-
21,3
4,17
2-te
nths
hund
redt
hsnu
mer
als
for
ratio
nal n
umbe
rs n
amed
with
com
mon
frac
tions
havi
ng d
enom
inat
ors
of 1
0,10
0,10
00.
For
exa
mpl
e:1;
3,16
5
thou
sand
ths
ten
thou
sand
ths
hund
red
thou
sand
ths
7 1t
/100
= 7
. 14.
24. G
iven
a n
umer
al s
uch
as 2
3.74
, the
stu
dent
can
writ
e th
eex
pand
ed n
umer
al in
the
follo
win
g w
ay: 2
3.74
= (
2x
10 )
+(
3 x
i)
+ (
7 x
1/1
0 )
+ (
4 x
1 /1
00).
25.G
iven
a n
umer
al s
uch
as 2
,47'
'.630
5, th
e st
uden
t can
rea
d22
9,24
0,26
012
L,19
221
-23,
34,1
64,
it an
d w
rite
it in
wor
ds.
204-
205
CO
NT
EN
T
NU
ME
RA
TIO
NG
RA
DE
SIX
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
26. G
iven
a n
umer
al s
uch
as .1
7856
, the
stu
dent
can
writ
eth
e ex
pand
ed n
umer
al in
the
follo
win
g w
ay:
.178
56 =
1/1
0 +
7/1
00 +
8/1
000
+ 5
/10,
000
+ 6
/100
,000
.
27. G
iven
num
eral
s su
ch a
s .3
3...
and
,5, t
he s
tude
nt c
andi
stin
guis
h be
twee
n re
peat
ing
and
term
inat
ing
deci
mal
frac
tions
.
28. T
he s
tude
nt c
an d
emon
stra
te th
at th
e co
mm
on fr
actio
n2/
3 is
a r
epea
ting
deci
mal
frac
tion.
230-
231,
240
255
255
116-
117,
120,
122
20-2
2,34
,188
,20
2-20
3,20
6
243,
252
Per
cent
not
atio
n29
. The
stu
dent
can
ren
ame
num
eral
s su
ch a
s 47
% a
s .4
726
4-26
9,28
012
3-12
4,23
-24,
109,
and/
or 4
7/10
0.20
8-20
916
5,17
3,19
1,24
6,25
0-25
1,26
6,28
1,34
3
30. G
iven
a s
et o
f num
eral
s su
ch a
s 3/
4, .6
4, 3
2/3
, 26%
,26
8-26
9,28
012
2-12
4,23
-24,
36,1
09th
e st
uden
t can
cla
ssify
them
as
com
mon
frac
tions
,20
8-20
918
8,24
3-24
6,de
cim
ai fr
actio
ns, m
ixed
num
eral
s, o
r pe
rcen
ts,
266,
289,
341
INT
EG
ER
S31
. Giv
en a
num
eral
suc
h as
8, th
e st
uden
t can
nam
e it
asne
gativ
e ei
ght o
r th
e op
posi
te o
f eig
ht.
284-
287,
295
88-8
930
8-31
0
IRR
AT
ION
AL
NU
MB
ER
S32
. The
stu
dent
can
rea
d an
d w
rite
the
sym
boliT
:28
2-28
325
394
-95
OT
HE
R N
OT
AT
ION
Rou
ndin
g33
. Giv
en a
num
eral
suc
h us
3,6
28.7
65, t
he s
tude
nt c
anro
und
it to
the
near
est h
undr
eth,
tent
h, o
ne, t
en, h
undr
ed,
and
thou
sand
.
8-9,
241,
248
204,
226
210-
211,
225
NU
ME
RA
TIO
N -
GR
AD
E S
IX
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
AW
SA
BC
Exp
onen
tial n
otat
ion
34. T
he s
tude
nt c
an w
rite
expa
nded
num
eral
s us
ing
expo
nent
ial
nota
tion
(see
obj
ectiv
es#
7 an
d 14
).10
-12
222-
223
34
35. G
iven
a n
umer
al s
uch
as35
, the
stu
dent
can
rena
me
it as
19,5
6,96
65,2
22-2
2310
5
(3x3
x3x3
x3)o
r 24
3.
36. G
iven
the
num
eral
s23
and
( 2
x 3
), th
e st
uden
t can
dis
tingu
ish
betw
een
them
and
sta
te th
at th
ey c
lo n
ot n
ame
the
sam
enu
mbe
r!65
,223
Sci
entif
ic n
otat
ion
37. T
he s
tude
nt c
an r
enam
e ci
giv
en n
umer
al u
sing
sci
entif
ic13
,257
225,
227
nota
tion.
For
exa
mpl
e93
,000
,000
= 9
.3 x
10'a
nd 3
4,58
9 =
3.4
589
x10
4.
CO
NT
EN
T
WH
OLE
NU
MB
ER
S
Add
ition
and
Sub
trac
tion
Inve
rse
rela
tions
hip
Bas
ic fa
cts
Thr
ough
sum
s of
18
Pro
pert
ies
Com
mut
ativ
e an
das
soci
ativ
e pr
oper
ties
of a
dditi
on
Iden
tity
elem
ent
for
addi
tion
Alg
orith
ms
Col
umn
addi
tion
and
subt
ract
ion
Oth
er n
otat
ion
OP
ER
AT
ION
SG
RA
DE
SIX
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
(Rev
iew
and
mai
ntai
n co
ncep
ts a
nd s
kills
.)
1. T
he s
tude
nt c
an s
olve
add
ition
or
subt
ract
ion
prob
lem
s w
ithm
issi
ng s
ums,
diff
eren
ces,
or
adde
nds.
For
exa
mpl
e:
+45
,987
=6,
000,
001
and
-500
,800
=1,
333,
708
2. T
he s
tude
nt c
an c
liPrk
sub
trac
tion
prob
lem
s by
add
ition
.
3. G
iven
any
sin
gle-
digi
t add
ition
or
subt
ract
ion
com
bina
tion,
the
stud
ent c
an im
med
iate
ly*n
ame
the
sum
or
diffe
renc
e.
4. G
iven
an
addi
tion
prob
lem
with
thre
eor
mor
e ad
dend
s, th
est
uden
t can
dem
onst
rate
how
to fi
nd th
esu
m in
the
easi
est
way
by
rena
min
g an
d re
arra
ngin
g th
e ad
dend
s.
5. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as 3
905
+=
390
5;54
77 -
5477
±;
0 =
- 38
0,35
7; a
nd8,
777,
300
=-
0,
6. G
iven
any
"re
ason
able
" ad
ditio
nor
sub
trac
tion
prob
lem
, the
stud
ent c
an n
ame
the
sum
or
diffe
renc
:2,
7. T
he s
tude
ntca
n id
entif
y an
d na
me
sum
s, d
iffer
ence
s, m
issi
ngod
oend
s, m
issi
ng d
igits
, and
mis
sing
ope
ratio
nal
sign
s in
c,ro
blem
s w
ritte
n in
bot
l, ho
rizon
tal a
nd v
ertic
alno
tatio
n.
imm
id!-
e; y
308
26 26, 4
1
34, 1
26
258
S 19 13,
148
-i49
14-1
7,25
-26,
330
23
35, 4
0, 4
418
-19,
46: L9,
2641
,H
4,51
55; .
8719
140:
2,
310-
311
12
AB
C
113-
114
115,
118
12, 1
4,42
-43,
115
39-4
1,H
O,
116-
117,
292-
293,
319
32, 2
93
29, 3
43L
,
44,
61, 6
5-66
69-7
2,10
5-10
6,11
8-1.
Y0,
123-
126
134,
152
,22
.:)
CO
NT
EN
T
OP
ER
AT
ION
S-
GR
AD
E S
IX
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
Mul
tiplic
atio
n an
d D
ivis
ion
(Rev
iew
and
mai
ntai
n co
ncep
ts a
nd s
kills
.)
AW
SA
BC
Inve
rse
rela
tions
hip
8. T
he s
tude
nt c
an s
olve
mul
tiplic
atio
nor
div
isio
n pr
oble
ms
27, 3
0812
0-12
1w
ith m
issi
ng p
rodu
cts,
quo
tient
s, o
r fa
ctor
s.F
or e
xam
ple:
x 31
7 =
1,5
95,1
44an
d-;
23
= 1
1,77
6
9. T
he s
tude
nt c
an c
heck
div
isio
n pr
oble
ms
by m
.ulti
plic
atio
n(w
ithou
t rem
aind
er)
or b
y m
ultip
licat
ion
and
addi
tion
(with
rem
aind
er).
(Not
e: S
ee o
b'oc
tive
# 18
.)
Bas
ic fa
cts
Thr
ough
pro
duct
s of
10. G
iven
any
sin
gle-
digi
t mul
tiplic
atio
nor
div
isio
n co
mbi
natio
n,81
the
stud
ent c
an im
med
iate
Iy*n
ame
the
prod
uct
or q
uotie
nt.
Pro
pert
ies
Com
mut
ativ
e an
das
soci
ativ
e pr
oper
ties
of m
ultip
licat
ion
elem
ent
for
mul
tiplic
atio
n
11. G
iven
a m
u,.,p
licat
ion
prob
lem
with
two
or m
ore
fact
ors,
the
stud
ent c
an d
emon
stra
te h
ow to
find
the
prod
uct i
n th
eea
sies
t way
by
rear
rang
ing
the
fact
ors.
For
exa
mpl
e:
4 x
359
x 25
= (
4 x
25
) x
359
=10
0x
359
35,9
00
12. T
he s
tude
nt c
an c
heck
mul
tiplic
atio
n pr
oble
ms
byre
vers
ing
the
orde
r of
the
fact
ors
and
mul
tiply
ing
agai
n.
13. T
he s
tude
ntca
n so
lve
equa
tions
suc
h as
1 x
896
7 -=
555
x=
555
; 89,
453
89,4
53 =
;34
9 ;
= 3
49;
and
870
= 8
70 x
* im
med
iate
,- is
def
ined
as
5 se
cond
s c-
- L-
ss.
22-2
5, 3
0-32
,13
, 41,
51
308
152-
153
34-3
5, 1
2614
-17,
48-4
925
-26,
54-5
633
0
36 3424
294
CO
NT
EN
T
OP
ER
AT
ION
SG
RA
DE
SIX
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
Mul
tiplic
ativ
e pr
oper
ty 1
4. T
he s
tude
nt c
an s
olve
equ
atio
nssu
ch O
E 7
320
x 0
=
of 0
0=x
4900
; 0 ;
685
--=
;0
x 1=
;an
d
15. G
iven
a d
ivis
ion
prob
lem
suc
h as
15
7. 0
=ti-
e st
uden
t can
27
dem
onst
rate
that
the
prob
lem
has
no
solu
tion
uy u
sing
rep
eate
dsu
btra
ctio
n cn
d/or
the
inve
rse
rela
tions
hip.
RE
PE
AT
ED
SU
BT
RA
CT
ION
INV
ER
SE
RE
LAT
ION
SH
IP
0 )
150
1
-15
- 0
3
15 025
15 etc.
etc.
etc.
0no
num
ber
beca
use
no n
umbe
r x
0 =
15
'73
A3C
Dis
trib
utiv
e pr
oper
tyof
mul
tiplic
atio
n ov
erad
ditio
n
16. G
iven
a p
robl
em s
uch
cs 5
3 x
624
=,
the
stud
ent
22-2
5, 2
S-2
935
, 38-
29LC
:,14
0.. 1
65
20-2
2,zu-,
-,
-Lo.
146,
148-
149
50-5
1,::.
-718
122
:-:';
eo-
297
.:an
dem
onst
rate
his
und
erst
andi
ngof
the
dist
ribut
ive
prin
cipl
e by
Inul
tiply
inc
in e
xpan
ded
horiz
onta
l for
m.
For
exa
mpl
e:
53 x
624
=(
50 +
3)
x62
4
=50
x 6
24)
(3
x 62
4 )
31,2
00÷
1872
33,0
72
Per
im
Are
a-5g
rela
ted
tle
ngth Rec
taP
aral
l
Vol
ume-
rela
ted
tle
ngth Liqu
i 0 Li
Tim
e Sec
o
Yea
Tim
e
CO
NT
EN
T
Ala
ori
ms
vert
nota
tion
divi
sion
OP
ER
AT
ION
S-
GR
AD
E S
IX
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
17. G
iven
any
"re
ason
able
" m
ultip
licat
ion
prob
lem
, the
stud
ent c
an n
ame
the
prod
uct.
18. G
iven
any
"re
ason
able
" di
visi
onpr
oble
m, t
he s
tude
nt
A
33, 5
1-53
82, 9
6, 1
84,
238,
311
18, 5
5,,
113,
151
,21
3
AE
C
29, 6
6,
can
nam
e th
e qu
otie
nt in
bot
h of
the
follo
win
gw
ays:
60-6
5, 7
0 -7
315
4-15
7,12
4;32
, 96,
224
,15
2, 1
591,
10-1
33,
238,
313
165,
191
,13
8-13
9,29
R 1
1an
d29
265,
328
141;
14S
23 )
678
23 -
j678
4646
218
218
207
207
1111
Che
ck :
( 23
x 2
9 )
+11
= 6
7823
x 2
9=
678
Sho
rt d
ivis
ion
19. G
iven
any
" r
easo
nabl
e"di
visi
on p
robl
em w
itha
sing
le-
61; 1
71,
1912
1di
git d
ivis
or, t
he s
tude
ntca
n us
e th
e sh
ort a
lgor
ithm
309
(sho
rt d
ivis
ion
form
) to
nam
e t:l
e qu
otie
nt a
nd r
emai
nder
.
Oth
er n
otat
ion
20. T
he s
tude
ntca
n id
entif
y an
d na
me
prod
ucts
, quo
tient
s,m
issi
ng fa
ctor
s, m
issi
ng d
igits
,an
d m
issi
ng o
p9ra
tiona
lsi
gns
in p
robl
ems
writ
ten
in b
oth
horiz
onta
l and
ver
tical
nota
tion.
12
Oth
er O
erat
ions
Ave
ragi
rr:::
21. G
iven
a se
t of n
umbe
rs s
uch
as 9
8, 7
5, 8
3, 1
00,
and
79, t
he s
tude
ntca
n na
me
the
aver
age
(arit
hmet
ic m
ean)
of th
e nu
mbe
rs.
66-6
7, 9
6,31
4
Wei
ght
Oun
cG
ram
Tem
pera
Fah
re
Cen
t
Ang
le Deg
n
RE
NA
M
Com
pari
Con
yers
OP
ER
AT
ION
SG
RA
DE
SIX
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
Gre
ates
t com
mon
fact
or22
. Giv
en a
set
of n
umbe
rs s
uch
as 2
8, 5
6,70
, and
126
, the
(gre
ates
t com
mon
div
isor
)st
uden
t can
lam
e th
e gr
eate
st c
omm
on fa
ctor
of th
e nu
mbe
rs.
Leas
t com
mon
mul
tiple
23. G
iven
a s
et o
f num
bers
suc
h as
12,
15,
35, a
nd 3
6, th
e
(leas
t com
mon
den
omin
ator
)st
uden
t can
nam
e th
e le
ast c
omm
onm
ultip
le o
f the
num
bers
.
Exp
onen
tiatio
n24
. Giv
en a
pro
blem
suc
h as
53=
,th
e st
uden
t can
iden
tify
A W
93, 9
9
94-9
5, 9
9,10
6, 1
22-
123
11, 1
9, 5
6,82
, 96,
311
119
S
58, 6
8, 7
7,11
3, 2
81,
328
61, 6
8,28
1, 3
28
65-6
7,22
2-22
5;26
5, 3
22
AB
C
179-
181
and
nam
e th
e ba
se, e
xpon
ent,
and
pow
er.
For
exa
mpl
e:
53=
125
5is
the
base
.3
is th
e ex
pone
nt12
5 is
the
third
pow
er o
f 5.
RA
TIO
NA
L N
UM
BE
RS
Add
ition
and
Sub
trac
tion
Def
initi
on25
. Giv
en a
n ad
ditio
n or
sub
trac
tion
prob
lem
suc
h as
(fra
ctio
ns w
ith li
ke a
nd2/
3 +
3/4
=or
2 5
r6 -
11/
2 =
,th
e st
uden
t can
unlik
e de
nom
.3to
rs)
dem
onst
rate
how
to fi
nd th
e su
m o
r di
ffere
nce
by u
sing
a
regi
on o
r nu
mbe
r lin
e m
odel
.
Inve
rse
rela
tions
hip
26. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as:
3/4
+=
7/8
2 2/
3 -
=5/
6
+ 3
/5=
12/
7-
3/4
11/
2
CO
MP
U
CO
NT
EN
T
Pro
pert
ies
Com
mut
ativ
e an
das
soci
ativ
e pr
oper
ties
of a
dditi
on
Iden
tity
elem
ent f
orad
ditio
n(0
= 0
/1 =
0/2
= 0
/3.
Alg
orith
ms
Fra
ctio
n no
tatio
nlik
e an
d un
like
deno
min
ator
s
Mix
ed n
umer
als
Dec
imal
not
atio
n(in
clud
ing
mon
ey)
OP
ER
AT
ION
SG
RA
DE
SIX
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
27. G
iven
an
addi
tion
prob
lem
with
thre
e or
mor
e ad
dend
s, th
est
uden
t can
dem
onst
rate
how
to fi
nd th
e su
m in
the
easi
est
way
by
resu
min
g an
d re
arra
ngin
g th
e ad
dend
s.F
or e
xam
ple:
7/8
+ 2
/3 +
5/8
+ 1
5/6
= (
7/8
+ 5
/8 )
+ (
4/6
+ 1
5/6
) =
1
28. T
he s
tude
nt c
an c
heck
sub
trac
tion
prob
lem
s by
add
ition
.
29. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as 1
/2 +
0/8
=-
4/7
= 0
; 0/7
+ 0
/10
=)
;an
d-
0//2
= 7
/15.
30. T
he s
tude
ni c
an n
ame
the
sum
s an
d di
ffere
nces
(as
frac
tions
in lo
wes
t ter
ms
and,
/or
as m
ixed
num
eral
s) fo
r pr
oble
ms
such
as:
3/7
+ 8
/9 +
13/
18 =
5/9
- 1/
4 =
31. T
he s
tude
rt c
an n
ame
the
sum
s an
d di
ffere
nces
(as
frac
tions
inlo
wes
t ter
ms
and/
or a
s m
ixed
num
eral
s) fo
r pr
oble
ms
such
as:
1'2
7 1/
4 =
73/
127
1/4
= 7
3/1
2 =
6 1
5 12
+ 4
2/3
= 4
8/12
- 4
2/3
= 4
8/1
2 =
48.
1211
111
22
7 12
32. G
iven
any
"re
ason
able
" ad
ditio
n or
sub
trac
tion
prob
lem
the
stud
ent c
an n
ame
the
sum
or
diffe
renc
e.
AW
126,
130
134,
142
,15
0-15
1
-1 -
1 1/
2 =
4
318
118-
121,
124-
125,
128-
132,
142-
143,
152,
165
131,
165
,18
1
49, 8
2, 2
34,
294,
314
,32
]
SA
BC
303,
320
31, 4
0,30
269
, 76,
73, 8
7,99
, 151
70-7
1, 7
3- 1
76-1
77,
74, 7
9-80
, 182
, 184
,86
, 113
,19
0, 1
92,
167,
190
,22
9, 2
60,
265,
28]
,31
432
9
116-
119,
45-4
6, 6
1-12
1, 1
25,
65, 7
1-72
,22
1, 2
33,
is.5
-106
,28
1, 3
13,
110,
135
-32
813
7, 1
52-
153,
176
-17
8, 1
82,
134,
190
,26
0,
SE
TS
WH
OLE
0- Prim
nurn
Ord
r.
CO
NT
EN
T
Mul
tiplic
atio
n an
d D
ivis
ion
Def
initi
on o
fm
ultip
l ica
tion oF
div
isio
n
OP
ER
AT
ION
SG
RA
DE
SIX
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
BC
33. G
iven
mul
tiplic
atio
n pr
oble
ms
such
as
2/3
x 3/
4 =
146-
148
176-
178
and
4 x
3/8
=,
the
stud
ent c
an d
emon
stra
te h
owto
find
the
prod
ucts
by
usin
g re
gion
s or
a n
umbe
r lin
e.F
or e
xam
ple:
3/4
0
2/3
of 3
/zi =
6/1
2 r
1. '2
)1
t1
III
12
4x, 8
121
1
Gi e
n a
divi
sion
equ
atio
n su
ch a
s 12
1.;
:;tud
ent c
an w
rite
and
scIv
e tn
ero
LIH
iplic
c-H
on
edua
t ion
,x
4,7
- 12
14.
16 -
-i;0
RA
TIO
NR
atic
Indi
c
Ord
INT
EG
ED
ire
IRR
AT
IC
CO
NT
EN
T
Inve
rse
rela
tions
hip
OP
ER
AT
ION
S -
GR
AD
E S
IX
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
35. G
iven
a m
odel
(re
gion
or
num
ber
line)
for
the
divi
sion
of
two
ratio
nal n
umbe
rs, t
he s
tude
nt c
an d
eter
min
e an
d na
me
the
quot
ient
.F
or e
xam
ple:
2/3
,,t/ t
..tl)
1/2
2/3
: 1/2
=
Look
at t
he m
odel
Thi
nk!
x 1/
2 =
2/3
11/
3 x
1/2
= 2
/31/
2
01
2/3
)
1/2
7:-
2/3
=T
hink
!x
2/3
= 1
/2
Look
at t
he m
odel
!3/
4 x
2/3
= 1
/2
36. T
he s
tude
ntca
n so
lve
equa
tions
suc
h as
:
1/3
x=
2/1
52/
73/
4
x 3/
8 =
5/9
.; 1/
5 =
4/1
1
AW
SA
BC
148
176
CO
NT
EN
T
Pro
pert
ies
Com
mut
ativ
e an
das
soci
ativ
e pr
oper
ties
of m
ultip
licat
ion
X
Iden
tity
elem
ent
for
mul
tiplic
atio
n(
1 =
1/1
= 2
/2 =
3/3
.. )
OP
ER
AT
ION
S -
GR
AD
E S
IX
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
37. T
he s
tude
nt c
an s
olve
equ
atio
ns s
uch
as:
1/2
x 3/
4=
3/4
x
( 1/
2 x
3/4
) x
4/7
= 1
/2 x
( 3
/4x
38. G
iven
a m
ultip
licat
ion
prob
lem
with
two
or m
ore
fact
ors,
the
stud
ent c
an d
emon
stra
te h
ow to
find
the
prod
uct i
nth
e ea
sies
t way
by
rear
rang
ing
the
fact
ors,
For
exa
mpl
e:
_/4
/X /.
2,_
id/
/.2as
- A
' 16
36'
/639
. The
stu
dent
can
sol
ve e
quat
ions
suc
h as
:
5/5
x 3/
7 =
5/6
13/1
3=
"r(
3/4
x=
3/4
2/3
2'1
40. T
he s
tude
nt c
an d
emon
stra
te h
ov, t
o re
nam
e a
give
n fr
actio
nsu
ch a
s 2,
/3 b
y m
ultip
lyin
g by
som
e na
me
for
the
iden
tity
elem
ent.
For
exa
mpl
e:
2/3
x 2/
2 =
4/6
2/3
x 3/
3 =
6/ 9
2/3
x 4/
4 =
8/1
9
15i.)
-151
,15
3-15
418 1
SO
Ais
:C
305
211-
213
Rom
(
thro
Nor
num
baSE
RA
T I
OI
Cor
a/b
Eqt
.,
wJ
OP
ER
AT
ION
S-
GR
AD
E S
IX
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
AW
AB
C
Mul
tiplic
ativ
e in
vers
es 4
1. G
iven
a s
et o
f rat
iona
l num
bers
suc
has
2/3
, 4, 7
/4, 1
,15
618
016
6-16
8(r
ecip
roca
ls)
and
0, th
e st
uden
t can
nam
e th
eir
mul
tiplic
ativ
e in
vers
es21
1-21
3(r
ecip
roca
ls)
and
dem
onst
rate
that
the
prod
uct o
fan
y-7
La.
-v
ratio
nal n
umbe
r an
d its
rec
ipro
cal i
s 1.
For
exa
mpl
e:
2/3
x 3/
2 =
14x
1/4
= 1
7/4
x 4/
7 =
1
1 x
1 =
10
x?
=1
0 ha
s nc
rec
ipro
cal
.
Mul
tiplic
ativ
e42
. The
stu
dent
can
sol
ve e
quat
ions
suc
has
:pr
oper
ty o
f 0(0
= 0
/1 =
0/2
= 0
/3. ;
.)2/
3 x
= 0
/50
= 2
/3 =
4/5
x 0/
13 x
9/1
7 =
43. T
he s
tude
nt c
an d
emon
stra
te th
at 0
/0 d
oes
not
nam
e a
23un
ique
rat
iona
l num
ber.
For
exa
mpl
e:
00
= 0
00
= 3
sinc
e0
x 0
= 0
sinc
e3
x 0
= 0
0 it
0 -=
17,
/35
sinc
e17
/35
x 0
=-
0
Dis
trib
utiv
e pr
oper
ty44
. Giv
en a
pro
blem
suc
h as
5 1
/2 x
3 =
,th
e st
uden
tof
mul
tiplic
atio
n ov
erca
n de
mon
stra
te h
is u
nder
stan
ding
of t
he d
istr
ibut
ive
addi
tion
prin
cipl
e by
mul
tiply
ing
in h
oriz
onal
form
.F
or e
xam
ple:
51 2
x 3
( 5
+ 1
/2 )
x 3
=(
5 x
3 )
( 1/
2 x
3 )
1 5
+ 1
12
161/
2
160,
180
20-2
212
2-12
318
729
6
CO
NT
EN
T
Alg
orith
ms
Fra
ctio
n no
tatio
n
OP
ER
AT
ION
SG
RA
DE
SIX
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
Mul
tipl ;
catio
n45
.T
he s
tude
nt c
an n
ame
the
prod
ucts
(as
frac
tions
in lo
i est
149,
152-
82-8
4,19
5-19
9,te
rms)
for
prob
lem
s su
ch a
s 14
/15
x 12
/35
=an
d15
4,15
6-86
,21
57/
5 x
15/1
8 x
10/2
1 =
and
use
the
redu
cing
157,
166,
178-
180
shor
tcut
whe
re a
ppro
pria
te (
see
obje
ctiv
e #
38 fo
r ju
stifi
-18
1,22
4,ca
tion)
.F
or e
xam
ple:
318
S--
-P
erc
46.
The
stu
dent
can
nam
e th
e pr
oduc
ts (
as fr
ac' i
ons
in lo
wes
t15
8-16
0,84
-85,
199-
202,
term
s m
id/o
r as
mix
ed n
umer
als)
for
prob
lem
s su
ch a
s18
0-18
1,18
2,23
1,31
6,
C.:
31
/2 x
4/7
=an
d 7
2/3
x 5
1/8
=by
ren
amin
g as
18.0
,318
186-
187,
341
impr
oper
frac
tions
and
/or
by a
pply
ing
the
dist
ribut
ive
prin
cipl
e.19
0,32
9
Div
isio
n47
.T
he s
tude
nt c
an n
ame
the
quot
ient
s (a
s fr
actio
ns in
low
est t
erm
s16
7-17
0,18
3-18
521
5,23
2,an
d 'o
r as
mix
ed n
umer
als)
for
prob
lem
s su
ch a
s 3.
'.5 =
7.'8
=18
6,31
926
.J, 2
65IN
TE
GE
For
exa
mpl
e:
33
75
157
e6 7
.5-
7
X -
7
3 57
3.6
IRR
AT
IC
OT
HE
R Rou
OP
ER
AT
ION
SG
RA
DE
SIX
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
SA
BC
48. T
he s
tude
nt c
an n
ame
the
quot
ient
s (a
s fr
actio
ns in
low
est
term
s an
d/or
as
mix
ed n
umer
als)
for
prob
lem
s su
ch a
s3
1/2
7. 4
/7 =
and
7 2/
3 7.
5 1
/8 =
-by
ren
amin
gas
impr
oper
frac
tions
and
div
idin
g.
Dec
imal
not
atio
n(in
clud
ing
mon
ey)
49. T
he s
tude
nt c
an n
ame
the
prod
ucts
and
quo
tient
s fo
r pr
oble
ms
such
as:
21,0
725
) 43
.75
x 8.
4
(Not
e:In
div
isio
n pr
oble
ms,
use
onl
y w
hole
num
ber
divi
sors
.)
Per
cent
not
atio
n50
. The
stu
dent
can
nam
e th
e pr
oduc
ts, q
uotie
nts,
and
mis
sing
fact
ors
for
prob
lem
s su
ch a
s:
25 %
of 1
60
56 x
0/0
7
x 50
% =
346
INT
EG
ER
S
Add
ition
and
Sub
trac
tion
Def
initi
on o
f add
ition
51. G
iven
a n
umbe
r lin
e m
odel
for
the
addi
tion
oftw
o in
tege
rs, t
hest
uden
t can
det
erm
ine
and
nam
e th
esu
m.
For
exa
mpl
e:32
3
168,
170,
319
186
215-
217,
316,
341,
344
76-7
7,82
,16
6,19
2-34
,105
-24
2 -2
45,
202,
205-
106,
139,
248-
251,
256,
207,
212,
141-
142,
260,
294,
281,
313,
202-
206,
321-
323,
325
322-
323,
218-
223,
328
231-
232,
263,
288,
341
273,
276-
277,
209-
210,
207,
247,
280-
281,
324
281:
313,
255-
257,
322
263,
341
286-
290
90,9
9,31
1-31
2
1-1g
1.14
4I
32
-10
12
34
56
7
6+ -
8 =
CO
NT
EN
T
OP
ER
AT
ION
SG
RA
DE
SIX
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
52. G
iven
an
addi
tion
prob
lem
suc
h as
-5
+ 1
3-=
286,
289,
the
stud
ent c
an n
ame
the
sum
and
dem
onst
rate
how
295
to fi
nd th
e su
m b
y us
ing
a nu
mbe
r lin
e.
Def
initi
on o
f53
. Giv
en a
sub
trac
tion
equa
tion
such
as
23
=su
btra
ctio
nth
e st
uden
t can
writ
e an
d so
lve
the
rela
ted
addi
tion
equa
tion,
+3
=2.
For
exa
mpl
e:
-2 -
-3
=
1 +
-3
= -
2
-3 -
2 -1
01
23
290-
291,
91,3
2329
5
W Ad
Inv
BaE
Prc
Al;
CO
NT
EN
T
GE
OM
ET
RIC
FIG
UR
ES
Pla
ne fi
gure
s(a
s se
ts o
f poi
nts)
Poi
ntP
ath
(cur
ve)
Line
4-A
rfLi
ne s
egm
ent
Ar
Ray
--K
g
Ang
le (
vert
ex)
L A
BC
Rig
ht a
ngle
Pol
ygon
(ve
rtic
es)
Tria
ngle
AB
C
Rig
ht tr
iang
leQ
uadr
ilate
ral=
AB
CD
Par
alle
logr
amS
quar
eR
ecta
ngle
Rho
mbu
s
Pen
tago
nH
exag
onO
ctag
on
GE
OM
ET
RY
- G
RA
DE
SIX
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
1. T
he s
tude
nt c
an d
escr
ibe
a gi
ven
plan
e fig
ure
as a
set o
f poi
nts.
For
exa
mpl
e:
A p
enta
gon
is th
e se
t of p
oint
s in
a s
impl
ecl
osed
cur
ve c
ompo
sed
of th
e un
ion
of fi
velin
e se
gmen
ts.
2. G
iven
mod
els
of th
e pl
ane
figur
es n
amed
on
the
left
(wire
, pap
er o
r fla
nnel
cut
outs
, pen
cil o
r ch
alk
outli
nes,
etc
.), t
he s
tude
nt c
an id
entif
y, n
ame,
and
dist
ingu
ish
amon
g th
em.
3. T
he s
tude
nt c
an r
ead
and
writ
e st
anda
rd n
otat
ion
for
the
plan
e fig
ures
nam
ed o
n th
e le
ft.(N
ote:
See
illu
stra
tion
of n
otat
ion
besi
de n
ames
on
the
left.
)
Circ
le Cen
ter
0R
adii
TO
- an
d W
5'D
iam
eter
EP
Cho
rd-"
ZA
rcC
ircum
fere
nce
AW
SA
BC
188-
189
10,
73-7
5,11
123
4-23
5,23
8-23
9,24
2-24
5
192-
193,
45,5
0,75
,80,
209
224,
84-8
7,10
7,30
6-30
711
2,15
1
192,
206-
4278
207,
213
CO
NT
EN
T
Spa
ce fi
gure
s(a
s se
ts o
f poi
nts)
Poi
ntP
lane
Pol
yhed
ron
Pris
m.
Pyr
amid
Sph
ere
Hem
isph
ere
Cyl
inde
rC
one
Par
ts o
f spa
ce fi
gure
sV
erte
xE
dge
Late
ral s
urfa
ce (
face
)B
ase
Alti
tude
(he
ight
)
PR
OP
ER
TIE
S
Par
alle
l lin
esIn
ters
ectin
g lin
esP
erpe
ndic
ular
line
s
GE
OM
ET
RY
- G
RA
DE
SIX
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
4. T
he s
tude
nt c
an d
raw
and
nam
e a
set o
f poi
nts
satis
fyin
ggi
ven
cond
ition
s.F
or e
xam
ple:
The
set
of a
ll po
ints
in s
pace
one
inch
from
a g
iven
line
is a
(n)
(cyl
inde
r)
5. T
he s
tude
nt c
an d
escr
ibe
a gi
ven
spac
e fig
ure
as a
set
of p
oint
s.F
or e
xam
ple:
A s
pher
e is
the
set o
f poi
nts
one
inch
from
agi
ven
poin
t in
spac
e.
6. G
iven
mod
els
of th
e sp
ace
figur
es n
amed
on
the
left
(woo
d or
pla
stic
sol
ids,
pap
er m
odel
s, s
ketc
hes,
etc
.),
the
stud
ent c
an id
entif
y, n
ame,
and
dis
tingu
ish
amon
g th
em.
7. G
iven
a s
et o
f spa
ce fi
gure
s, th
e st
uden
t can
iden
tify
and
nam
e th
e va
rious
par
ts o
f eac
h as
pla
ne fi
gure
s.F
or e
xam
ple:
The
late
ral s
urfa
ces
(fac
es)
of a
rig
ht r
ecta
ngul
arpr
ism
are
rec
tang
les.
The
bas
es o
f a c
ylin
der
are
circ
les.
8. T
he s
tude
nt c
an s
ketc
h, d
escr
ibe,
and
giv
e ex
ampl
es o
fpa
ralle
l, in
ters
ectin
g, a
nd p
erpe
ndic
ular
line
s.(N
ote:
See
obj
ectiv
es #
5, #
6, #
7, f
or G
rade
Fiv
efo
r ex
ampl
es.)
an O
MN
M M
apl
iNw
or
AW
188-
189,
209-
210,
212
SA
BC
104-
108,
9829
6-30
0,33
0-33
1
190-
191,
4420
8
210,
213
296
199,
202-
126
205,
207,
213
1 98 100
79,8
1,85
,
CO
NT
EN
T
Per
imet
er
Are
a
Vol
ume
GE
OM
ET
RY
GR
AD
E S
IX
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
9. T
he s
tude
nt c
an s
tate
and
app
ly a
rul
e fo
r de
term
inin
g th
e20
-21,
9639
88-8
9,97
,pe
rimet
er o
f any
pol
ygon
.F
or e
xam
ple:
The
per
imet
er11
2,19
0,of
a p
olyg
on is
equ
al to
the
sum
of t
he le
ngth
s of
its
side
s.31
7,34
5
10. G
iven
a c
ircle
(w
ith a
who
le n
umbe
r di
amet
er)
and
usin
g20
254
94-9
6,a
rule
r, s
trin
g, c
utou
ts, e
tc.,
the
stud
ent c
an d
eter
min
e28
2-28
322
7-22
8th
e ra
tio o
f the
circ
umfe
renc
e (p
erim
eter
) to
the
diam
eter
.
11. T
he s
tude
nt c
an s
tate
and
app
ly a
rul
e fo
r de
term
inin
g th
ear
ea o
f any
par
alle
logr
am.
For
exa
mpl
e: T
he a
rea
of a
para
llelo
gram
is e
qual
to th
e le
ngth
of t
he b
ase
mul
tiplie
dby
(th
e le
ngth
of)
the
altit
ude.
12. T
he s
tude
nt c
an d
emon
stra
te th
at th
e rr
reof
is e
qual
to o
ne-h
alf o
f the
leng
th o
f the
bas
e m
ultil
ied
by(t
he le
ngth
of)
the
altit
ude.
For
exa
mpl
e:
42-4
3,96
,10
090
-92,
97,
126
112,
229,
317,
346
916-
217
255-
258
`i3-9
4111
2
13. U
sing
uni
t cub
es, t
he s
tude
ntca
n de
mon
stra
te h
ow to
det
erm
ine
the
84-8
5,10
4-10
77O
2-10
396
,326
volu
me
of a
giv
en r
ight
rec
tang
ular
pris
m.
14T
he s
tude
nt c
an s
tate
and
app
ly a
rul
e fo
r de
term
inin
g `H
e. v
olum
e of
8410
4-10
510
1,an
y rig
ht r
ecta
ngul
ar p
rism
.F
or e
xam
ple:
The
vol
ume
of a
rig
ht10
3-10
4.re
ctan
gula
r pr
ism
is e
qual
to th
e ar
ea o
f the
bas
e rn
ulti;
Dlie
d by
112,
264
the
altit
ude.
CO
NT
EN
T
Con
grue
nce
GE
OM
ET
RY
- G
RA
DE
SIX
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
15. G
iven
a p
air
of li
ne s
egm
ents
, ang
les,
tria
ngle
s, o
r ot
her
poly
gons
, the
stu
dent
can
iden
iify
the
pairs
as
cong
ruen
tor
not
con
grue
nt b
y m
atch
ing
the
figur
es in
som
e m
anne
r(t
race
and
ove
rlay,
cut
outs
, etc
.).
16. T
he s
tude
nt c
an u
se th
e sy
mbo
l = to
exp
ress
the
rela
tions
hip
betw
een
cong
ruen
t fig
ures
.
17. T
he s
tude
nt c
an d
istin
guis
h be
twee
n eq
ual a
nd c
ongr
uent
figu
res.
zF
or e
xam
ple:
X
P
18. G
iven
two
cong
ruen
t tria
ngle
s, th
e st
uden
t can
nam
e th
e pa
irsof
con
grue
nt li
ne s
egm
ents
and
the
pairs
of c
ongr
uent
ang
les.
<A
BC
= <
YB
X
< A
BC
:-=
-7 <
ZIP
Sym
met
ry19
. The
stu
dent
can
dra
w li
nes
of s
ymm
etry
for
give
n pl
ane
figur
es-
if th
ey e
xist
.F
or e
xam
ple:
2 lin
es4
I ine
sN
o lin
es
AB
C
1 94
-1
96,
43,4
777
-78,
79,
197,
213
151,
194
194-
197
43
195-
-7,
4320
4-20
5,21
3
197
81-8
3
301-
312,
322-
323
CO
NT
EN
T
CO
NS
TR
UC
TIO
NS
Cop
y: Line
seg
men
tA
ngle
Tria
ngle
Ang
le b
isec
tor
Per
pend
icul
ar b
isec
tor
of a
line
seg
men
t
Per
pend
icul
ar to
a l
ine
at a
poi
nt o
f the
line
Per
pend
icul
ar to
a li
nefr
om a
poi
nt n
ot o
n th
elin
e
Line
par
alle
l to
agi
ven
line
Circ
le
GE
OM
ET
RY
- G
RA
DE
SIX
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
20. U
sing
a s
trai
ghte
dge
and
com
pass
, ihe
stu
dent
can
con
stru
cta
plan
e fig
ure
cong
ruen
t to
agi
ven
line
segm
ent,
angl
e,or
tria
ngle
.(N
ote:
See
obj
ectiv
e #
15 fo
r G
rade
Fiv
e fo
r ex
ampl
e.)
21. U
sing
a s
trai
ghte
dge
and
com
pass
, the
stu
dent
can
con
stru
ctc
c
the
bise
ctor
of a
giv
en a
ngle
.
22. U
sing
a s
trai
ghte
dge
and
com
pass
, the
stu
dent
can
con
stru
ctth
e pe
rpen
dicu
lar
bise
ctor
of a
giv
en li
ne s
egm
ent.
(Not
e: S
ee o
bjec
tive
# 16
for
Gra
de F
ive
for
exam
ple.
)
23. G
iven
a li
ne a
nd a
poi
nt o
f the
line
, the
stu
dent
can
con
stru
cta
line
perp
endi
cula
r to
the
give
n lin
e at
the
give
n po
int.
24. G
iven
a li
ne a
nd a
poi
nt n
ot o
n th
e lin
e, th
e st
uden
t can
cons
truc
t a li
ne p
erpe
ndic
ular
to th
e gi
ven
line
thro
ugh
the
give
n po
int.
25. G
iven
a li
ne a
nd a
poi
nt n
ot o
n th
e lin
e, th
e st
uden
t can
cons
truc
t a li
ne p
aral
lel t
o th
e gi
ven
l ine
thro
ugh
the
give
npo
int.
26. U
sing
a c
ompa
ss, t
he s
tude
nt c
on c
onst
ruct
a c
ircle
with
a g
iven
cent
er a
nd r
adiu
s (o
r di
amet
er).
AW
198,
200-
201
198
199
199
SA
BC
53-5
4,77
-78,
82,
134-
135
86-8
7,11
1
51-5
2
127
129
202-
203
130
45,
136-
138
82-8
3
CO
NT
EN
T
CO
NC
EP
TS
OF
ME
AS
UR
EM
EN
T
ME
AS
UR
EM
EN
T -
GR
AD
E S
IX
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
AB
C
Pro
cess
of m
easu
ring
1. G
iven
a m
easu
rabl
e ph
ysic
al p
rope
rty
such
as
leng
th,
area
,w
eigh
t, te
mpe
ratu
re, e
tc.,
the
stud
ent c
an s
elec
t a s
uita
ble
unit
and/
or m
easu
ring
devi
ce a
nd m
easu
re th
epr
oper
ty.
For
exam
ple:
An
angl
e ca
n be
mea
sure
d by
usi
ng a
(n)
Wha
t is
an a
ppro
pria
te u
nit w
hen
disc
ussi
ng th
e w
eigh
tof
dia
mon
ds?
hum
an b
eing
?of
coa
l?of
a
Arb
itrar
y se
lect
ion
of2.
The
stu
dent
can
nam
e at
leas
t tw
o un
its s
uita
ble
for
nam
ing
unit
the
mea
sure
of a
giv
en p
hysi
cal
prop
erty
.F
or e
xam
ple:
Spe
ed c
an b
e ex
pres
sed
in m
iles
per
hour
or
in fe
et p
erse
cond
.
187,
329
109,
251
App
roxi
mat
e na
ture
of
3. T
he s
tude
nt c
an d
emon
stra
te h
is u
nder
stan
ding
of t
he a
ppro
xi-
39,1
83m
easu
rem
ent
mat
e na
ture
of m
easu
rem
ent b
y st
atin
g th
e pr
ecis
ion
of th
em
easu
re.
For
exa
mpl
e:
The
circ
umfe
renc
e of
the
eart
h at
the
equa
tor
is 2
5,00
0m
iles
corr
ect t
o th
e ne
ares
t tho
usan
d m
iles.
The
thic
knes
s of
a p
iece
of
pape
r is
.003
inch
es c
orre
ctto
the
near
est t
hous
andt
h of
an
inch
.
CO
NT
EN
T
ME
AS
UR
EM
EN
T -
GR
AD
E S
IX
BE
HA
VIO
RA
L O
BJE
CT
IVE
S
4. G
iven
that
the
mea
sure
of a
line
seg
men
t is
3 1/
2 in
ches
corr
ect t
o th
e ne
ares
t hal
f inc
h, th
e st
uden
t can
sta
teth
at th
e ac
tual
leng
th is
bet
wee
n 3
1/4
and
3 3/
4 in
ches
.
3 1/
4 in
. ( a
ctua
l len
gth
< 3
3/4
in.
r4
23
4
ME
AS
UR
EM
EN
T O
F P
HY
SIC
AL
PR
OP
ER
TIE
S
Leng
thE
nglis
h un
itsM
etric
uni
tsLi
ght y
ears
Per
imet
er
Circ
umfe
renc
e
Are
a--s
quar
e un
itsre
late
d to
uni
ts o
fle
ngth
(ac
re)
Rec
tang
leP
aral
lelo
gram
Tria
ngle
Circ
le
5. T
he s
tude
nt c
an u
se v
ario
us m
easu
ring
devi
ces
(rul
er,
yard
stic
k, m
eter
stic
k, ta
pe)
to m
easu
re le
ngth
in w
hole
and
frac
tiona
l par
ts o
f uni
ts.
6. G
iven
the
mea
sure
s of
the
side
s of
a p
olyg
on, t
he s
tude
ntca
n co
mpu
te th
e pe
rimet
er.
(Not
e: S
ee o
bjec
tive
#9 fo
r G
EO
ME
TR
Y -
GR
AD
ES
IX.)
7. G
iven
the
mea
sure
of t
he d
iam
eter
or
radi
us o
f a c
ircle
, the
stud
ent c
an c
ompu
te th
e ci
rcum
fere
nce
(per
imet
er).
(Not
e: S
ee o
bjec
tive
#10
for
GE
OM
ET
RY
- G
RA
DE
SIX
.)
8. U
sing
pap
er fi
gure
s an
d sc
isso
rs, t
he s
tude
nt c
an d
emon
stra
teth
at th
e ar
ea o
f a tr
iang
le is
equ
al to
one
-hal
f of t
he a
rea
of a
par
alle
logr
am h
avin
g th
e sa
me
base
and
alti
tude
mea
sure
s.(N
ote:
See
obj
ectiv
e #1
2 fo
r G
EO
ME
TR
Y -
GR
AD
ES
IX.)
AW
68 144-
145,
162-
164,
176-
177,
262-
263
263
248
S
20-2
1,96
,32
,39,
195,
238,
278,
307
250
20,2
82-2
8325
3-25
4
216-
217,
296-
297
255
AB
C
330-
332,
354-
356
88-8
9,97
,112
,19
0,28
6,31
7,34
6
94-9
5,22
7-22
9
93-9
4,11
2
CO
NT
EN
T
Vol
ume-
-cu
bic
units
rela
ted
to u
nits
of
leng
th Liqu
id m
easu
reE
nglis
h un
itsM
etric
uni
ts
Tim
e Yea
r, d
ecad
e,ce
ntur
yB
.C. o
r A
.D.
Tim
e Z
ones
ME
AS
UR
EM
EN
TG
RA
DE
SIX
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
W
9. G
iven
the
mea
sure
s of
the
base
and
alti
tude
of a
rec
tang
le,
42-4
3,96
,126
,pa
ralle
logr
am, o
r tr
iang
le, t
he s
tude
nt c
an c
ompu
te th
e21
6- 2
17,2
26-
area
.22
7,23
8-23
9,(N
ote:
See
obj
ectiv
e #1
1 fo
r G
EO
ME
TR
Y -
GR
AD
E 2
78S
IX.)
10. G
iven
the
mea
sure
of t
he d
iam
eter
or
radi
us o
f a c
ircle
, the
297
stud
ent c
an c
ompu
te th
e ar
ea.
11. T
he s
tude
nt c
an c
ompu
te th
e su
rfac
e ar
ea o
f spa
ce fi
gure
s w
hose
face
s ar
e re
ctan
gles
, par
alle
logr
ams,
or
tria
ngle
s.96
,126
,307
12. G
iven
the
mea
sure
s of
the
edge
s of
a r
ight
rec
tang
ular
pris
m,
the
stud
ent c
an c
ompu
te th
e vo
lum
e.84
-85,
96,1
26(N
ote
See
obj
ectiv
e #1
4 fo
r G
EO
ME
TR
Y -
GR
AD
ES
IX.)
13. T
he s
tude
nt c
an n
ame
the
com
mon
sta
ndar
d un
its o
f liq
uid
262-
263
mea
sure
and
mea
sure
the
capa
city
of a
giv
en c
onta
iner
to th
e ne
ares
t who
le u
nit.
14. G
iven
that
a m
an w
as b
orn
in 1
9 B
.C. a
nd d
ied
in 4
2 A
.D.,
the
stud
ent c
an c
ompu
te th
e ag
e of
the
man
.
15. G
iven
that
a fo
otba
ll ga
me
begi
ns a
t 1:0
0 P
.M. E
aste
rnS
tand
ard
Tim
e, th
e st
uden
t can
nam
e th
e tim
e at
whi
ch to
wat
ch it
live
on
tele
visi
on in
Las
Veg
as.
SA
BC
100-
104,
247-
248
90-9
4,97
,112
,25
6-25
9,26
4,28
022
9,31
5,31
7,34
6
260
104-
108,
280,
322
109
110
96 98,1
01,1
12,2
29,
317
101-
104,
112,
264
ME
AS
UR
EM
EN
T -
GR
AD
E S
IX
CO
NT
EN
TB
EH
AV
IOR
AL
OB
JEC
TIV
ES
AW
SA
BC
Tem
pera
ture
16. U
sing
a th
erm
omet
er c
al ib
rate
din
eith
er F
ahre
nhei
t or
5925
2F
ahre
nhei
t deg
rees
Cen
tigra
de d
egre
es, t
he s
tude
nt c
an r
ead
the
tem
pera
ture
Cen
tigra
de d
egre
esto
the
near
est d
egre
e.
Ang
le17
. Usi
ng a
pro
trac
tor,
the
stud
ent c
an m
easu
re a
n an
gle
to10
0-10
1,11
6-48
-49
Deg
ree
the
near
est d
egre
e.11
7,22
4
Spe
ed18
. The
stu
dent
can
rea
d a
spee
dom
eter
.78
Fee
t/sec
ond
Mile
s/ho
ur
19. G
iven
a d
ista
nce
and
the
time
nece
ssar
y fo
r a
car
totr
avel
the
dist
ance
, the
stu
dent
can
com
pute
the
aver
age
spee
d of
the
car.
78,2
15,2
18
RE
NA
MIN
G M
EA
SU
RE
S
Com
paris
on o
f uni
ts20
. The
stu
dent
can
expr
ess
the
rela
tions
hips
bet
wee
n un
its o
f20
,185
,216
,10
0,10
2,10
7-90
,276
,284
,C
onve
rsio
n of
uni
tsm
easu
re a
ppro
pria
te to
the
grad
e le
vel a
nd c
an r
enam
e a
237,
262-
263
110,
112,
248,
251
336-
339
mea
sure
in o
ther
uni
ts.
For
exa
mpl
e:
1 cu
bic
foot
-=
cubi
c in
ches
.
If 1
gram
= .0
35 o
unce
,th
en 1
000
gram
s =
ounc
es =
app
roxi
mat
ely
45°
F=
° C
Not
e: C
6= 5
/9 (
F °
- 32
)
poun
ds.
CO
NT
EN
T
ME
AS
UR
EM
EN
T -
GR
AD
E S
IX
BE
HA
VIO
RA
L O
BJE
CT
IVE
SA
WS
A3C
CO
MP
UT
AT
ION
S W
ITH
ME
AS
UR
ES
21. T
he s
tude
nt c
an c
ompu
te w
ith m
easu
res
appr
opria
te to
the
grad
e le
vel,
assi
gn th
e pr
oper
uni
t to
the
resu
lt, a
ndre
nam
e if
nece
ssar
y.F
or e
xam
ple:
mile
spe
rho
ur =
mile
spe
rm
inut
e8
hour
s )
2880
mile
s
CD
184,320
107-
110,
163
336-
339