multiplying & dividing fractions · multiplying fractions on a number line and dividing...
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Mul
tipl
ying
&
Div
idin
g F
ract
ions
Storybook
Ess
ent
ial Less
ons
• Sh
arin
g V
anil
la W
afer
s•
Pai
nti
ng
a W
all-
Are
a an
d M
ult
ipli
cati
on
of
Fra
ctio
ns
• M
ult
iply
ing
Fra
ctio
ns
on
a N
um
ber
Lin
e•
Div
idin
g F
ract
ion
s I
• D
ivid
ing
Fra
ctio
ns
II•
Div
idin
g F
ract
ion
s: N
oti
cin
g P
atte
rns
• D
ivid
ing
Fra
ctio
ns
on
a N
um
ber
Lin
e•
Fra
ctio
n M
ult
ipli
cati
on
an
d D
ivis
ion
Pro
ble
m S
olv
ing
• H
ow
Acc
ura
te A
re Y
ou
?
For
mat
ive
Ass
essm
ent
#1
- H
ow
are
fra
cti
on
s a
nd
div
isio
n r
ela
ted
?U
se less
on S
ha
rin
g V
an
illa
Wa
fers
, quest
ions
11 a
nd 1
2, to
have s
tudents
expla
in t
he m
eanin
g o
f th
e f
ract
ions
in t
he c
onte
xt
of
sharing v
anill
a w
afe
rs. L
ook for
students
to c
onnect
the d
enom
inato
r of
the f
ract
ion t
o t
he n
um
ber
of
people
in t
he g
roup a
nd t
he n
um
era
tor
to t
he n
um
ber
of
vanill
a w
afe
rs.
Use
the less
on M
ak
ing
a Z
ipli
ne w
ith a
ttention t
o q
uest
ions
9-1
2 a
nd t
he s
um
mary
quest
ion. L
ook
for
students
to r
ela
te t
he d
ivis
ion p
roble
m w
ritt
en a
s st
andard
div
isio
n a
nd a
s a fra
ctio
n (
a m
ixed
num
ber
is a
lso a
ccepta
ble
, but
the fra
ctio
n form
is
ess
ential).
#2 -
Ho
w c
an
I m
od
el
an
d e
xp
lain
fra
cti
on
mu
ltip
lica
tio
n?
Use
less
on P
ain
tin
g a
Wa
ll:
Are
a a
nd
Fra
cti
on
s t
o h
ave s
tudents
physi
cally
build
a m
odel fo
r th
e
multip
lication o
f tw
o fra
ctio
ns.
H
ave s
tudents
expla
in, ora
lly o
r in
writing, w
hat
they a
re d
oin
g w
hen
multip
lyin
g t
wo fra
ctio
ns,
lookin
g for
som
e v
ers
ion o
f an e
xpla
nation t
hat
we a
re t
akin
g “
a p
iece
of
a
pie
ce”.
#3-
Wh
at
is t
he
me
an
ing
(in
co
nte
xt)
fo
r th
e d
ivis
ion
of
fra
cti
on
s?
gre
ate
r th
an o
r le
ss t
han 1
. U
se less
on D
ivid
ing
Fra
cti
on
s I
to h
ave s
tudents
expla
in a
measu
rem
ent
conte
xt
to d
ivis
ion o
f fr
act
ions,
such
as
2÷
1/4
=8 b
eca
use
there
are
8 q
uart
ers
(one-f
ourt
hs)
in 2
w
hole
s or
beca
use
I c
an jum
p o
ne-f
ourt
h a
mete
r 8 t
imes
in a
tota
l dis
tance
of
2 m
ete
rs. U
se less
on
Div
idin
g F
racti
on
s I
I beca
use
if
one-f
ourt
h o
f a p
izza
share
d e
qually
with t
wo p
eople
, I
cut
the fourt
h in h
alf a
nd t
hus
each
pers
on g
ets
one-e
ighth
of
a p
izza
. Y
ou c
an c
hoose
to g
ive c
onte
xtu
al pro
ble
ms
and h
ave s
tudents
pro
vid
e a
n a
nsw
er
and e
xpla
nation in c
onte
xt
or
allo
w t
hem
to m
ake u
p b
oth
the p
roble
m a
nd t
he
conte
xt.
#4-
Wh
at
is t
he
siz
e o
f th
e p
rod
uct
or
qu
oti
en
t in
re
lati
on
to
th
e s
ize
of
the
fa
cto
rs o
r d
ivid
en
d/d
ivis
or?
Use
less
ons
Mu
ltip
lyin
g F
racti
on
s o
n a
Nu
mb
er
Lin
e a
nd D
ivid
ing
Fra
cti
on
s o
n a
Nu
mb
er
Lin
e
to h
ave s
tudents
write
concl
usi
ons
about
the “
case
s” p
rese
nte
d;
e.g
. w
hen is
the p
roduct
or
quotient
less
than, equal to
or
gre
ate
r th
an 1
. H
ave s
tudents
use
the c
onte
xt
of
jum
pin
g fra
ctio
ns
of
mete
rs
and t
he n
um
ber
line t
o e
xpla
in h
ow
they k
now
the s
ize o
f th
e p
roduct
or
quotient.
Consi
der
usi
ng a
th
inkin
g m
ap t
o h
ave s
tudents
com
pare
fra
ctio
n m
ultip
lication a
nd d
ivis
ion w
ith w
hole
num
ber
fract
ion
and d
ivis
ion in t
erm
s of
both
what
is h
appenin
g a
nd t
he s
ize o
f th
e p
roduct
/quotient.
Look for
students
to
note
sim
ilarities
such
as
a n
um
ber
div
ided b
y its
elf is
one.
#5 -
:
Ho
w i
s t
he
re
lati
on
sh
ip b
etw
ee
n m
ult
ipli
ca
tio
n a
nd
div
isio
n e
vid
en
t w
ith
fra
cti
on
s?
want
to a
ssess
stu
dents
’ unders
tandin
g o
f how
this
rela
tionsh
ip w
ork
s w
ith f
ract
ions.
Look for
students
to
make a
n initia
l co
nnect
ion b
etw
een fra
ctio
n d
ivis
ion a
nd m
ultip
lication in t
he less
ons
Div
idin
g
Fra
cti
on
s I
an
d I
I.
Use
the less
on D
ivid
ing
Fra
cti
on
s:
No
ticin
g P
att
ers
as
a m
ore
form
al
form
ative a
ssess
ment,
havin
g s
tudents
use
the c
oncl
usi
on s
ect
ion t
o e
xpla
in t
he r
ela
tionsh
ip t
hat
exis
ts,
nam
ely
that
div
isio
n o
f fr
act
ions
is e
quiv
ale
nt
to m
ultip
lication b
y t
he m
ultip
licative invers
e.
Genera
l Str
ate
gie
s
For
Form
ative
Assessm
ents
str
ate
gie
s t
hro
ughout
the u
nit
sid
ew
ays
Ask s
tudents
to r
ate
their
means t
hey u
nders
tand t
he t
opic
,
thum
bs d
ow
n m
eans t
hey d
on’t
and in t
he m
iddle
means t
hey g
et
part
of
it b
ut
still
need a
dditio
nal
pro
ble
ms t
o s
olv
e o
n w
hite
board
s a
nd h
ave t
hem
rais
e t
heir
Sta
tem
ent
Ask s
tudents
to w
rite
a s
um
mary
stu
dents
rate
their u
nders
tandin
g
cla
ss,
giv
e s
tudents
a p
roble
m
or
two t
o c
om
ple
te o
n a
slip
of
need t
o s
ee t
hat
div
isio
n is n
ot
changin
g a
num
ber,
but
ch
angin
g h
ow
it
Div
isio
n o
nly
mean
s t
o m
ake e
qu
al
gro
up
s o
r sh
are
fair
ly
“Y
ou
rs i
s n
ot
to r
easo
n w
hy, ju
st
invert
an
d m
ult
iply
”
(or
oth
er
rule
s a
bo
ut
ho
w t
o d
ivid
e f
racti
on
s)
As t
he c
onceptu
al unders
tandin
g o
f th
e d
ivis
ion o
f fr
actions is n
ot
as
to s
implif
y t
he p
rocedure
to a
meanin
gle
ss s
hort
cut,
such a
s t
he o
ne
term
s o
f stu
dents
bein
g a
ble
to u
se it
quic
kly
and g
et
corr
ect
answ
ers
without
conceptu
al unders
tandin
g,
they w
ill n
ot
know
how
to a
pply
it
or
Ove
rvie
wSt
ud
ents
wil
l als
o u
se c
on
text
an
d c
on
cret
e m
od
els
to u
nd
erst
and
an
d
exp
lain
th
e m
ean
ing
of
frac
tio
n d
ivis
ion
. In
gra
de
5, d
ivis
ion
is
lim
ited
to
a
wh
ole
nu
mb
er a
nd
a u
nit
fra
ctio
n.
Stu
den
ts m
ust
be
"ex
ible
in
usi
ng
bo
th
a “f
air
shar
e” a
nd
a “
mea
sure
men
t” d
e#n
itio
n o
f d
ivis
ion
to
mo
del
th
e tw
o
maj
or
case
s: t
he
div
iso
r is
a p
osi
tive
nu
mb
er le
ss t
han
1, a
nd
th
e d
ivis
or
is a
wh
ole
nu
mb
er.
Stu
den
ts w
ill u
se a
rea
mo
del
s an
d n
um
ber
lin
es, a
nd
an
alyz
e th
e re
lati
on
ship
bet
wee
n t
he
size
of
the
div
iden
d, t
he
div
iso
r an
d
the
qu
oti
ent.
Wh
en m
od
elin
g d
ivis
ion
pro
ble
ms
wit
h a
rea
mo
del
s, s
tud
ents
w
ill n
oti
ce t
hat
th
ey s
eem
to
be
mu
ltip
lyin
g, a
nd
th
us
stu
den
ts w
ill s
tud
y th
e re
lati
on
ship
bet
wee
n f
ract
ion
div
isio
n a
nd
mu
ltip
lica
tio
n t
o c
on
clu
de
that
div
isio
n i
s eq
uiv
alen
t to
mu
ltip
lica
tio
n b
y th
e m
ult
ipli
cati
ve i
nve
rse.
St
ud
ents
wil
l use
fra
ctio
n m
ult
ipli
cati
on
an
d d
ivis
ion
to
pro
ble
m s
olv
e,
incl
ud
ing
anal
yzin
g m
easu
rem
ent
dat
a re
pre
sen
ted
on
a li
ne
plo
t.
Uni
t S
tory
TH
E R
EASO
NIN
G B
EH
IND
TH
E F
LO
W
The u
nit b
egin
s w
ith a
fam
iliar
pro
ble
m w
e f
ace in c
lassro
om
s:
som
eone h
as b
rought
a t
reat
to s
hare
for
a b
irth
day a
nd w
e
Sh
ari
ng
Van
illa
Wafe
rs,
stu
dents
build
vanill
a w
afe
rs f
rom
pla
y-d
oh a
nd
physic
ally
div
ide t
hem
to s
how
how
much e
ach s
tudent
would
sim
ple
, soon s
tudents
don’t h
ave a
n e
qual
num
ber
of
whole
cookie
s f
or
each s
tudent
or
they h
ave f
ew
er
cookie
s t
han s
tudents
and m
ust
dete
rmin
e h
ow
to c
ut
up a
nd s
hare
meth
ods o
thers
use,
stu
dents
com
e t
o s
ee f
ractions a
s a
means
Stu
dents
continue t
o
betw
een f
ractions a
nd
div
isio
n o
f w
hole
num
bers
in t
he lesson M
akin
g A
Zip
Lin
e
As in t
he p
rior
lesson,
stu
dents
connect
fractions t
o d
ivis
ion o
f
solu
tions t
o e
ach p
roble
m r
epre
sente
d o
n t
he n
um
ber
line s
o a
s
to c
onnect
their u
nders
tandin
g o
f fr
actions o
n t
he n
um
ber
line a
nd
Sta
ndard
s
Addre
ssed
Nu
mb
er
an
d O
pera
tio
ns–
Fra
cti
on
s
Ap
ply
an
d e
xte
nd
pre
vio
us
un
ders
tan
din
gs o
f m
ult
ipli
cati
on
an
d d
ivis
ion
to
mu
ltip
ly a
nd
div
ide
fracti
on
s.
div
isio
n o
f w
hole
num
bers
leadin
g
to a
nsw
ers
in t
he f
orm
of
fractions
vis
ual fr
action m
odels
or
equations t
o
of
rice e
qually
by w
eig
ht,
how
many
pounds o
f rice s
hould
each p
ers
on g
et?
Betw
een w
hat
two w
hole
num
bers
does
your
answ
er
lie?
unders
tandin
gs o
f m
ultip
lication t
o
multip
ly a
fra
ction o
r w
hole
num
ber
by
a p
art
s o
f a p
art
itio
n o
f q into
b e
qual
part
s;
equiv
ale
ntly,
as t
he r
esult o
f a
fractional sid
e length
s b
y t
iling it
with
unit s
quare
s o
f th
e a
ppro
priate
unit
fraction s
ide length
s,
and s
how
that
the a
rea is t
he s
am
e a
s w
ould
be
are
as o
f re
cta
ngle
s,
and r
epre
sent
& F
low
AN
D I
NTEN
TIO
N O
F E
ACH
LESSO
N
Pain
tin
g a
Wall
- A
rea a
nd
Mu
ltip
licati
on
of
Fra
cti
on
s, stu
dents
begin
usin
g p
lay-d
oh t
o r
epre
sent
a w
all
and
show
ing w
hat
it w
ould
look lik
e t
o p
ain
t a
port
ion o
f th
e w
all
would
be p
ain
ted if
they
follo
wed b
y r
epre
senting t
he s
cenario p
icto
rially
, stu
dents
see
solv
e m
ultip
le p
roble
ms involv
ing t
he m
ultip
lication o
f fr
actio
ns
for
patt
ern
s t
o c
onclu
de t
hat
they c
an a
rriv
e a
t th
e p
roduct
pro
cedura
lly b
y m
ultip
lyin
g t
he n
um
era
tors
and d
enom
inato
rs;
thus,
stu
dents
begin
the lesson c
onceptu
ally
with c
oncre
te
Once s
tudents
unders
tand f
raction m
ultip
lication c
onceptu
ally
and p
rocedura
lly,
they a
pply
their k
now
ledge t
o p
ractice a
nd
Mu
ltip
lyin
g F
racti
on
s o
n a
Nu
mb
er
Lin
e, stu
dents
will
stu
dy
on m
odelin
g f
raction m
ultip
lication o
n t
he n
um
ber
line,
with f
ocus
giv
en t
o u
nders
tandin
g h
ow
the w
hole
is d
ivid
ed t
o b
e a
ble
to
able
to u
se t
he n
um
ber
line t
o m
ultip
ly f
ractions,
they a
gain
be s
malle
r th
an,
equal to
or
gre
ate
r th
an t
he f
acto
rs a
s w
ell
as t
o
Sta
ndard
s
Addre
ssed
by:
of
the o
ther
facto
r, w
ithout
perf
orm
ing t
he
in a
pro
duct
gre
ate
r th
an t
he g
iven n
um
ber
why m
ultip
lyin
g a
giv
en n
um
ber
by a
fra
ction
the g
iven n
um
ber;
and r
ela
ting t
he p
rincip
le
of
div
isio
n t
o d
ivid
e u
nit f
ractions b
y w
hole
num
bers
and w
hole
num
bers
by u
nit
the r
ela
tionship
betw
een m
ultip
lication a
nd
num
ber
by a
unit f
raction,
and c
om
pute
the r
ela
tionship
betw
een m
ultip
lication
Com
mon
Mis
conc
epti
ons
Str
ug
gli
ng
to
In
terp
ret
Fra
cti
on
s a
s D
ivis
ion
stu
dents
will
str
uggle
unders
tandin
g f
ractions a
s d
ivis
ion o
f w
hole
to inte
rpre
t th
e d
enom
inato
r as t
he d
ivis
or
and t
he n
um
era
tor
as t
he
Mu
ltip
licati
on
alw
ays m
akes t
he a
nsw
er
big
ger
multip
lication w
ill g
reatly h
elp
stu
dents
avoid
thin
kin
g o
f m
ultip
lication
Div
isio
n a
lways m
akes n
um
bers
sm
all
er
Sim
ilar
to m
ultip
lication m
akin
g n
um
bers
larg
er,
stu
dents
als
o t
end
in a
quotient
sm
alle
r th
an t
he d
ivid
end,
rath
er
than t
hin
k o
f div
isio
n
mere
ly p
rocedura
lly,
stu
dents
need t
o u
nders
tand d
ivis
ion a
s b
oth
Sente
nce
Fra
mes &
Sta
rters
Her
e ar
e so
me
op
tio
ns
to p
rovi
de
to s
tud
ents
th
rou
gho
ut
the
acti
viti
es.
• I
agre
e w
ith
__
__
__
_
bec
ause
__
__
__
_.
• I
dis
agre
e w
ith
__
__
__
_
bec
ause
__
__
__
_.
• I
did
no
t u
nd
erst
and
_
__
__
__
__
__
__
__
.
• I
pre
fer
__
__
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eth
od
/st
rate
gy
bec
ause
_
__
__
__
.
• I
thin
k t
hat
__
__
__
_.
• W
hat
do
yo
u m
ean
by
__
__
__
_?
• I
thin
k _
__
__
__
mea
ns
__
__
__
__
__
__
_.
$is
un
it i
nvo
lves
stu
den
ts le
arn
ing
ho
w t
o m
ult
iply
fra
ctio
ns
and
d
ivid
e u
nit
fra
ctio
ns
by
wh
ole
nu
mb
ers.
His
tori
call
y, t
hes
e tw
o t
op
ics
wer
e ta
ugh
t u
sin
g p
roce
du
ral s
ho
rtcu
ts, l
eavi
ng
mo
st w
ith
ou
t an
y id
ea
of
wh
at t
hey
wer
e ac
tual
ly d
oin
g. W
hen
mu
ltip
lyin
g tw
o f
ract
ion
s b
etw
een
0 a
nd
1, t
he
pro
du
ct i
s sm
alle
r th
an e
ith
er f
acto
r; t
his
go
es
agai
nst
wh
at m
ost
stu
den
ts k
no
w a
bo
ut
mu
ltip
lica
tio
n (
thin
kin
g it
m
akes
nu
mb
ers
larg
er),
an
d t
hu
s, r
elyi
ng
sole
ly o
n s
ho
rtcu
ts le
aves
st
ud
ents
no
t u
nd
erst
and
ing
mat
h a
nd
ass
um
ing
mat
h i
s n
ow
ab
ou
t fo
llo
win
g st
eps
and
hav
ing
no
id
ea h
ow
rea
son
able
th
eir
answ
er i
s.
Rat
her
th
an p
erp
etu
ate
this
po
or
met
ho
d o
f te
ach
ing,
in
th
is u
nit
, st
ud
ents
wil
l use
co
nte
xt a
nd
han
ds-
on
mat
eria
ls t
o u
nd
erst
and
wh
at
frac
tio
n m
ult
ipli
cati
on
is
and
mea
ns.
Stu
den
ts w
ill u
se a
rea
mo
del
s an
d a
nu
mb
er li
ne
and
so
lve
pro
ble
ms
in c
on
text
, rea
son
ing
abo
ut
the
size
of
the
pro
du
ct a
nd
fac
tors
. St
ud
ents
wil
l stu
dy
pat
tern
s w
ith
th
eir
wo
rk t
o d
eriv
e th
e p
roce
du
re (
sho
rtcu
t).
Mu
ltip
lica
tio
n o
f fr
acti
on
s (i
ncl
ud
ing
mix
ed n
um
ber
s) s
ho
uld
be
mas
tere
d b
y th
e en
d o
f gr
ade
5.
Uni
t
The
Uni
t! (
Con
t.)
“Ho
w m
an
y o
ne
-fo
urt
hs
are
th
ere
in
2?
”
Stu
dent
Talk
Str
ate
gie
s
This
Top
ic F
it?
Gra
de 6
– H
igh
Sch
oo
l
num
bers
and u
nit f
ractions a
s t
hey n
ow
get
into
the m
ore
com
plic
ate
d c
ases o
f
have s
een w
hy d
ivis
ion o
f fr
actions c
an b
e r
epre
sente
d a
s m
ultip
lication b
y t
he
apply
their u
nders
tandin
g o
f fr
actions o
n t
he n
um
ber
line a
s t
hey learn
to locate
non-u
nit f
ractions,
and t
hus m
ultip
lication o
f fr
actions s
hould
be m
aste
red b
y
gra
de 7
on,
and t
hus s
tudent
maste
ry o
f fr
action o
pera
tions w
ill b
e r
elie
d u
pon
div
isio
n a
re invers
e o
pera
tions w
ill b
e u
sed n
ot
only
to s
olv
e e
quations,
but
late
r
to m
ultip
ly a
nd d
ivid
e f
ractions a
s t
hey learn
to m
ultip
ly a
nd
div
ide r
ational
Th
e s
tud
en
ts l
iste
n t
o t
he
ir
Types O
fKnow
ledge
• M
EM
OR
IZA
TIO
N
(QU
ICK
RE
CA
LL
)
• P
RO
CE
DU
RA
L
(FO
LL
OW
ST
EP
S/
DO
SO
ME
TH
ING
)
• C
ON
CE
PT
UA
L
(UN
DE
RS
TN
D B
IG
IDE
A/
EX
PL
AIN
/
DE
RIV
E)
• R
EL
AT
ION
AL
(AP
PLY
/ A
NA
LY
ZE
/
EV
AL
UA
TE
)
SBAC
Cla
ims
• • • •
Uni
t S
tory
Stu
dents
will
pra
ctice a
nd s
olv
e r
eal w
orld p
roble
ms involv
ing t
he
pra
ctice f
raction m
ultip
lication c
om
es in t
he f
orm
of
the g
am
e, T
he
Facto
r G
am
e:
Fra
cti
on
by F
racti
on
Mu
ltip
licati
on
are
obta
ined b
y s
ele
cting t
wo f
acto
rs f
rom
a lis
t, b
ut
only
be
ing a
ble
fraction m
ultip
lication,
stu
dents
reason t
o d
ete
rmin
e w
hat
facto
r to
not
use s
o t
hat
the o
pposin
g t
eam
cannot
make a
giv
en p
roduct
to
Div
idin
g
Fra
cti
on
s I
.
can e
asily
see t
here
are
tw
o h
alv
es in
one w
hole
, so t
hey c
onnect
this
concre
te
this
is a
gre
at
observ
ation,
as it
begin
s t
o p
lant
the s
eed t
o late
r
connect
to t
he f
raction d
ivis
ion a
lgorith
m,
nam
ely
multip
lyin
g b
y t
he
Div
idin
g F
racti
on
s I
I,
the d
ivid
end a
nd d
ivis
or
are
sw
itched s
o t
hat
they a
re n
ow
div
idin
g
div
isio
n u
sed t
o f
air s
hare
or
part
itiv
e
we h
ave a
nd t
hen d
ivid
e t
hat
am
ount
into
an e
qual num
ber
of
gro
ups,
Stu
dents
continue w
ith t
he u
se o
f pla
y-d
oh t
o b
uild
are
a m
odels
with
recta
ngle
s a
s t
hey n
ow
sta
rt w
ith o
nly
a f
ractional am
ount
and
then
dra
win
g t
hese m
odels
, stu
dents
notice t
hat
this
looks s
urp
risin
gly
Cohere
nce
Connections t
o o
ther
Gra
de 5
Topic
s
Th
is u
nit
bu
ild
s u
po
n w
ork
do
ne
wit
h w
ho
le
Real-W
orld
Application
• C
utt
ing
Ro
pe/
Wo
od
• Sh
arin
g o
r p
arti
tio
nin
g fo
od
• P
ain
tin
g•
Rel
ativ
e D
ista
nce
• M
easu
rem
ent
Dat
a•
Bak
ing
• A
rea
with c
onceptu
al unders
tandin
g o
f both
div
isio
n o
f w
hole
num
bers
by u
nit f
ractions a
nd u
nit f
ractions b
y w
hole
num
bers
, stu
dents
are
ready t
o look f
or
patt
ern
s in t
erm
s o
f w
hat
math
they a
re d
oin
g
Div
idin
g F
racti
on
s:
No
ticin
g P
att
ern
s,
and m
ultip
lication t
hey m
ay h
ave n
oticed o
ver
the p
ast
few
le
ssons
all
the p
roble
ms s
tudents
solv
ed in D
ivid
ing
Fra
cti
on
s I
an
d I
I, a
nd
then h
as a
corr
espondin
g f
raction m
ultip
lication p
roble
m t
hat
begin
s
with t
he s
am
e n
um
ber
and h
as t
he s
am
e s
olu
tion;
stu
dents
must
dete
rmin
e t
he m
issin
g f
acto
r to
make t
hat
multip
lication s
ente
nce
Thus,
stu
dents
are
able
to d
ivid
e u
sin
g a
n a
rea m
odel as w
ell
as
usin
g t
he s
tandard
pro
cedure
, w
ith t
he f
orm
er
bein
g m
uch m
ore
import
ant!
Stu
dents
will
furt
her
their u
nders
tandin
g o
f d
ivis
ion o
f
Div
idin
g F
racti
on
s o
n a
Nu
mb
er
Lin
e,
stu
dents
will
again
use m
easure
ment
div
isio
n t
o inte
rpre
t pro
ble
ms involv
ing a
pro
ble
ms involv
ing t
he s
am
e d
ivis
or
and t
hen s
tudy t
he r
ela
tionsh
ip
Stu
dents
develo
p f
raction n
um
ber
sense t
o s
ee w
hen a
nd w
hy t
he
verify
that
div
isio
n is e
quiv
ale
nt
multip
lication b
y t
he m
ultip
licative
Fra
cti
on
Mu
ltip
licati
on
an
d D
ivis
ion
Pro
ble
m S
olv
ing
, stu
dents
will
Ho
w F
ar
Can
Yo
u J
um
p?
, stu
dents
colle
ct
measure
ment
data
to t
he n
eare
st
half o
r quart
er
mete
r and r
epre
se
nt
The
Mat
h B
ehin
d
Where
Doe
s G
rad
es K
-4
unit,
stu
dents
als
o n
eed t
o c
alc
ula
te t
he a
rea o
f a r
ecta
ng
le w
ith f
ractional sid
e
num
bers
on a
num
ber
line a
s t
hey n
ow
multip
ly f
ractions o
n a
nu
mber
line in
of
pro
ble
ms a
nd
pers
evere
in s
olv
ing
arg
um
ents
and c
ritique
Math
Pra
ctice
Sta
ndard
s
The
Uni
t!
“Ho
w m
an
y _
__
_ (
div
iso
r) a
re t
he
re i
n _
__
__
(d
ivid
en
d)?
”
“I h
av
e _
__
(d
ivid
en
d)
an
d n
ee
d t
o d
ivid
e t
ha
t in
to _
__
(d
ivis
or)
eq
ua
l g
rou
ps.
H
ow
mu
ch d
oe
s e
ach
gro
up
ge
t?”
Academ
icLanguage
• Fa
ctor
•
Pro
duct
•
Num
era
tor
• D
enom
inato
r•
Div
idend
• D
ivis
or
•
Quotient
• M
ultip
licative
• I
nvers
e•
Reci
pro
cal
The
Mat
h B
ehin
d
Th
us
div
isio
n r
ela
ted?
multip
lication?
fractions?
pro
duct
or
quotient
in
div
isor?
betw
een m
ultip
lication
and d
ivis
ion e
vid
ent
with
fractions?
top related