Dear
P arents
a nd
C aregivers,
Thank
you
for
the
support
you
give
your
child
in
learning
mathematics.
We
w ould
l ike
t o
s hare
s ome
information
t o
h elp
y ou
b etter
u nderstand
Arizona’s
C ollege
a nd
C areer
R eady
S tandards.
This
is
one
in
our
series
of
letters
intended
to
help
you
understand
the
work
your
child
brings
home.
W e
w ill
highlight
s ome
n ew
l anguage
a nd
s trategies
w e
will
u se
t o
build
u nderstanding,
help
c hildren
m ake
sense
o f
n umbers,
a nd
k now
t he
c ommon
m ethods
w e
l earned
i n
school.
T his
l etter
a ddresses
equivalent
f ractions
i n
f ourth
g rade.
End-‐of-‐year
g oals
One
o f
t he
more
challenging
concepts
for
fourth
graders
is
that
of
equivalent
f ractions.
U sing
visuals
a nd
illustrations
i s
a
g reat
w ay
f or
t hem
t o
u nderstand
a nd
“ see”
e quivalent
fractions.
J ust
a s
5
+
5
o r
8
+
2
n ame
t he
same
a mount
a s
1 0,
t here
a re
d ifferent
f ractions
that
n ame
t he
s ame
a mount.
F or
e xample,
a nd
a ll
name
t he
s ame
a mount
that
i s
h alfway
b etween
z ero
a nd .
T hat
m akes
t hem
e quivalent.
H ere
a re
s ome
examples
y our
s tudent
m ay
u se
t o
v isualize
e quivalent
f ractions.
Rectangular
m odels
In
e ach
p icture
b elow
o f
t he
r ectangle
i s
s haded.
If
t he
r ectangle
i s
s plit
i nto
3
p arts,
Now
t he
r ectangle
h as
b een
This
r ectangle
s hows
half
o f
t he
r ectangle
i s
s till
s haded,
two
e qual
p arts,
w ith
1
divided
i nto
3 6
e qual
p arts.
T here
but
n ow
t here
a re
3
o f
t he
6
e qual
of
2
e qual
p arts
s haded.
are
1 8
s haded
p arts
i n
.
T his
i s
parts
s haded.
T his
i s
t he
s ame
a s
This
i s
w ritten
a s
a nd
multiplying
t he
n umerator
a nd
like
m ultiplying
b y
6 .
,
a nd
is
c alled
a
u nit
f raction.
’
denominator
o f
b y
3 .
a ll
n ame
t he
s ame
s haded
1
x
3
=
3
2
x
3
=
6
amount
a nd
a re
e quivalent
fractions.
The
n ew
f raction
n ame
i s
.
Multiplying
t he
n umerator
a nd
t he
denominator
o f
a
f raction
b y
t he
a nd
n ame
t he
s ame
s haded
same
n umber
c an
m ake
e quivalent
amount.
T hey
a re
c alled
fractions.
equivalent
f ractions.
a nd
all
n ame
t he
s ame
s haded
a mount
a nd
a re
e quivalent
f ractions.
T hey
a ll
e qual
b ecause
t hey
a ll
s how
the
s ame
s ize
e ven
t hough
t he
n umber
a nd
s ize
o f
p arts
d iffer.
Mesa
P ublic
S chools/Grade
4 /Equivalent
F ractions/2013
Authorization
t o
r eprint
o r
d isseminate
m ust
b e
g ranted
b y
M esa
P ublic
S chools
( February-‐2014).