Grade 5 Grade 5

Fifth
Fifth
Fifthgrade
grade
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students
studentswork
work
workwith
with
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division.
division.One
One
Onestrategy
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multiplyingup.
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students
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AAAstrategy
strategy
strategyaaafifth
fifth
fifthgrader
grader
gradermight
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mightuse
use
usefor
for
for
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division
divisionisisisproportional
proportional
proportionalreasoning.
reasoning.
reasoning.
768
768÷÷÷16
16
16===
768
768
768
768÷÷÷16
16
16
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384
384
384÷÷÷888
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192
192÷÷÷444
192
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96
96÷÷÷222
96
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46
46
46 ÷÷÷111===46
46
46
Parent
Parent
Roadmap
Roadmap
Grade
Grade 55
Students
Students
Studentsinin
ingrade
grade
grade555will
will
willuse
use
useequivalent
equivalent
equivalent
fractions
fractions
fractionsinin
inorder
order
ordertoto
to
add
add
addand
and
andsubtract.
subtract.
subtract.
+++
  
   +++   
This
This
Thisstudent
student
studenthas
has
hasused
used
usedthe
the
thepartial
partial
partialquotient
quotient
quotient
strategy
strategy
strategytoto
todivide
divide
dividethis
this
thisproblem.
problem.
problem.
634
634
634÷÷÷26
26
26===
===    
Fifth
Fifth
Fifthgraders
graders
graderssolve
solve
solvefraction
fraction
fractionword
word
wordproblems.
problems.
problems.
This
This
Thisexample
example
exampleinvolves
involves
involvesmultiplication
multiplication
multiplicationofof
ofaaa
whole
wholenumber
number
numberand
and
andaaafraction.
fraction.
fraction.
whole
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my
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How
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will
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four
fourtimes
times
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means
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that
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and
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requirement
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ininin
grade
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Fifth
Fifth
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grade
gradestudents
students
studentswork
work
workwith
with
withstrategies
strategies
strategies
when
when
wheninvestigating
investigating
investigatingdivision.
division.
division.One
One
Onestrategy
strategy
strategy
that
thatassists
assistsstudents
studentsisisismultiplying
multiplyingup.
up.
that
assists
students
multiplying
up.
Fifth
Fifth
Fifthgraders
graders
gradersexplore
explore
exploredivision
division
divisionofof
offractions.
fractions.
fractions.
the
theresult
result
resultofof
of333÷÷÷444and
and
andthey
they
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should
should
isisisthe
note
note
notethat
that
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multiplied
multipliedby
by
by444isisis3.3.
3.
IfIfIf333pizzas
pizzas
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were
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each
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has
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share
share
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ofsize
size
size
. ..
AAAstrategy
strategy
strategyaaafifth
fifth
fifthgrader
grader
gradermight
might
mightuse
use
usefor
for
for
division
division
divisionisisisproportional
proportional
proportionalreasoning.
reasoning.
reasoning.
768
768÷÷÷16
16
16===
768
768
768
768÷÷÷16
16
16
÷÷÷222 ÷÷÷222
384
384
384÷÷÷888
÷÷÷222÷÷÷222
192
192÷÷÷444
192
÷÷÷222÷÷÷222
96
96÷÷÷222
96
÷÷÷222÷÷÷ 222
46
46
46 ÷÷÷111===46
46
46
Key
Key
KeyConcepts:
Concepts:
Concepts:
Multiplication
Multiplication
Multiplication&&&Division
Division
Division
Working
Working
Workingwith
with
withFractions
Fractions
Fractions
Cobb
Cobb
CobbCounty
County
CountySchools
Schools
Schools
Strategies
Strategies
Strategiesfor
for
fordivision,
division,
division,
Working
Working
Workingwith
with
withdecimals
decimals
decimals
and
and
andfractions
fractions
fractions
2013-2014
2013-2014
2013-2014
Parent
Parent
Roadmap
Roadmap
Grade
Grade 55
Students
Students
Studentsinin
ingrade
grade
grade555will
will
willuse
use
useequivalent
equivalent
equivalent
fractions
fractions
fractionsinin
inorder
order
ordertoto
to
add
add
addand
and
andsubtract.
subtract.
subtract.
+++
This
This
Thisstudent
student
studenthas
has
hasused
used
usedthe
the
thepartial
partial
partialquotient
quotient
quotient
strategy
strategy
strategytoto
todivide
divide
dividethis
this
thisproblem.
problem.
problem.
634
634
634÷÷÷26
26
26===
  
   +++   
===    
Fifth
Fifth
Fifthgraders
graders
graderssolve
solve
solvefraction
fraction
fractionword
word
wordproblems.
problems.
problems.
This
This
Thisexample
example
exampleinvolves
involves
involvesmultiplication
multiplication
multiplicationofof
ofaaa
whole
whole
wholenumber
number
numberand
and
andaaafraction.
fraction.
fraction.
There
There
Thereare
are
are444sheets
sheets
sheetsofof
ofcolored
colored
coloredpaper,
paper,
paper,and
and
andI II
need
need
needtoto
touse
use
use  ofof
ofeach
each
eachsheet
sheet
sheettoto
to finish
finish
finishmy
my
my
art
art
artproject.
project.
project.How
How
Howmuch
much
muchpaper
paper
paperwill
will
willI Iuse?
Iuse?
use?
four
fourtimes
times
timesmeans
means
meansthat
that
that   ofof
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which
whichisisis333whole
whole
wholesheets
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and
and
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ofofofthe
Division
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by
by
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fraction
fractionisisis
not
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aaa
requirement
requirement
requirement
ininin
grade
grade
grade5.5.5.
Fifth
Fifth
Fifthgraders
graders
gradersexplore
explore
exploredivision
division
divisionofof
offractions.
fractions.
fractions.
the
theresult
result
resultofof
of333÷÷÷444and
and
andthey
they
theyshould
should
should
isisisthe
note
note
notethat
that
thatmultiplied
multiplied
multipliedby
by
by444isisis3.3.
3.
IfIfIf333pizzas
pizzas
pizzaswere
were
wereshared
shared
sharedequally
equally
equallyby
by
by
444people
people
peopleeach
each
eachperson
person
personhas
has
hasaaashare
share
share
ofof
ofsize
size
size
. ..
Key
Key
KeyConcepts:
Concepts:
Concepts:
Multiplication
Multiplication
Multiplication&&&Division
Division
Division
Working
Working
Workingwith
with
withFractions
Fractions
Fractions
Cobb
Cobb
CobbCounty
County
CountySchools
Schools
Schools
Strategies
Strategies
Strategiesfor
for
fordivision,
division,
division,
Working
Working
Workingwith
with
withdecimals
decimals
decimals
and
and
andfractions
fractions
fractions
2013-2014
2013-2014
2013-2014
Math
Math
Having
Having
Having
worked
worked
worked
with
with
with
addition,
addition,
addition,
subtraction,
subtraction,
subtraction,
multiplication
multiplication
multiplication
and
and
and
division
division
division
in
inin
both
both
both
third
third
third
and
and
and
fourth
fourth
fourth
grade,
grade,
grade,
fifth
fifth
fifth
grade
grade
grade
students
students
students
are
are
are
expected
expected
expected
to
toto
continue
continue
continue
apply
apply
apply
this
this
this
understanding
understanding
understanding
when
when
when
working
working
working
with
with
with
decimals.
decimals.
decimals.
Students
Students
Students
may
may
may
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solve
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aa decimal
adecimal
decimal
subtraction
subtraction
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problem
problem
problem
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an
anan
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open
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number
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line.
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23.6
23.6
23.6–– –0.79
0.79
0.79== =
88 8xx 2.5
x2.5
2.5== =
Fifth
Fifth
Fifth
grade
grade
grade
students
students
students
are
are
are
expected
expected
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toto
be
bebe
able
able
able
to
toto
fluently
fluently
fluently
multiply
multiply
multiply
multi-digit
multi-digit
multi-digit
whole
whole
whole
numbers
numbers
using
using
the
the
numbers
using
the
standard
standard
algorithm.
algorithm.
standard
algorithm.
Students
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may
may
may
solve
solve
solve
aa decimal
adecimal
decimal
subtraction
subtraction
subtraction
problem
problem
problem
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using
using
using
an
anan
open
open
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number
number
number
line.
line.
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strategy
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isis is
still
still
based
based
on
place
place
value
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strategy
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based
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place
value
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understanding.
understanding.
23.6
23.6
23.6–– –0.79
0.79
0.79== =
1.2
1.2
1.2xx 2.3
x2.3
2.3== =2.76
2.76
2.76
(1.0
(1.0
(1.0xx 2.0)
x2.0)
2.0)++ +(1.0
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2.0)++ +
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x0.3)
0.3)
(0.2
(0.2
2.0
2.0
2.0++ +0.3
0.3
0.3++ +0.4
0.4
0.4++ +0.06
0.06
0.06== =2.76
2.76
2.76
For
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AA fifth
Afifth
fifth
grader
grader
grader
should
should
should
apply
apply
apply
knowledge
knowledge
knowledge
of
ofof
multiplication
multiplication
multiplication
working
working
working
with
with
with
decimals.
decimals.
decimals.
22 2
•• •33 3
11 1
•• •
22 2
AA strategy
Astrategy
strategy
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used
used
in
inin
earlier
earlier
earlier
grades
grades
grades
isis is
working
working
working
with
place
value.
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aa written
example
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with
place
place
value.
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This
This
awritten
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example
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what
students
are
able
to
do
in
grade
5.
what
what
students
students
are
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inin
grade
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5.5.
Student
will
use
agrid
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the
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property.
1.8
1.8
1.8++ +2.86
2.86
2.86== =
The
The
The
strategy
strategy
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doubling
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halving
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isis is
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applied
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toto
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decimal
decimal
multiplication.
multiplication.
multiplication.
88 8xx 2.5
x2.5
2.5== =
Fifth
Fifth
Fifth
graders
graders
graders
also
also
also
do
dodo
this
this
this
with
with
with
subtraction.
subtraction.
subtraction.
11 1
Student
Student
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use
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the
distributive
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The
strategy
strategy
strategy
doubling
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doubling
and
and
and
halving
halving
halving
isis is
applied
applied
applied
to
toto
decimal
decimal
decimal
multiplication.
multiplication.
multiplication.
Having
Having
Having
worked
worked
worked
with
with
with
addition,
addition,
addition,
subtraction,
subtraction,
subtraction,
multiplication
multiplication
multiplication
and
and
and
division
division
division
in
inin
both
both
both
third
third
third
and
and
and
fourth
fourth
fourth
grade,
grade,
grade,
fifth
fifth
fifth
grade
grade
grade
students
students
students
are
are
are
expected
expected
expected
to
toto
continue
continue
continue
apply
apply
apply
this
this
this
understanding
understanding
understanding
when
when
when
working
working
working
with
with
with
decimals.
decimals.
decimals.
•• •33 3
•• •
1.8
1.8
1.8++ +2.86
2.86
2.86== =
Math
Math
22 2
22 2
AA strategy
Astrategy
strategy
used
used
used
in
inin
earlier
earlier
earlier
grades
grades
grades
isis is
working
working
working
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place
value.
isis is
aa written
example
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with
place
place
value.
value.This
This
This
awritten
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ofof
what
students
are
able
to
do
in
grade
5.
what
what
students
students
are
are
able
able
toto
dodo
inin
grade
grade
5.5.
Fifth
Fifth
Fifth
graders
graders
graders
also
also
also
do
dodo
this
this
this
with
with
with
subtraction.
subtraction.
subtraction.
AA fifth
Afifth
fifth
grader
grader
grader
should
should
should
apply
apply
apply
knowledge
knowledge
knowledge
of
ofof
multiplication
multiplication
multiplication
working
working
working
with
with
with
decimals.
decimals.
decimals.
1.2
1.2
1.2xx 2.3
x2.3
2.3== =2.76
2.76
2.76
(1.0
(1.0
(1.0xx 2.0)
x2.0)
2.0)++ +(1.0
(1.0
(1.0xx 0.3)
x0.3)
0.3)++ +(0.2
(0.2
(0.2xx 2.0)
x2.0)
2.0)++ +
(0.2xx 0.3)
x0.3)
0.3)
(0.2
(0.2
2.0
2.0
2.0++ +0.3
0.3
0.3++ +0.4
0.4
0.4++ +0.06
0.06
0.06== =2.76
2.76
2.76
Fifth
Fifth
Fifth
grade
grade
grade
students
students
students
are
are
are
expected
expected
expected
to
toto
be
bebe
able
able
able
to
toto
fluently
fluently
fluently
multiply
multiply
multiply
multi-digit
multi-digit
multi-digit
whole
whole
whole
numbers
numbers
using
using
the
the
numbers
using
the
standard
standard
algorithm.
algorithm.
standard
algorithm.
AA student’s
Astudent’s
student’s
model
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of
ofof
1.2
1.2
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xx 2.3
2.3
x 2.3
(which
(which
(which
means
means
means
11 1
and
and
and
2-tenths
2-tenths
2-tenths
of
ofof
22 and
2
and
and
3-tenths).
3-tenths).
3-tenths).Each
Each
Each
section
section
section
isis is
labeled
labeled
labeled
to
toto
show
show
show
the
the
the
product.
product.
product.
Los estudiantes de quinto grado trabajan
con las estrategias en la investigación de la
división. Una estrategia que ayuda a los
estudiantes se multiplica arriba.
Una estrategia que el estudiante de quinto
grado podría utilizar para la división es el
razonamiento proporcional.
768 ÷ 16
÷2 ÷2
384 ÷ 8
÷2 ÷ 2
192 ÷ 4
÷2 ÷ 2
96 ÷ 2
÷2÷ 2
48 ÷ 1 = 48
768 ÷ 16 =
Guía de ruta
para Padres
Grado 5
Los alumnos de quinto grado usarán
fracciones equivalentes con el fin de
sumar y restar.
 + 
Este estudiante ha utilizado la estrategia
cociente parcial para dividir este problema.
634 ÷ 26 =

+
 
=
 
Estudiantes del quinto grado resuelven
problemas de fracciones. Este ejemplo
implica la multiplicación de un número
entero y una fracción.
Hay 4 hojas de papel de colores, y tengo que
utilizar de cada hoja para terminar mi
proyecto de arte. ¿Cuánto papel voy a usar?

cuatro veces significa que
 de papel
ha sido usado el cual son 3 hojas enteras y
 de la última hoja.
División de una fracción por una fracción no es
un requisito en el grado 5.
Estudiantes del quinto grado exploran la
división de fracciones.  es el resultado de
3 ÷ 4 y se debe notar que  multiplicado
por 4 es 3. Si 3 pizzas son compartidas por
igual por 4 personas, cada persona
tiene un pedazo del tamaño de  .
Key Concepts:
Multiplication & Division
Working with Fractions
Escuelas del Condado
de Cobb
Estrategias para la división,
Trabajar con decimales
y fracciones
2013-2014
Matemáticas
Después de haber trabajado con la suma,
resta, multiplicación y división, tanto en
tercero y cuarto grado, se espera que los
alumnos de quinto grado continúen
aplicando este conocimiento al trabajar con
decimales.
Una estrategia utilizada en los grados
anteriores está trabajando con el valor de
posición. Este es un ejemplo escrito de lo que
los alumnos son capaces de hacer en quinto
grado.
1.8 + 2.86 =
Los estudiantes pueden resolver un problema
de resta decimal utilizando una línea
numérica abierta. Esta estrategia sigue
basándose con la comprensión del valor de
posición.
23.6 – 0.79 = 22.81
2
•
3
1
•
2
La estrategia de duplicación y la reducción a la
mitad, se aplica a la multiplicación decimal.
8 x 2.5 =
Estudiantes del quinto grado también hacen
esto con la resta.
Un estudiante de quinto grado debe aplicar
el conocimiento de la multiplicación
trabajando con decimales.
Se espera que los estudiantes de quinto grado
ser capaz de multiplicar fluidez conjunto de
varios dígitos de
números enteros con el
algoritmo estándar.
El estudiante usará una cuadrícula para
mostrar un modelo de un problema. El uso
de modelos continúa trabajando con la
propiedad distributiva.
1.2 x 2.3 = 2.76
(1.0 x 2.0) + (1.0 x 0.3) + (0.2 x 2.0) +
(0.2 x 0.3)
2.0 + 0.3 + 0.4 + 0.06 = 2.76
Modelo de un estudiante de 1.2 x 2.3 (lo que
significa que 1 y 2 décimas de 1 y 3 décimas).
Cada sección se etiqueta para mostrar el
producto.