NUMBER &
OPERATIONS
Not
Assessed
1
Student is unable to
explain the patterns in the
number of zeros of the
product when multiplying
or dividing by the powers
of 10 for both whole
numbers and decimals.
Fluently multiply
multi-digit whole
numbers
5.NBT.5
Student is unable to
accurately multiply a whole
number of up to 4- digits by
a 1-digit whole number
AND multiplies a 2-digit
whole number by a 2-digit
whole number.
Add decimals
(hundredths)
5.NBT.7
Student is unable to solve
division problems with up
to 4-digit dividends and 1digit divisors, including
problems that involve
remainders.
Student is unable to add two
decimals values.
Student is unable to subtract
two decimal values.
Subtract decimals
(hundredths)
5.NBT.7
Multiply decimals
(hundredths)
5.NBT.7
3
4
N/A
Demonstrate
understanding of
division procedures
5.NBT.1 and
5.NBT.2
Fluently divide
multi-digit numbers,
to find whole number
quotients
5.NBT.6
2
5th Grade
Mathematics Companion Document
Albany County School District #1
Student is unable to
multiply
two decimals values.
Student inconsistently
explains the patterns in the
number of zeros of the
product when multiplying or
dividing by the powers of 10
for both whole numbers and
decimals.
Student explains the
patterns in the number of
zeros of the product when
multiplying or
dividing by the powers of 10
for both whole numbers and
decimals.
Student accurately multiplies
a whole number of up to 4digits by a 1-digit whole
number AND multiplies a 2digit whole number by a 2digit whole number.
Student consistently and
accurately multiplies any
whole number by another
whole number.
Student accurately solves
division problems with up to
4-digit dividends and 1-digit
divisors, including problems
that involve remainders.
Student consistently and
accurately solves division
problems with up to 4- digit
dividends and 2-digit
divisors, including
problems that involve
remainders
Student consistently and
accurately divides any
whole number by another
whole number
Student is able to add two
decimal values to
hundredths using
understanding of place
value. This should include
multiple strategies
including: properties of
operations, relationship
between addition and
subtraction, models, or
traditional algorithm.
Student is able to
consistently and
accurately add any two
decimal values using
multiple strategies,
including the standard
algorithm.
N/A
Student is able to add two
decimal values (less than
hundredths) using
understanding of place value.
This should include multiple
strategies including:
properties of operations,
relationship between addition
and subtraction, models, or
traditional algorithm.
OR
Student is able to add two
decimal values to
hundredths using only one
strategy.
Student is able to subtract two
decimal values (less than
hundredths) using
understanding of place value.
This should include multiple
strategies including:
properties of operations,
relationship between addition
and subtraction, models, or
traditional algorithm.
OR
Student is able to subtract two
decimal values to hundredths
Student is able to subtract
two decimal values to
hundredths using
understanding of place value.
This should include multiple
strategies including:
properties of operations,
relationship between
addition and subtraction,
models, or traditional
algorithm.
Student is able to multiply
two decimal values (less than
hundredths) using
understanding of place value.
This should include multiple
strategies including:
properties of operations,
relationship between addition
and subtraction, models, or
traditional algorithm.
OR
Student is able to multiply
two decimals values to
hundredths
Student is able to multiply
two decimal values to
hundredths using
understanding of place
value. This should include
multiple strategies
including: properties of
operations, relationship
between addition and
subtraction, models, or
traditional algorithm.
Student is able consistently
and accurately subtract any
two decimal values using
multiple strategies,
including the standard
algorithm.
Student is able consistently
and accurately multiply any
two decimal values using
multiple strategies,
including the standard
algorithm.
Student is unable to
divide
two decimals values.
Divide decimals
(hundredths)
5.NBT.7
FRACTIONS
Add fractions with
unlike denominators
5.NF.1
Subtract fractions
with unlike
denominators
5.NF.1
Interpret a fraction
as division of the
numerator by the
denominator. Solve
word problems
involving the
division of whole
numbers leading to
answers in the form
of fractions.
Not
Assessed
1
5.NF.4
2
Student is able to divide
two decimal values to
hundredths using
understanding of place
value. This should include
multiple strategies
including: properties of
operations, relationship
between addition and
subtraction, models, or
traditional algorithm.
Student is able
consistently and
accurately divide any two
decimal values using
multiple strategies,
including the standard
algorithm.
3
4
Student is unable to add
fractions with unlike
denominators
Student inconsistently adds
fractions and/or mixed
numbers with like and unlike
denominators
Student consistently adds
fractions and/or mixed
numbers with like and
unlike denominators
N/A
Student is unable to
subtract fractions with
unlike denominators
Student inconsistently
subtracts fractions and mixed
numbers with like and unlike
denominators
Student consistently
subtracts fractions and
mixed numbers with like
and unlike denominators
N/A
Student does not
understand a fraction
as division of the
numerator by the
denominator.
5.NF.3
Apply and extend
previous
understandings of
multiplication to
multiply a fraction or
a whole number by a
fraction
Student is able to divide two
decimal values (less than
hundredths) using
understanding of place value.
This should include multiple
strategies including:
properties of operations,
relationship between addition
and subtraction, models, or
traditional algorithm.
OR
Student is able to divide two
decimal values to hundredths
using only one strategy
5th Grade
Mathematics Companion Document
Albany County School District #1
Student is unable to solve
problems that involve
multiplication of fractions
using visual fraction
models (i.e. area models,
tape diagrams, number
lines.).
Student accurately solves
word problems involving
the division of a whole
number leading to
answers in the form of
fractions or mixed
numbers, but does not
understand and interpret a
fraction as division of the
numerator by the denominator
OR Student inaccurately solves
word problems involving the
division of a whole number
leading to answers in the form
of fractions
or mixed numbers, but does
understand and interpret a
fraction as division of the
numerator by the
denominator.
Student can do some but not
all of the following
consistently: solves
problems involving
multiplication of a fraction
by a whole number and
fraction by a fraction.
Student understands and
explains the process of
multiplying a fraction by a
whole number and a
fraction by a fraction using
visual fraction models.
Student accurately solves
word problems
involving the division of a
whole number leading to
answers in the form of
fractions or mixed numbers
and
understands and interprets a
fraction as division of the
numerator by the
denominator.
Student can do ALL of
the following consistently:
solves problems involving
multiplication of a
fraction by a whole
number and fraction by a
fraction. Student
understands and explains
the process of multiplying
a fraction
by a whole number and a
fraction by a fraction
using visual fraction
models.
Student solves word
problems involving
division of fractions
by fractions using
visual fractions
models and equations
to represent the
problem.
N/A
Divide a unit fraction
by a whole number
5.NF.7
Student is unable to solve
problems that involve
division of a unit fraction by
a whole number.
Divide a whole
number by a unit
fraction
5.NF.7
GEOMETRY
Student is unable to
solve problems that
involve division of a
whole number by a
unit fraction.
Not
Assessed
Student is unable to find
the volume of a rectangular
prism with whole number
side lengths.
Find volume for a
rectangular prism
5.MD.5
MATHEMATICAL
PRACTICES
Make sense of
problems and
perseveres in solving
them
SMP1
1
Not
Assessed
Student inconsistently
solves problems that
involve division of a unit
fraction by a whole
number.
Student inconsistently
solves problems that
involve division of a
whole number by a unit
fraction
2
Student can do some but
not all of the following
consistently: finds the
volume of a rectangular
prism with whole number
side lengths using strategies
including packing it with
unit cubes and using the
formula for finding the
volume, and finds
volumes of solid figures
composed of two nonoverlapping right rectangular
prisms by adding the volumes
of non-overlapping parts.
5th Grade
Mathematics Companion Document
Albany County School District #1
Student consistently and
accurately solves problems
that involve division of a unit
fraction by a whole number.
Student consistently and
accurately solves problems
that involve division of a
whole number by a unit
fraction.
3
Student can do ALL of the
following consistently:
finds the volume of a
rectangular prism with
whole number side
lengths using strategies
including: packing it with
unit cubes and using the
formula for finding the
volume, and finds
volumes of solid figures
composed of two nonoverlapping right
rectangular prisms by
adding the volumes of
non-overlapping parts.
N/A
N/A
4
Student is able to find the
volume of a rectangular
prism with non-whole
number side lengths by
packing it with unit cubes,
and is able to apply the
formula for finding the
volume in the context of
solving real-world
problems.
1
2
3
4
When solving a problem the
student is unable to: 1.
Explain the meaning of
problem, 2. Look for
appropriate ways to solve it,
3. Evaluate the feasibility
and utility of alternatives, 4.
Continue to work on a
problem until a reasonable
solution is reached, 5.
Generalize strategies for use
in similar problem solving
contexts.
When solving a problem the
student is able to: 1. Explain
the meaning of problem, 2.
Look for appropriate ways to
solve it, 3. Evaluate the
feasibility and utility of
alternatives, and use those
alternative strategies to check
their own answers 4. Continue
to work on a problem until a
reasonable solution is reached,
5. Generalize strategies for use
in similar problem solving
contexts.
When solving a problem the
student is able to: 1. Explain
the meaning of problem, 2.
Look for appropriate ways
to represent and solve it, 3.
Evaluate the feasibility and
utility of alternatives, and
use those alternative
strategies to check their own
answers 4. Continue to work
on a problem until a
reasonable solution is
reached, 5. Generalize
strategies for use in similar
problem solving contexts.
N/A
5th Grade
Mathematics Companion Document
Albany County School District #1
Use numbers and
symbols to represent
a problem
SMP2
Communicate
effectively about
their learning and
respond
appropriately to
others’ perspectives
SMP3
Student may be able to
represent a problem using a
number sentence/equation
that represents the problem
solving process used.
Student is unable to clearly
explain and organize their
math thinking, verbally and
in writing, using formal
language. Student is unable
to use the reasoning of their
peers to look for accurate
and efficient strategies that
they can learn from and
apply in future problems.
Student is able to consistently
and accurately represent a
problem using a number
sentence/equation and the
equation represents the
problem solving process used,
with the answer represented
with appropriate units.
Student is also able to create a
problem based on a given
number sentence/equation.
Student is able to clearly
explain and organize their
mathematicalthinking,
verbally and in writing, using
formal language AND can
develop visual representations
of their thinking (for example
using an array to model a
multiplication problem).
Student uses the reasoning of
their peers to look for accurate
and efficient strategies that
they can learn from and apply
in future problems.
Student is able to
consistently and accurately
represent a problem using a
number sentence/equation
and the equation represents
the problem solving process
used, with the answer
represented with appropriate
units. Student is also able to
create a problem based on a
given number
sentence/equation. These
concepts can be applied to
both whole numbers and
fractions and decimals.
N/A
Student is able to clearly
explain and organize their
mathematical thinking,
verbally and in writing,
using formal language AND
can develop visual
representations of their
thinking (for example using
an array to model a
multiplication problem).
Student uses the reasoning
of their peers to look for
accurate and efficient
strategies that they can learn
from and apply in future
problems. Student
formulates questions to
understand or clarify the
mathematical thinking of
others.
N/A
5th Grade
Mathematics Companion Document
Albany County School District #1
Create mathematical
models to solve
problems and explain
thinking
SMP4
Student is unable to
represent problem situations
in multiple ways,
including: numbers, words
(mathematical language),
drawing pictures, using
objects, making a chart, list,
or graph, creating equations,
etc.
Student represents problem
situations in multiple ways,
including: numbers, words
(mathematical language),
drawing pictures, using
objects, making a chart, list, or
graph, creating equations, etc.
They use all of these
representations as needed.
Student connects the different
representations and explains
the connections.
Student represents problem
situations in multiple ways,
including: numbers, words
(mathematical language),
drawing pictures, using
objects, making a chart, list,
or graph, creating equations,
etc. They use all of these
representations as needed.
Student connects the
different representations and
explains the connections.
Student evaluates the utility
of models to determine the
models that are most useful
and efficient to solve
problems.
Student represents
problem situations in
multiple ways,
including: numbers,
words (mathematical
language),
drawing pictures, using
objects, making a chart,
list, or graph, creating
equations, and can use
these models to represent
two quantities
simultaneously. They use
all of these
representations as needed.
Student connects the
different representations
and explains the
connections. Student
evaluates the utility of
models to determine the
models that are most
useful and efficient to
solve problems.
N/A
Student is unable to select or
use appropriate
mathematical tools to
measure length/width or
model place value problems.
Appropriate tools may
include hundred charts,
number lines, place value
blocks, rulers, or measuring
tapes.
Student is able to select and
use appropriate mathematical
tools to measure length/width,
model place value problems.
Appropriate tools may include
hundred charts, number lines,
place value blocks, rulers, or
measuring tapes.
Student is able to select and
use appropriate
mathematical tools for
linear, weight, volume, angle
measure, etc. Student can
model place value problems,
and use tools in solving
problems. Appropriate tools
may include hundred charts,
number lines, place value
blocks, rulers, or measuring
tapes.
Student does not use grade
level vocabulary to
communicate descriptions
and explanations,
Student inconsistently uses
grade level vocabulary to
communicate descriptions and
explanations
Student consistently uses
grade level vocabulary to
communicate descriptions
and explanations
N/A
Student calculations are
consistently inaccurate
Student calculations are
inconsistently accurate
Student calculations are
consistentlyaccurate
N/A
Look for structure to
identify
mathematical
properties
SMP7
Student uses properties of
operations as strategies to
solve problems (for
example: commutative &
distributiveproperties)
Student uses properties of
operations as strategies to
solve and explain solutions to
problems (for example:
commutative & distributive
properties).
Student uses properties of
operations as strategies to
solve and explain solutions
to problems using the
commutative & distributive
properties. Examine
numerical patterns and relate
them to a rule or graphical
representation.
N/A
Develop and apply
formal strategies for
solving problems
SMP8
Student explains
calculations, but is unable to
explain how algorithms
work.
Student can explain
calculations and
understand how algorithms
work. Student also examines
patterns and generates
algorithms.
N/A
Use appropriate tools
SMP5
Attend to precision
(Academic
vocabulary) SMP6
Attend to precision
(Calculation)
SMP6
Student explains calculations
and understands how
algorithms work.