Grading Benchmarks – FIFTH GRADE
MATHEMATICS
1) Understands and applies mathematical concepts.
Trimester
1
2
3
4
1st
Numeration:
Student is unable or
rarely able to
demonstrate
understanding of
numeration
concepts.
Numeration: Student
demonstrates partial
understanding of
numeration concepts.
Numeration:
● Student consistently understands
place value concepts in the base
ten numeration system; that in a
multi-digit number, a digit in one
place represents 10 times as much
as it represents in the place to its
right and 1/10 of what it
represents in the place to its left.
5.NBT.A.1
● Student can apply and explain
patterns in zeros when
multiplying by powers of 10.
5.NBT.A.2
● Student can explain patterns in the
placement of a decimal point when
multiplying or dividing by a power
of 10. 5.NBT.A.2
● Student uses whole number
exponents to denote powers of 10.
5.NBT.A.2
Numeration:
Student consistently
makes insightful
connections to other
ideas and concepts
and independently
challenges
him/herself.
Grading Benchmarks – FIFTH GRADE
●
Student is able to read and write
decimals to thousandths using
base-ten numerals, number names,
and expanded form. 5.NBT.A.3.A
● Student can compare two decimals
to thousandths based on meanings
of the digits in each place, using >,
=, and < symbols to record the
results of comparisons.
5.NBT.A.3.B
● Student uses place value
understanding to round decimals
to any place. 5.NBT.A.4
Multiplication and
Division with MultiDigit Whole Numbers:
Student is unable or
rarely able to use
concepts of
multiplication and
division of whole
numbers.
Multiplication and
Division with MultiDigit Whole Numbers:
Student sometimes uses
concepts of
multiplication and
division of whole
numbers.
Multiplication and Division with MultiDigit Whole Numbers:
● Student can fluently multiply
multi-digit whole numbers using
the standard algorithm.
5.NBT.B.5
● Student consistently finds wholenumber quotients of whole
numbers with up to four-digit
dividends and two-digit divisors.
5.NBT.B.6
● Student consistently applies
strategies based on place value,
the properties of operations,
and/or the relationship between
Multiplication and
Division with MultiDigit Whole Numbers:
Student consistently
makes insightful
connections to other
ideas and concepts and
independently challenges
him/herself.
Grading Benchmarks – FIFTH GRADE
●
Operations with
Decimals to
Hundredths:
Student is
unable or rarely
able to use
concepts of
decimal
operations.
Operations with
Decimals to
Hundredths:
Student
sometimes uses
concepts of
decimal
operations.
multiplication and division to
solve problems. 5.NBT.B.6
Student can illustrate and explain
calculations by using equations,
rectangular arrays, and/or area
models. 5.NBT.B.6
Operations with Decimals to
Hundredths:
● Student fluently adds,
subtracts, multiplies and
divides decimals to
hundredths. 5.NBT.B.7
● Student uses concrete models or
drawings and consistently applies
strategies based on place value,
the properties of operations,
and/or the relationship between
inverse operations to solve
problems. 5.NBT.B.7
Operations with
Decimals to
Hundredths:
Student
consistently
makes insightful
connections to
other ideas and
concepts and
independently
challenges
him/herself.
Grading Benchmarks – FIFTH GRADE
2nd
Adding and
Subtracting Fractions:
Student is unable or
rarely able to use
concepts of addition
and subtraction of
fractions.
Adding and Subtracting
Fractions:
Student sometimes uses
concepts of addition and
subtraction of fractions.
Adding and Subtracting Fractions:
● Student can add and subtract
fractions and mixed numbers by
using equivalent fractions.
5.NF.A.1
● Student uses visual fraction
models and equations to solve
problems. 5.NF.A.2
● Student consistently uses
benchmark fractions and number
sense of fractions to estimate
mentally and assess the
reasonableness of answers.
5.NF.A.2
Multiplying Fractions:
●
Student can interpret the product
Adding and Subtracting
Fractions:
Student consistently
makes insightful
connections to other
ideas and concepts and
independently
challenges him/herself.
Grading Benchmarks – FIFTH GRADE
●
●
●
Multiplying Fractions:
Multiplying Fractions:
Student is unable or
rarely able to use
concepts of
multiplication of
fractions.
Student sometimes uses
concepts of
multiplication of
fractions.
(a/b) × q as a parts of a partition
of q into b equal parts;
equivalently, as the result of a
sequence of operations a × q ÷ b.
5.NF.B.4.A
Student can find the area of a
rectangle with fractional side
lengths by tiling it with unit squares
of the appropriate unit fraction side
lengths, and show that the area is
the same as would be found by
multiplying the side lengths.
5.NF.B.4.B
Student can multiply fractional side
lengths to find areas of rectangles,
and represent fraction products as
rectangular areas. 5.NF.B.4.B
Student can interpret multiplication
as scaling by:
- comparing the size of a product
to the size of one factor on the basis
of the size of the other factor,
without performing the indicated
multiplication. 5.NF.B.5.A
- explaining why multiplying a
given number by a fraction greater
than 1 results in a product greater
than the given number; explaining
why multiplying a given number by
a fraction less than 1 results in a
product smaller than the given
Multiplying Fractions:
Student consistently
makes insightful
connections to other
ideas and concepts and
independently
challenges him/herself.
Grading Benchmarks – FIFTH GRADE
●
number. 5.NF.B.5.B
Student can solve real world
problems involving multiplication
of fractions and mixed numbers by
using visual fraction models or
equations to represent the problem.
5.NF.B.6
Dividing Fractions:
●
●
●
●
●
Student can interpret a fraction as
division of the numerator by the
denominator (a/b = a ÷ b).
5.NF.B.3
Student can solve word problems
involving division of whole
numbers leading to answers in the
form of fractions or mixed
numbers, by using visual fraction
models or equations to represent
the problem. 5.NF.B.3
Student can interpret division of a
unit fraction by a non-zero whole
number, and compute such
quotients. 5.NF.B.7.A
Student can interpret division of a
whole number by a unit fraction,
and compute such quotients.
5.NF.B.7.B
Student can solve real world
Grading Benchmarks – FIFTH GRADE
Dividing Fractions:
Dividing Fractions:
Student is unable or
rarely able to use
concepts of dividing
fractions.
Student sometimes uses
concepts of division of
fractions.
problems involving division of unit
fractions by non-zero whole
numbers and division of whole
numbers by unit fractions, by using
visual fraction models and
equations to represent the problem.
5.NF.B.7.C
Volume Concepts:
●
●
●
●
Student recognizes that a cube with
side length 1 unit, called a "unit
cube," is said to have "one cubic
unit" of volume, and can be used to
measure volume. 5.MD.C.3.A
Student recognizes that a solid
figure, which can be packed
without gaps or overlaps
using n unit cubes is said to have a
volume of n cubic units.
5.MD.C.3.B
Student can measure volumes by
counting unit cubes, using cubic
cm, cubic in, cubic ft, and
improvised units. 5.MD.C.4
Student can find the volume of a
right rectangular prism with wholenumber side lengths by packing it
with unit cubes, and show that the
volume is the same as would be
found by multiplying the edge
Dividing Fractions:
Student consistently
makes insightful
connections to other
ideas and concepts and
independently
challenges him/herself.
Grading Benchmarks – FIFTH GRADE
●
Volume Concepts:
Volume Concepts:
Student is unable or
rarely able to use
volume concepts.
Student sometimes uses
volume concepts.
●
lengths, equivalently by
multiplying the height by the area
of the base. Represent threefold
whole-number products as
volumes, e.g., to represent the
associative property of
multiplication. 5.MD.C.5.A
Student can apply the
formulas V = l × w × h and V = b ×
h for rectangular prisms to find
volumes of right rectangular prisms
with whole-number edge lengths in
the context of solving real world
and mathematical problems.
5.MD.C.5.B
Student recognizes volume as
additive and can find volumes of
solid figures composed of two nonoverlapping right rectangular
prisms by adding the volumes of
the non-overlapping parts, applying
this technique to solve real world
problems. 5.MD.C.5.C
Converting Measurements:
● Student is able to convert among
different-sized standard
measurement units within a given
measurement system. 5.MD.5.A.1
Volume Concepts:
Student consistently
makes insightful
connections to other
ideas and concepts and
independently
challenges him/herself.
Grading Benchmarks – FIFTH GRADE
●
Student uses these conversions in
solving multi-step, real world
problems. 5.MD.5.A.1
Writing and Interpreting Numerical
Expressions:
● Student is able to use parentheses,
brackets, or braces in numerical
expressions, and evaluate
expressions with these symbols.
5.OA.A.1
● Student is able to write simple
expressions that record calculations
with numbers, and interpret
numerical expressions without
evaluating them. 5.OA.A.2
Grading Benchmarks – FIFTH GRADE
Converting
Measurements:
Student is unable or
rarely able to use
concepts of converting
measurements.
Converting
Measurements:
Student sometimes uses
concepts of converting
measurements.
Converting
Measurements:
Student consistently
makes insightful
connections to other
ideas and concepts and
independently
challenges him/herself.
Grading Benchmarks – FIFTH GRADE
Writing and
Interpreting Numerical
Expressions:
Student is unable or
rarely able to use
concepts of writing and
interpreting numerical
expressions.
Writing and Interpreting
Numerical Expressions:
Student sometimes uses
concepts of writing and
interpreting numerical
expressions.
Writing and
Interpreting Numerical
Expressions:
Student consistently
makes insightful
connections to other
ideas and concepts and
independently
challenges him/herself.
Grading Benchmarks – FIFTH GRADE
Grading Benchmarks – FIFTH GRADE
3rd
Representing and
Interpreting Data:
Student is unable or
rarely able to use
concepts of
representing and
interpreting data.
Points on the
Coordinate Plane:
Student is unable or
rarely able to use
concepts of points on
the coordinate plane.
Representing and
Interpreting Data:
Student sometimes uses
concepts of representing
and interpreting data.
Points on the Coordinate
Plane:
Student sometimes uses
concepts of points on the
coordinate plane.
Representing and Interpreting Data:
● Student can make a line plot to
display a data set of measurements
in fractions of a unit (1/2, 1/4, 1/8).
5.MD.B.2
● Student can use operations on
fractions for fifth grade (5.NF.A.2,
5.NF.B.6) to solve problems
involving information presented in
line plots. 5.MD.B.2
Points on the Coordinate Plane:
● Student can use a pair of
perpendicular number lines, called
axes, to define a coordinate system,
with the intersection of the lines
(the origin) arranged to coincide
with the 0 on each line and a given
point in the plane located by using
an ordered pair of numbers, called
its coordinates. 5.G.A.1
● Student understands that the first
number indicates how far to travel
from the origin in the direction of
one axis, and the second number
indicates how far to travel in the
direction of the second axis, with
Representing and
Interpreting Data:
Student consistently
makes insightful
connections to other
ideas and concepts and
independently
challenges him/herself.
Points on the
Coordinate Plane:
Student consistently
makes insightful
connections to other
ideas and concepts and
independently
challenges him/herself.
Grading Benchmarks – FIFTH GRADE
●
●
the convention that the names of
the two axes and the coordinates
correspond (e.g., x-axis and xcoordinate, y-axis and ycoordinate). 5.G.A.1
Student can represent real world
and mathematical problems by
graphing points in the first quadrant
of the coordinate plane. 5.G.A.2
Student can interpret coordinate
values of points in the context of
the situation. 5.G.A.2
Analyzing Patterns and Relationships:
● Student can generate two numerical
patterns using two given rules and
identify apparent relationships
between corresponding terms.
5.OA.B.3
● Student can form ordered pairs
consisting of corresponding terms
from the two patterns, and graph
the ordered pairs on a coordinate
plane. 5.OA.B.3 (5.G.A.2)
Classifying Two-Dimensional Figures:
● Student understands that attributes
belonging to a category of twodimensional figures also belong to
Grading Benchmarks – FIFTH GRADE
all subcategories of that category.
Analyzing Patterns and
Relationships:
Student is unable or
rarely able to use
concepts of analyzing
patterns and
relationships.
Analyzing Patterns and
Relationships:
Student sometimes uses
concepts of analyzing
patterns and
relationships.
Classifying TwoDimensional Figures:
Student is unable or
rarely able to use
concepts of classifying
two-dimensional
figures.
Classifying TwoDimensional Figures:
Student sometimes uses
concepts of classifying
two-dimensional figures.
(For example, all rectangles have four
right angles and squares are rectangles,
so all squares have four right angles.)
●
5.G.B.3
Student can classify twodimensional figures in a hierarchy
based on properties. 5.G.B.4
Analyzing Patterns and
Relationships:
Student consistently
makes insightful
connections to other
ideas and concepts and
independently
challenges him/herself.
Classifying TwoDimensional Figures:
Student consistently
makes insightful
connections to other
ideas and concepts and
independently
challenges him/herself.
Grading Benchmarks – FIFTH GRADE
Grading Benchmarks – FIFTH GRADE
2) Recalls math facts with speed and accuracy.
Trimester
1
2
ALL
Student is unable or
rarely able to recall
multiplication and
division facts with 1
through 12.
Student can
sometimes recall
multiplication and
division facts with
1 through 12.
3
Student can
consistently recall
multiplication and
division facts with
1 through 12.
4
Student is able to
apply and extend
content knowledge
independently.
Grading Benchmarks – FIFTH GRADE
Student is unable or
rarely able to
mentally calculate
products with
multiples of 10.
Student can
sometimes mentally
calculate products
with multiples of
10.
Student is unable to
mentally calculate
whole number
quotients with
divisors that are of
powers of 10.
Student can
sometimes mentally
calculate whole
number quotients
with divisors that
are powers of 10.
Student mentally
calculates products
with multiples of
10.
Student mentally
calculates whole
number quotients
with divisors that
are of powers of 10.
3) Understands and solves word problems accurately.
Trimester
1
2
3
4
ALL
●
●
●
Student is unable
or rarely able to
apply math
content
knowledge and
skills to solve
problems.
Student is unable
or rarely able to
●
Student
sometimes
applies math
content
knowledge and
skills to solve
problems.
Student
sometimes
chooses
●
●
●
Student consistently applies
math content knowledge and
skills to solve problems.
Student consistently chooses
appropriate tools (diagrams,
pictures, equations/number
sentences, tables, graphs,
number lines, formulas, etc.)
to solve problems.
●
Student
applies
content
knowledge
independently
to life
experiences.
Student
consistently
uses a variety
of processes
Grading Benchmarks – FIFTH GRADE
●
choose
appropriate tools
(diagrams,
pictures,
equations/numbe
r sentences,
tables, graphs,
number lines,
formulas, etc.) to
solve problems.
Student work
rarely includes
all necessary
calculations and
labels.
●
appropriate tools
(diagrams,
pictures,
equations/numbe
r sentences,
tables, graphs,
number lines,
formulas, etc.) to
solve problems.
Student work
sometimes
includes all
necessary
calculations and
labels.
●
Student work includes all
necessary calculations and
labels.
including
problem
solving,
reasoning,
communicating
, connecting,
and
representing
to extend
solutions to
other
situations, to
design other
strategies,
and/or to
apply
strategies to
life
experiences.
4) Computes accurately.
Trimester
ALL
1
Student is unable or
rarely able to identify
appropriate operations
and mathematically
compute the correct
answer.
2
3
4
Student sometimes
identifies appropriate
operations and
mathematically computes
the correct answer.
Student consistently
identifies appropriate
operations and
mathematically computes
the correct answer.
Student consistently
applies appropriate
operations and computes
accurately on more
complex problems, mental
Grading Benchmarks – FIFTH GRADE
math, and/or other
mathematical concepts.
5) Clearly expresses mathematical thinking in written and oral form.
Trimester
ALL
1
2
3
Student is unable or rarely
able to communicate
mathematical thinking
precisely and with
accurate vocabulary.
Student sometimes, but
not consistently,
communicates
mathematical thinking
precisely and with
accurate vocabulary.
Student communicates all
mathematical thinking
precisely and with
accurate vocabulary.
4
Student
communicates all
mathematical
thinking precisely and
with accurate
vocabulary.
Student communicates
logical arguments clearly
in oral, written, and/or
graphic form to
show why a result makes
sense.