2012-2013 Quarter 2 – 5th Grade Math Rubric
Mathematics
Rubric Key:
Standard
MCC5.OA.1 Use
parentheses, brackets, or
braces in numerical
expressions, and
evaluate expressions
with these symbols.
MCC5.OA.2 Write simple
expressions that record
calculations with
numbers, and interpret
numerical expressions
without evaluating
them.
Standard
MCC5.NBT.1 Recognize
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.
September 18, 2012
- Standards introduced and assessed
4
Uses and evaluates
problems with
parentheses, brackets,
and braces with no
procedural or
computational errors all
of the time.
Communicates
mathematical ideas by
writing simple
expressions that record
calculations with
numbers, and interprets
numerical expressions all
of the time.
4
Analyzes the effect on
the product when a
number is multiplied by
10, 100, 1000, 0.1 or
1/10, 0.01 or 1/100, and
0.001 or 1/1000 with no
procedural or
computational errors all
of the time.
- Standards maintained and assessed as needed
Operations and Algebraic Thinking
Write and interpret numerical expressions.
3
2
Consistently uses and
Shows progress, but
evaluates problems with inconsistently uses and
parentheses, brackets,
evaluates problems with
and braces with few
parentheses, brackets,
procedural or
and braces some of the
computational errors
time.
most of the time.
Consistently
Shows progress, but
communicates
inconsistently
mathematical ideas by
communicates
writing simple
mathematical ideas by
expressions that record
writing simple
calculations with
expressions that record
numbers, and interprets calculations with
numerical expressions
numbers, and interprets
with few procedural or
numerical expressions
computational errors
some of the time.
most of the time.
Number & Operations in Base Ten
Understand the place value system.
3
2
Consistently analyzes the Shows progress, but
effect on the product
inconsistently analyzes
when a number is
the effect on the product
multiplied by 10, 100,
when a number is
1000, 0.1 or 1/10, 0.01
multiplied by 10, 100,
or 1/100, and 0.001 or
1000, 0.1 or 1/10, 0.01
1/1000 with few
or 1/100, and 0.001 or
procedural or
1/1000 some of the time.
computational errors
most of the time.
1
Shows minimal progress
or seldomly uses and
evaluates problems
including parentheses,
brackets, and braces.
Notes
For example, evaluate
the numerical
expression:
2 x [(9x4) - (17 -6)] = 50
Shows minimal progress
or seldomly
communicates
mathematical ideas by
writing simple
expressions that record
calculations with
numbers, and interprets
numerical expressions.
For example, express the
calculation “add 8 and 7,
then multiply by 2” as 2 ×
(8 + 7). Recognize that 3
× (18932 + 921) is three
times as large as 18932 +
921, without having to
calculate the indicated
sum or product.
1
Shows minimal progress
or seldomly analyzes the
effect on the product
when a number is
multiplied by 10, 100,
1000, 0.1 or 1/10, 0.01
or 1/100, and 0.001 or
1/1000.
Notes
Grade 5: Quarter 2
1 of 10
Standard
MCC5.NBT.2 Explain
patterns in the number
of zeros of the product
when multiplying a
number by powers of 10,
and explain patterns in
the placement of the
decimal point when a
decimal is multiplied or
divided by a power of 10.
Use whole-number
exponents to denote
powers of 10.
MCC5.NBT.3 Read,
write, and compare
decimals to
thousandths.
a. Read and write
decimals to thousandths
using base-ten
numerals, number
names, and expanded
form.
MCC5.NBT.3 Read,
write, and compare
decimals to
thousandths.
b. Compare two
decimals to thousandths
based on meanings of
the digits in each place,
using >, =, and < symbols
to record the results of
comparisons.
September 18, 2012
4
Explain the patterns in
the number of zeros and
placement of decimals in
multiplication or division
problems when
multiplying or dividing by
a power of 10 (10, 100,
1,000, 0.1, 0.01, 0.001)
with no procedural or
computational errors all
of the time.
Number & Operations in Base Ten
Understand the place value system.
3
2
Consistently explains the Shows progress, but
patterns in the number
inconsistently explains
of zeros and placement
the patterns in the
of decimals in
number of zeros and
multiplication or division placement of decimals in
problems when
multiplication or division
multiplying or dividing by problems when
a power of 10 (10, 100,
multiplying or dividing by
1,000, 0.1, 0.01, 0.001)
a power of 10 (10, 100,
with few procedural or
1,000, 0.1, 0.01, 0.001)
computational errors
some of the time.
most of the time.
1
Shows minimal progress
or seldomly explains the
patterns in the number
of zeros and placement
of decimals in
multiplication or division
problems when
multiplying or dividing by
a power of 10 (10, 100,
1,000, 0.1, 0.01, 0.001).
Notes
Make sure to use
concepts of exponential
notation.
Standard has been
separated due to
complexity and length.
Read and write decimals
to thousandths place
value using base-ten
numerals, number
names, and expanded
form with no procedural
errors all of the time.
Consistently reads and
writes decimals to
thousandths place value
using base-ten numerals,
number names, and
expanded form with few
procedural errors most
of the time.
Shows progress, but
inconsistently reads and
writes decimals to
thousandths place value
using base-ten numerals,
number names, and
expanded form some of
the time.
Shows minimal progress
or seldomly reads and
writes decimals to
thousandths place value
using base-ten numerals,
number names, and
expanded form.
Compares two decimals
to the thousandths place
based on meanings of
the digits in each place,
using >, =, and < symbols
to record the results of
comparisons with no
procedural errors all of
the time.
Consistently compares
two decimals to the
thousandths place based
on meanings of the digits
in each place, using >, =,
and < symbols to record
the results of
comparisons with few
procedural errors most
of the time.
Shows progress, but
inconsistently compares
two decimals to the
thousandths place based
on meanings of the digits
in each place, using >, =,
and < symbols to record
the results of
comparisons some of the
time.
Shows minimal progress
or seldomly compares
two decimals to the
thousandths place based
on meanings of the digits
in each place, using >, =,
and < symbols to record
the results of
comparisons.
Grade 5: Quarter 2
Be sure to use wholenumber exponents to
denote powers of 10.
MCC5.NBT.3a
347.392 = 3 × 100 + 4 ×
10 + 7 × 1 + 3 × (1/10) + 9
× (1/100) + 2 × (1/1000).
2 of 10
Standard
MCC5.NBT.4 Use place
value understanding to
round decimals to any
place.
MCC5.NBT.5 Fluently
multiply multi-digit
whole numbers using the
standard algorithm.
MCC5.NBT.6 Find wholenumber quotients of
whole numbers with up
to four-digit dividends
and two digit divisors,
using strategies based on
place value, the
properties of operations,
and/or the relationship
between multiplication
and division. Illustrate
and explain the
calculation by using
equations, rectangular
arrays, and/or area
models.
September 18, 2012
Number & Operations in Base Ten
Understand the place value system.
4
3
2
1
Uses place value
Consistently uses place
Shows progress, but
Shows minimal progress
understanding to round
value understanding to
inconsistently uses place or seldomly uses place
decimals to any place
round decimals to any
value understanding to
value understanding to
with no procedural
place with few
round decimals to any
round decimals to any
errors all of the time.
procedural errors most
place some of the time.
place.
of the time.
Perform operations with multi-digit whole numbers and with decimals to hundredths.
Solves multi-digit
Consistently solves multi- Shows progress, but
Shows minimal progress
multiplication problems
digit multiplication
inconsistently solves
or seldomly uses
with no procedural or
problems with few
multi-digit multiplication strategies to solve multicomputational errors all
procedural or
problems some of the
digit multiplication
of the time.
computational errors
time.
problems.
most of the time.
Finds whole-number
quotients of whole
numbers with up to fourdigit dividends and two
digit divisors with no
procedural or
computational errors all
of the time.
Consistently finds wholenumber quotients of
whole numbers with up
to four-digit dividends
and two digit divisors
with few procedural or
computational errors
most of the time.
Shows progress, but
inconsistently finds
whole-number quotients
of whole numbers with
up to four-digit dividends
and two digit divisors
some of the time.
Shows minimal progress
or seldomly finds wholenumber quotients of
whole numbers with up
to four-digit dividends
and two digit divisors.
*See note.
*See note.
*See note.
*See note.
Grade 5: Quarter 2
Notes
Fluency has been
interpreted to mean that
a student solves multidigit multiplication
problems effortlessly and
correctly most of the
time.
Explore the meaning of
divisibility as a situation
with no remainder,
analyze divisibility, and
informally explain
divisibility relationships.
*Ensure use of strategies
based on place value, the
properties of operations,
and/or the relationship
between multiplication
and division. Illustrate
and explain the
calculation by using
equations, rectangular
arrays, and/or area
models.
3 of 10
Standard
MCC5.NBT.7 Add,
subtract, multiply, and
divide decimals to
hundredths, using
concrete models or
drawings and strategies
based on place value,
properties of operations,
and/or the relationship
between addition and
subtraction; relate the
strategy to a written
method and explain the
reasoning used.
MCC5.NF.1 Add and
subtract fractions with
unlike denominators
(including mixed
numbers) by replacing
given fractions with
equivalent fractions in
such a way as to produce
an equivalent sum or
difference of fractions
with like denominators.
September 18, 2012
Number & Operations in Base Ten
Perform operations with multi-digit whole numbers and with decimals to hundredths.
4
3
2
1
Adds, subtracts,
Consistently adds,
Shows progress, but
Shows minimal progress
multiplies, and divides
subtracts, multiplies, and inconsistently adds,
or seldomly adds,
decimals with no
divides decimals with
subtracts, multiplies, and subtracts, multiplies, and
procedural or
few procedural or
divides decimals some of divides decimals.
computational errors all
computational errors
the time.
of the time.
most of the time.
Number and Operations – Fractions
Use equivalent fractions as a strategy to add and subtract fractions
Add and subtract
Consistently adds and
Shows progress, but
Shows minimal progress
fractions and mixed
subtracts fractions and
inconsistently adds and
or seldomly adds and
numbers with unlike
mixed numbers with
subtracts fractions and
subtracts fractions with
denominators with no
unlike denominators
mixed numbers with
unlike denominators and
procedural or
with few procedural or
unlike denominators
mixed numbers.
computational errors all
computational errors
some of the time.
of the time.
most of the time.
Grade 5: Quarter 2
Notes
Ensure use of concrete
models or drawings and
strategies based on place
value, properties of
operations, and/or the
relationship between
addition and subtraction;
relate the strategy to a
written method and
explain the reasoning
used.
For example, 2/3 + 5/4 =
8/12 + 15/12 = 23/12. (In
general, a/b + c/d = (ad +
bc)/bd).
4 of 10
Standard
MCC5.NF.2 Solve word
problems involving
addition and subtraction
of fractions referring to
the same whole,
including cases of unlike
denominators.
Apply and extend
previous understandings
of multiplication and
division to multiply and
divide fractions.
MCC5.NF.3 Interpret a
fraction as division of the
numerator by the
denominator
(a/b = a ÷ b). Solve word
problems involving
division of whole
numbers leading to
answers in the form of
fractions or mixed
numbers.
September 18, 2012
Number and Operations – Fractions
Use equivalent fractions as a strategy to add and subtract fractions
4
3
2
1
Solve word problems
Consistently solve word
Shows progress, but
Shows minimal progress
involving addition and
problems involving
inconsistently solves
or seldomly solves word
subtraction of fractions
addition and subtraction word problems involving problems involving
with no procedural or
of fractions with few
addition and subtraction addition and subtraction
computational errors all
procedural or
of fractions some of the
of fractions.
of the time.
computational errors
time.
most of the time.
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Interpret a fraction as
Consistently interprets a Shows progress, but
Shows minimal progress
division of the numerator fraction as division of the inconsistently interprets
or seldomly interprets a
by the denominator (a/b numerator by the
a fraction as division of
fraction as division of the
= a ÷ b) and solve word
denominator (a/b = a ÷ b) the numerator by the
numerator by the
problems involving
and solves word
denominator (a/b = a ÷ b) denominator (a/b = a ÷ b)
division of whole
problems involving
and/or inconsistently
and/or solves word
numbers with no
division of whole
solves word problems
problems involving
procedural or
numbers with few
involving division of
division of whole
computational errors all
procedural or
whole numbers some of
numbers with no
of the time.
computational errors
the time.
procedural or
most of the time.
computational errors.
Grade 5: Quarter 2
Notes
Solve problems by using
visual fraction models or
equations to represent
the problem. Use
benchmark fractions and
number sense of
fractions (0, ½, 1) to
estimate mentally and
assess the
reasonableness of
answers.
For example, recognize
an incorrect result 2/5 +
½ = 3/7, by observing
that 3/7 < ½.
Use visual fraction
models or equations to
represent the problem.
For example, interpret ¾
as the result of dividing 3
by 4, noting that ¾
multiplied by 4 equals 3,
and that when 3 wholes
are shared equally
among 4 people each
person has a share of size
¾. If 9 people want to
share a 50-pound sack of
rice equally by weight,
how many pounds of rice
should each person get?
Between what two whole
numbers does your
answer lie?
5 of 10
Standard
MCC5.NF.4 Apply and
extend previous
understandings of
multiplication to multiply
a fraction or whole
number by a fraction.
a. Interpret the product
(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.
MCC5.NF.4 Apply and
extend previous
understandings of
multiplication to multiply
a fraction or whole
number by a fraction.
b. 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. Multiply
fractional side lengths to
find areas of rectangles,
and represent fraction
products as rectangular
areas.
September 18, 2012
Number and Operations – Fractions
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
4
3
2
1
Multiply a fraction or
Consistently multiplies a
Shows progress, but
Shows minimal progress
whole number by a
fraction or whole number inconsistently multiplies
or seldomly multiplies a
fraction by interpreting
by a fraction by
a fraction or whole
fraction or whole number
the product (a/b) × q as a interpreting the product
number by a fraction by
by a fraction by
parts of a partition of q
(a/b) × q as a parts of a
interpreting the product
interpreting the product
into b equal parts with no partition of q into b equal (a/b) × q as a parts of a
(a/b) × q as a parts of a
procedural or
parts with few
partition of q into b equal partition of q into b equal
computational errors all
procedural or
parts some of the time.
parts.
of the time.
computational errors
most of the time.
Multiply a fraction or
whole number by a
fraction by finding the
area of a rectangle by
tiling (modeling
multiplication of
fractions) it with unit
squares and multiply
fractional side lengths to
find areas of rectangles,
and represent fraction
products as rectangular
areas with no procedural
or computational errors
all of the time.
Consistently multiplies a
fraction or whole number
by a fraction by finding
the area of a rectangle by
tiling (modeling
multiplication of
fractions) it with unit
squares and multiply
fractional side lengths to
find areas of rectangles,
and represent fraction
products as rectangular
areas with few
procedural or
computational errors
most of the time.
Shows progress, but
inconsistently multiplies
a fraction or whole
number by a fraction by
finding the area of a
rectangle by tiling
(modeling multiplication
of fractions) it with unit
squares and multiply
fractional side lengths to
find areas of rectangles,
and represent fraction
products as rectangular
areas some of the time.
Notes
Use a visual fraction
model to show (2/3) × 4 =
8/3, and create a story
context for this equation.
Do the same with (2/3) ×
(4/5) =8/15. (In general,
(a/b) × (c/d) = ac/bd.)
Shows minimal progress
or seldomly multiplies a
fraction or whole number
by a fraction by finding
the area of a rectangle by
tiling (modeling
multiplication of
fractions) it with unit
squares and multiply
fractional side lengths to
find areas of rectangles,
and represent fraction
products as rectangular
areas.
Grade 5: Quarter 2
6 of 10
Number and Operations – Fractions
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Standard
4
3
2
1
MCC5.NF.5 Interpret
multiplication as scaling
(resizing), by:
a. 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.
Interpret multiplication
as scaling (resizing), 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
with no procedural or
computational errors all
of the time.
Shows progress, but
inconsistently interprets
multiplication as scaling
(resizing), 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 some of
the time.
Shows minimal progress
or seldomly interprets
multiplication as scaling
(resizing), 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.
MCC5.NF.5 Interpret
multiplication as scaling
(resizing), by:
b. 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 number; and
relating the principle of
fraction equivalence a/b
= (n×a)/(n×b) to the
effect of multiplying a/b
by 1.
Interpret multiplication
as scaling (resizing), by
explaining why
multiplying a given
number by a fraction
greater than 1 results in a
product greater than the
given number; and why
multiplying a given
number by a fraction less
than 1 results in a
product smaller than the
given number with no
procedural errors all of
the time.
Consistently interprets
multiplication as scaling
(resizing), 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 with few
procedural or
computational errors
most of the time.
Consistently interprets
multiplication as scaling
(resizing), by explaining
why multiplying a given
number by a fraction
greater than 1 results in a
product greater than the
given number; and why
multiplying a given
number by a fraction less
than 1 results in a
product smaller than the
given number with few
procedural errors most of
the time.
Shows progress, but
inconsistently interprets
multiplication as scaling
(resizing), by explaining
why multiplying a given
number by a fraction
greater than 1 results in a
product greater than the
given number; and why
multiplying a given
number by a fraction less
than 1 results in a
product smaller than the
given number some of
the time.
Shows minimal progress
or seldomly interprets
multiplication as scaling
(resizing), by explaining
why multiplying a given
number by a fraction
greater than 1 results in a
product greater than the
given number; and why
multiplying a given
number by a fraction less
than 1 results in a
product smaller than the
given number.
September 18, 2012
Grade 5: Quarter 2
Notes
Recognize multiplication
by whole numbers
greater than 1 as a
familiar case.
7 of 10
Number and Operations – Fractions
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Standard
MCC5.NF.6 Solve real
world problems
involving multiplication
of fractions and mixed
numbers.
MCC5.NF.7 Apply and
extend previous
understandings of
division to divide unit
fractions by whole
numbers and whole
numbers by unit
fractions.
a. Interpret division of a
unit fraction by a nonzero whole number, and
compute such quotients.
September 18, 2012
4
3
2
1
Solve real world
problems involving
multiplication of fractions
and mixed numbers with
no procedural or
computational errors all
of the time.
Apply and extend
previous understandings
of division to divide unit
fractions by whole
numbers and whole
numbers by unit fractions
by interpreting division of
a unit fraction by a whole
number, and compute
such quotients with no
procedural or
computational errors all
of the time.
Consistently solves real
world problems involving
multiplication of fractions
and mixed numbers with
few procedural or
computational errors
most of the time.
Consistently applies and
extends previous
understandings of
division to divide unit
fractions by whole
numbers and whole
numbers by unit fractions
by interpreting division of
a unit fraction by a whole
number, and compute
such quotients with few
procedural or
computational errors
most of the time.
Shows progress, but
inconsistently solves real
world problems involving
multiplication of fractions
and mixed numbers
some of the time.
Shows minimal progress
Use visual fraction
or seldomly solves real
models or equations to
world problems involving represent the problem.
multiplication of fractions
and mixed numbers
Shows progress, but
inconsistently applies
and extends previous
understandings of
division to divide unit
fractions by whole
numbers and whole
numbers by unit fractions
by interpreting division of
a unit fraction by a whole
number, and compute
such quotients some of
the time.
Shows minimal progress
or seldomly applies and
extends previous
understandings of
division to divide unit
fractions by whole
numbers and whole
numbers by unit fractions
by interpreting division of
a unit fraction by a whole
number, and compute
such quotients.
Grade 5: Quarter 2
Notes
For example, create a
story context for (1/3) ÷
4, and use a visual
fraction model to show
the quotient. Use the
relationship between
multiplication and
division to explain that
(1/3) ÷ 4 = 1/12 because
(1/12) × 4 = 1/3.
8 of 10
Standard
MCC5.MD.2 Make a
line plot to display a
data set of
measurements in
fractions of a unit
(1/2, 1/4, 1/8). Use
operations on
fractions for this
grade to solve
problems involving
information
presented in line
plots.
September 18, 2012
4
Makes line plots using
given data and solves
problems using the
data in the line plot
with no procedural
errors all of the time.
Measurement and Data
Represent and interpret data
3
2
Consistently makes line Shows progress, but
plots using given data
inconsistently makes
and solves problems
line plots using given
using the data in the
data and inconsistently
line plot with few
solves problems using
procedural errors most the data in the line plot
of the time.
some of the time.
1
Shows minimal
progress or seldomly
makes line plots using
given data and does
not solve problems
using the data in the
line plot.
Notes
For example, given
different measurements
of liquid in identical
beakers, find the amount
of liquid each beaker
would contain if the total
amount in all the beakers
were redistributed
equally.
Note: Line plots may
include whole numbers
or fractions, but
emphasis should be
given to fractional line
plots.
Grade 5: Quarter 2
9 of 10