2012-2013 Quarter 4 – 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.
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.
- 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.
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.
Grade 5: Quarter 4
1 of 15
Standard
MCC5.OA.3 Generate
two numerical patterns
using two given rules.
Identify apparent
relationships between
corresponding terms.
Form ordered pairs
consisting of
corresponding terms
from the two patterns,
and graph the ordered
pairs on a coordinate
plane.
4
Generates, identifies,
and forms numerical
patterns and ordered
pairs with no procedural
or computational errors
all of the time.
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.
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.
September 18, 2012
Number & Operations in Base Ten
Analyze patterns and relationships
3
2
Consistently generates,
Shows progress, but
identifies, and forms
inconsistently generates,
numerical patterns and
identifies, and forms
ordered pairs with few
numerical patterns and
procedural or
ordered pairs some of
computational errors
the time.
most of the time.
Understand the place value system
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 generates,
identifies, and forms
numerical patterns and
ordered pairs.
Notes
Notes: Students may need
to use data from a table or
a coordinate plane. For
example, given the rule
“Add 3” and the starting
number 0, and given the
rule “Add 6” and the
starting number 0,
generate terms in the
resulting sequences, and
observe that the terms in
one sequence are twice
the corresponding terms in
the other sequence.
Explain informally why this
is so.
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.
Grade 5: Quarter 4
2 of 15
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.
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.
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.
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.
Compares two decimals
Consistently compares
to the thousandths place two decimals to the
based on meanings of the thousandths place based
digits in each place, using on meanings of the digits
>, =, and < symbols to
in each place, using >, =,
record the results of
and < symbols to record
comparisons with no
the results of
procedural errors all of
comparisons with few
the time.
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 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.
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.
Shows minimal progress
or seldomly reads and
writes decimals to
thousandths place value
using base-ten numerals,
number names, and
expanded form.
Standard has been
separated due to
complexity and length.
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).
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 4
3 of 15
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 errors place with few
round decimals to any
round decimals to any
all of the time.
procedural errors most of place some of the time.
place.
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.
*See note.
*See note.
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.
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.
Grade 5: Quarter 4
4 of 15
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.
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).
Grade 5: Quarter 4
5 of 15
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
fraction as division of the inconsistently interprets or seldomly interprets a
numerator by the
numerator by the
a fraction as division of
fraction as division of the
denominator (a/b = a ÷
denominator (a/b = a ÷
the numerator by the
numerator by the
b) and solve word
b) and solves word
denominator (a/b = a ÷
denominator (a/b = a ÷
problems involving
problems involving
b) and/or inconsistently
b) and/or solves word
division of whole
division of whole
solves word problems
problems involving
numbers with no
numbers with few
involving division of
division of whole
procedural or
procedural or
whole numbers some of numbers with no
computational errors all
computational errors
the time.
procedural or
of the time.
most of the time.
computational errors.
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?
Grade 5: Quarter 4
6 of 15
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 4
7 of 15
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
Notes
Recognize multiplication
by whole numbers
greater than 1 as a
familiar case.
Grade 5: Quarter 4
8 of 15
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.6 Solve real
world problems involving
multiplication of
fractions and mixed
numbers.
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.
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 whole number by a unit
fraction, 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
or seldomly solves real
world problems involving
multiplication of fractions
and mixed numbers
Use visual fraction
models or equations to
represent the problem.
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.
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.
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 whole number by a unit
fraction, 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 whole number by a unit
fraction, and compute
such quotients.
For example, create a
story context for 4 ÷
(1/5), and use a visual
fraction model to show
the quotient. Use the
relationship between
multiplication and
division to explain that 4
÷ (1/5) = 20 because 20 ×
(1/5) = 4.
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.
MCC5.NF.7 Apply and
extend previous
understandings of
division to divide unit
fractions by whole
numbers and whole
numbers by unit
fractions.
b. Interpret division of a
whole number by a unit
fraction, and compute
such quotients.
September 18, 2012
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 whole number by a unit
fraction, and compute
such quotients with no
procedural or
computational errors all
of the time.
Notes
Grade 5: Quarter 4
9 of 15
Standard
MCC5.MD.1 Convert
among different-sized
standard measurement
units within a given
measurement system
(e.g., convert 5 cm to
0.05 m), and use these
conversions in solving
multi-step, real world
problems.
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.
Measurement and Data
Convert like measurement units within a given measurement system
4
3
2
1
Converts among
Consistently converts
Shows progress, but
Shows minimal progress
different-sized standard
among different-sized
inconsistently converts
or seldomly converts
measurement units
standard measurement
among different-sized
among different-sized
within a given
units within a given
standard measurement
standard measurement
measurement system
measurement system
units within a given
units within a given
with no procedural errors with few procedural
measurement system
measurement system.
all of the time.
errors most of the time.
some of the time.
Makes line plots using
given data and solves
problems using the data
in the line plot with no
procedural errors all of
the time.
Represent and interpret data
Consistently makes line
Shows progress, but
plots using given data and inconsistently makes line
solves problems using the plots using given data and
data in the line plot with
inconsistently solves
few procedural errors
problems using the data
most of the time.
in the line plot some of
the time.
Shows minimal progress
or seldomly makes line
plots using given data and
does not solve problems
using the data in the line
plot.
Notes
Notes: Include customary
and metric systems of
measurement for length,
weight and capacity.
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.
September 18, 2012
Grade 5: Quarter 4
10 of 15
Standard
MCC5.MD.3 Recognize
volume as an attribute of
solid figures and
understand concepts of
volume measurement.
a. 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.
MCC5.MD.3 Recognize
volume as an attribute of
solid figures and
understand concepts of
volume measurement.
b. 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.
MCC5.MD.4 Measure
volumes by counting unit
cubes, using cubic cm,
cubic in, cubic ft, and
improvised units.
September 18, 2012
Measurement and Data
Geometric Measurement: understand concepts of volume and relate volume to multiplication and division.
4
3
2
1
Identifies and
understands the use of a
cubic unit to measure
volume with no
procedural or
computational errors all
of the time.
Consistently identifies
and understands the use
of a cubic unit to measure
volume with few
procedural or
computational errors
most of the time.
Shows progress, but
inconsistently identifies
and understands the use
of a cubic unit to measure
volume some of the time.
Shows minimal progress
or seldomly identifies and
understands the use of a
cubic unit to measure
volume.
Always recognizes and
understands 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 all
of the time.
Consistently recognizes
and understands 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
with few procedural
errors most of the time.
Shows progress, but
inconsistently recognizes
and understands 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
some of the time.
Shows minimal progress
or seldomly recognizes or
understands 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.
Estimates and computes
the volume of a
rectangular prism with no
procedural or
computational errors all
of the time.
Consistently estimates
and computes the
volume of rectangular
prisms with few
procedural or
computational errors
most of the time.
Shows progress, but
inconsistently estimates
and computes the
volume of rectangular
prisms some of the time.
Shows minimal progress
or seldomly estimates or
computes the volume of
a rectangular prism.
Grade 5: Quarter 4
Notes
11 of 15
Measurement and Data
Geometric Measurement: understand concepts of volume and relate volume to multiplication and division.
Standard
MCC5.MD.5 Relate
volume to the operations
of multiplication and
addition and solve real
world and mathematical
problems involving
volume.
a. Find the volume of a
right rectangular prism
with whole-number side
lengths by packing it with
unit cubes, and show
that the volume is the
same as would be found
by multiplying the edge
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.
September 18, 2012
4
Computes the volume of
a rectangular prism with
no procedural or
computational errors all
of the time.
3
Consistently computes
the volume of rectangular
prisms with few
procedural or
computational errors
most of the time.
2
Shows progress, but
inconsistently computes
the volume of rectangular
prisms some of the time.
1
Shows minimal progress
or seldomly computes the
volume of rectangular
prisms.
Grade 5: Quarter 4
Notes
12 of 15
Measurement and Data
Standard
Geometric Measurement: understand concepts of volume and relate volume to multiplication and division.
4
3
2
1
MCC5.MD.5 Relate
volume to the operations
of multiplication and
addition and solve real
world and mathematical
problems involving
volume.
b. 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.
Uses formulas to
compute the volume of a
rectangular prism with no
procedural or
computational errors all
of the time.
Consistently uses
formulas to compute the
volume of rectangular
prisms with few
procedural or
computational errors
most of the time.
Shows progress, but
inconsistently uses
formulas to compute the
volume of rectangular
prisms some of the time.
Shows minimal progress
or seldomly uses
formulas to computes the
volume of rectangular
prisms.
MCC5.MD.5 Relate
volume to the operations
of multiplication and
addition and solve real
world and mathematical
problems involving
volume.
c. Recognize volume as
additive. Find volumes of
solid figures composed
of two non-overlapping
right rectangular prisms
by adding the volumes of
the non-overlapping
parts, applying this
technique to solve real
world problems.
Computes the volume of
two non-overlapping
rectangular prisms with
no procedural or
computational errors all
of the time.
Consistently computes
the volume of two nonoverlapping rectangular
prisms with few
procedural or
computational errors
most of the time.
Shows progress, but
inconsistently computes
the volume of two nonoverlapping rectangular
prisms some of the time.
Shows minimal progress
or seldomly computes the
volume of two nonoverlapping rectangular
prisms.
September 18, 2012
Notes
Note: In GPS terminology,
this standard is asking
students to find the
volume of irregular
prisms.
Grade 5: Quarter 4
13 of 15
Standard
MCC5.G.1 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. Understand
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 the
convention that the
names of the two axes
and the coordinates
correspond.
September 18, 2012
Geometry
Graph points on the coordinate plane to solve real-world and mathematical problems.
4
3
2
1
Understands, locates, and
graphs ordered pairs in
the first quadrant with no
procedural errors all of
the time.
Consistently understands,
locates, and graphs
ordered pairs in the first
quadrant with few
procedural errors most of
the time.
Shows progress, but
inconsistently,
understands, locates, and
graphs ordered pairs in
the first quadrant
(possibly reverses
coordinates) some of the
time.
Shows minimal progress
or seldomly understands,
locates, and graphs
ordered pairs in the first
quadrant (possibly
reverses coordinates).
Notes
(e.g., x-axis and xcoordinate, y-axis and ycoordinate)
Grade 5: Quarter 4
14 of 15
Standard
MCC5.G.2 Represent real
world and mathematical
problems by graphing
points in the first
quadrant of the
coordinate plane, and
interpret coordinate
values of points in the
context of the situation.
MCC5.G.3 Understand
that attributes belonging
to a category of twodimensional figures also
belong to all
subcategories of that
category.
MCC5.G.4 Classify twodimensional figures in a
hierarchy based on
properties.
September 18, 2012
Geometry
Graph points on the coordinate plane to solve real-world and mathematical problems.
4
3
2
1
Represents real world
Consistently represents
Shows progress, but
Shows minimal progress
and mathematical
real world and
inconsistently represents or seldomly represents
problems by graphing
mathematical problems
real world and
real world and
points in the first
by graphing points in the mathematical problems
mathematical problems
quadrant of the
first quadrant of the
by graphing points in the by graphing points in the
coordinate plane, and
coordinate plane, and
first quadrant of the
first quadrant of the
interprets coordinate
interprets coordinate
coordinate plane,
coordinate plane, and
values of points in the
values of points in the
interprets coordinate
seldomly interprets
context of the situation
context of the situation
values of points in the
coordinate values of
with no procedural errors with few procedural
context of the situation
points in the context of
all of the time.
errors most of the time.
some of the time.
the situation.
Classify two-dimensional figures into categories based on their properties.
Examines, classifies,
Consistently examines,
Shows progress, but
Shows minimal progress
compares, and contrasts
classifies, compares, and
inconsistently examines,
or seldomly examines,
the relationships among
contrasts the
classifies, compares, and
classifies, compares, or
two-dimensional figures
relationships among two- contrasts the
contrasts the
with no procedural errors dimensional figures with
relationships among two- relationships among twoall of the time.
few procedural errors
dimensional figures some dimensional figures.
most of the time.
of the time.
Classifies twodimensional figures in a
hierarchy based on
properties with no
procedural errors all of
the time.
Consistently classifies
two-dimensional figures
in a hierarchy based on
properties with few
procedural errors most of
the time.
Shows progress, but
inconsistently classifies
two-dimensional figures
in a hierarchy based on
properties some of the
time.
Notes
Note: When students are
looking at the quadrant,
they will use the
information given to
determine where a future
point within the plane
would lie.
For example, all
rectangles have four right
angles and squares are
rectangles, so all squares
have four right angles.
Notes: Here are some
examples of twodimensional figures to be
included: triangles
(classified by type),
quadrilaterals, irregular
figures etc.
Students should also be
familiar with the concept
of congruence.
Shows minimal progress
or seldomly classifies
two-dimensional figures
in a hierarchy based on
properties.
Grade 5: Quarter 4
15 of 15