Grade 4
Mathematics CCRS Standards and Alabama COS
CCRS Standard
Standard ID
1. Interpret a
multiplication
equation as a
comparison, e.g.,
interpret 35 = 5 × 7
as a statement that
35 is 5 times as many
as 7 and 7 times as
many as 5. Represent
verbal statements of
multiplicative
comparisons as
multiplication
equations.
Operations and
Algebraic Thinking
Use the four
operations with
whole numbers to
solve problems.
4.OA.1
Evidence of Student
Attainment
Students:
Given a multiplication
equation,
Create and explain
a corresponding verbal
multiplicative
comparison statement
(Table 2).
Teacher
Vocabulary
Multiplicative
comparison
See Table 2 for
problem types.
Knowledge
Students know:
Students are able to:
Characteristics
of multiplicative
comparisons
(Table 2).
Use mathematical
language to
communicate the
relationship between
verbal representations
of multiplicative
comparisons and the
related multiplication
equations,
Given a verbal (written
or oral) representation
of a multiplicative
comparison,
Operations and
Algebraic Thinking
Use the four
operations with
whole numbers to
solve problems.
4.OA.2
Franklin County Schools
Understanding
Resources
Students understand
that:
Click below to
access all ALEX
resources aligned
to this standard.
Multiplicative
comparisons relate the ALEX Resources
size of two quantities
and a scale factor,
Factors in
multiplication problems
have different roles
from each other in the
Write multiplication context of comparison
equations that
problems.
correspond to given
multiplicative
comparison statements,
Write and solve the
related multiplication
equation (e.g., given
"Johnny has 7 cards
and Shawna has 5
times as many cards as
Johnny," the student
will write 5 x 7 and
accurately find the
number of cards
Shawna has to be 35).
2. Multiply or divide
to solve word
problems involving
multiplicative
comparison, e.g., by
using drawings and
equations with a
symbol for the
unknown number to
represent the
problem,
distinguishing
multiplicative
comparison from
Skills
Write verbal
multiplicative
comparison descriptions
given a multiplication
equation.
Students:
Given multiplication
and division problems
involving multiplicative
comparisons,
Multiplicative
comparison
Find, explain and
justify solutions using
connections between
pictorial
representations and
related equations
involving a single
See (Tables 1
and 2) for problem
types.
Additive
comparison
Students know:
Students are able to:
Students understand
that:
Characteristics
of multiplicative
comparison
problems and
additive
comparison
problems,
Compare and
contrast mathematical
contexts in order to
determine the types of
mathematical
comparisons present,
Click below to
The operation of
access all ALEX
multiplication represents resources aligned
contexts of putting
to this standard.
together equal sized
groups or multiplicative
 ALEX
comparisons,
Resources
Represent
Addition,
The operation of
multiplicative
subtraction,
comparison contexts
division represents
multiplication, and physically, pictorially, or contexts of partitioning
Grade 4
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
additive comparison.1
Evidence of Student
Attainment
Teacher
Vocabulary
unknown.
(1 See Appendix A,
Table 2.)
Knowledge
Skills
Understanding
Resources
division strategies. symbolically,
into equal-sized shares
or contexts of
Strategically choose partitioning equally
and apply a variety of among a given number
representations to solve of groups or contexts
involving multiplicative
multiplicative
comparison problems, comparisons,
Given a mixture of
multiplicative
comparison and
additive comparison
problems,
Use symbols to
represent unknown
quantities in
multiplicative
comparison equations,
Apply their
understanding of
operations and a
variety of
representations to
explain and justify the
choice of operation in
solving the problem.
The operation of
subtraction represents
taking apart, taking
from, and additive
comparison contexts,
Accurately compute Mathematical
products and quotients, problems (four basic
operations) can be
solved using a variety of
Use mathematical
strategies, models,
language to
representations,
communicate the
connections among
Variables represent
contexts involving all
unknown quantities
four operations and
when modeling
related physical,
mathematical situations
pictorial, or symbolic
algebraically.
representations and
justify solutions/solution
paths.
3. Solve multistep
word problems posed
with whole numbers
and having wholenumber answers
using the four
operations, including
problems in which
remainders must be
interpreted.
Represent these
problems using
equations with a
Operations and
Algebraic Thinking
Use the four
operations with
whole numbers to
solve problems.
4.OA.3
Franklin County Schools
"Problems in
Students:
Given a variety of
which remainders
multistep word
must be interpreted"
problems involving all
four operations on
whole numbers
(including problems in
which remainders must
be interpreted),
Explain and justify
solutions using
Students know:
Students are able to:
Students understand
that:
Characteristics
(see Table 1 and
2) of addition,
subtraction,
multiplication and
division contexts,
Click below to
Represent quantities
access all ALEX
The operation of
and operations
(addition, subtraction, addition represents both resources aligned
to this standard.
multiplication, and
putting together and
division of whole
adding to contexts,
numbers) physically,
 ALEX
pictorially, or
Resources
The operation of
symbolically,
subtraction represents
Addition,
subtraction,
taking apart, taking
multiplication, and Strategically choose from, and additive
Grade 4
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
letter standing for the
unknown quantity.
Assess the
reasonableness of
answers using mental
computation and
estimation strategies
including rounding.
Evidence of Student
Attainment
Teacher
Vocabulary
connections between
the problems and
related equations
involving a single
(letter) unknown,
Knowledge
Skills
division strategies, and apply a variety of
representations to solve
Strategies for addition, subtraction,
multiplication, and
mentally
division multi-step word
computing and
estimating sums, problems,
Apply their
understanding of
operations and
estimation strategies
including rounding to
evaluate the
reasonableness of their
solutions.
differences,
products, and
quotients.
Use symbols to
represent unknown
quantities in equations
that represent multistep word problems,
Use logical
reasoning and
connections between
physical/pictorial
representations to
justify solutions and
solution paths and to
interpret remainders,
Understanding
Resources
comparison contexts,
The operation of
multiplication represents
contexts of putting
together equal sized
groups,
The operation of
division represents
contexts of partitioning
into equal-sized shares
or contexts of
partitioning equally
among a given number
of groups,
The interpretation
of the remainder in a
division problem is
dependent upon the
original context and
Estimate answers in question,
addition, subtraction,
multiplication and
Variables represent
division problems,
unknown quantities
Evaluate the
reasonableness of
answers by comparing
actual answers to
estimates.
4. Find all factor pairs
for a whole number
in the range 1–100.
Recognize that a
whole number is a
Operations and
Algebraic Thinking
Gain familiarity with
factors and multiples.
4.OA.4
Franklin County Schools
Students:
Given any whole
number from 1-100,
Use knowledge of
Factor
Students know:
Students are able to:
Factor pair
Strategies for
finding factor
Use models and
logical reasoning to
determine all possible
when modeling
mathematical situations
algebraically,
Solutions can be
evaluated by using
reasoning to compare
the actual solution with
estimated solutions.
Students understand
that:
Click below to
access all ALEX
resources aligned
A whole number is a to this standard.
multiple of each of its
Grade 4
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
multiple of each of its
factors. Determine
whether a given
whole number in the
range 1–100 is a
multiple of a given
one-digit number.
Determine whether a
given whole number
in the range 1–100 is
prime or composite.
Evidence of Student
Attainment
Teacher
Vocabulary
Multiple
multiplication and
division, models for
multiplication, and
Prime
logical reasoning to
decompose the given
Composite
number into all possible
factor pairs,
Determine if it is a
multiple of a given
single-digit number,
Knowledge
Skills
Understanding
factor pairs for a whole factors,
number between 1 100,
Vocabulary:
Numbers can be
factor, multiple,
classified as prime,
factor pair, prime, Accurately compute composite, or neither,
composite.
products and quotients, based on their
properties and
characteristics.
Use an
Resources
pairs,
ALEX Resources
understanding of prime
and composite to
classify numbers.
Use knowledge and
vocabulary of factors,
factor pairs, and
multiples to justify the
classification of
numbers as prime and
composite.
5. Generate a number
or shape pattern that
follows a given rule.
Identify apparent
features of the
pattern that were not
explicit in the rule
itself.
Example: Given the
rule “Add 3” and the
starting number 1,
generate terms in the
resulting sequence,
and observe that the
terms appear to
alternate between
odd and even
numbers. Explain
informally why the
numbers will continue
to alternate in this
way.
Operations and
Algebraic Thinking
Generate and
analyze patterns.
4.OA.5
Franklin County Schools
Students:
Given a number or
shape pattern in the
form of a rule,
Generate
successive members of
the pattern and identify
apparent features of
the pattern that were
not explicit in the rule
itself, (e.g., given the
rule “Add 3” and the
starting number 1,
generate terms in the
resulting sequence and
observe that the terms
appear to alternate
between odd and even
numbers),
Explain informally
Students know:
Students are able to:
Strategies for
generating and
recording number
or shape patterns
from rules,
Generate and
record number and
shape patterns from
rules,
Students understand
that:
Patterns in the
number system can be
used with logical
reasoning to make
conjectures and solve
Use logical
Click below to
Strategies for reasoning and informal problems,
access all ALEX
identifying and
language to explain
resources aligned
communicating
relationships between Identifying patterns
to this standard.
shape and number successive terms in a
in the number system
patterns.
pattern.
leads to a deeper
ALEX Resources
understanding of
numbers, their
characteristics, and their
properties.
Grade 4
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources
why the numbers will
continue to alternate in
this way.
6. Recognize that in a
multi-digit whole
number, a digit in
one place represents
ten times what it
represents in the
place to its right.
Example: Recognize
that 700 ÷ 70 = 10
by applying concepts
of place value and
division.
Number &
Operations in Base
Ten
Generalize place
value understanding
for multi-digit whole
numbers.2
Students:
7. Read and write
multi-digit whole
numbers using baseten numerals,
number names, and
expanded form.
Compare two multidigit numbers based
on meanings of the
digits in each place,
using >, =, and <
symbols to record the
results of
comparisons.
Number &
Operations in Base
Ten
Generalize place
value understanding
for multi-digit whole
numbers.2
Expanded form
Students:
Given multi-digit whole
numbers orally or in
<, =, and >
written form,
symbols
Explain, when
asked, how the value
of a digit differs in two
successive place
values, that the one to
the right is 1/10 of the
(2Grade 4
one to its left or that
expectations in this
the one on the left is
domain are limited to 10 times the one on
whole numbers less the right.
than or equal to
1,000,000)
4.NBT.1
Represent
quantities in a variety
of ways including
(2Grade 4
words, base-ten
expectations in this
numerals, and
domain are limited to expanded form,
whole numbers less
than or equal to
Explain
1,000,000)
relationships among
4.NBT.2
Franklin County Schools
Students know:
Students are able to:
Place values
Use logical
reasoning to explain the
relationship between
two successive place
values.
Place value
models
Students know:
Students are able to:
Students understand
that:
Values of digits in
any multi-digit number
are based on patterns
within a base-10 place Click below to
access all ALEX
value system,
resources aligned
to this standard.
Patterns created by
the use of 10 digits in a
ALEX Resources
place value system
make a place value to
the right 1/10 of the
previous place value
and a place value to the
left 10 times the
previous place value.
Students understand
that:
Place values,
Represent quantities
The same quantity
in a number of forms
Meanings and including words, base- can be represented with Click below to
words, mathematical
access all ALEX
appropriate use of ten numerals, and
expanded
form,
models, and expanded resources aligned
the mathematical
form based on the place to this standard.
symbols: <, =, >.
value of the digits,
Compare whole
numbers in equalities
and inequalities.
The value of a digit
in a multi-digit number
depends on the place
value spot it holds.
ALEX Resources
Grade 4
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources
representations.
Given two numbers
less than 1000,
Use place value
terminology and
concepts to explain and
justify the placement of
<, =, > to compare the
numbers and create
true equalities and
inequalities.
8. Use place value
understanding to
round multi-digit
whole numbers to
any place.
Number &
Operations in Base
Ten
Generalize place
value understanding
for multi-digit whole
numbers.2
Students:
Given any whole
number,
Justify the rounding
of the number to a
designated place value
using models and place
2
( Grade 4
value vocabulary (e.g.,
expectations in this
3,456 rounded to the
domain are limited to nearest ten is 3460
whole numbers less because it is between
than or equal to
the two tens 3450 and
1,000,000)
3460, but closer to
4.NBT.3
3460).
Students know:
Students are able to:
Place value
vocabulary: ones,
tens, hundreds,
thousands, tenthousands,
hundredthousands,
millions,
Count by 10s, 100s,
Rounding aids
1000s, 10,000s, etc.,
estimation of quantities
Determine what is by changing the original
number to the closest
halfway between two
consecutive multiples of multiple of a power of Click below to
powers of 10 (360 and 10.
access all ALEX
370, 36,000 and
resources aligned
37,000),
to this standard.
Place value
models (e.g.,
number lines,
place value
blocks),
Place value
strategies for
comparing and
ordering numbers.
Standard
9. Fluently add and
Number &
Students:
subtract multi-digit
Operations in Base Given a context which algorithms (addition
whole numbers using Ten
calls for the addition or and subtraction)
Franklin County Schools
Students know:
Students understand
that:
Compare whole
numbers,
ALEX Resources
Use place value
vocabulary, models, and
logical reasoning to
justify solutions to
rounding problems.
Students are able to:
Students understand
that:
Click below to
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resources aligned
Grade 4
CCRS Standard
the standard
algorithm.
Mathematics CCRS Standards and Alabama COS
Standard ID
Use place value
understanding and
properties of
operations to
perform multi-digit
arithmetic. 2
(2Grade 4
expectations in this
domain are limited to
whole numbers less
than or equal to
1,000,000)
4.NBT.4
Evidence of Student
Attainment
subtraction of two
whole numbers,
Choose the most
appropriate strategy for
computing the answer,
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources
to this standard.
Strategies for
computing
answers to
addition and
subtraction
problems.
Produce accurate
results efficiently using
the standard algorithm
when appropriate.
Strategically choose
and apply appropriate
methods for adding and
subtracting,
Accurately find
sums/differences using
the standard addition
and subtraction
algorithms.
Mathematical
problems can be solved ALEX Resources
using a variety of
strategies, models, and
representations,
Efficient application
of computation
strategies is based on
the numbers and
operations in the
problems.
The steps used in
the standard algorithm
for addition and
subtraction can be
justified by using
properties of operations
and understanding of
place value.
Among all
techniques and
algorithms that may be
chosen for accurately
performing multi-digit
computations, some
procedures have been
chosen with which all
should be fluent for
efficiency,
communication, and use
in other mathematics
situations.
10. Multiply a whole
number of up to four
digits by a one-digit
whole number, and
multiply two two-digit
Number &
Operations in Base
Ten
Use place value
understanding and
Franklin County Schools
Students:
Given multiplication
problems (four-digit
whole number by onedigit whole number, or
Students know:
Students are able to:
Place value
models for
Use strategies
based on an
Students understand
that:
Multiplication
Click below to
access all ALEX
resources aligned
to this standard.
Grade 4
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
numbers, using
strategies based on
place value and the
properties of
operations. Illustrate
and explain the
calculation by using
equations,
rectangular arrays,
and/or area models.
properties of
operations to
perform multi-digit
arithmetic. 2
11. Find wholenumber quotients and
remainders with up to
four-digit dividends
and one-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.
Number &
Operations in Base
Ten
Use place value
understanding and
properties of
operations to
perform multi-digit
arithmetic. 2
12. Explain why a
fraction a/b is
equivalent to a
fraction (n × a)/(n × b) by
Number &
Operations—
Fractions
Extend
Evidence of Student
Attainment
two-digit numbers by
two-digit numbers),
Use strategies
based on multiplication
(2Grade 4
models (e.g.,
expectations in this
rectangular arrays,
domain are limited to open arrays, area
whole numbers less models), place value
than or equal to
and properties of
1,000,000)
operations to find and
4.NBT.5
justify solutions and
solution paths.
Students:
Given division problems
(up to four-digit
dividends and one-digit
divisors),
Find whole-number
quotients and
remainders using
strategies that involve
(2Grade 4
using representations
expectations in this
based on place value,
domain are limited to properties of
whole numbers less operations, and/or the
than or equal to
relationship between
1,000,000)
multiplication and
4.NBT.6
division,
Teacher
Vocabulary
Knowledge
multiplying
numbers (e.g.,
area models, open
arrays, place value
blocks),
Franklin County Schools
Use visual models
Understanding
Resources
understanding of place
value and properties of
operations to find
products,
problems can be solved
using a variety of
ALEX Resources
strategies, models, and
representations.
Use a variety of
place value models of
multiplication problems
to justify solutions and
solution paths.
Efficient application
of multiplication
computation strategies
is based on the
numbers and operations
in the problems.
Students know:
Students are able to:
Students understand
that:
Tools for
modeling division
problems,
Model division
problems using
appropriate tools,
Strategies and
methods for
symbolically
(numerically)
recording
strategies for
solving division
problems.
Record strategies
for solving division
problems,
Strategies for
finding products
based on place
value and
properties of
operations.
Use logical
reasoning to
communicate the
relationship between
models and symbolic
(numeric)
representations of
solutions to division
problems,
Division problems
can be solved using a
variety of strategies,
models, and
representations,
Efficient application
of division computation
strategies is based on
the numbers and
operations in the
problems,
Click below to
access all ALEX
resources aligned
to this standard.
ALEX Resources
Relationships
between models of
division problems and
symbolic recordings of
Accurately compute those models can be
used to justify solutions.
quotients with
remainders.
Justify solutions
and solution paths
through equations,
rectangular arrays,
and/or area models.
Students:
Given a fraction a/b,
Skills
Students know:
Students are able to:
Students understand
that:
Strategies for
partitioning
Represent fractional
quantities using visual Two fractions are
Click below to
access all ALEX
resources aligned
to this standard.
Grade 4
Mathematics CCRS Standards and Alabama COS
CCRS Standard
using visual fraction
models, with
attention to how the
number and size of
the parts differ even
though the two
fractions themselves
are the same size.
Use this principle to
recognize and
generate equivalent
fractions.
Standard ID
understanding of
fraction equivalence
and ordering. 3
(3
Evidence of Student
Attainment
Teacher
Vocabulary
to create equivalent
fractions and explain
the generalized
pattern, a/b = (n x a) /
(n x b),
wholes,
Strategies for
representing
fractional parts of
a whole,
Grade 4
expectations in this
domain are limited to Use the generalized
fractions with
pattern to generate
denominators 2, 3, 4, equivalent fractions.
5, 6, 8, 10, 12, 100.)
4.NF.1
Skills
Knowledge
Multiplication
and division
strategies.
Understanding
Resources
models,
equivalent if they are
the same size share
ALEX Resources
(represent the same
Write fractions
related to visual models, amount) of the same
whole or name the
same point on a number
Generate equivalent
line.
fractions by modeling
the original fraction and
further partitioning
shares,
Explain the
equivalence of fractions
and the generalization
a/b = (n x a) / (n x b)
using logical reasoning,
patterns, and visual
models,
Generate equivalent
fractions using the
generalization a/b = (n
x a) / (n x b).
13. Compare two
fractions with
different numerators
and different
denominators, e.g.,
by creating common
denominators or
numerators or by
comparing to a
benchmark fraction
such as 1/2.
Recognize that
comparisons are valid
only when the two
fractions refer to the
same whole. Record
the results of
comparisons with
Number &
Operations—
Fractions
Extend
understanding of
fraction equivalence
and ordering. 3
Students:
Given two fractions
(having denominators
of 2,3, 4, 5, 6, 8, 10,
12, 100),
Use logical
reasoning and a variety
(3 Grade 4
of models to represent
expectations in this
and order the fractions
domain are limited to (using <, =, >) and
fractions with
justify their answers,
denominators 2, 3, 4,
5, 6, 8, 10, 12, 100.)
Communicate the
4.NF.2
reason why it is not
valid to make a
comparison between
Franklin County Schools
Benchmark
fraction
Students know:
Students are able to:
Strategies for
representing
fractional
quantities,
Strategically choose
Two fractions are
and apply
representations to
equivalent if they are
compare two fractions, the same size share
Click below to
(represent the same
access all ALEX
amount) of the same
Record the
resources aligned
whole or name the
comparison of two
to this standard.
same point on a number
fractions using <, =,
line,
and > notation,
ALEX Resources
Strategies for
comparing
fractions (e.g.,
comparing
numerators of like
fractions,
comparing
denominators of
fractions with like
numerators,
Use mathematical
language and logical
reasoning to justify
solutions.
Students understand
that:
Comparisons of
fractions are valid only
when the two fractions
refer to the same
whole.
Grade 4
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
symbols >, =, or <,
and justify the
conclusions, e.g., by
using a visual fraction
model.
14. Understand a
fraction a/b with a > 1
as a sum of fractions
1/ .
b
Number &
Operations—
Fractions
Build fractions from
unit fractions by
applying and
extending previous
understandings of
operations on whole
numbers.3
a. Understand
addition and
subtraction of
fractions as joining
and separating parts
referring to the same
(3 Grade 4
whole.
expectations in this
domain are limited to
b. Decompose a
fractions with
fraction into a sum of
denominators 2, 3, 4,
fractions with the
5, 6, 8, 10, 12, 100.)
same denominator in
4.NF.3
more than one way,
recording each
decomposition by an
equation. Justify
decompositions, e.g.,
by using a visual
fraction model.
Examples: 3/8 = 1/8 +
1/ + 1/ ; 3/ = 1/ +
8
8
8
8
2/ ; 2 1/ = 1 + 1 +
8
8
1/ = 8/ + 8/ + 1/ .
8
8
8
8
c. Add and subtract
Franklin County Schools
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
Understanding
fractions that refer to
different wholes (e.g.,
why it may not be valid
to say 1/2 > 1/4 if the
1/2 refers to a small
pizza and the 1/4
refers to an extra-large
pizza or "Susie said her
1/6 pizza was bigger
than my 1/2 pizza. Is
she correct?").
creating common
denominators, and
comparing to
landmark fractions
such as 1/2).
Students:
Given any fraction or
mixed number,
Students know:
Students are able to:
Characteristics
of addition and
subtraction
contexts for whole
numbers and like
fractions,
Represent quantities
Addition and
(whole numbers and
fractions) and
subtraction of fractions
operations (addition and are applied to fractions
subtraction) physically, referring to the same
pictorially, or
whole,
symbolically,
Strategies for
representing and
solving addition
and subtraction
problems involving
fractions.
The operation of
Strategically choose addition with whole
and apply a variety of numbers and/or
representations to solve fractions represents
addition and subtraction both putting together
word problems involving and adding to contexts,
like fractions,
Connect their
understanding of unit
fractions and their
understanding of
addition to decompose
the given fraction or
mixed number into the
sum of smaller
fractions/mixed
numbers, including unit
fractions.
Resources
Students understand
that:
The operation of
subtraction with whole
numbers and/or
fractions represents
taking apart, taking
from, and additive
comparison contexts,
Given a variety of
addition and
subtraction word
problems involving
fractions with like
denominators,
Use symbols to
represent unknown
quantities in addition
and subtraction
equations and solve
such equations,
Explain and justify
solutions using
connections among
unit fractions, pictorial
representations, and
related equations
Accurately compute The unit fraction
sums and differences of (1/b) names the size of
fractions,
the unit with respect to
the referenced whole
and that the numerator
Use logical
counts the parts
Click below to
access all ALEX
resources aligned
to this standard.
ALEX Resources
Grade 4
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
mixed numbers with
like denominators,
e.g., by replacing
each mixed number
with an equivalent
fraction, and/or by
using properties of
operations and the
relationship between
addition and
subtraction.
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
involving a single
unknown.
Skills
reasoning and
connections among
representations to
justify solutions and
solution paths.
Understanding
Resources
referenced and the
denominator tells the
number of parts into
which the whole was
partitioned,
The operations of
addition and subtraction
are performed on
counts with like
names/labels/denominat
ors and that the sum or
difference retains the
same
name/label/denominato
r,
d. Solve word
problems involving
addition and
subtraction of
fractions referring to
the same whole and
having like
denominators, e.g.,
by using visual
fraction models and
equations to
represent the
problem.
Mathematical
problems (addition and
subtraction of fractions)
can be solved using a
variety of strategies,
models,
representations,
Variables represent
unknown quantities
when modeling
mathematical situations
algebraically.
15. Apply and extend
previous
understandings of
multiplication to
multiply a fraction by
a whole number.
a. Understand a
fraction a/b as a
multiple of 1/b.
Example: Use a visual
Number &
Operations—
Fractions
Build fractions from
unit fractions by
applying and
extending previous
understandings of
operations on whole
numbers.3
Franklin County Schools
Students:
Given any fraction,
Use their
knowledge of multiples
of whole numbers to
connect a visual
representation of a
non-unit fraction to a
product of a whole
number and a unit
Multiple
Students know:
Students are able to:
Represent and
rename fractional
quantities as multiples
of whole numbers and
Characteristics unit fractions,
of multiplication
contexts for whole Strategically choose
numbers and
and apply a variety of
Associative
Property of
Multiplication,
Students understand
that:
Click below to
A fraction a/b is a access all ALEX
multiple of the unit
resources aligned
fraction 1/b, (e.g.., a/b to this standard.
= a x 1/b),
Multiplication may
be viewed as putting
ALEX Resources
Grade 4
CCRS Standard
fraction model to
represent 5/4 as the
product 5 × (1/4),
recording the
conclusion by the
equation 5/4 = 5 ×
(1/4).
Mathematics CCRS Standards and Alabama COS
Standard ID
(3 Grade 4
expectations in this
domain are limited to
fractions with
denominators 2, 3, 4,
5, 6, 8, 10, 12, 100.)
4.NF.4
b. Understand a
multiple of a/b as a
multiple of 1/b, and
use this
understanding to
multiply a fraction by
a whole number.
Example: Use a visual
fraction model to
express 3 × (2/5) as 6
× (1/5), recognizing
this product as 6/5.
(In general, n × (a/b)
= (n × a)/b.)
c. Solve word
problems involving
multiplication of a
fraction by a whole
number, e.g., by
using visual fraction
models and equations
to represent the
problem.
Example: If each
person at a party will
eat 3/8 of a pound of
roast beef, and there
will be 5 people at
the party, how many
pounds of roast beef
will be needed?
Between what two
whole numbers does
Franklin County Schools
Evidence of Student
Attainment
fraction.
Given a multiplication
problem involving a
whole number and a
fraction,
Use a visual
representation of the
problem,
understanding of unit
fractions, and
properties of the
operation of
multiplication to justify
n x (a/b) = (n x a)/b,
Given a word problem
involving the
multiplication of a
fraction by a whole
number,
Explain and justify
solutions and the
reasonableness of
solutions using
connections among
unit fractions, visual
representations, and an
understanding of
multiplication.
Teacher
Vocabulary
Knowledge
fractions,
Skills
representations to solve
multiplication word
problems involving
whole numbers and
fractions,
Strategies for
representing and
solving
multiplication
problems involving Apply knowledge of
whole numbers
the Associative Property
and fractions.
of Multiplication with
knowledge of unit
fractions to accurately
compute products of
whole numbers and
fractions,
Use logical
reasoning and
connections among
representations to
justify solutions,
reasonableness of
solutions, and solution
paths.
Understanding
together equal-sized
groups,
Mathematical
problems (multiplication
of whole numbers and
fractions) can be solved
using a variety of
strategies, models, and
representations,
A fractional quantity
can be modeled using a
variety of
representations (e.g.,
part of a whole, part of
a group, a distance on a
numberline) each of
which may reveal
important features of
given contexts.
Resources
Grade 4
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources
your answer lie?
16. Express a fraction
with denominator 10
as an equivalent
fraction with
denominator 100,
and use this
technique to add two
fractions with
respective
denominators 10 and
100.4
Example: Express 3/10
as 30/100, and add 3/10
+ 4/100 = 34/100.
Number &
Operations—
Fractions
Understand decimal
notation for
fractions, and
compare decimal
fractions.3
Students:
Given a fraction with a
denominator of 10,
Use visual models
and the generalized
pattern, a/b = (n x a) /
(n x b) to find the
equivalent fraction with
a denominator of 100.
(3 Grade 4
expectations in this
domain are limited to
fractions with
Given an addition
denominators 2, 3, 4,
problem with two
5, 6, 8, 10, 12, 100.)
fractions with
4
( Students who can
4.NF.5
respective
generate equivalent
denominators of 10
fractions can develop
and 100,
strategies for adding
fractions with unlike
Compute the sum
denominators in
by expressing the
general. But addition
fraction with a
and subtraction with
denominator of 10 as
unlike denominators
an equivalent fraction
in general is not a
with a denominator of
requirement at this
100 and then adding.
grade.)
17. Use decimal
notation for fractions
with denominators 10
or 100.
Example: Rewrite
0.62 as 62/100;
describe a length as
0.62 meters; locate
0.62 on a number
line diagram.
Number &
Operations—
Fractions
Understand decimal
notation for
fractions, and
compare decimal
fractions.3
Students:
Given a fraction with a
denominator of 10 or
100,
Write the
equivalent fraction
using decimal notation.
(3 Grade 4
expectations in this
Given a fraction in
domain are limited to
decimal notation
fractions with
(tenths or hundredths),
Franklin County Schools
Students know:
Students are able to:
Strategies for
generating
equivalent
fractions,
Represent fractional
quantities using visual Addition may be
models,
viewed as joining or
adding to,
Strategies for
adding fractions
with like
denominators.
Students know:
Students understand
that:
Write fractions
related to visual models, Two fractions are
equivalent if they are
Generate equivalent the same size share of
the same whole or are
fractions using the
generalization a/b = (n the same point on a
number line,
x a) / (n x b).
Click below to
access all ALEX
resources aligned
to this standard.
Accurately add
fractions.
The operations of
addition and subtraction ALEX Resources
are performed on
counts with like
names/denominators
and that the sum or
difference retains the
same
name/denominator.
Students are able to:
Students understand
that:
Decimal place Represent fractional
Two fractions are
value,
quantities including
Click below to
decimals using visual
equivalent if they are
access all ALEX
models,
the same size share
Decimal
resources aligned
(represent the same
notation,
to this standard.
amount) of the same
Write fractions
whole or name the
including decimals
Fraction
same point on a number ALEX Resources
related
to
visual
models.
notation.
line.
Grade 4
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources
denominators 2, 3, 4,
5, 6, 8, 10, 12, 100.) Write the
4.NF.6
equivalent fraction.
Given a fraction in
decimal notation,
Create a number
line diagram and justify
the placement of the
fraction on the number
line.
18. Compare two
decimals to
hundredths by
reasoning about their
size. Recognize that
comparisons are valid
only when the two
decimals refer to the
same whole. Record
the results of
comparisons with the
symbols >, =, or <,
and justify the
conclusions, e.g., by
using a visual model.
Number &
Operations—
Fractions
Understand decimal
notation for
fractions, and
compare decimal
fractions.3
(3 Grade 4
expectations in this
domain are limited to
fractions with
denominators 2, 3, 4,
5, 6, 8, 10, 12, 100.)
4.NF.7
19. Know relative
Measurement &
sizes of measurement Data
Franklin County Schools
Students:
Given two decimals,
Use logical
reasoning and a variety
of models to represent
and order the decimals
(using <, =, >) and
justify their answers,
Communicate the
reason why it is not
valid to make a
comparison between
decimals that refer to
different wholes (e.g.,
why it may not be valid
to say 0.5 > 0.25 if 0.5
refers to a small pizza
and the 0.25 refers to
an extra-large pizza, or
"Susie said her 0.25
pizza was bigger than
my 0.5 pizza. Is she
correct?").
Students:
Given a measurement
Students know:
Students are able to:
Students understand
that:
Strategies for Strategically choose
Two fractions
representing
and apply
decimal quantities, representations to
(decimals) are
compare two decimals, equivalent if they are
the same size share
Strategies for
(represent the same
Record the
comparing
amount) of the same
decimals (e.g.,
comparison of two
whole or name the
comparing
decimals using <, =,
Click below to
same point on a number access all ALEX
numerators of like and > notation,
line,
decimals creating
resources aligned
common
denominators,
comparing to
landmark fractions
such as 1/2).
Use mathematical
language and logical
reasoning to justify
solutions.
to this standard.
Comparisons of
fractions (decimals) are ALEX Resources
valid only when the two
fractions (decimals)
refer to the same
whole.
Students know:
Students are able to:
Students understand
that:
Click below to
access all ALEX
Grade 4
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
units within one
system of units
including km, m, cm;
kg, g; lb, oz.; l, ml;
and hr, min, sec.
Within a single
system of
measurement,
express
measurements in a
larger unit in terms of
a smaller unit. Record
measurement
equivalents in a twocolumn table.
Example: Know that
1 ft is 12 times as
long as 1 in. Express
the length of a 4 ft
snake as 48 in.
Generate a
conversion table for
feet and inches listing
the number pairs (1,
12), (2, 24), (3, 36),
...
Solve problems
involving
measurement and
conversion of
measurements from
a larger unit to a
smaller unit.
4.MD.1
20. Use the four
operations to solve
word problems
involving distances,
intervals of time,
liquid volumes,
masses of objects,
and money, including
problems involving
simple fractions or
decimals, and
problems that require
expressing
measurements given
in a larger unit in
terms of a smaller
Measurement &
Data
Solve problems
involving
measurement and
conversion of
measurements from
a larger unit to a
smaller unit.
4.MD.2
Franklin County Schools
Evidence of Student
Attainment
in a relatively large unit
(e.g., km, m, kg, lb., l,
hr., min.),
Accurately convert
the measurement to an
equivalent
measurement using
smaller units (e.g., m,
cm, g, oz., ml, min.,
sec.) within the same
measurement system
through the use of a
two column table.
(e.g., Express the
length of a 4 ft. snake
as 48 inches by
generating a
conversion table for
feet and inches listing
the number pairs
(1,12), (2,24), etc.).
Students:
Given word problems
involving distances
(km, m, cm), intervals
of time (hr., min.,
sec.), liquid volumes (l,
ml), mass (kg, g, lb.,
oz.), and money,
including problems
involving simple
fractions or decimals
and problems involving
measurements in
different units (within
the same measurement
system, conversions
Teacher
Vocabulary
Knowledge
Relative sizes
of measurement
units within one
system of units
including km, m,
cm; kg, g; lb., oz.;
l, ml; hr., min.,
sec.,
Skills
Multiply or use
repeated addition to
accurately generate
number pairs for
conversion tables,
Interpret tables to
solve problems.
Understanding
Resources
resources aligned
to this standard.
The relationships
among units within a
system of measurement ALEX Resources
(e.g., metric length,
time, standard mass,
etc.) are multiplicative
comparisons.
Strategies for
converting from
relatively large
units of measure
to smaller units of
measure within the
same system
including
multiplication and
two-column tables.
Students know:
Students are able to:
Students understand
that:
Relative sizes
of measurement
units within one
system of units
including: km, m,
cm; kg, g; lb., oz.;
L, mL; hr., min.,
sec.,
Strategically choose
an appropriate common
unit to use for
computations, when
working with problems
that contain
measurements in
different units,
Strategies for
converting from
relatively large
units of measure
Strategically choose The size of the unit
and apply
of measurement and
representations and
the number of units are
computation techniques
The relationships
among units within a
system of measurement
(e.g., metric length,
time, standard mass,
etc.) are multiplicative
comparisons,
Click below to
access all ALEX
resources aligned
to this standard.
ALEX Resources
Grade 4
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
unit. Represent
measurement
quantities using
diagrams such as
number line diagrams
that feature a
measurement scale.
21. Apply the area
and perimeter
formulas for
rectangles in realworld and
mathematical
problems.
Example: Find the
width of a rectangular
room given the area
of the flooring and
the length by viewing
the area formula as a
multiplication
equation with an
unknown factor.
Evidence of Student
Attainment
Teacher
Vocabulary
from larger to smaller
units only),
Justify choices of
units, solve the
problem, and justify
solutions.
Measurement &
Data
Solve problems
involving
measurement and
conversion of
measurements from
a larger unit to a
smaller unit.
4.MD.3
Area
Students:
Given real world and
mathematical problems Perimeter
involving area and
perimeter of
rectangular regions,
Use a variety of
representations (e.g.,
models, drawings, and
equations) based on
area and perimeter
formulas to find and
justify solutions and
solution paths.
Knowledge
to smaller units of
measure within the
same system
including
multiplication and
two-column tables,
Strategies for
solving word
problems involving
measurement
including number
line
representations.
Skills
Addition and
Accurately compute subtraction of
solutions,
measurements require
measurements in the
same unit and that the
Use logical
unit is maintained in the
reasoning to justify
answer.
solution paths.
Students are able to:
Strategies for
representing
contexts involving
area and perimeter
of rectangular
regions,
Discriminate
between contexts
asking for perimeter
and those asking for
area measurements,
Students understand
that:
Perimeter is
measured in length
units and is the distance
around a 2-D figure,
Strategically choose
and apply appropriate
methods for
representing and
calculating ,
The area of a plane
figure is measured by
Click below to
the number of samesize squares that exactly access all ALEX
cover the interior space resources aligned
to this standard.
of the figure and the
formula
for
the
area
of
Accurately compute
a rectangle is a result of ALEX Resources
measurements within
area and perimeter of this understanding,
rectangular region
The length and
problems.
width of a rectangular
region are related to
both the area and the
perimeter of that
region,
Addition and
Franklin County Schools
Resources
for solving real life
inversely related,
mathematical problems,
Students know:
Strategies
including standard
formulas (A = L x
W, P = 2L + 2W, P
=L+L+W+W
or P = 2 (L +W))
for computing
measurements
related to the area
and perimeter of
rectangular
regions.
Understanding
Grade 4
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources
subtraction of
measurements require
measurements in the
same unit and that the
unit is maintained in the
answer,
The multiplication
and division of
measurements result in
the units also being
multiplied or divided
and that a new unit is
created for the answer.
22. Make a line plot
to display a data set
of measurements in
fractions of a unit
(1/2, 1/4, 1/8). Solve
problems involving
addition and
subtraction of
fractions by using
information presented
in line plots.
Example: From a line
plot find and interpret
the difference in
length between the
longest and shortest
specimens in an
insect collection.
Measurement &
Data
Represent and
interpret data.
4.MD.4
Students:
Line plot
Make and use line
plots (with the scale
matching the unit of
measure) to represent
data generated by
measuring lengths (to
the nearest eighth
inch) of several objects
or by making repeated
measurements,
Students know:
Students are able to:
Students understand
that:
Techniques for Use standard units
constructing line
and related tools to
plots,
measure length to the
nearest eighth inch,
Questions
concerning
mathematical contexts
can be generated and
Standard units
answered by collecting,
and related tools Organize and
organizing, and
for measuring
represent length
length,
measurement data on a analyzing data and data Click below to
displays.
access all ALEX
line plot,
resources aligned
Strategies for
to this standard.
Choose and apply
adding and
subtracting
appropriate strategies
ALEX Resources
fractions.
to solve problems
generated by
conjectures from
examining data
displays,
Use information
from data displays to
generate questions and
solve problems
including problems that
involve addition and
subtraction of fractions.
Apply strategies for
solving problems
involving adding and
subtracting fractions.
23. Recognize angles Measurement &
as geometric shapes Data
Franklin County Schools
Students:
Angle
Students know:
Students are able to:
Students understand
that:
Click below to
access all ALEX
Grade 4
Mathematics CCRS Standards and Alabama COS
CCRS Standard
Standard ID
that are formed
wherever two rays
share a common
endpoint, and
understand concepts
of angle
measurement:
Geometric
measurement:
understand concepts
of angle and
measure angles.
4.MD.5
a. An angle is
measured with
reference to a circle
with its center at the
common endpoint of
the rays by
considering the
fraction of the circular
arc between the
points where the two
rays intersect the
circle. An angle that
turns through 1/360 of
a circle is called a
“one-degree angle”
and can be used to
measure angles.
Evidence of Student
Attainment
Teacher
Vocabulary
Skills
Knowledge
Understanding
Circular arc
Justify the result of
Ray
measuring angles (in
isolation and as parts
of polygons) as a
Endpoint
number of one-degree
angles contained
between the rays that
define the angle and
including language to
describe the number of
degrees through which
the angle has "turned."
Measurable
attributes of
geometric shapes,
specifically angle
size,
Students:
Given a variety of
angles,
Angle
Students know:
Students are able to:
Protractor
Measurable
attributes of
geometric shapes,
specifically angle
size,
Use a protractor to
The rotation of an
measure angles in
whole number degrees, angle is measured by
the number of onedegree angles that
Use a protractor
exactly cover the
and ruler to sketch
rotation of the angle.
angles of a given
Units of
measurement,
specifically onedegree angle
(degrees).
Communicate the
The rotation of an
process of measuring
angle is measured by
angles and the
the number of onerelationship of the
degree angles that
measurement to a one- exactly cover the
degree angle as the unit rotation of the angle.
of measure.
Resources
resources aligned
to this standard.
ALEX Resources
b. An angle that turns
through n one-degree
angles is said to have
an angle measure of
n degrees.
24. Measure angles in Measurement &
whole-number
Data
degrees using a
Geometric
protractor. Sketch
measurement:
angles of specified
understand concepts
measure.
of angle and
measure angles.
4.MD.6
Accurately measure
the angles in whole
number degrees using
a protractor.
Units of
measurement,
Franklin County Schools
measure.
Students understand
that:
Click below to
access all ALEX
resources aligned
to this standard.
ALEX Resources
Grade 4
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Evidence of Student
Attainment
Teacher
Vocabulary
Given a variety of angle
measurements,
Measurement &
Data
Geometric
measurement:
understand concepts
of angle and
measure angles.
4.MD.7
Skills
Understanding
Resources
specifically onedegree angle
(degrees),
Use a protractor
and ruler to sketch the
corresponding angles.
25. Recognize angle
measure as additive.
When an angle is
decomposed into
nonoverlapping parts,
the angle measure of
the whole is the sum
of the angle
measures of the
parts. Solve addition
and subtraction
problems to find
unknown angles on a
diagram in real-world
or mathematical
problems, e.g., by
using an equation
with a symbol for the
unknown angle
measure.
Knowledge
Procedures for
using a protractor.
Angle
Students:
Given real world and
mathematical problems
involving angle
measurement,
Use a variety of
representations
(including diagrams
and single unknown
equations) to show
angle measure as
additive and to find and
justify solutions and
solution paths.
Students know:
Students are able to:
Measurable
attributes of
geometric shapes,
specifically angle
size,
Strategically choose
and apply methods for
finding sums,
differences, products,
and quotients of whole
numbers,
Units of
measurement,
specifically onedegree angle
(degrees),
Strategies for
representing and
solving real world
problems,
Students understand
that:
The rotation of an
angle is measured by
the number of onedegree angles that
exactly cover the
rotation of the angle,
Accurately compute
Representations for
sums, differences,
products and quotients solving problems are
of whole numbers.
chosen based on the
context and numbers in
the problem.
Click below to
access all ALEX
resources aligned
to this standard.
ALEX Resources
Strategies for
finding sums,
differences,
products, and
quotients of whole
numbers.
26. Draw points,
lines, line segments,
rays, angles (right,
acute, obtuse), and
perpendicular and
parallel lines. Identify
these in twodimensional figures.
Geometry
Draw and identify
lines and angles, and
classify shapes by
properties of their
lines and angles.
4.G.1
Franklin County Schools
Students:
Given a written or an
oral prompt,
Lines
Students know:
Student are able to:
Line segments
Defining
characteristics of
geometric figures:
points, lines, line
segments, angles
(right, acute, and
obtuse), parallel
Strategically choose
and use tools to draw 2- Shapes are
D geometric figures,
categorized based on
attributes they possess
in common such as;
Decompose 2-D
angle size, side length,
figures in a variety of
side relationships
Strategically choose Rays
and use tools to draw
points, lines, line
Angles
segments, rays, angles
(right, acute, obtuse),
Students understand
that:
Click below to
access all ALEX
resources aligned
to this standard.
ALEX Resources
Grade 4
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Evidence of Student
Attainment
perpendicular lines,
and parallel lines to
specifications.
Teacher
Vocabulary
Knowledge
Skills
Understanding
Parallel
lines, and
perpendicular
lines.
ways in order to name (parallel and
and identify component perpendicular).
parts.
Students:
Given a variety of 2-D
figures,
Parallel
Students know:
Students are able to:
Perpendicular
Justify the
classification of the
shapes based on the
presence or absences
of parallel lines or
perpendicular lines, or
the presence or
absence of angles of a
specified size.
Right triangle
Defining
characteristics of
geometric figures:
quadrilateral,
trapezoid,
rhombus,
parallelogram,
rectangle, square,
right triangle,
acute triangle,
obtuse triangle,
angles (right,
acute, and
obtuse), parallel
lines, and
perpendicular
lines.
Justify classification
of shapes based on the Shapes are
characteristics of their categorized based on
attributes.
attributes they possess
in common such as:
angle size, side length,
side relationships
(parallel and
perpendicular).
Students:
Given a variety of 2-D
figures,
Line symmetry
Students know:
Students are able to:
Defining
characteristics of
line symmetry.
Draw lines of
symmetry and justify
their placement.
Perpendicular
Resources
Given 2-D figures,
Trace or highlight
specific components
such as angles, line
segments, rays,
perpendicular lines,
and parallel lines.
27. Classify twodimensional figures
based on the
presence or absence
of parallel or
perpendicular lines or
the presence or
absence of angles of
a specified size.
Recognize right
triangles as a
category, and identify
right triangles.
Geometry
Draw and identify
lines and angles, and
classify shapes by
properties of their
lines and angles.
4.G.2
28. Recognize a line
of symmetry for a
two-dimensional
figure as a line across
the figure such that
the figure can be
folded along the line
into matching parts.
Geometry
Draw and identify
lines and angles, and
classify shapes by
properties of their
lines and angles.
4.G.3
Franklin County Schools
Justify the
existence or nonexistence of line
symmetry within the
Students understand
that:
Click below to
access all ALEX
resources aligned
to this standard.
ALEX Resources
Students understand
that:
Click below to
access all ALEX
A line of symmetry resources aligned
divides a shape into two to this standard.
parts such that when
folded on the line the
ALEX Resources
two parts match.
Grade 4
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Identify linesymmetric figures
and draw lines of
symmetry.
Franklin County Schools
Evidence of Student
Attainment
figures by drawing the
lines of symmetry.
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources