Download Grade 3 Math CCRS Standard

Grade 3
Mathematics CCRS Standards and Alabama COS
CCRS Standard
Standard ID
1. Interpret
products of whole
numbers, e.g.,
interpret 5 × 7 as
the total number of
objects in 5 groups
of 7 objects each.
Example: Describe a
context in which a
total number of
objects can be
expressed as 5 × 7.
Operations and
Algebraic
Thinking
Represent and solve
problems involving
multiplication and
division.
3.OA.1
Evidence of Student
Attainment
Students:
Given any multiplication
problem in the form a x b
= c,
Represent the
problem physically or
pictorially and describe
the relationship between
the factors and the
product in the equation
and the attributes of the
representation (i.e., given
3 x 5 = 15, students
make 3 piles of buttons
with 5 buttons in each
pile. They explain that 15
represents the total
number of buttons, 3 is
the number of piles and 5
is the number of buttons
in each pile) ,
Teacher
Vocabulary
Knowledge
Students know:
Skills
Students are able to:
Understanding
Resources
Students understand
that:
Characteristics of Represent quantities
Putting together
multiplication
and operations
contexts.
(multiplication)
equal sized groups may
physically, pictorially, or be represented by
symbolically,
multiplication equations
and totals found
Use mathematical through multiplication.
language to
communicate the
connections between
multiplication equations
and related
representations,
Click below to
access all ALEX
resources
aligned to this
standard.
ALEX Resources
Write word
problems containing
multiplication contexts.
Write a corresponding
word problems containing
a multiplication context.
2. Interpret wholenumber quotients of
whole numbers,
e.g., interpret 56 ÷
8 as the number of
objects in each
share when 56
objects are
partitioned equally
into 8 shares, or as
a number of shares
when 56 objects are
partitioned into
equal shares of 8
objects each.
Operations and
Algebraic
Thinking
Represent and solve
problems involving
multiplication and
division.
3.OA.2
Franklin County Schools
Students:
Given any division
problem in the form a ÷ b
= c,
Represent the
problem physically or
pictorially and describe
the relationship between
the dividend, divisor, and
quotient in the equation
and the attributes of the
representation (e.g.,
given 15 ÷ 3 = 5,
students make 3 piles of
Students know:
Students are able to:
Students understand
that:
Characteristics of Represent quantities
Both partitioning
division contexts.
and operations
(division) physically,
into equal-sized shares
pictorially, or
and partitioning equally
symbolically,
among a given number
of groups may be
Use mathematical modeled by division
equations and the
language to
desired results found
communicate the
through division.
connections between
division equations and
Click below to
access all ALEX
resources
aligned to this
standard.

ALEX
Resources
Grade 3
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Example: Describe a
context in which a
number of shares or
a number of groups
can be expressed as
56 ÷ 8.
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
buttons with 5 buttons in
each pile and explain that
15 represents the total
number of buttons, 3 is
the number of piles the
total was shared among
and 5 is the number of
buttons in each pile),
Skills
Understanding
Resources
related representations,
Write word
problems containing
division contexts.
Write a corresponding
word problem containing
a division context.
3. Use multiplication
and division within
100 to solve word
problems in
situations involving
equal groups,
arrays, and
measurement
quantities, e.g., by
using drawings and
equations with a
symbol for the
unknown number to
represent the
problem.1
Operations and
Algebraic
Thinking
Represent and solve
problems involving
multiplication and
division.
3.OA.3
(1See Appendix A,
Table 2.)
See glossary
Students:
Given a variety of
for problem types
multiplication and division (Table 2).
word problems within
100,
Explain and justify
solutions and solution
paths using connections
among a variety of
representations (e.g.,
place value blocks,
drawings, open arrays,
and equations with a
symbol for the unknown).
Students know:
Students are able to:
Characteristics of Represent quantities
Multiplication is
multiplication and
and operations
division contexts,
(multiplication and
putting together equal
division) physically,
sized groups and
pictorially,
or
division is sharing into
Multiplication and
symbolically,
equal-sized shares or is
division strategies.
sharing equally among a
Strategically use a given number of
Click below to
groups,
variety of
access all ALEX
representations to solve
resources
Mathematical
multiplication and
aligned to this
division word problems, problems can be solved standard.
using a variety of
strategies, models,
Use informal and
 ALEX
mathematical language representations,
Resources
to communicate the
Variables represent
connections among
multiplication and
unknown quantities
division contexts and
when representing
related physical,
mathematical situations
pictorial, or symbolic
algebraically.
representations,
Accurately compute
products and quotients,
Franklin County Schools
Students understand
that:
Grade 3
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources
Use symbols to
represent unknown
quantities in equations.
4. Determine the
unknown whole
number in a
multiplication or
division equation
relating three whole
numbers.
Example: Determine
the unknown
number that makes
the equation true in
each of the
equations 8 × ? =
48, 5 = _ ÷ 3, 6 ×
6 = ?.
Operations and
Algebraic
Thinking
Represent and solve
problems involving
multiplication and
division.
3.OA.4
5. Apply properties
of operations as
strategies to
multiply and divide.2
Examples: If 6 × 4
= 24 is known, then
4 × 6 = 24 is also
known.
(Commutative
property of
multiplication) 3 × 5
× 2 can be found by
3 × 5 = 15, then 15
× 2 = 30, or by 5 ×
2 = 10, then 3 × 10
= 30. (Associative
property of
multiplication)
Knowing that 8 × 5
= 40 and 8 × 2 =
16, one can find 8 ×
Operations and
Algebraic
Thinking
Understand
properties of
multiplication and
the relationship
between
multiplication and
division.
3.OA.5
Franklin County Schools
Students:
Students know:
Students are able to:
Solve single operation
multiplication/division
equations containing a
single unknown (e.g. 8x?
= 48, 5= __ ÷3, 6x6 =
___).
Strategies for
solving simple
equations with one
unknown.
Efficiently apply
strategies for solving
simple equations with
one unknown,
Students:
Given multiplication and
division problems within
100,
Students understand
that:
Equalities contain
phrases that name the
same amount on each
side of the equal sign.
Justify solutions for
single unknown
equations.
Commutative
Property of
Multiplication
Associative
Use the properties of Property of
operations and descriptive Multiplication
language for the property
to justify their products
Distributive
and quotients (e.g., If I
Property
know that 8 x 5 is 40, and
two more groups of 8
would be 16, then 8 x 7
must be 40 + 16 or 56).
Students know:
Students are able to:
Commutative,
Associative, Identity
and Zero Properties
of Multiplication and
the Distributive
Property,
Strategically and
efficiently apply
properties of
multiplication and
division in order to find
products and quotients.
Strategies for
finding products and
quotients.
Click below to
access all ALEX
resources
aligned to this
standard.

ALEX
Resources
Students understand
that:
The order in which
factors are multiplied
does not change the
Click below to
product.
access all ALEX
resources
aligned to this
standard.

ALEX
Resources
Grade 3
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources
7 as 8 × (5 + 2) =
(8 × 5) + (8 × 2) =
40 + 16 = 56.
(Distributive
property)
(2Students need not
use formal terms for
these properties.)
6. Understand
division as an
unknown-factor
problem.
Example: Find 32 ÷
8 by finding the
number that makes
32 when multiplied
by 8.
Operations and
Algebraic
Thinking
Understand
properties of
multiplication and
the relationship
between
multiplication and
division.
3.OA.6
Students:
Given a division problem
with an unknown
quotient,
Use a pictorial or
physical model to explain
the connection between
the division problem and
the related unknown
factor equation.
Factor
Students know:
Students are able to:
Students understand
that:
Strategies for
Use symbols to
The relationship
finding quotients and represent unknown
products.
quantities in equations, between multiplication
and division (that one
Use mathematical "undoes" the other) can
be used to solve
language to
problems,
communicate the
connections between an
unknown quotient
problem and the related
unknown factor
problem,
Efficient application
of computation
strategies are based on
the numbers in the
problems.
Click below to
access all ALEX
resources
aligned to this
standard.

ALEX
Resources
Use the inverse
relationship between
multiplication and
division to find
quotients.
7. Fluently multiply
and divide within
100, using
strategies such as
the relationship
between
multiplication and
division (e.g.,
knowing that 8 × 5
= 40, one knows 40
÷ 5 = 8) or
Operations and
Algebraic
Thinking
Multiply and divide
within 100.
3.OA.7
Franklin County Schools
Students:
Given any single digit
multiplication problem or
a division problem with a
single digit divisor and an
unknown single digit
quotient,
Use an efficient
strategy (e.g., recall,
inverse operations,
Students know:
Students are able to:
Students understand
that:
Click below to
access all ALEX
Strategies for
Use multiplication
resources
finding products and and division strategies Efficient application
aligned to this
quotients.
efficiently based on the of computation
standard.
numbers in the
strategies are based on
problems.
the numbers in the
 ALEX
problems.
Resources
Grade 3
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
properties of
operations. By the
end of Grade 3,
know from memory
all products of two
one-digit numbers.
8. Solve two-step
word problems
using the four
operations.
Represent these
problems using
equations with a
letter standing for
the unknown
quantity. Assess the
reasonableness of
answers using
mental computation
and estimation
strategies including
rounding.3
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources
arrays, derived facts,
properties of operations,
etc.) to name the product
or quotient.
Operations and
Algebraic
Thinking
Solve problems
involving the four
operations, and
identify and explain
patterns in
arithmetic.
3.OA.8
(3This standard is
limited to problems
posed with whole
numbers and having
whole-number
answers; students
should know how to
perform operations
in the conventional
order when there
are no parentheses
to specify a
particular order
(Order of
Operations).)
Students:
Given a variety of twostep word problems
involving all four
operations,
Apply their
understanding of
operations to explain and
justify solutions and
solution paths using the
connections among a
variety of representations
including equations with
symbols for unknown
quantities,
Apply their
understanding of
operations and estimation
strategies including
rounding to evaluate the
reasonableness of their
solutions, (e.g., "The
answer had to be around
125 because it's a put
together problem, and 72
is close to 75, and 56 is
close to 50, and 75 plus
50 is 125.").
Students know:
Students are able to:
Characteristics of
addition, subtraction,
multiplication, and
division situations,
Strategically use a
Multiplication is
variety of
representations to solve putting together equal
two-step word problems sized groups,
involving all four
operations,
Division is sharing
Addition,
subtraction,
multiplication, and
division strategies,
into equal-sized shares
or as sharing equally
among a given number
of groups,
Click below to
Strategies for
access all ALEX
Mathematical
mentally computing
resources
and estimating sums,
problems can be solved aligned to this
Use mathematical using a variety of
differences,
standard.
products, and
language and
strategies, models, and
quotients.
contextual situations to representations,
 ALEX
communicate the
Resources
connections among the Solutions can be
four operations and
evaluated by using
related physical,
reasoning to compare
pictorial, or symbolic
the actual solution with
representations and
estimated solutions.
justify solutions/solution
paths,
Use symbols to
represent unknown
quanities in equations
that relate to word
problem contexts,
Accurately compute
sums, differences,
products and quotients,
Use logical
Franklin County Schools
Students understand
that:
Grade 3
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources
reasoning, mental
computation strategies,
and estimation
strategies to justify the
reasonableness of
solutions.
9. Identify
arithmetic patterns
(including patterns
in the addition table
or multiplication
table), and explain
them using
properties of
operations.
Example: Observe
that 4 times a
number is always
even, and explain
why 4 times a
number can be
decomposed into
two equal addends.
Operations and
Algebraic
Thinking
Solve problems
involving the four
operations, and
identify and explain
patterns in
arithmetic.
3.OA.9
Students:
Students know:
Identify arithmetic
patterns (including
patterns in the addition
table or multiplication
table), and explain them
using properties of
operations. (e.g., observe
that 4 times a number is
always even, and explain
why 4 times a number
can be decomposed into
two equal addends).
Characteristics of Identify arithmetic
numbers and
patterns in number
properties of
sequences, in the
operations (e.g.,
addition table or
odd, even),
multiplication table,
Properties from
Table 3, etc.
Use logical
reasoning and
properties of numbers
and operations to
explain arithmetic
patterns.
10. Use place value
understanding to
round whole
numbers to the
nearest 10 or 100.
Number &
Operations in
Base Ten
Use place value
understanding and
properties of
operations to
perform multi-digit
arithmetic. 4
Students:
Given any number less
than 1,000,
Students know:
Students are able to:
Place value
(ones, tens,
hundreds),
Count by 10s and
100s,
(4 A range of
algorithms may be
used.)
3.NBT.1
Franklin County Schools
Round it to the
nearest 10 or 100 and
justify the answer using
place value vocabulary,
(e.g., "Rounding 147 to
the nearest 10 is 150
because 147 is between
140 and 150 and is more
than half way to 150).
Rounding.
Students are able to:
Determine what is
halfway between two
multiples of 10 or 100,
Round to the
nearest 10 or 100,
Use place value
vocabulary and logical
reasoning to justify
solutions to rounding
problems.
Students understand
that:
Characteristics of
Click below to
numbers and properties access all ALEX
of operations justify
resources
patterns which can be aligned to this
used to reason about
standard.
mathematical situations,
form conjectures, and
 ALEX
solve problems.
Resources
Students understand
that:
Rounding and place
value can be used to
estimate quantities by
changing the original
number to the closest
multiple of a power of
10.
Click below to
access all ALEX
resources
aligned to this
standard.

ALEX
Resources
Grade 3
CCRS Standard
11. Fluently add and
subtract within 1000
using strategies and
algorithms based on
place value,
properties of
operations, and/or
the relationship
between addition
and subtraction.
Mathematics CCRS Standards and Alabama COS
Standard ID
Number &
Operations in
Base Ten
Use place value
understanding and
properties of
operations to
perform multi-digit
arithmetic. 4
(4 A range of
algorithms may be
used.)
3.NBT.2
12. Multiply onedigit whole numbers
by multiples of 10 in
the range 10–90
(e.g., 9 × 80, 5 ×
60) using strategies
based on place
value and properties
of operations.
Number &
Operations in
Base Ten
Use place value
understanding and
properties of
operations to
perform multi-digit
arithmetic. 4
(4 A range of
algorithms may be
used.)
3.NBT.3
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
Understanding
Students:
Students know:
Students are able to:
Fluently add and
subtract within 1000,
using strategies based on
place values, properties of
operations, and/or the
relationship between
addition and subtraction,
Tools for
modeling addition
and subtraction,
Methods for
symbolically
(numerically)
recording strategies
for solving addition
and subtraction
problems.
Model addition and
Relationships
subtraction problems
using appropriate tools, between models of
addition and subtraction
problems and symbolic
Record strategies
for solving addition and recordings of those
subtraction problems, models can be used to
justify solutions and
solution strategies.
Communicate the
relationship between
models and symbolic
(numeric)
representations of
solutions to addition
and subtraction
problems.
Students:
Students know:
Students are able to:
Efficiently use
strategies based on place
value and properties of
operations to multiply
one-digit numbers by
multiples of 10 (from 1090) and justify their
answers.
Place value
models for
multiplying numbers
(e.g., open arrays,
place value blocks),
Justify solutions
including those which
required regrouping by
relating the strategy to a
written method and
explain the reasoning.
Strategies for
solving addition and
subtraction
problems,
Use mental
strategies based on an
understanding of place
value, properties of
operations, and
knowledge of one-digit
multiplication to find
Strategies for
multiplying one-digit products,
numbers,
Use a variety of
place value models of
Strategies for
mentally multiplying multiplication problems
one-digit numbers by to justify strategies and
multiples of powers solutions.
Resources
Students understand
that:
Click below to
access all ALEX
resources
aligned to this
standard.

ALEX
Resources
Students understand
that:
Patterns in the place
Click below to
value system and
properties of operations access all ALEX
resources
can be used to
aligned to this
efficiently compute
standard.
products.

ALEX
Resources
of 10.
13. Understand a
fraction 1/b as the
quantity formed by
1 part when a whole
is partitioned into b
Number &
Operations—
Fractions
Develop
understanding of
Franklin County Schools
Students:
Given any fraction in the
form a/b,
Students know:
Fractions,
Students are able to:
Students understand
that:
Click below to
access all ALEX
resources
Write fractions that
correspond to pictorial Fractional parts are aligned to this
standard.
Grade 3
CCRS Standard
equal parts;
understand a
fraction a/b as the
quantity formed by
a parts of size 1/b.
Mathematics CCRS Standards and Alabama COS
Standard ID
fractions as
numbers.5
(5Grade 3
expectations in this
domain are limited
to fractions with
denominators 2, 3,
4, 6, 8.)
3.NF.1
Evidence of Student
Attainment
Create a model of the
fraction and explain the
relationship between the
fraction and the model
including the
corresponding sum of unit
fractions (fractions with
numerator = 1). (e.g.,
3/5 = 1/5 + 1/5 + 1/5).
Teacher
Vocabulary
Knowledge
Strategies for
creating models of
fractional quantities
(e.g., folding,
repeatedly dividing
the whole in half,
etc.).
Write the
corresponding fraction
and explain the
relationship of the
numerator and
denominator to the
model.
Number &
Operations—
Fractions
Develop
understanding of
fractions as
numbers.5
a. Represent a
fraction 1/b on a
number line
diagram by defining
the interval from 0
to 1 as the whole
and partitioning it
into b equal parts.
Recognize that each
part has size 1/b
and that the
endpoint of the part
(5Grade 3
expectations in this
domain are limited
to fractions with
denominators 2, 3,
4, 6, 8.)
3.NF.2
Franklin County Schools
Students:
Given any common
fraction a/b between 0
and 1 (denominators of 2,
3, 4, 6, 8),
Create a number line
diagram and justify the
partitioning of the interval
from 0 to 1 and the
placement of the point
that corresponds to the
fraction.
or physical models,
Understanding
created when a whole is
partitioned into equal
sized pieces (using up
the whole),
Create models of
fractions that
correspond to fractions
written in the form a/b, The unit fraction
(1/b) names the size of
the unit with respect to
Communicate the
the referenced whole,
relationship between
Resources

ALEX
Resources
models of fractions and
The numerator
the corresponding
written fraction.
counts the parts
referenced and that the
denominator tells the
number of parts into
which the whole was
partitioned.
Given a model of a
fraction,
14. Understand a
fraction as a
number on the
number line;
represent fractions
on a number line
diagram.
Skills
Students know:
Students are able to:
Students understand
that:
Represent fractions
A fractional quantity
in the form a/b on a
number line including
can be modeled using a
Strategies for
Click below to
creating number line correctly partitioning the variety of
interval
from
0
to
1
into
representations
(e.g.,
access all ALEX
models of fractions
"b"
equal
parts
and
part
of
a
whole,
part
of
resources
less than 1 (e.g.,
counting "a" parts to
a group, a distance on a aligned to this
marking off equal
place the fraction,
numberline) each of
standard.
lengths by
which
may
reveal
estimation, recursive
Explain and justify important features of
halving).
 ALEX
given contexts.
the creation and
Resources
Fractions,
placement of a fraction
less than 1 on a number
line.
Grade 3
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources
based at 0 locates
the number 1/b on
the number line.
b. Represent a
fraction a/b on a
number line
diagram by marking
off a lengths 1/b
from 0. Recognize
that the resulting
interval has size a/b
and that its
endpoint locates the
number a/b on the
number line.
15. Explain
equivalence of
fractions in special
cases, and compare
fractions by
reasoning about
their size.
Number &
Operations—
Fractions
Develop
understanding of
fractions as
numbers.5
a. Understand two
fractions as
equivalent (equal) if
they are the same
size or the same
point on a number
line.
(5Grade 3
expectations in this
domain are limited
to fractions with
denominators 2, 3,
4, 6, 8.)
3.NF.3
b. Recognize and
generate simple
equivalent fractions,
e.g., 1/2 = 2/4, 4/6 =
2/ ). Explain why
3
the fractions are
equivalent, e.g., by
Franklin County Schools
Students:
Students know:
Students are able to:
Use visual models
(e.g., fraction
manipulatives, number
lines, or pictures) to
generate simple
equivalent fractions
including fractions
equivalent to whole
numbers,
Strategies for
comparing fractions
(e.g., comparing
numerators of like
fractions, comparing
denominators of
fractions with like
numerators,
comparing to
landmark fractions
such as 1/2),
Generate simple
equivalent fractions
using visual models,
Given two fractions,
use logical reasoning and
a variety of models to
represent and order the
fractions (using <, =, >)
and justify their answers,
Communicate the
reason why it is not valid
to make a comparison
Students understand
that:
Two fractions are
equivalent if they are
the same portion of the
Express the same same whole or are the Click below to
same point on the
whole number in
access all ALEX
number line,
multiple ways as
resources
fractions (4 = 4/1 = 8/2
aligned to this
Comparisons of
= 16/4) and explain
standard.
their answers,
fractions are valid only
when the two fractions
 ALEX
Strategically choose refer to the same
Resources
Strategies for
and apply a variety of whole,
generating
representations or use
equivalent fractions logical reasoning to
Any fraction can be
using visual models justify the comparison named in many ways
(e.g., fraction circles, of two fractions,
(equivalent fractions)
fraction bars,
and different names are
diagrams, pictures,
useful for different
Represent the
etc.).
comparison of fractions problem situations.
Grade 3
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
using a visual
fraction model.
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
between 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?").
c. Express whole
numbers as
fractions, and
recognize fractions
that are equivalent
to whole numbers.
Examples: Express
3 in the form 3 =
3/ ; recognize that
1
6/ = 6; locate 4/
1
4
and 1 at the same
point of a number
line diagram.
Skills
Understanding
Resources
using <, =, and >
notation.
d. Compare two
fractions with the
same numerator or
the same
denominator by
reasoning about
their size. Recognize
that comparisons
are valid only when
the two fractions
refer to the same
whole. Record the
results of
comparisons with
the symbols >, =,
or <, and justify the
conclusions, e.g., by
using a visual
fraction model.
16. Tell and write
time to the nearest
minute, and
measure time
intervals in minutes.
Measurement &
Data
Solve problems
involving
measurement and
Franklin County Schools
Students:
Students know:
Students are able to:
Students understand
that:
Tell and write time to
the nearest minute using
Conventions for
time notation,
Accurately read and
Analog and digital
write time to the
nearest minute from
clocks represent the
Click below to
access all ALEX
resources
aligned to this
standard.
Grade 3
Mathematics CCRS Standards and Alabama COS
CCRS Standard
Standard ID
Solve word
problems involving
addition and
subtraction of time
intervals in minutes,
e.g., by
representing the
problem on a
number line
diagram.
estimation of
intervals of time,
liquid volumes, and
masses of objects.
3.MD.1
Evidence of Student
Attainment
Teacher
Vocabulary
Time sequence
patterns,
analog and digital clocks,
Use strategies (e.g.,
watch the movement of a
second or minute hand,
count the changing of
digits) to estimate and
measure time intervals in
minutes,
Measurement &
Data
Solve problems
involving
measurement and
estimation of
intervals of time,
liquid volumes, and
masses of objects.
3.MD.2
(6Excludes
compound units
such as cm3 and
Franklin County Schools
Students:
Liquid volume
Accurately measure
Mass
the liquid volume and
mass of objects by
selecting and using
appropriate tools such as
balance and spring scales,
graduated cylinders,
beakers, and measuring
cups to determine
measures to the nearest
whole unit.
Given a variety of onestep word problems
involving same unit
volume or mass
measurements,
Explain and justify
solutions using a variety
Skills
analog and digital
clocks,
Understanding
time at any particular
moment,
Measure time
Clocks show the
Strategies for
determining elapsed intervals in minutes,
passage of time with
time (e.g., using
the movement of the
number lines).
Strategically select hands or the changing
and apply methods for of digits,
showing elapsed time to
Representations for
solve word problems.
use in solving problems
are selected based on
the context and
numbers in the
problem.
Solve word problems
involving addition and
subtraction of time
intervals using
representations of time
passage such as arrows
on open number lines.
17. Measure and
estimate liquid
volumes and
masses of objects
using standard units
of grams (g),
kilograms (kg), and
liters (l).6 Add,
subtract, multiply,
or divide to solve
one-step word
problems involving
masses or volumes
that are given in the
same units, e.g., by
using drawings
(such as a beaker
with a measurement
scale) to represent
the problem.7
Knowledge
Students know:
Students are able to:
Personal
benchmarks for
metric standard units
of mass (gram &
kilogram) and liquid
volume (liter)
measure and the use
of related tools for
measurement to
those units,
Measure liquid
volume and mass in
metric standard units,
Resources

ALEX
Resources
Students understand
that:
The liquid volume of
the object is expressed
as the number of unit
Choose appropriate volumes needed to fill
Click below to
measurement tools and the same space,
access all ALEX
units of measure,
resources
The mass of an
aligned to this
Represent quantities object is expressed as standard.
the number of standard
and operations
physically, pictorially, or units needed to balance
 ALEX
Characteristics of symbolically,
the object,
Resources
addition, subtraction,
multiplication, and
Mathematical
Strategically use a
division contexts that
problems can be solved
variety of
involve
representations to solve using a variety of
measurements.
one-step word problems strategies, models, and
representations.
that involve
measurement.
Grade 3
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
finding the
geometric volume of
a container.)
(7Excludes
multiplicative
comparison
problems (problems
involving notions of
“times as much”).)
(See Appendix A,
Table 2.)
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources
of representations.
18. Draw a scaled
picture graph and a
scaled bar graph to
represent a data set
with several
categories. Solve
one- and two-step
“how many more”
and “how many
less” problems using
information
presented in scaled
bar graphs.
Example: Draw a
bar graph in which
each square in the
bar graph might
represent 5 pets.
Measurement &
Data
Represent and
interpret data.
3.MD.3
19. Generate
measurement data
by measuring
lengths using rulers
marked with halves
and fourths of an
inch. Show the data
by making a line
plot where the
horizontal scale is
Measurement &
Data
Represent and
interpret data.
3.MD.4
Students:
Organize and
represent data with
several categories using
picture graphs
(pictographs) and bar
graphs with scales other
than 1,
Scaled
pictograph
Scaled bar
graph
Reason quantitatively
to answer one- and twostep "how many more?"
and "how many less?"
problems using
information presented in
the scaled pictographs
and bar graph.
Franklin County Schools
Students:
Make and use line
plots (scale to match unit
of measure) to represent
data generated by
measuring lengths (to the
nearest inch, half inch, or
quarter inch) of several
objects (e.g., measure
Students know:
Students are able to:
Strategies for
collecting,
organizing, and
recording data
(including scaled
pictographs and
scaled bar graphs),
Choose and apply
appropriate strategies
for organizing and
recording data,
Strategies for
counting and
comparing
quantities,
Strategies for
solving addition and
subtraction one and
two-step problems.
Line plots
Students know:
Line plots,
Students understand
that:
Questions
concerning
mathematical contexts
can be answered by
collecting and
organizing data scaled
pictographs and bar
graphs,
Read and interpret
graphical
representations
(pictographs and bar
graphs with scales other
Understand that
than 1) of data,
logical reasoning and
Communicate and connections between
representations provide
defend solutions and
justifications for
solutions paths.
solutions.
Students are able to:
Students understand
that:
Use standard units
and the related tools to Questions
Standard units, measure length to the concerning
nearest quarter inch,
mathematical contexts
can be answered by
Related tools for
collecting, organizing,
Organize
and
measuring length.
and analyzing data and
represent length
measurement data on a data displays.
Click below to
access all ALEX
resources
aligned to this
standard.

ALEX
Resources
Click below to
access all ALEX
resources
aligned to this
standard.

ALEX
Resources
Grade 3
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
marked off in
appropriate units—
whole numbers,
halves, or quarters.
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
the length of all class
members' fingers) or by
making repeated
measurements (e.g.,
measuring how far a
marble rolls under certain
conditions),
Skills
Understanding
Resources
line plot,
Form conjectures
based on the display of
the data.
Communicate
questions and
descriptions related to the
data display.
20. Recognize area
as an attribute of
plane figures, and
understand
concepts of area
measurement.
a. A square with
side length 1 unit
called “a unit
square,” is said to
have “one square
unit” of area and
can be used to
measure area.
Measurement &
Data
Geometric
measurement:
understand
concepts of area
and relate area to
multiplication and to
addition.
3.MD.5
Students:
Area
Explain the result of
Plane figure
measuring the area of a
plane figure as a number Unit square
of "unit squares" needed
to cover the object
without gaps or overlaps.
Students know:
Students are able to:
Students understand
that:
Measureable
Measure area using
The area of a plane
attributes of objects, manipulative square
specifically area,
units to cover a plane figure is measured by
figure,
the number of samesize squares that exactly
Units of measure
Click below to
Explain and justify cover the interior space access all ALEX
for area (unit
of the figure.
squares).
procedures for
resources
determining the area of
aligned to this
a plane figure.
standard.

ALEX
Resources
b. A plane figure
which can be
covered without
gaps or overlaps by
n unit squares is
said to have an area
of n square units.
21. Measure areas
by counting unit
squares (square cm,
square m, square
in, square ft, and
Measurement &
Data
Geometric
measurement:
understand
Franklin County Schools
Students: Given a variety
of plane figures,
Accurately measure
area by counting standard
Students know:
Students are able to:
Students understand
that:
Click below to
access all ALEX
resources
Measurable
Accurately measure
attributes of objects, area using standard and The area of a plane aligned to this
non-standard square
figure is measured by standard.
Grade 3
CCRS Standard
improvised units).
Mathematics CCRS Standards and Alabama COS
Standard ID
concepts of area
and relate area to
multiplication and to
addition.
3.MD.6
22. Relate area to
the operations of
multiplication and
addition.
Measurement &
Data
Geometric
measurement:
understand
a. Find the area of a concepts of area
and relate area to
rectangle with
whole-number side multiplication and to
lengths by tiling it, addition.
3.MD.7
and show that the
area is the same as
would be found by
multiplying the side
lengths.
b. Multiply side
lengths to find areas
of rectangles with
whole-number side
lengths in the
context of solving
real world and
mathematical
problems, and
represent wholenumber products as
rectangular areas in
mathematical
reasoning.
c. Use tiling to show
in a concrete case
that the area of a
rectangle with
Franklin County Schools
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
(square centimeter,
square meter, square
inch, and square foot)
and non-standard unit
squares (e.g., orange
pattern blocks, floor tiles,
etc.).
specifically area,
Distributive
Students:
Given a polygon that may Property
be decomposed into 2 or
more rectangles,
Rectilinear
figures
Find the total area by
decomposing the figure
into non-overlapping
rectangles, finding the
area of each, and find the
sum of the areas.
Given a rectangle with
whole number length
sides,
Find and justify the
area of the rectangle by
relating a tile covered
model to a corresponding
multiplication problem
(counting unit squares in
rows and columns
compared to multiplying
length by width).
Using array cards or tiles,
Create and explain
rectangular models to
show that the area of a
Skills
Understanding
units (to the nearest
whole unit).
counting the number of
same-size squares (unit
squares) that exactly
cover the interior space
of the figure.
Students know:
Students are able to:
Students understand
that:
Relationships
between rectangular
arrays and the
corresponding
multiplication
problems (counting
unit squares in rows
and columns
compared to
multiplying length by
width),
Communicate the
relationships between
rectangular array
models of areas and
multiplication and
addition problems
including modeling the
Distributive Property,
Strategies for
measuring area.
Strategies for
finding sums and
products of whole
numbers.
Resources

ALEX
Resources
The area of a plane
figure is measured by
the number of samesize squares that exactly
cover the interior space
of the figure,
Multiplication is
Model the area of putting together equal
rectangles using
sized groups,
Click below to
manipulatives or graph
access all ALEX
paper,
Rectangular arrays resources
represent groups (rows) aligned to this
Strategically and
of equal size (number of standard.
fluently choose
columns),
strategies for finding
 ALEX
sums and products,
Resources
Multiplication is
distributive over the
Accurately compute addition of whole
sums and products.
numbers.
Grade 3
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
whole-number side
lengths a and b + c
is the sum of a × b
and a × c. Use area
models to represent
the distributive
property in
mathematical
reasoning.
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources
rectangle with wholenumber side lengths a
and d (where d=b+c) is
the same as the area of
two smaller rectangles
with area a x b and a x c.
(the Distributive
Property).
d. Recognize area
as additive. Find
areas of rectilinear
figures by
decomposing them
into nonoverlapping
rectangles and
adding the areas of
the nonoverlapping
parts, applying this
technique to solve
real-world
problems.
23. Solve real-world
and mathematical
problems involving
perimeters of
polygons, including
finding the
perimeter given the
side lengths, finding
an unknown side
length, and
exhibiting
rectangles with the
same perimeter and
different areas or
with the same area
and different
perimeters.
Measurement &
Data
Geometric
measurement:
recognize perimeter
as an attribute of
plane figures and
distinguish between
linear and area
measures.
3.MD.8
Franklin County Schools
Students:
Perimeter
Find and justify
Area
solutions to real world
and mathematical
Polygons
problems involving
perimeters of polygons,
including finding the
perimeter given the side
lengths, finding an
unknown side length, and
exhibiting rectangles with
the same perimeter and
different areas, or with
the same area and
different perimeters.
Students know:
Students are able to:
Measureable
attributes of objects,
specifically perimeter
and area,
Strategically use a
variety of models and
representations to solve
measurement problems
involving area and
perimeter,
Strategies for
modeling
measurement
problems involving
perimeter and area,
Students understand
that:
Perimeter is
measured in length
Click below to
units and is the distance access all ALEX
around a 2-D figure,
resources
aligned to this
The area of a plane standard.
Accurately compute figure is measured by
using whole numbers, the number of same ALEX
size squares that exactly
Resources
cover the interior space
Use logical
of the figure.
Strategies for
reasoning to justify
representing and
solutions and solution
computing perimeter paths by connecting
and area.
models to equations
and computations.
Grade 3
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Evidence of Student
Attainment
24. Understand that
shapes in different
categories (e.g.,
rhombuses,
rectangles, and
others) may share
attributes (e.g.,
having four sides),
and that the shared
attributes can
define a larger
category (e.g.,
quadrilaterals).
Recognize
rhombuses,
rectangles, and
squares as
examples of
quadrilaterals, and
draw examples of
quadrilaterals that
do not belong to
any of these
subcategories.
Geometry
Students:
Reason with shapes
and their attributes. Justify their
3.G.1
identification/sorting of
shapes (triangles,
quadrilaterals, pentagons,
hexagons, squares,
rectangles, rhombuses)
by referring to their
shared attributes,
25. Partition shapes
into parts with equal
areas. Express the
area of each part as
a unit fraction of the
whole.
Example: Partition a
shape into 4 parts
with equal area, and
describe the area of
each part as 1/4 of
the area of the
shape.
Geometry
Students:
Reason with shapes Given squares,
and their attributes. rectangles, or circles,
3.G.2
Teacher
Vocabulary
Franklin County Schools
Express the area of
each part as a unit
fraction of the whole
(e.g., partition a shape
into 4 parts with equal
area, and describe the
Skills
Understanding
Resources
Rhombus
Students know:
Students are able to:
Rectangle
Names for 2-D
shapes, (e.g.triangle,
quadrilateral,
pentagon, hexagon,
square, rectangle,
rhombus),
Identify attributes of
Shapes may be
2-D shapes, (e.g.,
number of sides, equal assigned to different
sides, right angles,
categories of shapes
parallel sides),
based on different
Click below to
selections of shared
access all ALEX
attributes
and
that
the
Classify 2-D shapes
resources
shared attributes can
based on their
aligned to this
define
a
larger
category.
attributes,
standard.
Square
Quadrilateral
Students understand
that:
Defining
attributes for 2-D
shapes, (e.g., right
angles, equal length Draw shapes based
sides, parallel sides, on specified attributes.
straight sides, closed
figure).
Draw corresponding
shapes when given a list
of attributes.
Cut or draw lines to
divide the shapes into
equal shares and justify
their divisions by
reasoning about equal
area,
Knowledge
Students are able to:

Area
Students know:
Partition
Strategies for
Decompose circles,
decomposing shapes squares, and rectangles The same fractional
into equal shares,
into equal shares,
parts of same- size 2-D
shapes have equal area
but do not have to be
Fraction
Communicate the
vocabulary; halves, size of shares using the congruent (e.g., When
two same-size
thirds, fourths,
appropriate fraction
rectangles are cut in
quarters, fifths,
terminology,
half vertically,
eighths, and tenths.
horizontally, or
Justify equal area of
diagonally, the pieces
congruent and nonare all one half of the
congruent shares as
original rectangle, have
equal shares of the
equal area but are not
same size whole.
all congruent).
ALEX
Resources
Students understand
that:
Click below to
access all ALEX
resources
aligned to this
standard.

ALEX
Resources
Grade 3
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Evidence of Student
Attainment
area of each part as 1/4
of the area of the shape).
Franklin County Schools
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources