Mississippi College and Career Readiness Standards for
Mathematics Scaffolding Document
Grade 3
September 2016 Page 1 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Operations and Algebraic Thinking
Represent and solve problems involving multiplication and division
3.OA.1
Interpret products of
whole numbers, e.g.,
interpret 5 • 7 as the
total number of
objects in 5 groups of
7 objects each. For
example, describe a
context in which a
total number of
objects can be
expressed as 5 × 7.
Desired Student Performance
A student should know
• Repeated addition is
connected to multiplication.
• Equal groups can be modeled
by partitioning rectangles.
• How to skip count by 2s, 5s
and 10s.
• How to use a rectangular
array to find the total number
of objects.
• Interpretation means to
communicate symbolically,
numerically, abstractly, and/or
with a model.
• How to add using the
commutative and identity
properties.
• Patterns connecting addition
and subtraction.
A student should understand
• Multiplication means “groups
of.”
• Multiply by using a set of
equal groups.
• Arrays can be used to
represent multiplication.
• How to define the terms factor
and product.
• Properties (rules about how
numbers work) of
multiplication can be used to
solve problems.
• Patterns are found in the
multiplication table.
• Find products of whole
numbers as the total number
of objects in n groups of n
objects each.
• Solve multiplication problems
by using equal groups, arrays,
area, and/or measurement
quantities.
• Represent a multiplication
situation as an equation.
• For example, choose the
equation that represents the
picture:
a) 4 + 4 + 4 + 4
b) 2 x 6
c) 2 + 6
d) 6 ÷ 2
September 2016 Page 2 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Operations and Algebraic Thinking
Represent and solve problems involving multiplication and division
3.OA.2
Interpret whole-
number 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. For
example, describe a
context in which a
number of shares or a
number of groups can
be expressed as 56 ÷
8.
Desired Student Performance
A student should know
• Repeated subtraction is
related to division.
• How to skip count by 2s, 5s,
10s, and 100s.
• Patterns are found in the
multiplication table.
• How to partition shapes and
groups of objects into equal
shares.
• Interpretation means to
communicate symbolically,
numerically, abstractly,
and/or with a model.
• Patterns connecting addition
and subtraction.
A student should understand
• Division means to separate
into parts.
• A quotient describes how
many groups there are or how
many objects are in each
group.
• The numbers in a division
equation represent a number
of equal shares and the
number of items in each share.
• The relationship between
multiplication and division is an
inverse relationship.
• Models and arrays can be
used to solve division
problems.
• Explain what division means
and how it relates to equal
shares.
• Interpret quotients as the
number of objects (shares) or
the number of groups when a
set of objects is divided
equally.
• Solve division problems by
using equal groups, arrays,
area, and/or measurement
quantities.
• Represent a division situation
as an equation.
• For example, choose the
division number sentence that
represents the picture:
a) 12 ÷ 4 = 3
b) 12 ÷ 6 = 2
c) 6 ÷ 6 = 1
d) 12 ÷ 1 = 12
September 2016 Page 3 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Operations and Algebraic Thinking
Represent and solve problems involving multiplication and division
3.OA.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
Desired Student Performance
A student should know
• How to solve one- and two-
step addition and subtraction
word problems.
• Addition can be used to find
the total number of objects
arranged in rectangular
arrays.
• How to skip count by 2s, 5s,
and 10s.
• A variable represents the
unknown number.
• How to solve equations for
the unknown.
• Multiplication and division are
related.
• Multiplication is repeated
addition and division is
repeated subtraction.
• How to find products and
quotients within 100.
A student should understand
• Multiplication is used to find
the sum of equal groups.
• Division is used to find the
number of objects in a share
or the number of equal
shares.
• Arrays can be used to model
multiplication and division
problems.
• The rows and columns of an
array differ based on
orientation of the array.
• The relationship between
multiplication and division
(inverse operations) can be
used to find the unknown.
• Solve a variety of problem
solving situations including the
product, the group size, or the
number of groups.
• Represent a word problem
using a picture, an equation
with a symbol for the unknown
number, or in other ways.
• Solve real-life multiplication
and division problems where
the product/quotient is greater
than 5.
• For example, Maria cuts 12
feet of ribbon into three equal
pieces so she can share it with
her two sisters. Use words,
numbers, and/or pictures to
show how long each piece is.
September 2016 Page 4 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Operations and Algebraic Thinking
Represent and solve problems involving multiplication and division
3.OA.4
Determine the
unknown whole
number in a
multiplication or
division equation
relating three whole
numbers, with factors
0-10. For example,
determine the
unknown number that
makes the equation
true in each of the
equations 8 × ? = 48,
5 = ? ÷ 3, 6 × 6 = ?
Desired Student Performance
A student should know
• How to find an unknown
whole number in an addition
and subtraction equation.
• Addition can be used to find
the total number of objects
arranged in rectangular
arrays.
• How to skip count by 2s, 5s,
and 10s.
• A variable represents the
unknown number.
• How to multiply and divide
within 100 using basic
multiplication facts.
• How to express the
relationship between
multiplication and division as
fact families.
A student should understand
• How to use related facts and
properties of operations to
find the unknown number.
• The relationship between
multiplication and division
(inverse operations) can be
used to find the unknown.
• Factors and products and
divisors and dividends
express part-whole
relationships in multiplication
and division.
• The meaning of the equal
sign as “the same as” to
interpret an equation with an
unknown.
• Products from single digit
factors 0-9 and 10.
• Select the operation
(multiplication or division)
needed to determine the
unknown whole number.
• Solve to find the unknown
whole number (factor, product,
quotient) in a multiplication or
division equation where
products and quotients are
greater than 5.
• For example, solve the
equations below:
24= ? x 6
72 ÷ ? = 9
• For example, Candace has
four bags. There are three
marbles in each bag. How
many marbles does Candace
have altogether (4 x 3 = m)?
September 2016 Page 5 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Operations and Algebraic Thinking
Understand properties of multiplication and the relationship between multiplication and division
3.OA.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 × 7 as 8 × (5
+ 2) = (8 × 5) + (8 × 2) =
40 + 16 = 56.
(Distributive property.)
Desired Student Performance
A student should know
• Understand and apply the
properties of operations
(commutative, associative,
and identity) to add and
subtract.
• Addition can be used to find
the total number of objects
arranged in rectangular
arrays.
• How to multiply and divide
within 100.
• How to use arrays, bar
diagrams, and drawings as
strategies to multiply and
divide.
• Fact families are expressions
of the relationship between
multiplication and division.
A student should understand
• The commutative property
states that the order in which
the factors are multiplied does
not change the product.
• The associative property
states the way in which
numbers are grouped does
not change their product.
• The distributive property
states that a sum may be
found by multiplying each
addend separately and then
adding the products.
• The identity property of
multiplication states that the
product of 1 and a number is
the number itself.
• Factors can be decomposed
as a strategy for finding a
product.
• Explain how the properties of
operations work.
• Apply properties of operations
as strategies to multiply and
divide.
• Find products and quotients by
using known facts.
• For example, for each
expression in A–D, answer
Yes or No if the expression is
equivalent to the product of 7
and 9.
a) 7 x (1 + 8) Yes No
b) 9 x (3 + 6) Yes No
c) (2 x 5) + (5 x 4) Yes No
September 2016 Page 6 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Operations and Algebraic Thinking
Understand properties of multiplication and the relationship between multiplication and division
3.OA.6
Understand division
as an unknown-factor
problem, where a
remainder does not
exist. For example,
find 32 ÷ 8 by finding
the number that
makes 32 when
multiplied by 8 with no
remainder.
Desired Student Performance
A student should know
• How to find an unknown
whole number in an addition
and subtraction equation.
• Addition can be used to find
the total number of objects
arranged in rectangular
arrays.
• How to skip count by 2s, 5s,
and 10s.
• The equal sign is an
expression of equality.
• How to use models and
arrays to find quotients to
division problems.
• A variable represents the
unknown number.
• How to multiply and divide
within 100.
A student should understand
• How to use multiplication to
find the unknown number in
a division problem.
• The relationship between
multiplication and division
(inverse operations) can be
used to find the unknown.
• Factors and products and
divisors and dividends
express part-whole
relationships in multiplication
and division.
• The difference between
division with and without a
remainder and the impact to
factors in multiplication.
A student should be able to do
• Find quotients to division
problems by using
multiplication facts.
• Recognize multiplication and
division as related operations
and explain how they are
related.
• For example,
3 x 5 =15; 5 x 3= 15
15 ÷ __ = 5 (3)
15 ÷ __ = 3 (5)
• For example, a student knows
that 4 x 6 = 24. How can he
use that fact to determine the
answer to the following
problem:
Twenty-four students are
divided into four groups in Art
class. How many students are
in each group? Write a division
equation and explain your
reasoning.
September 2016 Page 7 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Operations and Algebraic Thinking
Multiply and divide within 100
3.OA.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 properties of
operations. Know
from memory all
products of two one-
digit numbers; and
fully understand the
concept when a
remainder does not
exist under division.
Desired Student Performance
A student should know
• How to add and subtract
fluently within 20 and recall
single-digit sums from
memory.
• Patterns and relationships
are found in the multiplication
table.
• The relationship between
multiplication and division is
an inverse relationship.
• Multiplication is used to find
the sum of equal groups.
• Division is used to find the
number of objects in a share
or the number of equal
shares.
A student should understand
• Visual images and numerical
patterns of multiplication and
division can be used to solve
problems.
• Various strategies are used to
attain fluency with basic
multiplication and division
facts.
• Numbers can be used flexibly
to solve multiplication and
division problems.
• Fluently means quickly and
accurately.
• Multiplication and division
within 100.
• Analyze a multiplication or
division problem in order to
choose an appropriate strategy
to fluently multiply or divide
within 100.
• Recall from memory all
products of two one-digit
numbers.
• For example:
6 x 7 = 42
8 x 8 = 64
42 ÷ 6 = 7
72 ÷ 9 = 8
September 2016 Page 8 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Operations and Algebraic Thinking
Solve problems involving the four operations, and identify and explain patterns in arithmetic
3.OA.8
Solve two-step (two
operational steps)
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
Include problems with
whole dollar amounts.
Desired Student Performance
A student should know
• How to solve two-step word
problems involving addition
and subtraction.
• How to recall multiplication
and division facts from
memory.
• How to use problem-solving
structures for area/arrays and
for equal groups.
• How to define the meaning of
addition, subtraction,
multiplication, and division.
• A variable represents the
unknown number.
• Rounding is an estimation
strategy.
• How to describe the order of
operations (without
parentheses).
A student should understand
• How to construct an equation
with a letter standing for the
unknown quantity.
• How to describe strategies for
solving problems involving
addition, subtraction,
multiplication, and division.
• Using strategies for estimating.
• How to represent whole dollar
amounts.
• How to subtract across zeros
when working with whole dollar
amounts.
• Solve two-step problems
involving addition, subtraction,
multiplication, and division.
• Solve for an unknown in
various positions.
• Justify answers using various
estimation strategies.
• For example, a roller skating
team has 10 members. Each
team member has two skates.
Each skate has four wheels.
What is the total number of
skate wheels that the team
has? __________ wheels
Show how you got your
answer.
September 2016 Page 9 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Operations and Algebraic Thinking
Solve problems involving the four operations, and identify and explain patterns in arithmetic
3.OA.9
Identify arithmetic
patterns (including
patterns in the
addition table or
multiplication table),
and explain them
using properties of
operations. For
example, observe that
4 times a number is
always even, and
explain why 4 times a
number can be
decomposed into two
equal addends.
Desired Student Performance
A student should know
• How to use an addition table,
a multiplication table, and a
hundreds chart.
• Arithmetic patterns are
patterns that change by the
same rate, such as adding the
same number.
• The properties of operations
can be used to identify
arithmetic patterns.
• How to determine whether a
number is even or odd.
A student should understand
• Patterns can be found in the
addition and multiplication
tables.
• Visual images and numerical
patterns of multiplication and
division will help in solving
problems.
• Identifying arithmetic patterns
related to the properties of
operations.
• Identifying patterns (such as
even and odd numbers,
patterns in an addition table,
patterns in a multiplication
table, patterns regarding
multiples and sums).
• Identify arithmetic patterns
(including patterns in the
addition or multiplication
tables).
• Explain rules for a pattern
using properties of operations.
• Explain relationships between
the numbers in a pattern.
• For example, the products of
which numbers are
always even?
a) 4
b) 6
c) 8
d) all of the above
September 2016 Page 10 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Numbers and Operations in Base Ten
Use place value understanding and properties of operations to perform multi-digit arithmetic
3.NBT.1
Use place value
understanding to
round whole numbers
to the nearest 10 or
100.
Desired Student Performance
A student should know
• Each digit in a three-digit
number represents an amount
of hundreds, tens, and ones.
• Three-digit numbers can be
compared based on the
hundreds, tens, and ones
digits, and >, =, and < symbols
are used to record the results
of comparisons.
• A hundreds chart and a
number line illustrate place-
value relationships.
A student should understand
• Rounding is a method of
approximating an answer.
• There are rules for rounding.
• The digits in the ones, tens,
and hundreds places are used
to round whole numbers.
• A number line and a hundreds
chart are tools to support
rounding.
• Rounding applies to real life.
• When rounding to the nearest
10, the ones digit is used to
determine if the number is
rounded up or down.
• When rounding to the nearest
100, the tens digit is used to
determine if the number is
rounded up or down.
A student should be able to do
• Use a number line, hundreds
chart, and/or rounding rules to
round whole numbers to the
nearest 10 or 100.
• Model the rounding process
and reasoning for rounding to
represent the structure of the
base-ten number system.
• Use patterns in the number
system in the rounding
process.
• For example, when rounding
to the nearest 10:
What is the smallest whole
number that will round to 50?
What is the largest whole
number that will round to 50?
How many different whole
numbers will round to 50?
September 2016 Page 11 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Numbers and Operations in Base Ten
Use place value understanding and properties of operations to perform multi-digit arithmetic
3.NBT.2
Fluently add and
subtract (including
subtracting across
zeros) within 1000
using strategies and
algorithms based on
place value,
properties of
operations, and/or the
relationship between
addition and
subtraction. Include
problems with whole
dollar amounts.
Desired Student Performance
A student should know
• How to add and subtract
fluently within 100.
• How to apply various
strategies (i.e., the standard
algorithm, concrete models,
make 10, and make 100) to
add and subtract.
• The properties of operations
(associative, commutative,
and distributive properties)
can be used to solve addition
and subtraction problems.
• The relationship between
addition and subtraction is an
inverse relationship.
A student should understand
• A variety of strategies can be
used to attain fluency with
addition and subtraction.
• These strategies can include
the standard algorithm
(borrowing or regrouping) and
thinking about multi-digit
numbers as groups of
hundreds, tens, and ones.
• Numbers can be used flexibly
to solve addition and
subtraction problems such as
using the properties of
operations.
• Fluently means quickly and
accurately.
• Strategies for subtracting
across zeros using place
value understanding.
• Add and subtract within 1,000
without context.
• Model algorithms based on
place value, properties of
operations, and/or the inverse
relationship between addition
and subtraction.
• Demonstrate fluency (speed,
accuracy, and understanding)
with addition and subtraction
problems within 1,000.
• For example,
272 – 189 = ___.
• Subtract across zeros using
understanding of place value.
September 2016 Page 12 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Numbers and Operations in Base Ten
Use place value understanding and properties of operations to perform multi-digit arithmetic
3.NBT.3
Multiply one-digit
whole numbers by
multiples of 10 in the
range of 10-90 (e.g., 9
x 80, 5 x 60) using
strategies based on
place value and
properties of
operations.
Desired Student Performance
A student should know
• How to count by multiples of
10.
• How to compose and
decompose multiples of 10 as
groups of 10.
• How to find the product of two
one-digit numbers; develop
fluency with basic
multiplication facts.
• Rectangular arrays can be
constructed to find the sum of
a repeated addition problem.
A student should understand
• Base-ten blocks, diagrams,
and a hundreds chart can be
used to multiply a one-digit
number by multiples of 10.
• The patterns in place value
connect the products of one-
digit numbers to the products
of one-digit numbers multiplied
by multiples of 10. For
example, 6 x 8 = 48 and
6 x 80 = 480.
• Multiply one-digit numbers by
a multiple of 10 using various
strategies.
• Recognize patterns in
multiplying by multiples of 10.
• For example, 30 is 3 tens and
70 is 7 tens; 2 x 40 is 2 groups
of 4 tens or 8 groups of ten; 5
x 60 is 5 groups of tens or 30
tens; and 30 tens is 300.
• For example,
40 x 5 = n.
September 2016 Page 13 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Numbers and Operations – Fractions
Develop understanding of fractions as numbers
3.NF.1
Understand a fraction
1/b as the quantity
formed by 1 part when
a whole is partitioned
into b equal parts;
understand a fraction
a/b as the quantity
formed by a parts of
size 1/b.
Desired Student Performance
A student should know
• How to divide shapes (circles
and rectangles) into no more
than four equal parts.
• Fraction models include area
(parts of a whole) models
(circles, rectangles, and
squares) and number lines.
• A fraction is written with a
numerator/denominator.
• A fraction represents
quantities where a whole is
divided into equal parts.
• The numerator of a fraction
is the number of parts.
• The denominator of a
fraction represents the total
number of parts that make
up the whole.
• Equal shares of the same
whole need not have the
same shape.
A student should understand
• The size of the fractional part
is relative to the size of the
whole.
• Fractions are composed of
unit fractions, which have a
numerator of 1. For example,
the fraction
3
4
�
is composed
of three pieces that each
have a size of
1
4
�
.
• Fractions represent quantities
where a whole is divided into
equal-sized parts using
models, manipulatives,
words, and/or number lines.
• Fractions can be used as a
tool to model and understand
quantities and relationships.
A student should be able to do
• Represent a whole using unit
fractions.
• Use the terms numerator for
the number of relevant parts
and denominator for the total
number of parts in the whole.
• Use accumulated unit fractions
to represent numbers equal to,
less than, and greater than one
(
1
3
�
and
1
3
�
is
2
3
�
;
1
3
�
,
1
3
�
,
1
3
�
,
and
1
3
�
is
4
3
�
).
• For example, four children
share one chocolate bar that
was broken into six pieces.
What portion of the chocolate
bar will each child receive?
• For example, six children share
one chocolate bar that was
broken into four pieces. What
portion of the chocolate bar will
each child receive?
September 2016 Page 14 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Numbers and Operations – Fractions
Develop understanding of fractions as numbers
3.NF.2a
Understand a fraction
as a number on the
number line;
represent fractions on
a number line
diagram.
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 based at 0
locates the number
1/b on the number
line.
Desired Student Performance
A student should know
• How to divide shapes (circles
and rectangles) into no more
than four equal parts.
• How to share a whole that
was partitioned or split.
• Fraction models include area
models (parts of a whole
using circles, rectangles, and
squares) and number lines.
• The numerator of a fraction is
the number of relevant parts.
• The denominator of a fraction
represents the total number of
parts that make up a whole.
• Fractions are composed of
unit fractions.
A student should understand
• Fractions can be used as a
tool to model and understand
quantities and relationships.
• Fractions can be
represented on a number
line. The whole is divided
into equal-sized parts
between whole numbers.
• How to define the interval
from 0 to 1 on a number line
as the whole.
• The equal parts between 0
and 1 have a fractional
representation.
• The size of the fractional part
is relative to the size of the
whole.
• Divide a number line diagram
into equal segments and label
the appropriate fractional
parts.
• Explain that the end of each
equal part is represented by a
fraction (1/the number of equal
parts).
• For example, in a number line
diagram, the space between 0
and 1 is divided (partitioned)
into four equal regions. The
distance from 0 to the first
segment is 1 of the 4
segments from 0 to 1 or
1
4
�
.
September 2016 Page 15 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Numbers and Operations- Fractions
Develop understanding of fractions as numbers
3.NF.2b
Understand a fraction
as a number on the
number line;
represent fractions on
a number line
diagram.
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.
Desired Student Performance
A student should know
• How to divide shapes (circles
and rectangles) into no more
than four equal parts.
• Sharing of a whole being
partitioned or split.
• Fraction models include area
models (parts of a whole using
circles, rectangles, and
squares) and number lines.
• The numerator of a fraction is
the number of relevant parts.
• The denominator of a fraction
represents the total number of
parts that make up the whole.
A student should understand
• Fractions can be used as a
tool to model and
understand quantities and
relationships.
• The size of the fractional
part is relative to the size of
the whole.
• Fractions represent
quantities where a whole is
divided into equal-sized
parts using number lines.
• How to define the interval
from 0 to 1 on a number line
as the whole.
• How to divide on a number
line into equal parts.
A student should be able to do
• Represent each equal part
on a number line with a
fraction.
• Explain that the endpoint of
each equal part represents
the total number of parts.
• For example, on a number
line, the space between 0
and 1 is partitioned into four
equal regions. The distance
from 0 to the first segment is
one of the four segments
from 0 to 1 or
1
4
�
. The
distance from 0 to
2
4
�
represents two of the four
segments between 0 and 1.
September 2016 Page 16 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Numbers and Operations – Fractions
Develop understanding of fractions as numbers
3.NF.3a
Explain equivalence of
fractions in special
cases, and compare
fractions by reasoning
about their size.
Understand two
fractions as
equivalent (equal) if
they are the same
size, or the same point
on a number line.
Recognize that
comparisons are valid
only when the two
fractions refer to the
same whole.
Desired Student Performance
A student should know
• How to divide shapes (circles
and rectangles) into no more
than four equal parts.
• Measure length and
represent that data in a line
plot.
• Fraction models include area
models (parts of a whole
using circles, rectangles, and
squares) and number lines.
• The numerator of a fraction is
the number of relevant parts.
• The denominator of a fraction
represents the total number
of parts that make up a
whole.
A student should understand
• Fractions that represent
equal-sized quantities or
parts of a whole are
equivalent.
• Two fractions are equivalent
if they are the same size, or
represent the same portion
on a number line.
• Visual fraction models (area
models) and number lines
are helpful in exploring
equivalence.
• What makes fractions
equivalent.
A student should be able to do
• Represent different fractions
as parts of a whole and
compare the shaded or
relevant parts.
• Compare fractions by
reasoning about their size to
determine equivalence.
• Model equivalent fractions
using manipulatives, pictures,
or number line diagrams and
explain in words why the
fractions are equivalent.
• For example: Which statement
is true about the diagrams
below?
September 2016 Page 17 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Numbers and Operations – Fractions
Develop understanding of fractions as numbers
3.NF.3b
Explain equivalence of
fractions in special
cases, and compare
fractions by reasoning
about their size.
Recognize and
generate simple
equivalent fractions,
e.g., 1/2 = 2/4, 4/6 =
2/3. Explain why the
fractions are
equivalent, e.g., by
using a visual fraction
model.
Desired Student Performance
A student should know
• How to divide shapes (circles
and rectangles) into no more
than 4 equal parts and use
vocabulary terminology to
describe.
• How to measure length and
represent that data in a line
plot.
• Fraction models include area
models (parts of a whole
using circles, rectangles, and
squares) and number lines.
• The numerator of a fraction is
the number of relevant parts.
• The denominator of a fraction
represents the total number of
parts that make up a whole.
A student should understand
• Fractions that represent
equal-sized quantities or
parts of a whole are
equivalent.
• Visual fraction models (area
models) and number lines
are helpful in exploring
equivalence.
• What makes fractions
equivalent.
• Two fractions are equivalent
(equal) if they are the same
size, or represent the same
portion on a number line.
• Compare fractions by
reasoning about their size to
determine equivalence.
• Recognize and construct
equivalent fractions using
manipulatives, pictures, or
number line diagrams and
explain in words why the
fractions are equivalent.
• For example, which symbol
can be used to compare the
following fractions?
3
6
-
1
2
a) > b) < c) =
September 2016 Page 18 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Numbers and Operations – Fractions
Develop understanding of fractions as numbers
3.NF.3c
Explain equivalence of
fractions in special
cases, and compare
fractions by reasoning
about their size.
Express whole
numbers as fractions,
and recognize
fractions that are
equivalent to whole
numbers. Examples:
Express 3 in the form
3 = 3/1; recognize that
6/1 = 6; locate 4/4 and
1 at the same point of
a number line
diagram.
Desired Student Performance
A student should know
• How to divide shapes (circles
and rectangles) into no more
than four equal parts and use
correct terms to describe
(halves, thirds, fourths).
• Fraction models include area
models (parts of a whole
using circles, rectangles, and
squares) and number lines.
• The numerator of a fraction is
the number of relevant parts.
• The denominator of a fraction
represents the total number of
parts that make up a whole.
• Fractions that represent
equal-sized quantities are
equivalent.
A student should understand
• Writing whole numbers as
fractions relates to fractions
as division problems. For
example,
6
2
�
is six wholes
divided into two groups.
• The difference between a
whole number and a fraction.
• Two fractions are equivalent
(equal) if they are the same
size, or represent the same
portion on a number line.
• Equivalence of fractions
depends upon the same
whole.
A student should be able to do
• Explain how a fraction relates
to or is equivalent to a whole
number.
• Represent whole numbers as
fractions using area models,
number line diagrams, and
numbers.
• For example, if a small pie is
cut into four pieces and shared
between three people, what
fraction of the pie would each
person receive?
• For example, which fraction is
equivalent to the number 1?
a)
1
4
�
b)
2
4
�
c)
3
4
�
d)
4
4
�
How do you know that the fraction
you selected is equal to 1?
September 2016 Page 19 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Numbers and Operations- Fractions
Develop understanding of fractions as numbers
3.NF.3d
Explain equivalence of
fractions in special
cases, and compare
fractions by reasoning
about their size.
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.
Desired Student Performance
A student should know
• How to divide shapes (circles
and rectangles) into no more
than four equal parts and use
correct vocabulary to describe
(halves, thirds, fourths).
• Two fractions are equivalent
(equal) if they are the same
size, or represent the same
portion on a number line.
• Fraction models include area
models (parts of a whole
using circles, rectangles, and
squares) and number lines.
• The numerator of a fraction is
the number of relevant parts.
• The denominator of a fraction
represents the total number of
parts that make up the whole.
• The size of the fractional part
is relative to the size of the
whole.
A student should understand
• Fractions can be compared
with or without visual fraction
models including number
lines.
• When fractions have
common denominators, the
larger numerator has the
larger number of equal parts,
i.e.,
2
6
�
<
5
6
�
.
• When fractions have
common numerators, each
fraction has the same
number of relevant equal
parts, but the total number of
parts is different. The whole
with more parts has smaller
pieces than the whole with
fewer parts, i.e.,
3
8
�
<
3
4
� .
• Determine that comparisons
are valid only when the two
fractions refer to same-sized
wholes.
• Compare two fractions with the
same numerator and compare
two fractions with the same
denominator using visual
fraction models, symbols, and
words.
• Record the results of fraction
comparisons using the
symbols >, <, or =.
• Justify conclusions about the
equivalence of fractions.
• For example, Mary checked
out six books from the library.
Of these,
2
3
�
were fiction and
2
6
�
were nonfiction. Mary had
more of which type of book?
How do you know?
September 2016 Page 20 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Measurement and Data
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects
3.MD.1
Tell and write time to
the nearest minute
and measure time
intervals in minutes.
Solve word problems
involving addition and
subtraction of time
intervals in minutes,
e.g., by representing
the problem on a
number line diagram.
Desired Student Performance
A student should know
• How to tell and write time to
the nearest hour, half-hour,
and 5 minutes using digital
and analog clocks.
• How to skip count by 5s.
• How to add and subtract
within 100.
• An analog clock has an hour
and minute hand. Sometimes
an analog clock has a second
hand.
• A.M. represents time from
midnight to noon. P.M.
represents time from noon to
midnight.
• Sixty minutes is equivalent to
1 hour.
A student should understand
• The space between two
consecutive tick marks on an
analog clock represents 1
minute.
• Elapsed time is the interval of
time, given a specific unit, from
a starting time to an ending
time.
• A number line is a tool that may
be used to represent time on an
analog clock and may be used
as a tool for finding elapsed
time.
• Compare an analog clock face
to a number line.
• Tell and write time to the
nearest minute.
• Use a number line to add and
subtract time intervals in hours
and minutes.
• Create and solve word
problems involving addition and
subtraction of time intervals in
hours and minutes.
• For example, Jonathan wakes
us at 5:45 a.m. It takes him 5
minutes to shower, 10 minutes
to get dressed, and 15 minutes
to eat breakfast. What time will
he be ready for school?
September 2016 Page 21 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Measurement and Data
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects
3.MD.2
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
Desired Student Performance
A student should know
• Objects have measurable
attributes including length and
mass.
• How to measure and estimate
the length of an object using
units of inches, feet,
centimeters, and meters.
• How to solve one-step
addition and subtraction word
problems within 100 involving
the same unit.
A student should understand
• Capacity is the amount of
liquid that a container can hold
and can be measured in liters.
• Mass is the amount of matter
that an object has and can be
measured in grams or
kilograms.
• Mass is different than weight.
• Liters, grams, and kilograms
are all units used to measure
in the Metric System.
• How to solve one-step word
problems involving mass and
one-step word problems
involving capacity. (Given in
the same unit.)
A student should be able to do
• Measure and estimate capacity
using liters and mass using
grams and kilograms.
• Solve one-step, addition,
subtraction, multiplication, or
division word problems
involving capacity and mass.
(Problems contain only one unit
of measure. No conversions
between units.)
• For example, a paper clip
weighs about (a) 1 gram, (b) 10
grams, or (c) 100 grams?
• For example, Mrs. Smith uses a
backpack on a hiking trip. Her
backpack had a mass of 8 kg.
She took 2 kg of food out of her
backpack. What is the mass of
the backpack now?
September 2016 Page 22 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Measurement and Data
Represent and interpret data
3.MD.3
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. For
example, draw a bar
graph in which each
square in the bar
graph might represent
5 pets.
Desired Student Performance
A student should know
• How to draw a single-unit
scale picture graph and a bar
graph to represent a data set
with up to four categories.
• How to solve simple one-step
problems using information
from picture graphs and bar
graphs (with single-unit
scale).
• Scaled pictographs include
symbols that represent units.
Graphs should include a title,
labeled categories, a key, and
data.
• Scaled bar graphs can be
horizontal or vertical and use
bars of different lengths/
heights to show data. Graphs
include a title, labeled scale,
labeled categories, and data,
• How to skip count by 5s, 10s,
and 100s.
A student should understand
• Information (data) can be
represented using scaled bar
and picture graph forms.
These graphs can be used to
solve one- and two-step math
problems.
• The scale of a graph can be
greater than one.
• How to find “how many more,”
“how many less,” and “how
many fewer.”
• How to find the difference
between the greatest and the
least values.
• Two-step word problems
involving the four operations.
A student should be able to do
• Create a scaled picture graph or
scaled bar graph to show data
in multiple categories.
• Interpret a bar/picture graph to
solve one- or two-step problems
asking “how many more” and
“how many less.”
• Analyze a scaled graph with a
scale greater than one and
solve problems.
• For example, Ms. Bennett
collected data to show the
number of students in the third
grade who were wearing each
color of shirt. Draw a bar graph
to show the information below:
Blue – 28, Red – 15, Green –
23, and Yellow – 17
September 2016 Page 23 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Measurement and Data
Represent and interpret data
3.MD.4
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 marked off in
appropriate units—
whole numbers,
halves, or quarters.
Desired Student Performance
A student should know
• How to draw a picture graph
and a bar graph to represent
a data set.
• How to measure length in
whole units using both metric
and U.S. customary systems
and represent that data in a
line plot.
• X’s are drawn above the
number line to represent data
values.
• How to read and use a
standard ruler, including
halves and quarter inch marks
on a ruler.
• Fractions are related to
measuring one-half and one-
quarter inch.
• Measuring is approximate.
A student should understand
• How to use a line plot to
represent data.
• The horizontal scale is marked
off in appropriate units.
• Some items will not measure
exactly
1
4
�
,
1
2
�
, or 1 inch.
• How to determine an
appropriate scale for the line
plot.
• Fractions on a number line.
A student should be able to do
• Generate measurement data by
measuring lengths using rulers
marked with halves and fourths
of an inch.
• Create a line plot where the
horizontal scale is marked off in
appropriate units—whole
numbers, halves, or quarters.
• Analyze data from a line plot.
• For example, Measure the
objects in your art supply box to
the nearest
1
2
�
or
1
4
�
of an inch
and display data collected on a
line plot. How many objects
measured
1
4
�
,
1
2
�
,
etc.?
September 2016 Page 24 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Measurement and Data
Geometric measurement: understand concepts of area and relate area to multiplication and to addition
3.MD.5a
Recognize area as an
attribute of plane
figures and
understand concepts
of area measurement.
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.
Desired Student Performance
A student should know
• How to partition a rectangle
into rows and columns of
same-size squares and count
to find the total number of
them.
• Plane figures are two-
dimensional shapes that
include triangles,
quadrilaterals, pentagons,
and hexagons.
• What it means to find the
length of an object.
• How to measure the length of
an object using the customary
and metric units of inches,
feet, centimeters, and meters.
A student should understand
• Area as the amount of two-
dimensional space in a
bounded region.
• A square unit is used to
measure the area of a given
plane figure or surface.
• Area can be measured in
square units.
• How to find area by
decomposing figures using
cutting and folding techniques.
A student should be able to do
• Cover the area of a plane figure
with unit squares without gaps or
overlaps.
• Relate the number (n) of unit
squares to the area of a plane
figure.
• For example, determine the area
in square units of the rectangle
below.
3
one square unit
4
September 2016 Page 25 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Measurement and Data
Geometric measurement: understand concepts of area and relate area to multiplication and to addition
3.MD.5b
Recognize area as an
attribute of plane
figures and
understand concepts
of area measurement.
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.
Desired Student Performance
A student should know
• Area can be found by
partitioning a rectangle into
rows and columns of same-
size squares and counting the
squares.
• How to measure length in
whole units using both metric
and U.S. customary systems.
• Plane figures are two-
dimensional shapes that
include triangles,
quadrilaterals, pentagons,
and hexagons.
• Everyday objects have a
variety of attributes each of
which can be measured in
different ways.
A student should understand
• A two-dimensional geometric
figure that is covered by a
certain number of squares
without gaps or overlaps has an
area of that number of square
units.
• Area can be measured in
square units.
• How to use square units to
measure area by filling in an
area with the same sized
square units and counting the
number of square units
• Plane figures have different
attributes such as length and
area.
• Relate the number of unit
squares (n) to the area of a
plane figure.
• Cover a plane figure with
square tiles and count the
number of units (tiles) to find
the area.
• Find the area of plane figures.
• For example, which of the three
rectangles covers the most
area?
September 2016 Page 26 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Measurement and Data
Geometric measurement: understand concepts of area and relate area to multiplication and to addition
3.MD.6
Measure areas by
counting unit squares
(square cm, square m,
square in, square ft,
and improvised units).
Desired Student Performance
A student should know
• Area can be found by
partitioning a rectangle into
rows and columns of same-
size squares and counting the
squares.
• How to use a ruler to measure
length including the length of
a side on a plane figure.
• Area can be measured in
units of centimeters (cm),
meters (m), inches (in), and
feet (ft).
• Addition problem-solving
strategies.
A student should understand
• Area is the amount of two-
dimensional space in a bound
region, and it is measured by
choosing a unit of area, often a
square, and iterating it over the
entire space.
• Squares units can be square
centimeters, square meters,
square inches, square feet, or
other improvised square units.
• Everyday objects have a variety
of attributes each of which can
be measured in different ways.
• Area and addition are related.
• Place square tiles on a surface
without gaps or overlays and
count the number of units
(tiles) to find the area of the
surface.
• For example, find the area in
square units of the figure
below.
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
September 2016 Page 27 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Measurement and Data
Geometric measurement: understand concepts of area and relate area to multiplication and to addition
3.MD.7a
Relate area to the
operations of
multiplication and
addition. Find the area
of a rectangle with
whole-number side
lengths by tiling it,
and show that the
area is the same as
would be found by
multiplying the side
lengths.
Desired Student Performance
A student should know
• How to partition rectangles
into equal-sized groups of
rows and columns using
square units.
• Problem-solving structures for
area/arrays and for equal-
sized groups.
• How to skip count by 5s, 10s,
and 100s.
• Multiplication facts for all
single digits 1 through 9 and
10.
A student should understand
• Area is additive.
• There is a relationship
between area and
multiplication.
• The properties of operations
will help in finding area.
• Find the area of a rectangle by
tiling it in unit squares.
• Find the side lengths of a
rectangle in units.
• Skip counting and
multiplication to determine the
number of squares in an array.
• Area models of multiplication.
A student should be able to do
• Tile areas of rectangles and
determine the area in square
units. Record the length and
width of the rectangle, and
investigate the patterns in the
numbers (equal-sized groups in
rows and columns).
• Compare the area found by
counting the tiles in a rectangle
to the area found by adding
equal-sized groups of tiles. If
there are three rows and four
columns, find the area by
adding 3 + 3 + 3 + 3 or
4 + 4 + 4.
• Compare the area found by
tiling a rectangle to the area
found by multiplying the side
lengths and discover that the
area is the length times the
width.
September 2016 Page 28 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Measurement and Data
Geometric measurement: understand concepts of area and relate area to multiplication and to addition
3.MD.7b
Relate area to the
operations of
multiplication and
addition. Multiply side
lengths to find areas
of rectangles with
whole-number side
lengths (where factors
can be between 1 and
10, inclusively) in the
context of solving real
world and
mathematical
problems, and
represent whole-
number products as
rectangular areas in
mathematical
reasoning.
Desired Student Performance
A student should know
• How to model with equal-
sized groups by partitioning
rectangles.
• Problem-solving structures for
area/arrays and for equal
groups.
• Addition problem-solving
strategies.
• Multiplication facts for all
single digits 1 through 9 and
10
A student should understand
• Area is additive.
• There is a relationship between
area and multiplication.
• The properties of operations will
help in finding area.
• Multiply side lengths to find
areas of rectangles.
• Area is a square measure.
• Solve real-world and
mathematical area problems
by multiplying whole-number
side lengths of rectangles.
• Use rectangular arrays to
represent whole-number
products in multiplication
problems.
• For example, Betsy wants to
tile the bathroom floor using
square foot tiles. How many
square foot tiles will she need?
6 ft.
8 ft.
September 2016 Page 29 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Measurement and Data
Geometric measurement: understand concepts of area and relate area to multiplication and to addition
3.MD.7c
Relate area to the
operations of
multiplication and
addition. Use tiling to
show in a concrete
case that the area of a
rectangle with 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.
Desired Student Performance
A student should know
• How to model with equal-
sized groups by partitioning
rectangles.
• Problem-solving structures for
area/arrays and for equal
groups.
• Addition problem-solving
strategies.
• Multiplication facts for all
single digits 1 through 9 and
10.
A student should understand
• Area is additive.
• There is a relationship between
area and multiplication.
• The properties of operations,
specifically the distributive
property, will help in finding
area.
• How to multiply using an area
model or array.
• How to use the distributive
property to represent a real-
world problem:
a x (b + c) = a x b + a x c
• Relate area of a rectangle to
multiplication and addition by
modeling the distributive
property.
• For example, in the picture
below, the area of a 6 x 7
figure can be determined by
finding the area of a 6 x 5 and
6 x 2 figure and adding the two
products.
6 x 7= (6 x 5) + (6 x 2)
(30) + (12) = 42
6 x 5
6 x 2
September 2016 Page 30 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Measurement and Data
Geometric measurement: understand concepts of area and relate area to multiplication and to addition
3.MD.7d
Relate area to the
operations of
multiplication and
addition. Find areas of
rectilinear figures by
decomposing them
into non-overlapping
rectangles and adding
the areas of the non-
overlapping parts,
applying this
technique to solve
real world problems.
Recognize area as
additive.
Desired Student Performance
A student should know
• How to decompose figures.
• A rectilinear figure is a
polygon that has all right
angles.
• How to find areas of
rectangles.
• How to add areas of
rectangles.
• Problem-solving structures for
area/arrays and for equal
groups.
• Multiplication facts for all
single digits 1 through 9 and
10.
A student should understand
• Area is additive.
• There is a relationship between
area and multiplication.
• The properties of operations will
help in finding area.
• Areas of each rectangle in a
rectilinear (straight line) figure
can be added together to find
the area of the figure.
• Decompose rectilinear figures
into different rectangles and
find the area of each rectangle
that is part of a larger figure.
• Find the area of each larger
figure by adding the areas of
each of the rectangles. See
the example below.
The area for the above figure is
(9 x 4) + (2 x 6) = 48 square feet.
9 ft
10 ft
2 ft
6 ft
September 2016 Page 31 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Measurement and Data
Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area
measures
3.MD.8
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 (including,
but not limited to:
modeling, drawing,
designing, and
creating) rectangles
with the same
perimeter and
different areas or with
the same area and
different perimeters.
Desired Student Performance
A student should know
• How to relate addition and
subtraction to length.
• How to measure and estimate
lengths in standard units.
• How to relate to an open
array used in multiplication
and area problems.
• Addition problem-solving
strategies.
• A polygon is a closed, flat
figure formed using line
segments that meet only at
their ends.
• For a polygon, the length of
the perimeter is the sum of
the lengths of the sides.
• Perimeter equals the distance
around a closed figure.
A student should understand
• Perimeter and addition are
related and connected to the
commutative property of
multiplication.
• Patterns exist when finding the
sum of the lengths and widths
of rectangles.
• The difference between
perimeter and area.
• The length of all sides in a
polygon must be known to find
the perimeter of the polygon.
• Unknown side lengths may be
found by measuring or
reasoning using given sides.
• Solve real-world and
mathematical problems
involving perimeters of
polygons.
• Find the perimeter of a
polygon given the side lengths.
• Find the perimeter of a
polygon when there is an
unknown side length.
• Exhibit (design, create, draw,
model, etc.) rectangles with
the same perimeter and
different areas.
• Exhibit rectangles with the
same area and different
perimeters.
• Solve real-world and
mathematical problems
involving perimeters of
September 2016 Page 32 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Geometry
Reason with shapes and their attributes
3.G.1
Understand that
shapes in different
categories (e.g.,
rhombuses,
rectangles, circles,
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.
Desired Student Performance
A student should know
• How to recognize and draw
shapes having specified
attributes such as a given
number of angles and sides.
Identify triangles,
quadrilaterals, pentagons,
and hexagons.
• Triangles, quadrilaterals,
pentagons, etc. are two-
dimensional shapes.
• How to identify and count
angles and sides within a
shape to label a shape.
A student should understand
• Shapes can be described
and compared using their
geometric attributes.
• Shapes are categorized
according to their attributes
including the number of
sides and angles within the
shape. Those categories
can contain subcategories,
for example, rhombuses,
rectangles, squares,
trapezoids, parallelograms,
etc.
• Attributes of a circle.
A student should be able to do
• Describe, analyze, and
compare properties of two-
dimensional shapes.
• Compare and classify shapes
by attributes, sides and angles.
• Group shapes with shared
attributes to define a larger
category (e.g., quadrilaterals).
• Draw examples and non-
examples of quadrilaterals with
specific attributes.
• For example, if a student writes,
“All quadrilaterals are squares,
rectangles, or rhombuses.”
Draw a quadrilateral on the grid
that proves this statement is
false.
September 2016 Page 33 of 33
College- and Career-Readiness Standards for Mathematics
GRADE 3
Geometry
Reason with shapes and their attributes
3.G.2
Partition shapes into
parts with equal areas.
Express the area of
each part as a unit
fraction of the whole.
For 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.
Desired Student Performance
A student should know
• A whole shape can be divided
into equal parts. The equal
parts may not be the same
shape.
• How to divide shapes (circles
and rectangles) into two,
three, or four equal parts and
use the terms halves, thirds,
or fourths to describe the
parts.
• A fraction represents
quantities where a whole is
divided into equal-sized parts.
• How to use the term
numerator to indicate the
number of parts and
denominator to represents the
total number of parts a whole
is portioned into.
A student should understand
• Unit fractions can be used to
describe a whole that has
been divided into parts.
• The size of the fractional part
is relative to the size of the
whole.
• Composition and
decomposition of rectangular
regions.
• How to partition a rectangle
into equal squares.
• Divide shapes into parts with
equal areas.
• Represent the area of each
part as a unit fraction.
• For example, which of these
shows
1
3
�
of the shaded
figure?