Download 3rd Grade Math Curriculum Pacing Guide

COURSE CONTENT
MATHEMATICS
THIRD GRADE
CCRS
EVIDENCE OF STUDENT ATTAINMENT
CONTENT STANDARDS
RESOURCES
FIRST SIX WEEKS
8
[3.OA.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
(3This standard is limited to problems posed
with whole numbers and having wholenumber 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).)
9
[3.OA.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.
Students:
Given a variety of two-step 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:

Go Math
Chapter 1
AMSTI
Year One Units
Collections and Travel Stories
Inv. 1: Sess. 1.4-1.5, Inv. 2: Sess. 2.1-2.2, 2.4, Inv. 3: 3.43.7, Inv. 4: 4.1-4.4
Year Two Units
How Many Hundreds?:
Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.3, Inv. 3: Sess. 3.63.9
Solids and Boxes:
CC 4A.3
Other Units
Trading Stickers:
Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.3, 2.5, 2.7-2.8
Go Math
Chapter 1
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).
AMSTI
Year One Units
Collections and Travel Stories:
Inv. 1: Sess. 1.1-1.2, 1.5-1.6, Inv. 2: Sess. 2.3-2.7, Inv. 3:
Sess. 3.3, Inv. 4: Sess. 4.4
Equal Groups:
Inv. 1: Sess. 1.3, Inv. 2: Sess. 2.1-2.6, Inv. 3: Sess. 3.13.4
CC 3.5A, 3.5B, 3.7A
Year Two Units
How Many Hundreds?:
Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.1-2.5, Inv. 3: Sess.
3.1-3.9
Other Units
1
COURSE CONTENT
MATHEMATICS
THIRD GRADE
10
[3.NBT.1] Use place value understanding to
round whole numbers to the nearest 10 or 100.
Students:
Given any number less than 1,000,

11
[3.NBT.2] 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.
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).
Students:


Fluently add and subtract within 1000, using
strategies based on place values, properties of
operations, and/or the relationship between
addition and subtraction,
Justify solutions including those which
required regrouping by relating the strategy to
a written method and explain the reasoning.
Trading Stickers, Combining Coins:
Inv. 1: Sess. 1.2, 1.4, Inv. 2: Sess. 2.2-2.3, 2.6
Stories, Tables, & Graphs:
TMM
Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.1-2.3, Inv. 3: Sess.
3.1-3.7
Go Math
Chapter 1
AMSTI
Year One Units
Collections and Travel Stories:
CC 1.7A
Perimeter, Angles, & Area:
CC 2.5A
Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.4-2.5, Inv. 3: Sess.
3.5-3.6
Year Two Units
Finding Fair Shares:
Inv. 1: Sess. 1.1-1.3, Inv. 2: Sess. 2.1-2.4
CC 1.4A, 1.4B
Solids and Boxes:
Inv. 2: Sess. 2.1-2.3
CC 4A.1, 4A.2, 4A.3
Other Units
Stories, Tables, & Graphs:
Inv. 2: Sess. 2.2, Inv. 3: Sess. 3.1, 3.3-3.4
Go Math
Chapter 1
AMSTI
Year One Units
Collections and Travel Stories:
Inv. 1: Sess. 1.1-1.6, Inv. 2: Sess. 2.1-2.7, Inv. 3: Sess.
3.2-3.7, Inv. 4: Sess. 4.1-4.6
Perimeter, Angles, & Area:
Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.4-2.5, Inv. 3: Sess.
3.2, 3.5-3.6
CC2.5A
Year Two Units
Finding Fair Shares:
Inv. 1: Sess. 1.1-1.3, Inv. 2: Sess. 2.1-2.4
2
COURSE CONTENT
MATHEMATICS
THIRD GRADE
18
19
[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.
Example: Draw a bar graph in which each
square in the bar graph might represent 5 pets.
Students:
[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.
Students:




CC1.4A, 1.4B
How Many Hundreds?:
Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.1-2.5, Inv. 3: Sess.
3.1-3.9
Solids and Boxes:
Inv. 2: Sess. 2.1-2.3
CC 4A.1, 4A.2, 4A.3
Other Units
Trading Stickers, Combining Coins:
Inv. 1: Sess. 1.1-1.9, Inv. 2: Sess. 2.2-2.8
Stories, Tables, & Graphs:
TMM
Inv. 1: Sess. 1.2-1.4, Inv. 2: Sess. 2.1-2.3, Inv. 3: Sess.
3.1-3.4
Go Math
Chapter 2
Organize and represent data with several
categories using picture graphs (pictographs)
and bar graphs with scales other than 1,
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.
AMSTI
Other Units
Surveys and Line Plots:
Inv. 1: Sess. 1.2-1.8, Inv. 2: Sess. 2.1-2.2, Inv. 3: Sess.
3.5
CC 2.3A
Go Math
Chapter 2
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 the length of all class members'
fingers) or by making repeated measurements
(e.g., measuring how far a marble rolls under
certain conditions),
Communicate questions and descriptions
related to the data display
AMSTI
Other Units
Surveys and Line Plots:
Inv. 3: Sess. 3.1-3.4
3
COURSE CONTENT
MATHEMATICS
THIRD GRADE
1
[3.OA.1] Interpret products of whole numbers,
e.g., interpret 5 x 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 x 7.
Students:
Given any multiplication problem in the form a x b = c,


3
5
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) ,
Write a corresponding word problems
containing a multiplication context.
[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.
Students:
Given a variety of multiplication and division word
problems within 100,
[3.OA.5] Apply properties of operations as
strategies to multiply and divide.2
Examples: If 6 x 4 = 24 is known, then 4 x 6 =
24 is also known. (Commutative property of
multiplication) 3 x 5 x 2 can be found by 3 x 5
= 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3
x 10 = 30. (Associative property of
multiplication) Knowing that 8 x 5 = 40 and 8
Students:
Given multiplication and division 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).
Use the properties of operations and
descriptive language for the property to justify
their products and quotients (e.g., If I 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
Go Math
Chapter 3
AMSTI
Year One Units
Equal Groups:
Inv. 1: Sess. 1.1-1.4, Inv. 2: Sess. 2.1-2.6, Inv. 3: Sess.
3.1-3.4, 3.6, Inv. 4: Sess. 4.7
Year Two Units
How Many Hundreds?
Inv. 3.5
Go Math
Chapter 3
AMSTI
Year One Units
Equal Groups:
Inv. 1: Sess. 1.1-1.4, Inv. 2: Sess. 2.3-2.6, Inv. 3: Sess.
3.1, 3.3-3.4, Inv. 4: Sess. 4.1-4.3, 4.5-4.7
Year Two Units
Finding Fair Shares:
Inv. 1: Sess. 1.1, Inv. 2: Sess. 2.1
Other Units
Stories, Tables, & Graphs:
Inv. 3: Sess. 3.1-3.7
Go Math
Chapter 3
AMSTI
Year One Units
Equal Groups:
Inv. 1: Sess. 1.4, Inv. 2: Sess. 2.2-2.6, Inv. 3: Sess. 3.13.4, 3.6
CC3.5A, 3.5B, 3.7A
4
COURSE CONTENT
MATHEMATICS
THIRD GRADE
56).
x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8
x 5) + (8 x 2) = 40 + 16 = 56. (Distributive
property)
8
[3.OA.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.
Students:
Given a variety of two-step 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.").
Other Units
Ten-Minute Math Unit 6
Stories, Tables, & Graphs:
Inv. 2: Sess. 2.1-2.3, Inv. 3: Sess. 3.1-3.6
Go Math
Chapter 3
AMSTI
Year One Units
Collections and Travel Stories
Inv. 1: Sess. 1.4-1.5, Inv. 2: Sess. 2.1-2.2, 2.4, Inv. 3: 3.43.7, Inv. 4: 4.1-4.4
Year Two Units
How Many Hundreds?:
Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.3, Inv. 3: Sess. 3.63.9
Solids and Boxes:
CC 4A.3
Other Units
Trading Stickers:
Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.3, 2.5, 2.7-2.8
SECOND SIX WEEKS
3
5
[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.
Students:
Given a variety of multiplication and division word
problems within 100,
[3.OA.5] Apply properties of operations as
strategies to multiply and divide.2
Students:
Given multiplication and division 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).
Go Math
Chapter 4
AMSTI
Year One Units
Equal Groups:
Inv. 1: Sess. 1.1-1.4, Inv. 2: Sess. 2.3-2.6, Inv. 3: Sess.
3.1, 3.3-3.4, Inv. 4: Sess. 4.1-4.3, 4.5-4.7
Year Two Units
Finding Fair Shares:
Inv. 1: Sess. 1.1, Inv. 2: Sess. 2.1
Other Units
Stories, Tables, & Graphs:
Inv. 3: Sess. 3.1-3.7
Go Math
Chapter 4
5
COURSE CONTENT
MATHEMATICS
THIRD GRADE
Examples: If 6 x 4 = 24 is known, then 4 x 6 =
24 is also known. (Commutative property of
multiplication) 3 x 5 x 2 can be found by 3 x 5
= 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3
x 10 = 30. (Associative property of
multiplication) Knowing that 8 x 5 = 40 and 8
x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8
x 5) + (8 x 2) = 40 + 16 = 56. (Distributive
property)
7
8

Use the properties of operations and
descriptive language for the property to justify
their products and quotients (e.g., If I 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).
[3.OA.7] Fluently multiply and divide within
100, using strategies such as the relationship
between multiplication and division (e.g.,
knowing that 8 x 5 = 40, one knows 40 ÷ 5 =
8) or properties of operations. By the end of
Grade 3, know from memory all products of
two one-digit numbers.
Students:
Given any single digit multiplication problem or a
division problem with a single digit divisor and an
unknown single digit quotient,
[3.OA.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.
Students:
Given a variety of two-step word problems involving all
four operations,



Use an efficient strategy (e.g., recall, inverse
operations, arrays, derived facts, properties of
operations, etc.) to name the product or
quotient.
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
AMSTI
Year One Units
Equal Groups:
Inv. 1: Sess. 1.4, Inv. 2: Sess. 2.2-2.6, Inv. 3: Sess. 3.13.4, 3.6
CC3.5A, 3.5B, 3.7A
Other Units
Ten-Minute Math Unit 6
Stories, Tables, & Graphs:
Inv. 2: Sess. 2.1-2.3, Inv. 3: Sess. 3.1-3.6
Go Math
Chapter 4
AMSTI
Year One Units
Equal Groups:
Inv. 3: Sess. 3.4, 3.6, Inv. 4: Sess. 4.5-4.6
CC 3.5A, 3.5B, 3.7A
Year Two Units
Finding Fair Shares:
CC 1.4A
How Many Hundreds?:
Inv. 1: Sess. 1.4
Go Math
Chapter 4
AMSTI
Year One Units
Collections and Travel Stories
Inv. 1: Sess. 1.4-1.5, Inv. 2: Sess. 2.1-2.2, 2.4, Inv. 3: 3.43.7, Inv. 4: 4.1-4.4
Year Two Units
How Many Hundreds?:
Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.3, Inv. 3: Sess. 3.63.9
Solids and Boxes:
CC 4A.3
Other Units
Trading Stickers:
Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.3, 2.5, 2.7-2.8
6
COURSE CONTENT
MATHEMATICS
THIRD GRADE
50 is 125.").
9
4
9
[3.OA.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.
Students:
[3.OA.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 x ? = 48, 5 = _ ÷ 3, 6 x 6 = ?.
Students:
[3.OA.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
Students:



Go Math
Chapter 4
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).
Solve single operation multiplication/division
equations containing a single unknown (e.g.
8x? = 48, 5= __ ÷3, 6x6 = ___).
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
AMSTI
Year One Units
Collections and Travel Stories:
Inv. 1: Sess. 1.1-1.2, 1.5-1.6, Inv. 2: Sess. 2.3-2.7, Inv. 3:
Sess. 3.3, Inv. 4: Sess. 4.4
Equal Groups:
Inv. 1: Sess. 1.3, Inv. 2: Sess. 2.1-2.6, Inv. 3: Sess. 3.13.4
CC 3.5A, 3.5B, 3.7A
Year Two Units
How Many Hundreds?:
Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.1-2.5, Inv. 3: Sess.
3.1-3.9
Other Units
Trading Stickers, Combining Coins:
Inv. 1: Sess. 1.2, 1.4, Inv. 2: Sess. 2.2-2.3, 2.6
Stories, Tables, & Graphs:
TMM
Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.1-2.3, Inv. 3: Sess.
3.1-3.7
Go Math
Chapter 5
AMSTI
Year One Units
Equal Groups:
Inv. 1: Sess. 1.3-1.4, Inv. 2: Sess. 2.6, Inv. 4: Sess. 4.14.6
CC3.5A, 3.5B, 3.7A
Go Math
Chapter 5
AMSTI
Year One Units
Collections and Travel Stories:
7
COURSE CONTENT
MATHEMATICS
THIRD GRADE
always even, and explain why 4 times a
number can be decomposed into two equal
addends
3
number is always even, and explain why 4
times a number can be decomposed into two
equal addends).
[3.NBT.3] Multiply one-digit whole numbers
by multiples of 10 in the range 10-90 (e.g., 9 x
80, 5 x 60) using strategies based on place
value and properties of operations.
Students:
[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.
Example: Describe a context in which a
number of shares or a number of groups can be
expressed as 56 ÷ 8.
Students:
Given any division problem in the form a ÷ b = c,

Efficiently use strategies based on place value
and properties of operations to multiply onedigit numbers by multiples of 10 (from 10-90)
and justify their answers.
Inv. 1: Sess. 1.1-1.2, 1.5-1.6, Inv. 2: Sess. 2.3-2.7, Inv. 3:
Sess. 3.3, Inv. 4: Sess. 4.4
Equal Groups:
Inv. 1: Sess. 1.3, Inv. 2: Sess. 2.1-2.6, Inv. 3: Sess. 3.13.4
CC 3.5A, 3.5B, 3.7A
Year Two Units
How Many Hundreds?:
Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.1-2.5, Inv. 3: Sess.
3.1-3.9
Other Units
Trading Stickers, Combining Coins:
Inv. 1: Sess. 1.2, 1.4, Inv. 2: Sess. 2.2-2.3, 2.6
Stories, Tables, & Graphs:
TMM
Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.1-2.3, Inv. 3: Sess.
3.1-3.7
Go Math
Chapter 5
Year One Units
Equal Groups:
CC 3.7A
THIRD SIX WEEKS
2


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 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),
Write a corresponding word problem
Go Math
Chapter 6
AMSTI
Year One Units
Equal Groups:
Inv. 4: Sess. 4.1-4.7
8
COURSE CONTENT
MATHEMATICS
THIRD GRADE
containing a division context.
3
5
[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
Students:
Given a variety of multiplication and division word
problems within 100,
[3.OA.5] Apply properties of operations as
strategies to multiply and divide.2
Examples: If 6 x 4 = 24 is known, then 4 x 6 =
24 is also known. (Commutative property of
multiplication) 3 x 5 x 2 can be found by 3 x 5
= 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3
x 10 = 30. (Associative property of
multiplication) Knowing that 8 x 5 = 40 and 8
x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8
x 5) + (8 x 2) = 40 + 16 = 56. (Distributive
property)
Students:
Given multiplication and division 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).
Use the properties of operations and
descriptive language for the property to justify
their products and quotients (e.g., If I 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).
Go math
Chapter 6
AMSTI
Year One Units
Equal Groups:
Inv. 1: Sess. 1.1-1.4, Inv. 2: Sess. 2.3-2.6, Inv. 3: Sess.
3.1, 3.3-3.4, Inv. 4: Sess. 4.1-4.3, 4.5-4.7
Year Two Units
Finding Fair Shares:
Inv. 1: Sess. 1.1, Inv. 2: Sess. 2.1
Other Units
Stories, Tables, & Graphs:
Inv. 3: Sess. 3.1-3.7
Go Math
Chapter 6
AMSTI
Year One Units
Equal Groups:
Inv. 1: Sess. 1.4, Inv. 2: Sess. 2.2-2.6, Inv. 3: Sess. 3.13.4, 3.6
CC3.5A, 3.5B, 3.7A
Other Units
Ten-Minute Math Unit 6
Stories, Tables, & Graphs:
Inv. 2: Sess. 2.1-2.3, Inv. 3: Sess. 3.1-3.6
(2Students need not use formal terms for these
properties.)
6
[3.OA.6] Understand division as an unknownfactor problem.
Example: Find 32 ÷ 8 by finding the number
that makes 32 when multiplied by 8.
Students:
Given a division problem with an unknown quotient,

Use a pictorial or physical model to explain
the connection between the division problem
Go Math
Chapter 6
AMSTI
Year One Units
Equal Groups:
Inv. 4: Sess. 4.1-4.6
9
COURSE CONTENT
MATHEMATICS
THIRD GRADE
and the related unknown factor equation.
7
4
7
8
[3.OA.7] Fluently multiply and divide within
100, using strategies such as the relationship
between multiplication and division (e.g.,
knowing that 8 x 5 = 40, one knows 40 ÷ 5 =
8) or properties of operations. By the end of
Grade 3, know from memory all products of
two one-digit numbers.
Students:
Given any single digit multiplication problem or a
division problem with a single digit divisor and an
unknown single digit quotient,
[3.OA.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 x ? = 48, 5 = _ ÷ 3, 6 x 6 = ?.
Students:
[3.OA.7] Fluently multiply and divide within
100, using strategies such as the relationship
between multiplication and division (e.g.,
knowing that 8 x 5 = 40, one knows 40 ÷ 5 =
8) or properties of operations. By the end of
Grade 3, know from memory all products of
two one-digit numbers.
Students:
Given any single digit multiplication problem or a
division problem with a single digit divisor and an
unknown single digit quotient,
[3.OA.8] Solve two-step word problems using
the four operations. Represent these problems
Students:
Given a variety of two-step word problems involving all



Use an efficient strategy (e.g., recall, inverse
operations, arrays, derived facts, properties of
operations, etc.) to name the product or
quotient.
Solve single operation multiplication/division
equations containing a single unknown (e.g.
8x? = 48, 5= __ ÷3, 6x6 = ___).
Use an efficient strategy (e.g., recall, inverse
operations, arrays, derived facts, properties of
operations, etc.) to name the product or
quotient.
Go Math
Chapter 6
AMSTI
Year One Units
Equal Groups:
Inv. 3: Sess. 3.4, 3.6, Inv. 4: Sess. 4.5-4.6
CC 3.5A, 3.5B, 3.7A
Year Two Units
Finding Fair Shares:
CC 1.4A
How Many Hundreds?:
Inv. 1: Sess. 1.4
Go Math
Chapter 7
AMSTI
Year One Units
Equal Groups:
Inv. 1: Sess. 1.3-1.4, Inv. 2: Sess. 2.6, Inv. 4: Sess. 4.14.6
CC3.5A, 3.5B, 3.7A
Go Math
Chapter 7
AMSTI
Year One Units
Equal Groups:
Inv. 3: Sess. 3.4, 3.6, Inv. 4: Sess. 4.5-4.6
CC 3.5A, 3.5B, 3.7A
Year Two Units
Finding Fair Shares:
CC 1.4A
How Many Hundreds?:
Inv. 1: Sess. 1.4
Go Math
Chapter 7
10
COURSE CONTENT
MATHEMATICS
THIRD GRADE
using equations with a letter standing for the
unknown quantity. Assess the reasonableness
of answers using mental computation and
estimation strategies including rounding.3
(3This standard is limited to problems posed
with whole numbers and having wholenumber 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).)
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.").
AMSTI
Year One Units
Collections and Travel Stories
Inv. 1: Sess. 1.4-1.5, Inv. 2: Sess. 2.1-2.2, 2.4, Inv. 3: 3.43.7, Inv. 4: 4.1-4.4
Year Two Units
How Many Hundreds?:
Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.3, Inv. 3: Sess. 3.63.9
Solids and Boxes:
CC 4A.3
Other Units
Trading Stickers:
Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.3, 2.5, 2.7-2.8
FOURTH SIX WEEKS
13
[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 aparts of
size 1/b.
Students:
Given any fraction in the form a/b,

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).
Go Math
Chapter 8
AMSTI
Year Two Units
Finding Fair Shares:
Inv.1: Sess. 1.1-1.6, Inv. 2: Sess. 2.1-2.4, Inv. 3: Sess.
3.1-3.4
Given a model of a fraction,

14
[3.NF.2] Understand a fraction as a number on
the number line; represent fractions on a
number line diagram.
Write the corresponding fraction and explain
the relationship of the numerator and
denominator to the model.
Students:
Given any common fraction a/b between 0 and 1
(denominators of 2, 3, 4, 6, 8),
Go Math
Chapter 8
AMSTI
11
COURSE CONTENT
MATHEMATICS
THIRD GRADE
a.
b.
15
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.
Represent a fraction a/b on a number
line diagram by marking off a
lengths 1/bfrom 0. Recognize that the
resulting interval has size a/band that
its endpoint locates the
number a/b on the number line.
[3.NF.3] [3.NF.3] Explain equivalence of
fractions in special cases, and compare
fractions by reasoning about their size.
a.
b.
c.
d.
Understand two fractions as
equivalent (equal) if they are the
same size or the same point on a
number line.
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.
Express whole numbers as fractions,
and recognize fractions that are
equivalent to whole numbers.
Examples: Express 3 in the form 3
=3/1; recognize that6/1 = 6;
locate 4/4and 1 at the same point of a
number line diagram.
Compare two fractions with the
same numerator or the same
denominator by reasoning about

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.
Students:



Year Two Units
Finding Fair Shares:
CC 1.4A, 1.4B
Go Math
Chapter 8-9
Use visual models (e.g., fraction
manipulatives, number lines, or pictures) to
generate simple equivalent fractions including
fractions equivalent to whole numbers,
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 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?").
AMSTI
Year Two Units
Finding Fair Shares:
a. Finding Fair Shares:
Inv.1: Sess. 1.1-1.2, 1.4-1.6, Inv. 2: Sess. 2.1-2.4, Inv. 3:
Sess. 3.1-3.4
CC 1.4A, 1.4B
b. Finding Fair Shares:
Inv.1: Sess. 1.5, Inv. 2: Sess. 2.1-2.4, Inv. 3: Sess. 3.1-3.4
c. Finding Fair Shares:
Inv.1: Sess. 1.3, Inv. 2: Sess. 2.1-2.4, Inv. 3: Sess. 3.4
CC 1.4A, 1.4B
d. Finding Fair Shares:
Inv.1: Sess. 1.2-1.3
CC 1.4B
12
COURSE CONTENT
MATHEMATICS
THIRD GRADE
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.
FIFTH SIX WEEKS
16
[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.
Students:



17
[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
(6Excludes compound units such as cm3 and
finding the geometric volume of a container.)
(7Excludes multiplicative comparison
Go Math
Chapter 10
Tell and write time to the nearest minute using
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,
Solve word problems involving addition and
subtraction of time intervals using
representations of time passage such as arrows
on open number lines.
Students:

Accurately measure 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.
AMSTI
Year One Units
Collections and Travel Stories:
Inv. 3: Sess. 3.2-3.7, Inv. 4: Sess. 4.1-4.6
CC 1.7A
Equal Groups:
Inv. 1: Sess. 1.1-1.4, Inv. 3: Sess. 3.1-3.3, Inv. 4: Sess.
4.1-4.7
CC 3.1A
Year Two Units
Finding Fair Shares:
Inv. 1: Sess. 1.4-1.6, Inv. 3: Sess. 3.1-3.4
Other Units
Stories, Tables, & Graphs:
TMM
Go Math
Chapter 10
AMSTI
Year Two Units
Solids and Boxes:
CC 4A.1, 4A.2, 4A.3
Given a variety of one-step word problems involving
13
COURSE CONTENT
MATHEMATICS
THIRD GRADE
problems (problems involving notions of
"times as much").)
same unit volume or mass measurements,

19
[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.
Explain and justify solutions using a variety of
representations.
Students:


Go Math
Chapter 10
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 the length of all class members'
fingers) or by making repeated measurements
(e.g., measuring how far a marble rolls under
certain conditions),
Communicate questions and descriptions
related to the data display
AMSTI
Other Units
Surveys and Line Plots:
Inv. 3: Sess. 3.1-3.4
SIXTH SIX WEEKS
20
[3.MD.5] Recognize area as an attribute of
plane figures, and understand concepts of area
measurement.
a.
b.
21
Students:

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.
A plane figure which can be covered
without gaps or overlaps byn unit
squares is said to have an area
of n square units.
[3.MD.6] Measure areas by counting unit
squares (square cm, square m, square in,
square ft, and improvised units).
Go Math
Chapter 11
Explain the result of measuring the area of a
plane figure as a number of "unit squares"
needed to cover the object without gaps or
overlaps.
Students: Given a variety of plane figures,

Accurately measure area by counting standard
AMSTI
Year One Units
Perimeter, Angles, and Area:
Inv. 2
a. Perimeter, Angles, and Area:
Inv. 2: Sess. 2.2-2.6, Inv. 3: Sess. 3.6
CC 2.5A
b. Perimeter, Angles, and Area:
Inv. 2: Sess. 2.1-2.6, Inv. 3: Sess. 3.6
CC 2.5A
Go Math
Chapter 11
AMSTI
14
COURSE CONTENT
MATHEMATICS
THIRD GRADE
(square centimeter, square meter, square inch,
and square foot) and non-standard unit squares
(e.g., orange pattern blocks, floor tiles, etc.).
22
[3.MD.7] Relate area to the operations of
multiplication and addition.
a.
b.
c.
d.
23
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.
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 whole-number
products as rectangular areas in
mathematical reasoning.
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 xb and a x c. Use area models to
represent the distributive property in
mathematical reasoning.
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.
[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
Students:
Given a polygon that may be decomposed into 2 or more
rectangles,

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 rectangle with whole-number
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).
Students:

Year One Units
Perimeter, Angles, and Area:
Inv. 2: Sess. 2.1-2.6, Inv. 3: Sess. 3.6
CC 2.5A
Go Math
Chapter 11
AMSTI
Year One Units
Perimeter, Angles, and Area:
Inv. 2
Equal Groups:
Inv. 3
a. Perimeter, Angles, and Area:
Inv. 2: Sess. 2.4
Equal Groups:
Inv. 3: Sess. 3.1-3.4
CC 3.1A, 3.5A
b. Perimeter, Angles, and Area:
Inv. 2: Sess. 2.4
Equal Groups:
Inv.3: Sess. 3.1, 3.3-3.4, 3.6
CC 3.1A, 3.5A
c. Equal Groups:
CC 3.1A, 3.5A
d. Perimeter, Angles, & Area:
Inv. 2: Sess. 2.3-2.5
CC 2.5A
Equal Groups:
CC 3.1A, 3.5A
Go Math
Chapter 11
Find and justify solutions to real world and
AMSTI
15
COURSE CONTENT
MATHEMATICS
THIRD GRADE
exhibiting rectangles with the same perimeter
and different areas or with the same area and
different perimeters.
24
25
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.
[3.G.1] 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.
Students:
[3.G.2] 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.
Students:
Given squares, rectangles, or circles,




Year One Units
Perimeter, Angles, and Area:
Inv. 1: Sess. 1.2-1.5
CC 2.5A
Go Math
Chapter 12
Justify their identification/sorting of shapes
(triangles, quadrilaterals, pentagons, hexagons,
squares, rectangles, rhombuses) by referring to
their shared attributes,
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,
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 area of
each part as 1/4 of the area of the shape).
AMSTI
Year One Units
Perimeter, Angles, and Area:
Inv. 3: Sess. 3.1-3.6
Year Two Units
Solids & Boxes
Inv. 1
Go Math
Chapter 12
AMSTI
Year Two Units
Finding Fair Shares:
Inv.1: Sess. 1.1-1.6, Inv. 2: Sess. 2.1-2.4, Inv. 3: Sess.
3.1-3.4
Getting Ready Lessons 1 – 20
16