Pacing Guide - Math Grade 3 - Gaston County Schools

3 rd Grade Mathematics Resource & Pacing Guide Overview
…Putting it all Together!
Objectives: The North Carolina Standard Course of Study for mathematics is listed in this column. It determines the curriculum and assessments for each grade level.
Students Should Be Able To: This section gives a detailed description of the concepts that are included for each objective in the NC Standard Course of Study. Broad objectives leave many
teachers questioning if they have taught all concepts that need to be covered. The detailed descriptions promote comprehensive planning for teaching and assessing students.
DPI Strategies: These activities are designed for introducing math concepts. They are kinesthetic in nature and promote a deeper understanding for each objective. Teachers are highly
encouraged to introduce new concepts with these lessons before utilizing the textbook. In addition, these activities can be revisited for tutoring students.
Textbook: This column paces the blended program to assure that instruction is aligned with the NC Standard Course of Study. To optimize understanding of concepts, the topics from enVision
and the units from Investigations have been strategically placed. It is important to keep the standard course of study in mind when teaching the topic/units that are listed in this column. In rare
cases you may discover an objective that needs additional attention for mastery.
Week By Week: This document was designed to be used as a spiraling review. The column documents the number of times each objective is addressed in the Week By Week Essentials.
Lessons 1-9 are designated to occur during the first quarter, lessons 10-18 during the second quarter, lessons 19-27 during the third quarter, and lessons 28-36 during the fourth quarter. These
lessons can be revisited and adapted for additional review, tutoring, and/or assessing students.
Problem Solving Cards: All of these activity cards can be classified as problem solving and often times include more than one objective. If an objective is prominent, the card will be listed
beside that objective; however, it may not be limited to that objective. These cards can be used to check the students’ ability to apply concepts to demonstrate mastery. For students already
proficient in a particular concept, these activities can be used to replace lessons that may be too low for advanced math students. Problem Solving Cards are available in three levels for
elementary students. Set A is designated for first and second grade students. Set B is designated for third and fourth grade students. Set C is designated for fifth and sixth grade students.
Teachers are encouraged to use the Problem Solving Cards above or below them for enrichment and/or tutoring purposes.
Math Stars: These activities are challenging! They promote reasoning skills through math concepts. Math Stars can be used to replace activities/problems that insufficiently challenge the
top math students. Math Stars can also be utilized to facilitate team work, discussions about math, and math competitions. Teachers are encouraged to use Math Star activities from previous
grade levels that reinforce the standard course of study and provide additional practice for all students.
Key Mathematics Vocabulary: The vocabulary, listed in this section, builds a foundation for understanding and mastering the NC Standard Course of Study for each grade level.
Understanding these terms will facilitate math discussions and math journals which promotes comprehension and mastery of the objectives.
Readers for Math Integration: The books listed in this column offer opportunities to integrate reading selections with math concepts. These books can stimulate a desire for students to utilize
and master mathematical concepts. The reading selections reinforce the importance of math concepts in every day life. These short stories can be used as guided reading before or after the math
concepts are taught.
Gaston County Schools (July 2009 – Sharon W. White)

Third Grade Mathematics Resource & Pacing Guide
2009-2010
Third Grade - First Nine Weeks Weekly Spiraling Review
1
Differentiation
st Quarter 2 nd Quarter 3 rd Quarter 4 th Quarter
1-9 10-18 19-27 28-36
Objective Students should be able to… DPI enVision DPI
Week By Week
Problem Math
Strategies Investigations Indicators
Essentials
Solving Cards Stars
1.01 Develop number sense for whole
numbers through 9,999.
1.01a Connect model, number word, and
number using a variety of
representations.
1.01b Build understanding of place value
(ones through thousands).
1.01c Compare and order.
1.02 Develop fluency and multi-digit
addition and subtraction through
9,999 using:
1.02a Strategies for adding and
subtracting numbers.
1.02b Estimation of sums and differences
in appropriate situations.
1.02c Relationships between operations.
1.04 Use basic properties (identity,
commutative, associative, order of
operations) for addition,
subtraction, multiplication, and
division.
Recognize and represent a number in standard
form, expanded form, picture form, and written
form.
Compose and decompose a quantity in a variety of
representations.
Compare and decompose a quantity in a variety of
representations.
Compare number using diagrams, models, and
symbols
( , =, ≥, ≤, ≠).
Estimate to the nearest tens, hundreds and
thousands place.
Justify, explain and/or prove responses.
Understand and apply appropriate vocabulary.
Use a variety of strategies to add and subtract to
find sums and differences.
Apply estimation strategies to find sums and
differences.
Demonstrate how addition and subtraction are
related to one another.
Understand and apply appropriate vocabulary.
Understand and apply appropriate vocabulary.
Apply appropriate properties to solve problems.
Apply order of operations.
objective letter
page #
Introduce
Concepts
a:1-5
b:6-8
c:9-11
a:12-14
b:15
c:16
topic #. lesson(s) #
unit, investigation(s)
PACING
Practice
enVision Topics
(goal 1)
1.1-9
2.1-10
3.1-5
4.1-6
Investigations
(goal 1)
7.1-2
page # week # - page # Set B newsletter #
card #
activity #
Determine
Spiraling Review Applied Strategies High Level
Mastery
Enrichment
7-13
14-21
29-30 29-30 1-1
* * * * * First Nine Weeks Continued - Next Page * * * * *
a:4-13 a:13-49 a:18-69 a:28-109
b:4-14 b:5-18 b:7-26 b:11-42
b:12-45 b:12-46 b:26-103 b:27-105
b:35-137
c:2-5 c:5-18 c:6-21 c:15-57
c:16-63 c:34-133
a:28-110 a: 31-121
c:15-58
5 7 9
13 14 30
45 46 47
62
1 2 4
11 14 17
18 19 20
22 29 30
42
a:8 a:15 a:26
a:33 a:40 a:46
a:50 a:57 a:61
a:64
7.4
9.8
2.3
2.8
2.9
3.4
3.5
3.7
4.9
8.4
10.6

Third Grade - First Nine Weeks Continued... Weekly Spiraling Review
1
Differentiation
st Quarter 2 nd Quarter 3 rd Quarter 4 th Quarter
1-9 10-18 19-27 28-36
Objective Students should be able to… DPI enVision DPI
Week By Week Problem Math
Strategies Investigations Indicators
Essentials
Solving Stars
1.05 Use area or region models and set
models of fractions to explore part-
whole relationships.
1.05a Represent fractions concretely and
symbolically (halves, fourths, thirds,
sixths, eighths).
1.05b Compare and order fractions (halves,
fourths, thirds, sixths, eighths) using
models and benchmark numbers (zero,
one-half, one); describe comparisons.
1.05c Model and describe common
equivalents, especially relationships
among halves, fourths, and eighths, and
thirds and sixths.
1.05d Understand that the fractional
relationships that occur between zero
and one also occur between every two
consecutive whole numbers.
1.05e Understand and use mixed numbers and
their equivalent fraction forms.
1.06 Develop flexibility in solving problems
by selecting strategies and using mental
computation, estimation, calculators or
computers, and paper and pencil.
Recognize and represent fractions in a variety of
ways using models.
Compare and order fractions using models and
benchmark numbers.
Understand and apply appropriate vocabulary.
Recognize equivalent fractions among families
(halves, fourths, eighths, thirds, and sixths).
Using models, find the fractions between any two
consecutive whole numbers.
Using models, recognize, identify and use mixed
numbers and their equivalent fraction forms.
Recognize and represent fractions in a variety of
ways using models.
Compare and order fractions using models and
benchmark numbers.
Understand and apply appropriate vocabulary.
Recognize equivalent fractions among families
(halves, fourths, eighths, thirds, and sixths).
Using models, find the fractions between any two
consecutive whole numbers.
Using models, recognize, identify and use mixed
numbers and their equivalent fraction forms.
Use strategies such as making a table or diagram,
using guess-and-check, looking for patterns,
simplifying the problem, drawing pictures, spatial
visualization, working backwards- solve problems
Use strategies such as decomposing numbers,
benchmark numbers, models, manipulatives,
estimation, and mental computation.
Identify and use efficient, accurate and effective
strategies including calculators to solve problems.
Verify solutions by using appropriate methods
including using paper/pencil, calculator, computer.
Determine if solution is reasonable.
Solve multi-step problems.
objective letter
page #
Introduce
Concepts
a: 31-33
b: 34-35
c: 36-38
d: 39
e: 40
topic #. lesson(s) #
unit, investigation(s)
PACING
Practice
Listed Above On
Previous Page
page # week # - page # Set B
card #
Determine
Spiraling Review Applied
Mastery
Strategies
31-41 36-141
a:25-98 a:26-102 a:27-105 a:27-
106
b:21-81
d:6-21
41-52 42-46 4-13 4-15 5-17 5-19 6-2
6-23 7-27 8-29 8-31 9-33
10-37 11-43 12-45 12-47 13-49
13-51 14-53 14-55 15-57 16-61
17-65 17-67 18-71 19-73 19-75
20-77 21-81 21-83 22-85 23-89
23-91 24-95 25-97 25-99 26-103
27-107 28-111 29-113 29-114 29-115
30-117 30-119 31-121 32-125 32-127
33-129 34-135 35-137 35-138 36-143
10
38
41
64
4
6
14
19
20
27
55
61
63
newsletter #
activity #
High Level
Enrichment
4.6
4.8
6.2
6.4
7.1
8.2
9.1
9.2
10.1
10.7
2.4 2.6
4.5 4.7
5.2 5.5
5.6 6.1
6.6 6.7
7.6 8.3
8.6 10.2
10.4 10.5
10.8 10.9

Objectives to Maintain from Previous Grade Levels
These objectives are important concepts that need to be revisited throughout the year to maintain understanding.
- length and time - addition and subtraction of multi-digit numbers - Venn diagrams
- symmetry and congruence - line plots, tallies and pictographs
Second through Fourth Nine Weeks
Objectives taught in previous nine weeks should be continuously taught to maintain understanding and develop mastery.
Each grading period will include the objectives introduced during the current nine weeks and any objectives already addressed.
A spiraling curriculum allows students to reinforce and connect objectives.
Third Grade – Second Nine Weeks Weekly Spiraling Review Differentiation
1 st Quarter 2 nd Quarter 3 rd Quarter 4 th Quarter
1-9 10-18 19-27 28-36
Objective Students should be able to… DPI
Strategies
3.01 Use appropriate vocabulary to
compare, describe, and classify two-
and three-dimensional figures.
3.02 Use rectangular coordinate system
to solve problems.
3.02a Graph and identify points with
whole number and/or letter
coordinates.
3.02b Describe the path between given
points on the plane.
4.01 Collect, organize, analyze, and
display data (including circle graphs
and tables) to solve problems.
Recognize and name geometric figures
(two-dimensional and three-dimensional figures).
Graph and identify points with whole numbers
and/or letter coordinates.
Describe the paths between given points on the
plane.
Make predictions based on data.
Choose appropriate chart/graph/diagram to
display data.
objective letter
page #
Introduce
Concepts
71-76
a:77-83
b:84-86
enVision
Investigations
topic #. lesson(s) #
unit, investigation(s)
PACING
Practice
enVision Topics
(goal 1)
12.1-7
enVision Topics
(goal 3)
10.1-8
11.1-4
DPI
Indicators
Week By Week
Essentials
Problem
Solving Cards
Math
Stars
page # week # - page # Set B newsletter
card #
activity #
Determine
Spiraling Review Applied Strategies High Level
Mastery
Enrichment
58-59 3-9 7-25 9-33 10-37
10-38 11-41 12-45 14-53
16-61 17-65 18-69 19-73
24-93 28-109 29-113 30-117
36-141
35 39
48 49
52 59
3.8 5.3
5.7 9.3
9.6
10.10
60-61 13-49 13-50 44 2.2 3.2
4.3 6.5
7.2 7.7
8.8 9.9
87-91 enVision Topics
(goal 4)
20.1-9
62-63 2-5 3-9 4-13 9-33
10-37 11-41 13-49 14-53
15-57 17-65 22-85 23-89
24-93 26-101 27-105 30-117
enVision Topics
(goal 5)
9.1-8
32-125
* * * * * Second Nine Weeks Continued - Next Page * * * * *
12
20
53
2.1 2.5
3.3 5.1
6.7 7.3
7.5 8.1
10.3

Third Grade – Second Nine Weeks Continued... Weekly Spiraling Review Differentiation
1 st Quarter 2 nd Quarter 3 rd Quarter 4 th Quarter
1-9 10-18 19-27 28-36
Objective Students should be able to… DPI
Strategies
4.02 Determine the number of
permutations and combinations of
up to three items.
4.03 Solve probability problems using
permutations and combinations.
5.01 Describe and extend numeric and
geometric patterns.
5.02 Extend and find missing terms of
repeating and growing patterns.
objective letter
page #
Introduce
Concepts
enVision
Investigations
topic #. lesson(s) #
unit, investigation(s)
PACING
Practice
DPI
Indicators
Week By Week
Essentials
Problem
Solving Cards
Math
Stars
page # week # - page # Set B newsletter
card #
activity #
Determine
Spiraling Review Applied Strategies High Level
Mastery
Enrichment
Know when order matters. 92-94
64-65 28-109 29-113 33-131 34-133
Listed Above On
35-137
Previous Page
35-139
Determine the list of outcomes.
95-104 66-67 28-110 31-123 34-133 34-134
Determine the probability of the desired outcome.
35-137
36-141
Not provide by DPI
105-109 68-69 1-1 3-9 3-11 4-13 5-17
Given numeric and geometric patterns, accurately
8-29 9-33 9-35 10-37 11-41
determine the pattern and extend it an
13-49 14-55 15-59 18-69 20-77
appropriate number of times
20-79 21-81 22-85 23-89 24-93
25-97 26-101 27-105 28-109 29-
113
32-125 34-133 35-
137
Not provided by DPI
110-114
70-71 8-29 15-57 22-85 24-93 26-
Identify and extend repeating and growing
101
patterns
28-109 33-129 35-
Identify missing terms based on the pattern
137
2 6-8 12 13
15 24 25 43
44 45 54
3.5
4.2
8.5
58 3.1 7.8
9.4
26
32
36
47
53
26 32
37 53
2.7
3.6
4.4
5.8
6.3

Third Grade - Third Nine Weeks Weekly Spiraling Review Differentiation
1 st Quarter 2 nd Quarter 3 rd Quarter 4 th Quarter
1-9 10-18 19-27 28-36
Objective Students should be able to… DPI
Strategies
1.03 Develop fluency with multiplication
from 1x1 to 12x12 and division up to
two-digit by one-digit numbers using:
1.03a Strategies for multiplying and dividing
numbers.
1.03b Estimation of products and quotients
in appropriate situations.
1.03c Relationships between operations.
1.04 Use basic properties (identity,
commutative, associative, order of
operations) for addition, subtraction,
multiplication, and division.
2.01 Solve problems using measurement
concepts and procedures involving:
2.01a Elapsed time.
2.01b Equivalent measures within the same
measurement system.
2.02 Estimate and measure using
appropriate units.
2.02a Capacity (cups, pints, quarts, gallons,
liters)
2.02b Length (miles, kilometers)
2.02c Mass (ounces, pounds, grams,
kilograms).
2.02d Temperature
(Fahrenheit, Celsius).
Recognize and represent multiplication and division in
a variety of ways to find products and quotients.
Comprehend and apply appropriate vocabulary /
symbols ( x, , 12 , 4 12 )
4
Use known facts to find less familiar facts.
Apply estimation strategies to find products and
quotients.
Demonstrate how products and quotients are related to
one another.
Understand and apply appropriate vocabulary.
Apply appropriate properties to solve problems.
Apply order of operations.
Solve multi-step problems using elapsed time including
problems to nearest minute.
Solve problems and follow procedures using equivalent
units within the same measurement system.
time: seconds, minutes, hours, days, weeks, months,
years money: pennies/nickels/dimes/quarter/halfdollars/dollars/bills
capacity: cups, pints, quarts,
gallons, liters length: inches/feet/yards/miles,
centimeters/meters/kilometers mass: ounce/pounds,
grams/kilograms
Estimate and measure with appropriate units.
Select and use the appropriate tools and units for the
attribute being measured.
letter
page #
Introduce
Concepts
a:17-25
b: 26
c:27-28
enVision
Investigations
topic #. lesson(s) #
unit, investigation(s)
PACING
Practice
Investigations
(goal 1)
5.1-4
enVision Topics
(goal 2)
14.1-6
15.1-5
17.1-6
DPI
Indicators
29-30 29-30
a:53-55
b:56-58
a:59-60
b:61-65
c:66-68
d:69-70
Week By Week
Essentials
Problem
Solving
page # week # - page # Set B
card #
Determine
Spiraling Review Applied
Mastery
Strategies
22-28 31-122 36-141
a:1-1 a:1-3 a:2-5 a: 3-9 a:3-10
a:4-15 a:5-17 a:5-19 a: 6-21 a:8-29
a:9-33 a:11-41 a:12-45 a:12-47 a:13-49
a:13-50 a:13-51 a:14-53 a:14-54 a:14-55
a:15-57 a:16-61 a:16-62 a:16-63 a:17-65
a:17-66 a:18-70 a:19-73 a:19-74 a:20-77
a:21-81 a:21-82 a:22-86 a:23-89 a:25-97
a:26-101 a:27-105 a:27-107 a:28-109
a:28-111 a:29-113 a:29-114 a:29-115
a:30-117 a:30-118 a:30-119 a:31-121
a:32-125 a:32-127 a:33-129 a:34-133
a:35-135 a:36-142 a:36-143
b:21-81 b:22-85
47-54 7-25
c:25-97 c:22-87 c:30-118 c:32-127
a:2-6 a:4-13 a:15-57
a:15-59 a:16-61 a:30-117 a:31-
121
b:7-25 b:8-30 b:9-34
b:18-69 b:26-101 b:36-141
55-57 23-90 32-126
b:21-81 b:24-94
c:20-77
10
11
21
23
24
28
31
34
36
37
40
47
51
60
64
11
16
10
32
56
62
Math
Stars
newsletter #
activity #
High Level
Enrichment
2.3
2.8
4.9
5.5
8.3
9.7
5.4
8.7
9.5
4.1

Third Grade - Fourth Nine Weeks Weekly Spiraling Review Differentiation
1 st Quarter 2 nd Quarter 3 rd Quarter 4 th Quarter
1-9 10-18 19-27 28-36
Objective Students should be able to… DPI
Strategies
5.03 Use symbols to represent unknown
quantities in number sentences.
5.04 Find the value of the unknown
quantities in number sentences.
Define: variable, unknown
Use symbols of unknown quantities in number
sentences
Use a variety of strategies to determine the
unknown quantity in a number sentence.
objective letter
page #
Introduce
Concepts
enVision
Investigations
topic #. lesson(s) #
unit, investigation(s)
PACING
Practice
DPI
Indicators
Week By Week
Essentials
Problem
Solving
Cards
page # week # - page # Set B
card #
Determine
Spiraling Review Applied
Mastery
Strategies
115
72-73 20-77
116-118
Investigations
(goal 5)
6.1-3
74 20-77 50
Great Review! Fantastic Five – Countdown to EOG’s - Sample EOG Questions Great Review!
Math
Stars
newsletter
activity #
High Level
Enrichment

Key Mathematics Vocabulary – Third Grade
Goal 1 Goal 2 Goal 3 Goal 4 Goal 5
6÷2, 2 6 , 6
2
least
leftover
AM/PM
analog
justify
kilograms
(D, 2) or (4, 2)
acute
ordered pair
parallel
1 out of 3 = 1
3
balance
complete the pattern
2 (3), 2 x 3, 2 3 less than < appropriate units kilometer attributes parallelogram 1 st , 2 nd , 3 rd , etc. continue the pattern
about less than or equal to ≤ before/after length/long axes path 3 items create a pattern
act out the problem make a diagram/picture Celsius linear axis pentagon analyze equation
add make table/chart/graph centimeter liters base plane figures / 2-D arrange equivalent
addend make an organized list convert measure circle point arrangement(s) expression
approximately mixed number cups meter stick cone polygon certain extend
arrays multiples customary metric congruent polyhedrons / 3-D circle graph extend the pattern
cents multiply decreasing miles cube prism collect form
compare not equal to ≠ degrees minutes curved/straight quadrilateral combinations geometric patterns
compose numerator digital months cylinder ray create a table growing patterns
decompose ones place earlier/later non-standard decagon rectangle different orders missing terms
demonstrate order elapsed ounces diagonal regular display number sentence(s)
denominator parentheses equivalent pints east rhombus double Venn Diagram numeric patterns
difference pattern equivalent measures pounds edge right angle how many different pattern
digit product estimate quarter hour endpoints shapes impossible pattern core
divide proper fractions Fahrenheit quarts face side less likely pattern unit
dividend prove feet reasonable flat south likely position
division quotient gallons ruler grid sphere line plot repeating patterns
divisor reasonable grams season height square list represent
dollars regions/area half past seconds hexagon square angle more likely symbol(s)
equal portions relationship half-hour standard irregular surface no repeats unknown
equal to = remainder height/tall tape measure kite symmetric order unknown quantities
equivalent repeated addition hours trundle wheel line of symmetry symmetry organize value
estimate repeated subtraction inches until/after/past line segment edge trapezoid organized list variable
evaluate sets increasing width/wide line(s) triangle outcomes
expanded form share equally increments yard stick north vertex permutations
expanded notation skip count intervals yards obtuse vertices/vertexes pictograph
explain solve a simpler problem years octagon west possible
factor standard form possible outcomes
fair share standard notation predictions
find a pattern subtract survey
fraction bar 3
4
sum
tens place
table
tallies
greater than > thousands place triple Venn Diagram
greater than or equal to ≥ using objects
greatest value
groups Venn diagram
guess and check/test whole number
hundreds place work backwards
improper fractions
justify
written form

Amanda Bean’s Amazing Dream: A Mathematical Story. Cindy Neuschwander & Marilyn Burns. Scholastic
Arithme-Tickle: An Even Number of Odd Riddle-Rhymes. J. Patrick Lewis, Frank Remkiewicz. Silver Whistle
Arithmetricks. Edward H. Julius. John Wiley & Sons
Bats on Parade. Kathi Appelt. William Morrow
Can You Count to a Googol? Robert E. Wells. Albert Whitman & Co.
A Cloak for the Dreamer. Aileen Friedman. Scholastic
Do You Wanna Bet? Your Chance to Find Out About Probability. Jean Cushman. Houghton Mifflin
Einstein Anderson, Science Detective: On-line Spacemen and Other Cases. Seymour Simon. Avon Books
Esio Trot. Roald Dahl. Demco Media
Fraction Fun. David Adler. Holiday House
The Go-Around Dollar. Barbara Johnston Adams. Simon & Schuster Children’s
A Grain of Rice. Helna C. Pittman Bantam. Doubleday Dell
Grandfather Tang’s Story: A Tale Told with Tangrams. Ann Tompert. Demco Media
How Much Is a Million? David M. Schwartz. William Morrow
If You Made a Million. David M. Schwartz. William Morrow
Readers for Math Integration – Third Grade
The King’s Commissioners. Aileen Friedman. Scholastic
Logic for Space Age Kids. Lyn McClure Butrick. University Classics
Math Mysteries: Stories and Activities fo Build Problem Solving Skills. Jack Silbert. Scholastic
Math-Terpieces. Greg Tang, Greg Paprocki. Scholastic
Measuring Penny. Loreen Leedy. Henry Holt
Pigs at Odds: Fun With Math and Games. Amy Axelrod, Sharom McGinley-Nally. Simon & Schuster
Sam Johnson and the Blue Ribbon Quilt. Lisa Campbell Renst. William Morrrow
Sir Cumference and the First Round Table: A Math Adventure. Cindy Neuschwander. Charlesbridge
Spaghetti and Meatballs for All: A Mathematical Story. Marilyn Burns. Scholastic
Three Pigs, One Wolf, and Seven Magic Shapes. Grace MacCarone, David Neuhaus, Marilyn Burns.
Scholastic
Tiger Math: Learning to Graph From a Baby Tiger. AnnWhitehead Nagda, Cindy Bickel.
Henry Holt & Co
Time. Henry Pluckrose. Children’s Press