# Standard: by HC111123173735

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• pg 1
```									                                                        Math Curriculum
Standard: 4.1 (NUMBER AND NUMERICAL OPERATIONS)

Strand: A Number Sense
Cumulative Progress                              Resources                  Suggested Teaching
Date/Notes                                                          Assessments
Indicator                                        (Materials)                Strategies/Activities
A. 1   Use real-life experiences,                         Trailblazers Unit         Games                     Teacher
physical materials, and                             Resource Guide:           Cooperative Group          Observation using
technology to construct                            Unit 3, “Number and        Work                       Assessment
meanings for number (unless                         Number Operations”        Journal Prompts            Record in URG
otherwise noted, all indicators                     Lessons 4 p. 220          Teacher Observation       Journal Prompts
for grade 4 pertain to these sets                  Lesson 5 p. 231            Modeling                  Related DPPs
of numbers as well).                               Unit 6, “ Place Value     Use of meter sticks,      Unit 3
Whole numbers through                               Patterns” Lessons 1-6      fraction strips, place    Place Value + and
millions                                            pp. 418-445                value charts, and base     – quiz
Commonly used fractions                            Unit 10, “Using            ten pieces                Written
(denominators of 2, 3, 4, 5, 6,                     Decimals”                                             explanation of +
8, 10, 12, and 16) as part of a                    Lessons 1-3 pp.755-775                                 and – process
whole, as a subset of a set, and
 Oral explanation
as a location on a number line
of place value
Decimals through hundredths
 SG p. 76 #16
 Unit 6
writing of large
numbers
 DAB p. 69 URG
439
 SG p. 163,
homework
questions5-7
 Check Up Time
URG p. 463
 Making Money
SG p. 175
 Unit 10

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Math Curriculum
 Grace‟s Base Ten
Pieces DAB p.
151
 DAB p. 150 #7
 Linda‟s Base Ten
Pieces URG p.
776
 Measure
classroom items
A. 2   Demonstrate an understanding     Trailblazers Unit          Small Group Instruction    Teacher
of place value concepts.          Resource Guide             Journal Writing             Observation
 Unit 3, “Numbers and       Use of number line,        Assessment
Number Operations”,         place value chart, and      Record Sheet
Lessons 4 p. 220            base ten pieces            Student Oral
Lesson 5 p. 231            Modeling                    Explanation of
 Unit 6, “Place Value                                    Place Value
Patterns” Lessons 1 p.                                 Journal Prompts
418 and Lesson 3 p. 432                                Unit 3
 Unit 11,                                               SG p. 76 #16
“Multiplication”                                       URG p. 243
Lessons 2 p. 835 and                                    Unit 6
Lesson 4 p. 845                                          Students Read
 Unit 13, “Division”                                     Numbers orally
Lessons 2 p.993                                         Assessment
Record
 DAB p. 69
 URG p. 439
 Unit 11
 Homework
Questions SG p.
306+307
 Practice problems
 Quiz URG p. 850
A. 3   Demonstrate a sense of the       Trailblazers Unit          Use of number line,        Read Aloud
relative magnitudes of            Resource Guide              place value chart,          Numbers
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Math Curriculum
numbers.                         Unit 6, “ Place Value          newspaper, and megabit     Assessment
Patterns” Lessons 1-6 pp.      base ten pieces             Record Sheet
418-445                       Cooperative Learning       Journal Prompt
 Physical Modeling          DPP Letter P
 Choral Reading of          DAB p. 69
Numbers                    URG p. 439
 Journal Writing            SG p. 163 #5-7
 Small Group Instruction    Check Up Time
 How Much Is A Million       URG p. 463
 SG p. 175 Making
Money

A. 4   Understand the various uses of     Trailblazers Unit          Modeling                   Teacher
numbers.                            Resource Guide             Journal Writing             Observation:
Counting, measuring, labeling      Units 1-16                 Cooperative Learning        student
(e.g., numbers on baseball         Lab Activities             Think Pair Share            demonstrate skill
uniforms), locating (e.g.,         Unit 1, “Data About        Small Group Instruction    Group discussion
Room 235 is on the second           Us” Lesson 1 -5 pp. 28-    Journal Writing            Lab Activities:
floor)                              73                         Teacher Observation         refer to rubric
 Arms Span vs. Height       Modeling                    provided in URG
Lab p. 63
 Unit 2, “Geometric
Investigations: A
Baseline Assessment
Unit” Lesson 2-5 pp.
128-154
 Perimeter vs. Length
Lab p.128
 Unit 3, “Numbers and
Number Operations”
Lesson 1-6 pp.201-244
249
 Unit 5, “Using Data to

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Math Curriculum
Predict” Bouncing Ball
Lesson 4 p.359
Lesson 1-5 pp. 336-374
 Unit 8, “Measuring Up:
An Assessment Unit”
Lesson 595
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
A. 5   Use concrete and pictorial          Trailblazers Unit           Use of fraction strips,    Assessment
models to relate whole               Resource Guide               fraction circles, and       Record Sheet
numbers, commonly used              Unit 10, “Using              paper folds                Journal Prompt
fractions, and decimals to each      Decimals” Lessons 1-3       Cooperative Groups         Teacher
other, and to represent              pp.755-776                  Game Playing                Observation:
equivalent forms of the same        Unit 12, “Exploring         Small Group Instruction     students complete
number.                              Fractions” Lessons 4- 5     Teacher Observation         tasks-
pp. 915-924                 Modeling                   Unit 10
 Measure
classroom objects
 Grace‟s Base Ten
Pieces DAB p.
151
 DAB p. 150 #7
 Linda‟s Base Ten
Pieces URG p.
776
 Teacher
Observation:
students

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Math Curriculum
demonstrate skill
and
understanding-
Unit 12
 DAB p. 179-183
 Frabble Game
 Order Fractions
 SG p. 345 #6-15
A. 6   Compare and order numbers.             Trailblazers Unit        Mega- Bit                  Teacher
Resource Guide           Estimation                  Observation-
 Unit 6, “ Place Value    Manipulate Physical         student
Patterns” Lessons 1-6     Placement of Numbers        demonstrates and
pp. 418-445               on Number Line              explains how to
 Digit Cards                 compare and order
 Journal Writing             numbers
 Modeling                   Assessment
 Cooperative Learning        Record Sheet
 Use of the base ten        Journal Prompt
pieces and boards          SG p. 163 #5-7
 Think Pair Share           URG p. 463
 Small Group Instruction    SG p. 175 Making
Money
A. 7   Explore settings that give rise        Trailblazers Unit        Physical Placement on      Teacher
to negative numbers.                    Resource Guide            Number Line                 Observation-
Temperatures below 0°, debts           Unit 3, “Numbers and     Thermometer                 group discussion
Extension of the number line            Number Operations”       Below Zero                 Student
Lesson 6 p. 244          DPP letter K                demonstrates task:
 Large Group Instruction     URG p. 249
 Cooperative Learning
 Journal Writing
 Modeling
 Small Group Instruction
Standard: 4.1 (NUMBER AND NUMERICAL OPERATIONS)

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Math Curriculum
Strand: B. Numerical Operations
Cumulative Progress                            Resources                    Suggested Teaching
Date/Notes                                                               Assessments
Indicator                                      (Materials)                  Strategies/Activities
B. 1   Develop the meanings of the                      Trailblazers Unit           Journal Writing              Assessment
four basic arithmetic                             Resource Guide              Games                         Record Sheet
operations by modeling and                       Unit 3, “Numbers and        TIMS student rubric          Journal Prompts-
discussing a large variety of                     Number Operations”          Modeling                      Explain place
problems.                                         Lessons 4 -5 pp. 220 -      Use of flashcards, graph      value using base
Addition and subtraction:                         245                          paper, color tiles, and       ten pieces
joining, separating, comparing                   Unit 4, “Products and        base ten pieces              SG pg. 76
Multiplication: repeated                          Factors” Lessons 1-5        Multiplication Rock           question 16
addition, area/array                              pp. 283-309                  video                        URG pg. 243
Division: repeated subtraction,                  Unit 7, “Patterns in        Paper-Pencil problems        Teacher
sharing                                           Place Value” Lessons 2-     Small Group Instruction       observation-
5 pp.505-538                Cooperative Groups           Journal Writing:
 Unit 11,                    Multiplication fact Music     Have students
“Multiplication”             CD                            explain different
Lessons 1- 5 pp. 826-                                      ways of solving
853                                                        subtraction
 Unit 12, “Exploring                                        process
Fractions” Lessons 2                                      Teacher
p.907                                                      observation:
 Unit 13, “Division”                                        student
Lessons 2- 4 pp. 993-                                      demonstrates
1007                                                       skill: Unit 4
 Solve
multiplication
and division
problems
 TIMS student
rubric
 Prime Numbers
 Unit 7
 Divisibility

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Math Curriculum
 SG p. 194 #9
 Teacher
Observation:
Portfolio
Assessment
 Broken
Calculator
 URG p. 527
 Unit 13
 Division
problems
 Lesson 3 quiz
 URG p. 1007
B. 2   Develop proficiency with basic      Trailblazers Unit          Journal Prompts              Teachers
multiplication and division          Resource Guide             Practice                      Observation:
number facts using a variety of     Unit 3, “Numbers and       Use of flashcards, tiles,     demonstration of
fact strategies (such as “skip       Number Operations”          connecting cubes, and         skills verbal and
counting” and “repeated              Lessons 4 -5 pp. 220-       calculator                    Written-
subtraction”) and then commit        243                        Doubles                      Assessment
them to memory.                     Unit 4, “Products and      Skip Counting                 Record Sheet
Factors” Lessons 1-5       Counting up or down          Teacher
pp. 283-309                 from a known fact             Observation:
 Unit 7, “Patterns in       Arrays                        class discussion-
Place Value” Lessons 2-    Forgiving Method              Triangle
5 pp.505-538               Mad Minute-timed sheets       Flashcards
 Unit 11,                    (enrichment)                 Journal Prompts
“Multiplication”            Cooperative groups           Unit 3
Lessons 1- 5 pp. 826-      Small Group Instruction      DPP letters Q and
853                        Games                         F
 Unit 12, “Exploring                                      Unit 4
Fractions” Lessons 2                                     Determining
p.907                                                     Multiples
 Unit 13, “Division”                                      URG p. 305+306
Lessons 2- 4 pp. 993-                                    Unit 7
1007                                                     Determining
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Math Curriculum
Divisibility
 SG p. 194 #9
 Portfolio
 Teacher
Observation
 Unit 11
 SG p. 302 #20-22
 Multiplication
problems
 SG p. 310
selected teacher
homework
questions
 URG p. 850
 SG p. 320
 Unit 13
 Computing
Forgiving
Method
 Division
problems
 Lesson 3-Unit 13
quiz
B. 3   Construct, use, and explain       Trailblazers Unit          Journal Prompts            Teacher
procedures for performing          Resource Guide             Estimation                  Observation-
whole number calculations and     Units 1-16                 Reasonableness of           demonstration of
with:                             Lab Activities              Answer                      skills.
Pencil-and-paper                  Unit 1, “Data About        Modeling                   Class discussion
Mental math                        Us” Lesson 1 -5 pp. 28-    Practice                   URG 8
Calculator                         73                         Games                      Mid Year Test
 Arms Span vs. Height       Use of Manipulatives       URG 16
Lab p. 63                  Small Group Instruction    End of Year
 Unit 2, “Geometric         Teacher Observation         Exam
Investigations: A
Baseline Assessment
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Math Curriculum
Unit” Lesson 2-5 pp.
128-154
 Perimeter vs. Length
Lab p.128
 Unit 3, “Numbers and
Number Operations”
Lesson 1-6 pp.201-244
249
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359
Lesson 1-5 pp. 336-374
 Unit 8, “Measuring Up:
An Assessment Unit”
Lesson 595
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
B. 4   Use efficient and accurate         Trailblazers Unit           Journal Writing            Assessment
pencil-and-paper procedures         Resource Guide              All-Partials Method         Record Sheet
for computation with whole         Unit 3, “Numbers and        Forgiving Method           Journal Prompts
numbers.                            Number Operations”          Break Apart Computing      Unit 3
Addition of 3-digit numbers        Lesson 5 p. 231              Use of base ten pieces,    URG p. 243
Subtraction of 3-digit numbers     Unit 11,                     tiles, and calculator      Subtraction
Multiplication of 2-digit           “Multiplication”            Practice problems using     methods
numbers                             Lessons 1-5 pp. 826-         various tools and          Unit 11
Division of 3-digit numbers by    853                            strategies                 SG p. 302 #20-22
1-digit numbers                    Unit 13, “Division “        Games                      Multiplication
Lessons 2 - 3 pp. 993-      Teacher Observation         problems

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Math Curriculum
1004                      Modeling                   SG p. 310
selected teacher
homework
questions
 URG p. 850
 SG p. 320
 Teacher
Observation-
demonstration of
of the process.
 Unit 13
 Forgiving
Method
 Division
problems
 Lesson 3 quiz
 URG 1007 Unit
13 quiz
B. 5   Construct and use procedures     Teacher created math     NJ Test Prep Activities    Teacher
for performing decimal            enrichment activities    Journal Prompts             Observation
addition and subtraction.                                  Reasonableness of          NJ Test Prep
 Modeling
 Practice
 Games
 Small Group Instruction
 Teacher Observation
B. 6   Count and perform simple         Teacher created math     Test Prep review           Teacher
computations with money.          enrichment activities     Activities                  Observations
Standard dollars and cents                                 Reasonableness of          Quizzes
notation                                                    Answer                     NJ Test Prep
 Modeling                    Activities
 Practice
 Games
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Math Curriculum
 Small Group Instruction
 Teacher Observation
B. 7   Select pencil-and-paper,            Trailblazers Unit          Journal Prompts            Teacher
mental math, or a calculator as      Resource Guide             Estimation                  Observations-
the appropriate computational       Units 1-16                 Reasonableness of           Student
method in a given situation         Lab Activities              Answer                      demonstration of
depending on the context and        Unit 1, “Data About        Modeling                    skills
numbers.                             Us” Lesson 1 -5 pp. 28-    Practice                   URG 1-16 all
73                         Games                       Labs- refer to
 Arms Span vs. Height       Use of Manipulatives        rubric supplied in
Lab p. 63                  Small Group Instruction     teachers edition
 Unit 2, “Geometric         Teacher Observation        URG 8
Investigations: A                                      Mid Year Test
Baseline Assessment                                    URG 16
Unit” Lesson 2-5 pp.                                   End of Year
128-154                                                 Exam
 Perimeter vs. Length
Lab p.128
 Unit 3, “Numbers and
Number Operations”
Lesson 1-6 pp.201-244
249
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359
Lesson 1-5 pp. 336-374
 Unit 8, “Measuring Up:
An Assessment Unit”
Lesson 595
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186

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Math Curriculum
 Unit 15, “Using Patterns
Lesson 1 p. 1106
B. 8   Check the reasonableness of     Trailblazers Unit           Journal Prompts            Teachers
results of computations.         Resource Guide              Estimation                  Observation-
 Units 1-16                  Reasonableness of           class discussion
 Unit 1, “Data About         Modeling                   Teacher and
Us” Lesson 1 -5 pp. 28-     Practice                    student
73                          Games                       conference
 Arms Span vs. Height        Use of Manipulatives       URG 1-16- Labs-
Lab p. 63                   Small Group Instruction     refer to rubrics in
 Unit 2, “Geometric          Teacher Observation         teachers edition
Investigations: A                                       URG 8
Baseline Assessment                                     Mid Year Test
Unit” Lesson 2-5 pp.                                    URG 16
128-154                                                 End of Year
 Perimeter vs. Length                                     Exam
Lab p.128
 Unit 3, “Numbers and
Number Operations”
Lesson 1-6 pp.201-244
249
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359
Lesson 1-5 pp. 336-374
 Unit 8, “Measuring Up:
An Assessment Unit”
Lesson 595
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.

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Math Curriculum
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
B. 9   Use concrete models to                 Trailblazers Unit           Journal Prompts           Assessment
explore addition and                    Resource Guide              Paper folding              Record Sheet
subtraction with fractions.            Unit 12 “ Exploring         Use of pattern blocks,    Journal Prompts
fractions” Lessons 1- 6     fraction strips, and      Teacher
pp.894-924                  centimeter grid paper      Observation-
 Modeling                  Student folding
 Cooperative Groups         of paper
 Games                     SG p. 335
 Teacher
Observation- use
of fraction stripes
 Class Discussion
B. 10 Understand and use the inverse          Trailblazers Unit           Journal Writing           Assessment
relationships between addition           Resource Guide              Flashcards                 Record Sheet
and subtraction and between             Unit 3, “ Numbers and       Forgiving Method          Journal Prompts
multiplication and division.             Number Operations”          All Partials Method       Unit 3
Lesson 5 p. 231             Think Pair Share          URG p. 243
 Unit 4, “ Products and      Modeling                  Unit 4
Factors” Lessons 1 p.                                  Multiples
283 Lesson 5 p. 307                                    Teacher
 Unit 13, “ Division”                                    Observation-
Lesson 4 p. 1005                                        student
demonstrates
understanding of
skill
 Unit 13 quiz
 Class discussion-
fact families
Standard: 4.1 (NUMBER AND NUMERICAL OPERATIONS)

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Math Curriculum
Strand: C. Estimation
Cumulative Progress                           Resources                    Suggested Teaching
Date/Notes                                                            Assessments
Indicator                                     (Materials)                  Strategies/Activities
C. 1   Judge without counting                          Trailblazers Unit           Estimation Jars within    Teacher
whether a set of objects has                     Resource Guide               10%                        Observation:
less than, more than, or the                    Unit 6, “ Place Value       Journal Writing            Class discussion
same number of objects as a                      and Patterns” Lesson 1-     Flashcards                Teacher
reference set.                                   7 pp. 418-467               Forgiving Method           Observation:
 All Partials Method        student
 Think Pair Share           demonstrates skill
 Modeling                  Journal Prompt
C. 2   Construct and use a variety of                  Trailblazers Unit           Journal Writing           Teacher
estimation strategies (e.g.,                     Resource Guide              Flashcards                 Observation:
rounding and mental math) for                   Units 1-16                  Forgiving Method           Class discussion
estimating both quantities and                  Lab Activities              All Partials Method       Teacher
the results of computations.                    Unit 1, “Data About         Think Pair Share           Observation:
Us” Lesson 1 -5 pp. 28-     Modeling                   student
73                                                      demonstrates skill
 Arms Span vs. Height                                   Journal Prompt
Lab p. 63                                              Final and Mid
 Unit 2, “Geometric                                      Term Exam
Investigations: A                                      Quizzes
Baseline Assessment
Unit” Lesson 2-5 pp.
128-154
 Perimeter vs. Length
Lab p.128
 Unit 3, “Numbers and
Number Operations”
Lesson 1-6 pp.201-244
249
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
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Math Curriculum
1-5 pp. 336-374
 Unit 8, “Measuring Up:
An Assessment Unit”
Lesson 595
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
C. 3   Recognize when an estimate is        Trailblazers Unit           Journal Writing        Teacher
appropriate, and understand           Resource Guide              Flashcards              Observation:
the usefulness of an estimate as     Units 1-16                  Forgiving Method        Class discussion
distinct from an exact answer.       Lab Activities              All Partials Method    Teacher
 Unit 1: Arms Span vs.       Think Pair Share        Observation:
Height Lab                  Modeling                student
 Unit 1, Lesson 1 ,2, 3 &                             demonstrates skill
5                                                   Journal Prompt
 Unit 2 Perimeter vs.                                Final and Mid
Length Lab                                           Term Exam
 Unit 2, Lesson 2,5, & 6                             Quizzes
 Unit 3: Professor
Peabody: Invents a Ball
 Unit 3, Lesson 1, 4,6, &
7
 Unit 5: Bouncing Ball :
Lesson 4
 Unit 5, Lesson 1, 2, &3
 Unit 8
 Volume vs. Number
 Unit 4, Lesson 2, 3, & 6
 Unit 16
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Math Curriculum
 Area Vs. Length
 Unit 15, “Using
Patterns”
Group
C. 4   Use estimation to determine     Trailblazers Unit          Journal Writing        Teacher
whether the result of a          Resource Guide             Flashcards              Observation:
computation (either by          Units 1-16                 Forgiving Method        Class discussion
calculator or by hand) is       Lab Activities             All Partials Method    Teacher
reasonable.                     Unit 1, “Data About        Think Pair Share        Observation:
Us” Lesson 1 -5 pp. 28-    Modeling                student
73                                                  demonstrates skill
 Arms Span vs. Height                               Journal Prompt
Lab p. 63                                          Final and Mid
 Unit 2, “Geometric                                  Term Exam
Investigations: A                                  Quizzes
Baseline Assessment
Unit” Lesson 2-5 pp.
128-154
 Perimeter vs. Length
Lab p.128
 Unit 3, “Numbers and
Number Operations”
Lesson 1-6 pp.201-244
249
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 8, “Measuring Up:
An Assessment Unit”
Lesson 595
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309

Page 16
Math Curriculum
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
Standard: 4.2 (GEOMETRY AND MEASUREMENT)

Strand: A. Geometric Properties
Cumulative Progress                            Resources                     Suggested Teaching
Date/Notes                                                               Assessments
Indicator                                      (Materials)                   Strategies/Activities
A. 1   Identify and describe spatial                    Teacher created              NJ Test Prep Activities     Teacher
relationships of two or more                      enrichment activities        Journal Prompts              Observation:
objects in space.                                                              Estimation                   Class Discussion
Direction, orientation, and                                                    Reasonableness of           Teacher
perspectives (e.g., which is on                                                 Answer                       Observation:
your left when you are                                                         Modeling                     student
standing here?)                                                                Practice                    demonstrates skill
Relative shapes and sizes
 Games                       Teacher
 Use of Manipulatives         Observation:
everyday objects                                                                                             Hand-On
 Small Group Instruction
 Teacher Observation          Activities both
small and large
group
 Map skill
activities-
following a
sequence of
problem solving
activities related
to map skills
A. 2   Use properties of standard                       Trailblazers Unit           Journal Writing              Assessment
three-dimensional and two-                        Resource Guide              Use of protractors, angle     Record Sheet
dimensional shapes to identify,                  Unit 2, “Geometric           circles, pattern blocks,     Teacher
classify, and describe them.                      Investigation: An            geometric solids,             Observation &
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Math Curriculum
Vertex, edge, face, side, angle       Assessment Unit‟           Identify shapes and         class discussion
3D figures-cube, rectangular          Lessons 1- 6 pp. 121-       angles within the          Teacher
prism, sphere, cone, cylinder,        164                         classroom                   Observation-
and pyramid                          Unit 9, “Shapes and        Cooperative Groups          students complete
2D figures-square, rectangle,         Solids” Lessons 1-3 pp.    Drawing shapes              tasks
circle, triangle, quadrilateral,      662-687                                                Unit 6
pentagon, hexagon, octagon           Lesson 5 p. 695                                        Students use
Inclusive relationships-squares                                                               circles to identify
are rectangles, cubes are                                                                     angles URG 164
rectangular prisms                                                                            Unit 9
 SG p. 242
Questions 5-8
 Teacher
Observation
 SG p. 260
Homework
Questions
A.3    Identify and describe                Trailblazers Unit          Journal Writing            Assessment
relationships among two-              Resource Guide             Paper folding               Record Sheet
dimensional shapes.                  Unit 9, “Shapes and        Modeling                   Teacher
Congruence                            Solids” Lessons 3 - 4      Kinesthetic Activities      Observation:
Lines of symmetry                     pp.678-698                 Games                      Explore line and
 Cooperative Learning        turn symmetry
 Think Pair Share           Journal Prompt
 Small Group Instruction    Class Discussion
 Teacher Observation
A. 4   Understand and apply concepts        Trailblazers Unit          Journal Writing            Assessment
involving lines, angles, and          Resource Guide             Use of rulers, pattern      Record Sheet
circles.                             Unit 2, “Geometric          blocks, protractors,       Teacher
Point, line, line segment,            Investigation: An          Identifying angles and      Observation-
endpoint                              Assessment Unit”            lines in everyday life      student
Parallel, perpendicular               Lesson 6 p. 155            Cooperative groups          demonstrates
Angles-acute, right, obtuse          Unit 9, “Shapes and                                     knowledge of
Circles-diameter, radius, center      Solids” Lessons 1-2 pp.                                 skills:
662-677                                                Unit 2
Page 18
Math Curriculum
 Using Angle
Circles
 Unit 9
 SG p. 242 #5-8
SG p. 238-240 ,
Map Skills
activity page
 Teacher
Observation
measuring angles
quiz
 Journal prompts
A. 5   Recognize, describe, extend,                   Teacher created          NJ Test Prep Activities     Teacher
and create space-filling                        enrichment math          Journal Prompts              Observation:
patterns.                                       activities               Estimation                   Class Discussion
 Reasonableness of           Teacher
 Modeling                     student
 Practice                    demonstrates skill
 Games                       Teacher
 Use of Manipulatives         Observation:
 Small Group Instruction      Hand-On
 Teacher Observation          Activities both
small and large
group
Standard: 4.2 (GEOMETRY AND MEASUREMENT)

Strand: B. Transforming Shapes
Cumulative Progress                          Resources                  Suggested Teaching
Date/Notes                                                           Assessments
Indicator                                    (Materials)                Strategies/Activities
 Teacher created math      NJ Test Prep Activities    Teacher
Use simple shapes to cover an
B. 1                                                   enrichment activities     Journal Prompts             Observation:
area (tessellations).
 Estimation                  Class Discussion

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Math Curriculum
 Reasonableness of           Teacher
 Modeling                     student
 Practice                    demonstrates skill
 Games                       Teacher
 Use of Manipulatives         Observation:
 Small Group Instruction      Hand-On
 Teacher observation          Activities both
small and large
group
B. 2   Describe and use geometric        Teacher created math       NJ Test Prep Activities     Teacher
transformations (slide, flip,      enrichment activities      Journal Prompts              Observation:
turn).                                                        Estimation                   Class Discussion
 Reasonableness of           Teacher
 Modeling                     student
 Practice                    demonstrates skill
 Games                       Teacher
 Use of Manipulatives         Observation:
 Small Group Instruction      Hand-On
 Teacher Observation          Activities both
small and large
group
B. 3   Investigate the occurrence of     Trailblazers Unit          Journal Writing             Assessment
geometry in nature and area.       Resource Guide             Use of geometric solids,     Record Sheet
 Unit 2, “Geometric          protractors, rulers,        Journal Prompts
Investigation: An           pattern blocks, tiles       Teacher
Assessment Unit‟           Explore Nature               Observation:
Lessons 1- 6 pp. 121-      Drawings                     students perform
164                        Modeling                     various activities
 Unit 9, “Shapes and        Cooperative Groups           that show mastery
Solids” Lessons 1-3 pp.                                  of area and
662-687 Lesson 5 p.                                      perimeter
695                                                     Unit 2
 Find perimeter

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Math Curriculum
and area of shapes
 SG p. 36
 Drawings
 TIMS Lab
 Unit 9
 Observe students
measuring angles
Standard: 4.2 (GEOMETRY AND MEASUREMENT)

Strand: C. Coordinate Geometry
Cumulative Progress                           Resources                  Suggested Teaching
Date/Notes                                                           Assessments
Indicator                                     (Materials)                Strategies/Activities
C. 1   Locate and name points in the                   Teacher created math      NJ Test Prep Activities    Teacher
first quadrant on a coordinate                   enrichment activities     Journal Prompts             Observation: class
grid.                                                                      Estimation                  discussion
 Reasonableness of          Teacher
 Modeling                    Small group
 Practice                    activities
 Games-“Battleship”
 Use of manipulatives
 Small Group Instruction
 Teacher Observation
C. 2   Use coordinates to give or                      Teacher created math      NJ Test Prep Activities    Teacher
follow directions from one                       enrichment activities     Journal Prompts             Observation: class
point to another on a map or                                               Estimation                  discussion
grid.                                                                      Reasonableness of          Teacher
 Modeling                    Small group
 Practice                    activities
 Games
 Use of Manipulatives
 Small Group Instruction
 Teacher Observation
Page 21
Math Curriculum
Standard: 4.2 (GEOMETRY AND MEASUREMENT)

Strand: D. Units of Measurement
Cumulative Progress                              Resources                  Suggested Teaching
Date/Notes                                                           Assessments
Indicator                                        (Materials)                Strategies/Activities
D. 1   Understand that everyday                           Trailblazers Unit         Journal Writing            Assessment
objects have a variety of                           Resource Guide            Cooperative Groups          Record Sheet
attributes, each of which can                      Unit 8, “Measuring Up:    Oral discussion of         Journal prompts
be measured in many ways.                           An Assessment Unit”        concepts in Adventure      Unit 2
Lesson 1 p.577             book                       Angle Circles
 Unit 2, “Geometric        Exploring objects          Teacher
Investigation: An         Use of solid shapes,        Observation:
Assessment Unit‟           pattern blocks,             student completes
Lessons 6 p.155            protractors, rulers         task
 Unit 9, “Shapes and                                   Unit 9
Solids” Lessons 1-3 pp.                               Measuring angles
662-687
Lesson 5 p. 695
D. 2   Select and use appropriate                         Trailblazers Unit         Use of rulers,             Assessment
standard units of measure and                       Resource Guide             protractors, graduated      Record Sheet
measurement tools to solve                         Unit 2, “Geometric         cylinders, measuring       Journal prompts
real-life problems.                                 Investigation: An          tools                      Unit 2
Length-fractions of an inch                         Assessment Unit‟          Journal writing            Find perimeter
(1/8, 1/4, 1/2), mile, decimeter,                   Lessons 1- 2 pp. 121-     Cooperative Groups          and area of shapes
kilometer                                           139                       Measuring items in room    SG p. 36
Area-square inch, square                           Unit 9, “Shapes and       Journal Writing            Drawings
centimeter                                          Solids” Lessons 6 p.      Games                      TIMS Lab
Volume-cubic inch, cubic                            709                       Discuss units of           Teacher
centimeter                                         Unit 8, “Measuring Up:     measurement, both           Observation- class
Weight-ounce                                        An assessment Unit”        standard and metric         discussion
Capacity-fluid ounce, cup,                          Lessons 1-3 pp. 577-603                               Unit 8
gallon, milliliter                                 Unit 10, “Using                                       Spinner Game:
Decimals” Lesson 1                                     Operation Target
p.755                                                  SG p. 226
 Unit 16, “Assessing Our
Page 22
Math Curriculum
Learning” Lesson 3 p.                                   Unit 9
1186                                                    SG p. 266-267
 Unit 10
 Measuring to
nearest metric unit
 Unit 16
 TIMS Lab-refer to
rubric in URG
 Teacher
Observation-
observe students
completing lab-
teacher and
student
conferencing
D. 3   Develop and use personal             Trailblazers Unit          Measuring items in room    Teacher
referents to approximate              Resource Guide             Journal Writing             Observation:
standard units of measure (e.g.,     Unit 1, “Data About        Games                       student
a common paper clip is about          Us” Lesson 1 -5 pp. 28-    Discuss units of            demonstrates
an inch long).                        73                          measurement, both           understanding of
 Arms Span vs. Height        standard and metric         skills
Lab p. 63                  Cooperative Learning       Teacher
 Unit 10, “Using            Think Pair Share            Observation:
Decimals” Lesson 1         Small Group Instruction     student explains
p.755                      Teacher Observation         reason for picking
unit of measure
 Lab- refer to
rubrics
D. 4   Incorporate estimation in            Trailblazers Unit          Measuring items in room    Teacher
measurement activities (e.g.,         Resource Guide             Journal Writing             Observation:
estimate before measuring).          Unit 10, “Using            Games                       student
Decimals” Lesson 1 p.      Discuss units of            demonstrates
755                         measurement, both           understanding of
 Unit 1, “Data About         standard and metric         skills
Us” Lesson 1 -5 pp. 28-    Games                      Teacher

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Math Curriculum
73                        Cooperative Learning        Observation:
 Arms Span vs. Height      Think Pair Share            student explains
Lab p. 63                 Small Group Instruction     reason for picking
 Teacher Observation         unit of measure
 Lab- refer to
rubrics
D. 5   Solve problems involving                       Teacher created math      Large group Discussion     Teacher
elapsed time.                                   enrichment activities     Clock                       Observation: class
 Journal Writing            Teacher
 NJ Test Prep Activities     Observation:
 Cooperative Learning        Small group
Activities                  activities
 DPP‟s Units 1-16
Standard: 4.2 (GEOMETRY AND MEASUREMENT)

Strand: E. Measuring Geometric Objects
Cumulative Progress                          Resources                   Suggested Teaching
Date/Notes                                                           Assessments
Indicator                                    (Materials)                 Strategies/Activities
E. 1   Determine the area of simple                   Trailblazers Unit          Journal Writing           Assessment
two-dimensional shapes on a                     Resource Guide             Use of tiles               Record Sheet
square grid.                                   Unit 2, “Geometric         Think, Pair, Share        Teacher
Investigation: An          Cooperative Groups         Observation-
Assessment Unit”                                       students finding
Lessons 1-2 pp.121-139                                 area and perimeter
 TIMS Lab- refer
to rubric in URG

 Journal prompt
E. 2   Distinguish between perimeter                  Trailblazers Unit         Journal Writing            Assessment
and area and use each                           Resource Guide            Use of tiles                Record Sheet
appropriately in problem-                      Unit 2, “Geometric        Think, Pair, Share         Teacher
solving situations.                             Investigation: An         Cooperative Groups          Observation-
Assessment Unit”          Journal Writing             students finding

Page 24
Math Curriculum
Lessons 1-2 pp.121-139                                     area and perimeter
 TIMS Lab-refer to
rubric in URG
 Journal prompt
E. 3   Measure and compare the                         Trailblazers Unit          Journal Writing              Rubric- refer to
volume of three-dimensional                      Resource Guide             Use of graduated              URG- Journal
objects using materials such as                 Unit 9, “Shapes and         cylinders, geometric          prompt
rich or cubes.                                   Solids” Lessons 6 p.        solids, connecting cubes,    SG p. 266-267
709                         base ten pieces,             Teacher
 Determine volume of           Observation:
everyday objects              Class
 Cooperative Groups            discussion/class
 Modeling                      activities
Standard: 4.3 (PATTERNS AND ALGEBRA)

Strand: A. Patterns
Cumulative Progress                           Resources                    Suggested Teaching
Date/Notes                                                              Assessments
Indicator                                     (Materials)                  Strategies/Activities
A.1    Recognize, describe, extend,                    Trailblazers Unit           Journal writing             Assessment
and create patterns.                             Resource Guide              Use of calculator            Record Sheet
Descriptions using words,                       Unit 1, “Data About         Practice problems           Journal prompt
number sentences/expressions,                    Us” Lesson 1 -5 pp. 28-     Think, Pair, Share          Students
graphs, tables, variables (e.g.,                 73                          Modeling                     Observation:
shape, blank, or letter)                        Arms Span vs. Height        Game                         students complete
Sequences that stop or that                      Lab p. 63                   Groups share methods         task
continue infinitely                             Unit 2, “Geometric           for solving                 Unit 1
Whole number patterns that                       Investigation: An                                        Students make
grow or shrink as a result of                    Assessment Unit”                                          and interpret bar
repeatedly adding, subtracting,                  Lessons 1-2 pp.121-139                                    graphs
multiplying by, or dividing by                  Unit 6, “Place Value                                     SG p. 6 #7
a fixed number (e.g., 5, 8, 11,                  Patterns” Lesson 2                                       SG p. 10 #1
… or 800, 400, 200, …                            p.424                                                    DPP letter J and T
Sequences can often be                          Unit 15, “Using
extended in more than one way                                                                             Unit 2
Patterns” Lessons 3 – 4                                  TIMS Lab
(e.g., the next term after 1, 2,
Page 25
Math Curriculum
4, could be 8, or 7, or…)                      pp. 1121-1135                                         Unit 6
 DPP letter P
 Unit 15, “Using
Patterns”
 URG 1130-1131
 Quiz
Standard: 4.3 (PATTERNS AND ALGEBRA)

Strand: B. Functions and Relationships
Cumulative Progress                          Resources                    Suggested Teaching
Date/Notes                                                          Assessments
Indicator                                    (Materials)                  Strategies/Activities
B. 1   Use concrete and pictorial                     Trailblazers Unit           Journal Writing         Assessment
models to explore the basic                     Resource Guide              Guess My Rule Game       Record Sheet
concept of a function.                         Unit 1, “Data About         Use of calculator       Journal Prompts
Input/output tables, T-charts                   Us” Lesson 1 -5 pp. 28-     Practice problems       Teacher
Combining two function                          73                          Think, Pair, Share       Observation-
machines                                       Arms Span vs. Height        Modeling                 students
Reversing a function machine                    Lab p. 63                   Game                     demonstrate:
 Unit 5, “Using Data To      Groups share methods    Unit 1
Predict” Lesson 4 p.359      for solving             Students create
 Unit 15, “Using                                       and interpret a bar
Patterns” Lesson 4 p.                                 graph
1132                                                 DPP letter J and T
 TIMS Lab- URG
Rubric
 Unit 5
 TIMS Lab
 Student Rubric
 Unit 15, “Using
Patterns”
 SG. P. 413-414
 Quizzes
Standard: 4.3 (PATTERNS AND ALGEBRA)

Page 26
Math Curriculum
Strand: C. Modeling
Cumulative Progress                          Resources                    Suggested Teaching
Date/Notes                                                              Assessments
Indicator                                    (Materials)                  Strategies/Activities
C. 1   Recognize and describe change                  Trailblazers Unit           Journal writing             Teacher
in quantities.                                  Resource Guide              Use of manipulatives for     Observation- class
Graphs representing change                     Unit 1, „Data About Us”      each TIMS lab.               discussion
over time (e.g., temperature,                   Lesson 5 p.63               Think, Pair, Share          Assessment
height)                                        Unit 3,” Numbers and        Cooperative Groups           Record Sheet
How change in one physical                      Number Operations”          Modeling                    Journal Prompts
quantity can produce a                          Lesson 6 p.244              Discussion of student       Unit 1
corresponding change in                        Unit 5, “Using data To       rubrics for labs.           SG. p. 23
another (e.g., pitch of a sound                 Predict “ Lesson 4 p.                                    URG p. 74-76
depends on the rate of                          359                                                      Unit 3
vibration)                                     Unit 10 “Using                                           URG p. 249
Decimals” Lesson 4                                       Unit 5
p.777                                                    TIMS Lab
 Unit 13, “Division “                                     Student Rubric
Lesson 5 p.1008                                           Solving
 Unit 15, “Using                                          SG p. 143-144 #
Patterns” Lessons 1 – 3                                   10 and 12
pp.1106-1131                                             Unit 10
 Unit 16, “Assessing Our                                  TIMS Lab
“Learning Lessons 3 – 4
 URG p. 787-788
pp. 1186-1209
 Unit 13
 TIMS Lab
 Unit 15, “Using
Patterns”
 SG p. 402-403
 URG p. 1130-
1131
 Unit 16
 TIMS Lab
 URG p. 1206-
1209
Page 27
Math Curriculum
C. 2   Construct and solve simple                        Trailblazers Unit           Journal Writing             Teacher
open sentences involving any                       Resource Guide              Games                        Observation-
one operation (e.g., 3 x 6 = __,                  Unit 4, “Products and       Think, Pair, Share           students
n = 15, 3, 3 x __ = 0, 16 – c =                    Factors” Lessons 1 p. 28     methods of solving           demonstrate:
7).                                                Lesson 5 p.63                equations                    simple facts
 Unit 7, “Patterns in        Use of fraction strips,      understanding
Multiplication” Lessons      calculators,                Journal Prompts
1-5 pp. 500-538             Review of basic facts       Fact quizzes
 Unit 12, “Exploring          and families                Unit 4
Fractions „Lessons 2        Modeling/discussion of      Identify multiples
p.907                        inverse operations          Unit 7
 Practice Sheets             Quiz
 URG p. 527
 SG p. 194 #9
 Unit 12
 SG p. 335 #1-7
Standard: 4.3 (PATTERNS AND ALGEBRA)

Strand: D. Procedures
Cumulative Progress                             Resources                  Suggested Teaching
Date/Notes                                                              Assessments
Indicator                                       (Materials)                Strategies/Activities
D. 1   Understand, name, and apply                       Trailblazers Unit         Journal Writing               Teacher
the properties of operations                       Resource Guide            Use of flashcards, tiles,      Observation- class
and numbers.                                      Unit 3, “Numbers and       calculator,                    discussion &
Commutative (e.g., 3 x 7 = 7 x                     Number Operations”        Practice sheets                complete tasks
3)                                                 Lesson 1 p.201            Methods of break apart,        related to skills
Identity element for                              Unit 4, “Products and      divisibility/multiplicatio    Assessment
multiplication is 1 (e.g., 1 x 8                   Factors “ Lesson 4         n rules and chart              Record Sheet
=8)                                                p.300                     Games                         Journal Prompts
Associative (e.g., 2 x 4 x 25                     Unit 7, “Patterns in      Modeling                      Unit 3
can be found by first                              Multiplication” Lessons                                  DPP letter Q
multiplying either 2 x 4 or 4 x                    1 p. 500 Lesson 7 p.544                                  Identify 5s and
25)                                               Unit 11,                                                  10s
Division by zero is undefined                      “Multiplication”                                         Unit 4
Page 28
Math Curriculum
Any number multiplied by           Lessons 1 – 2 pp. 121-                               Unit 4 Test
zero is zero                       139                                                  Student Rubric
Telling
 Finding Prime
Factors
 Unit 7
 Order of
Operations quiz
 URG p. 547
 Unit 11
 Informal
Assessment
SG p. 302 #20-22
D. 2   Understand and use the             Trailblazers Unit        Journal Writing           Assessment
concepts of equals, less than,      Resource Guide           Games                      Record Sheet
and greater than in simple         Unit 12, “Exploring      Think, Pair, Share        Journal Prompts
number sentences (=, <, >)          Fractions” Lessons 3      methods                   Class Discussion
p.910                    Modeling/discussion       Teacher
 Practice sheets            Observation:
 Independent Practice       Explain how to
 Large Group Discussion     identify a number
 Small Group Activities     is larger than
another number
 Teacher
Observation-
students
demonstrate
understanding of
skill
 Unit 12
 Use fraction strips
to compare
 SG p. 338 # 6-8

Page 29
Math Curriculum
Standard: 4.4 DATA ANALYSIS, PROBABILITY, AND DISCRETE MATHEMATICS

Strand: A. Data Analysis
Cumulative Progress                             Resources                  Suggested Teaching
Date/Notes                                                      Assessments
Indicator                                       (Materials)                Strategies/Activities
A. 1   Collect, generate, organize,                      Trailblazers Unit         Journal Prompt        Assessment
and display data in response to                    Resource Guide            Modeling               Record Sheet
questions, claims, or curiosity.                  Unit 1, “Data About       Cooperative Groups    Journal Prompts
Data collected from the school                     Us” Lesson 1 -5 pp. 28-   Student Rubrics       Unit TIMS Labs
environment                                        73                                               Unit 1
 Arms Span vs. Height                             SG p. 5 #7
Lab p. 63                                        Teacher
 Unit 5, “Using Data To                            Observation-Make
Predict” Lesson 4 p.359                           a bar graph
 Unit 10, “Using                                  Unit 5
Decimals” Lesson 4                               Student Rubric
p.777                                             Solving
 Unit 13, „Division‟                              SG p. 143+144
Lesson 5 p.1008                                   #10-12
 Unit 14, „Chancy                                 Unit 10
Predictions: An                                  URG p. 787-788
Introductory to                                  Unit 13
Probability‟ Lesson 3                            Lab-rubric
p.1052
 Unit 14
 Unit 15, “Using                                  Assessment:
Patterns” Lesson 1                                Check Up
p.1106                                            Assessment p.
1060
 Unit 15, “Using
Patterns”
 Creating and
Interpreting a
Graph
 TIMS LAB
Page 30
Math Curriculum
Activities- refer to
rubrics in Unit
Resource Guides
rubrics
A. 2   Read, interpret, construct,       Trailblazers Unit          Journal Writing              Teacher
analyze, generate questions        Resource Guide             Student Rubrics               Observation-
about, and draw inferences        Unit 1, “Data About        Practice Problems             students complete
from displays of data.             Us” Lesson 1 -5 pp. 28-    Cooperative Groups            and demonstrate
Pictograph, bar graph, line        73                         Group Discussions             understanding of
plot, line graph, table           Arms Span vs. Height       Modeling                      skills.
Average (mean), most frequent      Lab p. 63                  Create and discuss           Class discussion
(mode), middle term (median)      Unit 5, “Using Data To      various graphs and tables    Assessment
Predict” Lesson 4 p.359                                   Record Sheet
 Unit 10, “Using                                          Journal Prompts
Decimals” Lesson 4                                       Unit 1
p.777                                                    SG p. 5 + 6
 Unit 13, „Division‟                                      URG p. 37
Lesson 5 p.1008                                          DPP letter T
 Unit 14, „Chancy                                         SG p. 10 #1
Predictions: An                                          Unit 5
Introductory to                                          SG p. 131 #3
Probability‟ Lesson 3                                    URG p. 358
p.1052                                                   Student Rubric
 Unit 15, “Using                                           Telling
Patterns” Lesson 1                                       Student Rubric
p.1106                                                    Solving
 Unit 16, „Assessing Our                                  Unit 10
Learning” Lessons 2-4
 URG p. 787+788
pp. 1184-1209
 Unit 13
 Lab
 Unit 15, “Using
Patterns”
 SG p. 401 #11-15
 Student Rubric
Page 31
Math Curriculum
Telling
 SG p. 419-421 #
13-15
 Unit 16
 URG p. 1206-
1209
 TIMS LAB
Activities- refer to
rubrics in Unit
Resource Guides
rubrics
Standard: 4.4 DATA ANALYSIS, PROBABILITY, AND DISCRETE MATHEMATICS

Strand: B. Probability
Cumulative Progress                           Resources                     Suggested Teaching
Date/Notes                                                              Assessments
Indicator                                     (Materials)                   Strategies/Activities
B. 1   Use everyday events and                         Trailblazers Unit            Journal Writing            Teacher
chance devices, such as dice,                    Resource Guide               Cooperative Learning        Observation &
coins, and unevenly divided                     Unit 14, „Chancy             Think Pair Share            class discussion
spinners, to explore concepts                    Predictions: An              Small Group Instruction    Student
of probability.                                  Introductory to              Teacher Observation         demonstrates
Likely, unlikely, certain,                       Probability‟ Lesson 2-7      Modeling                    understanding by
impossible                                       pp.1050-1080                                              explaining
More likely, less likely,                                                                                  probability
equally likely
B. 2   Determine probabilities of                      Trailblazers Unit           Journal Writing             Teacher
simple events based on equally                   Resource Guide              Cooperative Learning         Observation: class
likely outcomes and express                     Unit 14, „Chancy            Think Pair Share             discussion
them as fractions.                               Predictions: An             Small Group Instruction     Students explain
Introductory to             Teacher Observation          and demonstrate
Probability‟ Lesson 1 p.    Modeling                     skill
1106 Lesson 3 p.1052                                     Journal Prompts
B. 3   Predict probabilities in a                      Trailblazers Unit           Cooperative Learning        Teacher
variety of situations (e.g.,                     Resource Guide              Think Pair Share             Observation: class
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Math Curriculum
given the number of items of                        Unit 14, „Chancy           Small Group Instruction      discussion
each color in a bag, what is the                     Predictions: An            Journal Writing             Students explain
probability that an item picked                      Introductory to            Teacher Observation          and demonstrate
will have a particular color).                       Probability‟ Lesson 1-7    Modeling                     skill
What students think will                             pp.1006-1080                                            Journal Prompts
happen (intuitive)                                                                                           TIMS LAB
Collect data and use that data                                                                                Activities- refer to
to predict the probability                                                                                    rubrics in Unit
(experimental)                                                                                                Resource Guides
rubrics
Standard: 4.4 DATA ANALYSIS, PROBABILITY, AND DISCRETE MATHEMATICS

Strand: C. Discrete Mathematics-Systematic Listing and Counting
Cumulative Progress                               Resources                    Suggested Teaching
Date/Notes                                                               Assessments
Indicator                                         (Materials)                  Strategies/Activities
C. 1   Represent and classify data                         Trailblazers Unit           Cooperative Learning       Teacher
according to attributes, such as                     Resource Guide              Small Group Instruction     Observation:
shape or color, and                                 Units 1-16                  Journal Writing             Students explain
relationships.                                      Unit 14, „Chancy            Teacher Observation         the difference
Venn diagrams                                        Predictions: An             Modeling                    between
Numerical and alphabetical                           Introductory to                                          categorical and
order                                                Probability‟ Lesson 1-7                                  numerical
pp.1006-1080                                             variables
 Numerical and
Categorical
Variable
discussion
 Teacher
Observation:
Classification of
Items based on
certain
characteristics
 Student explains
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Math Curriculum
why they have
grouped items
 TIMS LAB
Activities- refer to
rubrics in Unit
Resource Guides
rubrics
 Teacher
Observation-
 Student explains
patterns within
multiplication
C. 2   Represent all possibilities for a     Trailblazers Unit          Journal Prompts            Teacher
simple counting situation in an        Resource Guide             Estimation                  Observation: class
organized way and draw                Units 1- 16                Reasonableness of           discussion
representation.                        Us” Lesson 1 -5 pp. 28-    Modeling                    Observation:
Organized lists, charts, tree          73                         Practice                    student
diagrams                              Arms Span vs. Height       Games                       demonstrates
Dividing into categories (e.g.,                                                                knowledge of
Lab p. 63                  Use of Manipulatives
to find the total number of           Unit 2, “Geometric         Small Group Instruction    skills
rectangles in a grid, find the         Investigations: A          Teacher Observation        Teacher
number or rectangles of each           Baseline Assessment                                     Observation:
size and add the results)              Unit” Lesson 2-5 pp.                                    students complete
128-154                                                 and explain lab
 Perimeter vs. Length                                    activities
Lab p.128                                              URG 8
 Unit 3, “Numbers and                                   Mid Year Test
Number Operations”                                     URG 16
Lesson 1-6 pp.201-244                                  End of Year Exam
249                                                    TIMS LAB
 Unit 5, “Using Data to                                  Activities- refer to
Predict” Bouncing Ball                                  rubrics in Unit
Lesson 4 p.359 Lesson                                   Resource Guides
1-5 pp. 336-374
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Math Curriculum
 Unit 4, “Products and                                   and teacher Made
Factors” Lesson 2 -6                                    rubrics.
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15 “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
Standard: 4.4 DATA ANALYSIS, PROBABILITY, AND DISCRETE MATHEMATICS

Strand: D. Discrete Mathematics-Vertex-Edge Graphs and Algorithms
Cumulative Progress                             Resources                    Suggested Teaching
Date/Notes                                                                 Assessments
Indicator                                       (Materials)                  Strategies/Activities
D. 1   Follow, devise, and describe                      Trailblazers Unit           Journal Prompts            Teacher
practical sets of directions                       Resource Guide              Estimation                  Observation: class
(e.g., to add two 2-digit                         Unit 1-16                   Reasonableness of           discussion
numbers).                                         Unit 3: “Numbers and         Answer                     Teacher
Number Operations”          Modeling                    Observation:
 Unit 4: “Products and       Practice                    student
Factors”                    Games                       demonstrates
 Use of Manipulatives        knowledge of
 Small Group Instruction    skills
 Teacher Observation        Teacher
Observation:
students complete
and explain lab
activities URG 8
 Mid Year Test

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Math Curriculum
 URG 16
 End of Year Exam
D. 2   Play two-person games and           Trailblazers Unit          Cooperative Learning       Teacher
devise strategies for winning        Resource Guide             Think Pair Share            Observation
the games (e.g., “make 5”           Unit Resource Guide        Small Group Instruction    Class Discussion
where players alternately add 1     Unit 4, „Products and      Journal Writing            Teacher
or 2 and the person who              Factors” Lesson 3 p.297    Teacher Observation         Observation:
reaches 5, or another                Lesson 5 p. 307            Modeling                    small group
designated number, is the           Unit 6, “Decimals”                                      activities
winner).                             Lesson 5 p. 446
 Unit 12, “Exploring
Fractions” Lesson 4 p.
915 Lesson 8 p. 935
 Unit 14, “Chancy
Predictions: An
Introductory to
Probability” Lesson 2
p.1050
 Unit 15, “Using
Patterns” Lesson 4 p.
1132
 Games
D. 3   Explore vertex-edge graphs          Teacher created            Cooperative Learning       Teacher
and tree diagrams.                   enrichment math            Think Pair Share            Observation
Vertex, edge,                        activities to teach and    Small Group Instruction    Class Discussion
neighboring/adjacent, number         reinforce skill            Journal Writing            Teacher
of neighbors                      (addressed in Daily           Teacher Observation         Observation:
Path, circuit (i.e., path that    Practice Problems (DPP‟s)     Modeling                    small group
ends at its starting point)       Units 1-16)                                                activities
D. 4   Find the smallest number of         Teacher created            Cooperative Learning       Teacher
colors needed to color a map         enrichment activities      Think Pair Share            Observation
or a graph.                          (covered in social         Small Group Instruction    Class Discussion
studies curriculum)        Journal Writing            Teacher
 Teacher Observation         Observation:
 Modeling                    small group

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Math Curriculum
activities
Standard: 4.5 (MATHEMATICAL PROCESSES)

Strand: A. Problem Solving
Cumulative Progress                          Resources                   Suggested Teaching
Date/Notes                                                            Assessments
Indicator                                    (Materials)                 Strategies/Activities
A. 1   Learn mathematics through                      Trailblazers Unit          Journal Prompts            Teacher
problem solving, inquiry, and                   Resource Guide             Estimation                  Observation-
discovery.                                     Units 1-16                 Reasonableness of           student
Us” Lesson 1 -5 pp. 28-    Modeling                    understanding of
73                         Practice                    skill
 Unit 2, “Geometric         Games                      Students complete
Investigations: A          Use of Manipulatives        and explain lab
Baseline Assessment        Small Group Instruction     activities
Unit” Lesson 2-5 pp.       Teacher Observation        Class Discussion
128-154                                                URG 8
 Perimeter vs. Length                                   Mid Year Test
Lab p.128                                              URG 16
 Unit 3, “Numbers and                                   End of Year Exam
Number Operations”                                     TIMS LAB
Lesson 1-6 pp.201-244                                   Activities- refer to
249                                                     rubrics in Unit
 Unit 5, “Using Data to                                  Resource Guides
Predict” Bouncing Ball                                  and teacher Made
Lesson 4 p.359 Lesson                                   rubrics.
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns

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Math Curriculum
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
 Unit 10, “Using
Decimals” Lesson
4p.777
 Unit 14, Chancy
Predictions: An
Introductory to
Probability Lesson 3 p.
1052
A. 2   Solve problems that arise in       Trailblazers Unit          Journal Prompts            Teacher
mathematics and in other            Resource Guide             Estimation                  Observation-
contexts (cf. workplace            Units 1-16                 Reasonableness of           student
Open-ended problems                 Us” Lesson 1 -5 pp. 28-    Modeling                    understanding of
Non-routine problems                73                         Practice                    skill
Problems with multiple             Arms Span vs. Height       Games                      Students complete
solutions                                                                                   and explain lab
Lab p. 63                  Use of Manipulatives
Problems that can be solved in     Unit 2, “Geometric                                      activities
 Small Group Instruction
several ways                        Investigations: A          Teacher Observation        Class Discussion
Baseline Assessment                                    URG 8
Unit” Lesson 2-5 pp.                                   Mid Year Test
128-154                                                URG 16
 Perimeter vs. Length                                   End of Year Exam
Lab p.128                                              TIMS LAB
 Unit 3, “Numbers and                                    Activities- refer to
Number Operations”                                      rubrics in Unit
Lesson 1-6 pp.201-244                                   Resource Guides
 Unit 5, “Using Data to                                  rubrics.

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Math Curriculum
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
A. 3   Select and apply a variety of        Trailblazers Unit           Journal Prompts            Teacher
appropriate problem-solving           Resource Guide              Estimation                  Observation-
strategies (e.g., “try a simpler     Units 1-16 Unit 1, “Data    Reasonableness of           student
diagram”) to solve problems.          pp. 28-73                   Modeling                    understanding of
 Arms Span vs. Height        Practice                    skill
Lab p. 63                   Games                      Students complete
 Unit 2, “Geometric          Use of Manipulatives        and explain lab
Investigations: A           Small Group Instruction     activities
Baseline Assessment         Teacher Observation        Class Discussion
Unit” Lesson 2-5 pp.                                    URG 8
128-154                                                 Mid Year Test
 Perimeter vs. Length                                    URG 16
Lab p.128                                               End of Year Exam
 Unit 3, “Numbers and                                    TIMS LAB
Number Operations”                                       Activities- refer to
Lesson 1-6 pp.201-244                                    rubrics in Unit
249                                                      Resource Guides

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Math Curriculum
 Unit 5, “Using Data to                                  and teacher Made
Predict” Bouncing Ball                                  rubrics.
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
A. 4   Pose problems of various types     Trailblazers Unit           Journal Prompts            Teacher
and levels of difficulty.           Resource Guide              Estimation                  Observation-
 Units 1-16                  Reasonableness of           student
Us” Lesson 1 -5 pp. 28-     Modeling                    understanding of
73                          Practice                    skill
 Arms Span vs. Height        Games                      Students complete
Lab p. 63                   Use of Manipulatives        and explain lab
 Unit 2, “Geometric          Small Group Instruction     activities
Investigations: A           Teacher Observation        Class Discussion
Baseline Assessment                                     URG 8
Unit” Lesson 2-5 pp.                                    Mid Year Test
128-154                                                 URG 16
 Perimeter vs. Length                                    End of Year Exam
Lab p.128                                               TIMS LAB
 Unit 3, “Numbers and                                     Activities- refer to
Number Operations”                                       rubrics in Unit

Page 40
Math Curriculum
Lesson 1-6 pp.201-244                                   Resource Guides
 Unit 5, “Using Data to                                  rubrics.
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
A. 5   Monitor their progress and          Trailblazers Unit           Journal Prompts            Teacher
reflect on the process of their      Resource Guide              Estimation                  Observation-
problem solving activity.           Units 1-16                  Reasonableness of           student
Us” Lesson 1 -5 pp. 28-     Modeling                    understanding of
73                          Practice                    skill
 Arms Span vs. Height        Games                      Students complete
Lab p. 63                   Use of Manipulatives        and explain lab
 Unit 2, “Geometric          Small Group Instruction     activities
Investigations: A           Teacher Observation        Class Discussion
Baseline Assessment                                     URG 8
Unit” Lesson 2-5 pp.                                    Mid Year Test
128-154                                                 URG 16
 Perimeter vs. Length                                    End of Year Exam
Lab p.128                                               TIMS LAB

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Math Curriculum
 Unit 3, “Numbers and                                Activities- refer to
Number Operations”                                  rubrics in Unit
Lesson 1-6 pp.201-244                               Resource Guides
 Unit 5, “Using Data to                              rubrics.
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
Standard: 4.5 (MATHEMATICAL PROCESSES)

Strand: B. Communication
Cumulative Progress                       Resources                     Suggested Teaching
Date/Notes                                                         Assessments
Indicator                                 (Materials)                   Strategies/Activities
B. 1   Use communication to                        Trailblazers Unit            Journal Prompts       Teacher
organize and clarify their                   Resource Guide               Estimation             Observation-
mathematical thinking.                      Unit Resource Guide          Reasonableness of      student
Discussion, listening, and                  Unit 1, “Data About          Modeling               understanding of
questioning                                  Us” Lesson 1 -5 pp. 28-      Practice               skill
73                           Games                 Students complete
and explain lab
Page 42
Math Curriculum
 Arms Span vs. Height        Use of Manipulatives        activities
Lab p. 63                   Small Group Instruction    TIMS LAB
 Unit 2, “Geometric          Teacher Observation         Activities- refer to
Investigations: A                                        rubrics in Unit
Baseline Assessment                                      Resource Guides
Unit” Lesson 2-5 pp.                                     and teacher Made
128-154                                                  rubrics.
 Perimeter vs. Length                                    Class Discussion
Lab p.128                                               URG 8
 Unit 3, “Numbers and                                    Mid Year Test
Number Operations”                                      URG 16
Lesson 1-6 pp.201-244                                   End of Year Exam
249
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
B. 2   Communicate their                    Trailblazers Unit           Journal Prompts            Teacher
mathematical thinking                 Resource Guide              Estimation                  Observation-
coherently and clearly to peers,     Units 1-16                  Reasonableness of           student
orally and in writing.
Page 43
Math Curriculum
Us” Lesson 1 -5 pp. 28-     Modeling                    understanding of
73                          Practice                    skill
 Arms Span vs. Height        Games                      TIMS LAB
Lab p. 63                   Use of Manipulatives        Activities- refer to
 Unit 2, “Geometric          Small Group Instruction     rubrics in Unit
Investigations: A           Teacher Observation         Resource Guides
Unit” Lesson 2-5 pp.                                     rubrics.
128-154                                                 Class Discussion
 Perimeter vs. Length                                    URG 8
Lab p.128                                               Mid Year Test
 Unit 3, “Numbers and                                    URG 16
Number Operations”                                      End of Year Exam
Lesson 1-6 pp.201-244
249
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
B. 3   Analyze and evaluate the      Trailblazers Unit           Journal Prompts            Teacher
mathematical thinking and      Resource Guide              Estimation                  Observation: class
strategies of others.
Page 44
Math Curriculum
 Units 1-16                  Reasonableness of           discussion
Us” Lesson 1 -5 pp. 28-     Modeling                    Observation:
73                          Practice                    small group
 Arms Span vs. Height        Games                       activities
Lab p. 63                   Use of Manipulatives       TIMS LAB
 Unit 2, “Geometric          Small Group Instruction     Activities- refer to
Investigations: A           Teacher Observation         rubrics in Unit
Baseline Assessment                                      Resource Guides
Unit” Lesson 2-5 pp.                                     and teacher Made
128-154                                                  rubrics.
 Perimeter vs. Length                                    URG 8
Lab p.128                                               Mid Year Test
 Unit 3, “Numbers and                                    URG 16
Number Operations”                                      End of Year Exam
Lesson 1-6 pp.201-244
249
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008

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Math Curriculum
B. 4   Use the language of               Trailblazers Unit           Journal Prompts            Class Discussion
mathematics to express             Resource Guide              Estimation                 Teacher
mathematical ideas precisely.     Units 1-16                  Reasonableness of           Observation:
Us” Lesson 1 -5 pp. 28-     Modeling                    verbally
73                          Practice                   TIMS LAB
 Arms Span vs. Height        Games                       Activities- refer to
Lab p. 63                   Use of Manipulatives        rubrics in Unit
 Unit 2, “Geometric          Small Group Instruction     Resource Guides
Investigations: A           Teacher Observation         and teacher Made
Baseline Assessment                                      rubrics.
Unit” Lesson 2-5 pp.                                    URG 8
128-154                                                 Mid Year Test
 Perimeter vs. Length                                    URG 16
Lab p.128                                               End of Year Exam
 Unit 3, “Numbers and
Number Operations”
Lesson 1-6 pp.201-244
249
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777

Page 46
Math Curriculum
 Unit 13, “Division”
Lesson 5 p.1008
Standard: 4.5 (MATHEMATICAL PROCESSES)

Strand: C. Connections
Cumulative Progress                        Resources                    Suggested Teaching
Date/Notes                                                             Assessments
Indicator                                  (Materials)                  Strategies/Activities
C. 1   Recognize recurring themes                   Trailblazers Unit           Journal Prompts            Teacher
across mathematical domains                   Resource Guide              Estimation                  Observation: class
(e.g., patterns in number,                   Units 1-16                  Reasonableness of           discussion
algebra, and geometry).                      Unit 1, “Data About          Answer                     URG 8
Us” Lesson 1 -5 pp. 28-     Modeling                   Mid Year Test
73                          Practice                   URG 16
 Arms Span vs. Height        Games                      End of Year Exam
Lab p. 63                   Use of Manipulatives
 Unit 2, “Geometric          Small Group Instruction
Investigations: A           Teacher Observation
Baseline Assessment
Unit” Lesson 2-5 pp.
128-154
 Perimeter vs. Length
Lab p.128
 Unit 3, “Numbers and
Number Operations”
Lesson 1-6 pp.201-244
249
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our

Page 47
Math Curriculum
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
C. 2   Use connections among               Teacher created math        Connect literature where    Teacher
mathematical ideas to explain        enrichment activities        applicable                   observation of
concepts (e.g., two linear                                       Inquiry Strategies           student response
equations have a unique                                          Think Pair Share             tin group
solution because the lines they                                  Cooperative Learning         discussion
represent intersect at a single                                   Groups
point).
C. 3   Recognize that mathematics is       Trailblazers Unit           Journal Prompts             URG 8
used in a variety of contexts        Resource Guide              Estimation                  Mid Year Test
outside of mathematics.             Unit Resource Guide         Reasonableness of           URG 16
 Units 1-16                   Answer                      End of Year Exam
 Unit 1, “Data About         Modeling                    TIMS LAB
Us” Lesson 1 -5 pp. 28-     Practice                     Activities- refer to
73                          Games                        rubrics in Unit
 Arms Span vs. Height        Use of Manipulatives         Resource Guides
Lab p. 63                   Small Group Instruction      and teacher Made
 Unit 2, “Geometric          Teacher Observation          rubrics.
Investigations: A
Baseline Assessment
Unit” Lesson 2-5 pp.
128-154
 Perimeter vs. Length
Lab p.128
 Unit 3, “Numbers and
Number Operations”

Page 48
Math Curriculum
Lesson 1-6 pp.201-244
249
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
C. 4   Apply mathematics in                  Trailblazers Unit           Journal Prompts            URG 8
practical situations and in other      Resource Guide              Estimation                 Mid Year Test
disciplines.                          Unit Resource Guide         Reasonableness of          URG 16
 Units 1-16                   Answer                     End of Year Exam
 Unit 1, “Data About         Modeling
Us” Lesson 1 -5 pp. 28-     Practice
73                          Games
 Arms Span vs. Height        Use of Manipulatives
Lab p. 63                   Small Group Instruction
 Unit 2, “Geometric          Teacher Observation
Investigations: A
Baseline Assessment
Unit” Lesson 2-5 pp.
128-154
 Perimeter vs. Length

Page 49
Math Curriculum
Lab p.128
 Unit 3, “Numbers and
Number Operations”
Lesson 1-6 pp.201-244
249
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
C. 5   Trace the development of            Trailblazers Unit           Modeling                   Teacher
mathematical concepts over           Resource Guide              Practice                    Observation: class
time and across cultures (cf.       Unit 3, “Numbers and        Games                       discussion
world languages and social           Number Operations”          Small Group Instruction
studies standards).                  Lesson 2 p.206              Teacher Observation
C. 6   Understand how mathematical         Trailblazers Unit           Journal Prompts            Teacher
ideas interconnect and build on      Resource Guide              Estimation                  Observation: class
one another to produce a            Units 1-16                  Reasonableness of           discussion
Us” Lesson 1 -5 pp. 28-     Modeling                   Mid Year Test
73                          Practice                   URG 16
 Arms Span vs. Height        Games                      End of Year Exam
Page 50
Math Curriculum
Lab p. 63                   Use of Manipulatives
 Unit 2, “Geometric          Small Group Instruction
Investigations: A           Teacher Observation
Baseline Assessment
Unit” Lesson 2-5 pp.
128-154
 Perimeter vs. Length
Lab p.128
 Unit 3, “Numbers and
Number Operations”
Lesson 1-6 pp.201-244
249
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
Standard: 4.5 (MATHEMATICAL PROCESSES)

Strand: D. Reasoning
Cumulative Progress                 Resources                     Suggested Teaching
Date/Notes                                                             Assessments
Indicator                           (Materials)                   Strategies/Activities
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Math Curriculum
D. 1   Recognize that mathematical       Trailblazers Unit           Journal Prompts            Teacher
facts, procedures, and claims      Resource Guide              Estimation                  Observation:
must be justified.                Unit 1, “Data About         Reasonableness of           students complete
73                          Modeling                   Class Discussion
 Arms Span vs. Height        Practice                   Quizzes
Lab p. 63                   Games                      TIMS LAB
 Unit 2, “Geometric          Use of Manipulatives        Activities- refer to
Investigations: A           Small Group Instruction     rubrics in Unit
Baseline Assessment         Teacher Observation         Resource Guides
Unit” Lesson 2-5 pp.                                     and teacher Made
128-154                                                  rubrics.
 Perimeter vs. Length                                    URG 8
Lab p.128                                               Mid Year Test
 Unit 3, “Numbers and                                    URG 16
Number Operations”                                      End of Year Exam
Lesson 1-6 pp.201-244
249
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”

Page 52
Math Curriculum
Lesson 5 p.1008
D. 2   Use reasoning to support their     Trailblazers Unit           Journal Prompts            Teacher
mathematical conclusions and        Resource Guide              Estimation                  Observation
problem solutions.                 Unit 1, “Data About         Reasonableness of          Units 1-16 Lab
Us” Lesson 1 -5 pp. 28-      Answer                      activities- refer to
73                          Modeling                    rubric
 Arms Span vs. Height        Practice                   Teacher
Lab p. 63                   Games                       Observation:
 Unit 2, “Geometric          Use of Manipulatives        students complete
Investigations: A           Small Group Instruction     task
Baseline Assessment         Teacher Observation        TIMS LAB
Unit” Lesson 2-5 pp.                                     Activities- refer to
128-154                                                  rubrics in Unit
 Perimeter vs. Length                                     Resource Guides
 Unit 3, “Numbers and                                     rubrics.
Number Operations”                                      Class Discussion
Lesson 1-6 pp.201-244                                   Quizzes
249                                                     URG 8
 Unit 5, “Using Data to                                  Mid Year Test
Predict” Bouncing Ball                                  URG 16
Lesson 4 p.359 Lesson                                   End of Year Exam
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777

Page 53
Math Curriculum
 Unit 13, “Division”
Lesson 5 p.1008
D. 3   Select and use various types of     Trailblazers Unit           Journal Prompts            Teacher
reasoning and methods of             Resource Guide              Estimation                  Observation:
proof.                              Unit Resource Guide         Reasonableness of          Class Discussion
 Units 1-16                   Answer                     Teacher
 Unit 1, “Data About         Modeling                    Observation:
Us” Lesson 1 -5 pp. 28-     Practice                    students complete
 Arms Span vs. Height        Use of Manipulatives       Class Discussion
Lab p. 63                   Small Group Instruction    TIMS LAB
 Unit 2, “Geometric          Teacher Observation         Activities- refer to
Investigations: A                                        rubrics in Unit
Baseline Assessment                                      Resource Guides
Unit” Lesson 2-5 pp.                                     and teacher Made
128-154                                                  rubrics.
 Perimeter vs. Length                                    Quizzes
Lab p.128                                               URG 8
 Unit 3, “Numbers and                                    Mid Year Test
Number Operations”                                      URG 16
Lesson 1-6 pp.201-244                                   End of Year Exam
249
 Unit 5, “Using Data to
predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106

Page 54
Math Curriculum
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
D. 4   Rely on reasoning, rather than      Trailblazers Unit           Journal Prompts            Teacher
answer keys, teachers, or            Resource Guide              Estimation                  Observation
peers, to check the correctness     Units 1-16                  Reasonableness of          Units 1-16 Lab
of their problem solutions.         Unit 1, “Data About          Answer                      activities- refer to
Us” Lesson 1 -5 pp. 28-     Modeling                    rubric
73                          Practice                   Teacher
 Arms Span vs. Height        Games                       Observation:
Lab p. 63                   Use of Manipulatives        students complete
 Unit 2, “Geometric          Small Group Instruction     task
Investigations: A           Teacher Observation        Class Discussion
Baseline Assessment                                     Quizzes
Unit” Lesson 2-5 pp.                                    URG 8
128-154                                                 Mid Year Test
 Perimeter vs. Length                                    URG 16
Lab p.128                                               End of Year Exam
 Unit 3, “Numbers and
Number Operations”
Lesson 1-6 pp.201-244
249
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns

Page 55
Math Curriculum
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
D. 5   Make and investigate              Trailblazers Unit          Journal Prompts            Teacher
mathematical conjectures.          Resource Guide             Estimation                  Observation
Counterexamples as a means        Units 1-16                 Reasonableness of          Units 1-16 Lab
of disproving conjectures         Unit 1, “Data About         Answer                      activities- refer to
Verifying conjectures using        Us” Lesson 1 -5 pp. 28-    Modeling                    rubric
informal reasoning or proofs.      73                         Practice                   Teacher
 Arms Span vs. Height       Games                       Observation:
Lab p. 63                  Use of Manipulatives        students complete
 Unit 2, “Geometric         Small Group Instruction     task
Investigations: A          Teacher Observation        Class Discussion
Baseline Assessment                                    Quizzes
Unit” Lesson 2-5 pp.                                   URG 8
128-154                                                Mid Year Test
 Perimeter vs. Length                                   URG 16
Lab p.128                                              End of Year Exam
 Unit 3, “Numbers and
Number Operations”
Lesson 1-6 pp.201-244
249
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.

Page 56
Math Curriculum
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
D. 6   Evaluate examples of           Trailblazers Unit           Journal Prompts            Teacher
mathematical reasoning and      Resource Guide              Estimation                  Observation
determine whether they are     Unit 1-16                   Reasonableness of          Units 1-16 Lab
Us” Lesson 1 -5 pp. 28-     Modeling                    rubric
73                          Practice                   Teacher
 Arms Span vs. Height        Games                       Observation:
Lab p. 63                   Use of Manipulatives        students complete
 Unit 2, “Geometric          Small Group Instruction     task
Investigations: A           Teacher Observation        Class Discussion
Baseline Assessment                                     Quizzes
Unit” Lesson 2-5 pp.                                    URG 8
128-154                                                 Mid Year Test
 Perimeter vs. Length                                    URG 16
Lab p.128                                               End of Year Exam
 Unit 3, “Numbers and
Number Operations”
Lesson 1-6 pp.201-244
249
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309

Page 57
Math Curriculum
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
Standard: 4.5 (MATHEMATICAL PROCESSES)

Strand: E. Representations
Cumulative Progress                           Resources                     Suggested Teaching
Date/Notes                                                              Assessments
Indicator                                     (Materials)                   Strategies/Activities
E. 1   Create and use representations                  Trailblazers Unit            Journal Prompts            Teacher
to organize, record, and                         Resource Guide               Estimation                  Observation
communicate mathematical                        Unit 1, “Data About          Reasonableness of          Units 1-16 Lab
ideas.                                           Us” Lesson 1 -5 pp. 28-       Answer                      activities- refer to
Concrete representations (e.g.,                  73                           Modeling                    rubric
base-ten blocks or algebra                      Arms Span vs. Height         Practice                   Teacher
tiles)                                           Lab p. 63                    Game                        Observation:
Pictorial representations (e.g.,                Unit 2, “Geometric           Use of Manipulatives        students complete
Investigations: A            Small Group Instruction
Symbolic representations (e.g.,                  Baseline Assessment          Teacher Observation        Class Discussion
a formula)                                       Unit” Lesson 2-5 pp.                                     Quizzes
Graphical representations (e.g.,                 128-154                                                  URG 8
a line graph)                                   Perimeter vs. Length                                     Mid Year Test
Lab p.128                                                URG 16
 Unit 3, “Numbers and                                     End of Year Exam
Number Operations”
Lesson 1-6 pp.201-244
249

Page 58
Math Curriculum
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
E. 2   Select, apply, and translate     Trailblazers Unit           Journal Prompts            Teacher
among mathematical                Resource Guide              Estimation                  Observation
representations to solve         Units 1- 16                 Reasonableness of          Units 1-16 Lab
Us” Lesson 1 -5 pp. 28-     Modeling                    rubric
73                          Practice                   Teacher
 Arms Span vs. Height        Games                       Observation:
Lab p. 63                   Use of Manipulatives        students complete
 Unit 2, “Geometric          Small Group Instruction     task
Investigations: A           Teacher Observation        Class Discussion
Baseline Assessment                                     Quizzes
Unit” Lesson 2-5 pp.                                    URG 8
128-154                                                 Mid Year Test
 Perimeter vs. Length                                    URG 16
Lab p.128                                               End of Year Exam
 Unit 3, “Numbers and
Number Operations”

Page 59
Math Curriculum
Lesson 1-6 pp.201-244
249
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
 Unit 15, “Using
Patterns” , Using
Patterns Lesson 1, 3, 4,
5, and 6
E. 3   Use representations to model        Trailblazers                Journal Prompts             Units 1-16 Lab
and interpret physical, social,     Unit Resource Guide         Estimation                   activities- refer to
and mathematical phenomena.         Units 1-16                  Reasonableness of            rubric
Us” Lesson 1 -5 pp. 28-     Modeling                     Observation-
73                          Practice                     Class discussion
 Arms Span vs. Height        Games                       Teacher
Lab p. 63                   Use of Manipulatives         Observation-
 Unit 2, “Geometric          Small Group Instruction      students
Investigations: A           Teacher Observation          demonstrates
knowledge after
Baseline Assessment         Discrete Math Activities
Page 60
Math Curriculum
Unit” Lesson 2-5 pp.        NJ Test Prep Activities         and giving
128-154                                                      reasoning for
 Perimeter vs. Length                                         his/her answers
Lab p.128                                                    (Discrete Math
 Unit 3, “Numbers and                                         Activities)
Number Operations”                                          URG 8
Lesson 1-6 pp.201-244                                       Mid Year Test
249                                                         URG 16
 Unit 5, “Using Data to                                      End of Year Exam
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using Patterns
Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
Standard: 4.5 (MATHEMATICAL PROCESSES)

Strand: F. Technology
Cumulative Progress                      Resources                     Suggested Teaching
Date/Notes                                                                 Assessments
Indicator                                (Materials)                   Strategies/Activities
F. 1   Use technology to gather,                  Teacher created math         Computer Software             Teacher
analyze, and communicate                    enrichment activities        Computer generated             Observation of
mathematical information.                                                 math activities to present     student
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Math Curriculum
math information
F. 2   Use computer spreadsheets,            Teacher created math       Computer Software           Teacher
software, and graphing utilities       enrichment activities      Visual presentation of       Observation of
to organize and display                                            quantitative information     student
F. 3   Use graphing calculators and          Teacher created math       Computer Software to        Teacher
computer software to                   enrichment activities       make connections with        Observation of
investigate properties of                                          math and technology re:      student
functions and their graphs.                                        graphs and their             tasks/activities
functions
 Graphing Activities
F. 4   Use calculators as problem-           Trailblazers Unit          Journal Prompts             Teacher
solving tools (e.g., to explore        Resource Guide             Estimation                   Observation
patterns, to validate solutions).     Units 1-16                 Reasonableness of           Units 1-16 Lab
Us” Lesson 1 -5 pp. 28-    Modeling                     rubric
73                         Practice                    Teacher
 Arms Span vs. Height       Games                        Observation:
Lab p. 63                  Use of manipulatives         students complete
 Unit 2, “Geometric         Small group instruction      task
Investigations: A          Teacher observation         Class Discussion
Baseline Assessment                                     Quizzes
Unit” Lesson 2-5 pp.                                    URG 8
128-154                                                 Mid Year Test
 Perimeter vs. Length                                    URG 16
Lab p.128                                               End of Year Exam
 Unit 3, “Numbers and
Number Operations”
Lesson 1-6 pp.201-244
249
 Unit 5, “Using Data to
Predict” Bouncing Ball
Lesson 4 p.359 Lesson
1-5 pp. 336-374
 Unit 4, “Products and

Page 62
Math Curriculum
Factors” Lesson 2 -6
pp.292- 309
 Unit 16, “Assessing Our
Learning” Lesson 3 p.
1186
 Unit 15, “Using
Patterns, Make Your
Own” Lesson 1 p. 1106
 Unit 10, “Using
Decimals” Lesson 4
p.777
 Unit 13, “Division”
Lesson 5 p.1008
F. 5   Use computer software to          Teacher created            Computer Software to     Teacher
make and verify conjectures        enrichment math             enhance understanding     Observation of
about geometric objects.           activities                  of geometry               student