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									                                                        Math Curriculum
                                                         Fourth Grade
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
                                                                                                                Oral reading and
                                                                                                                 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

                                                              Page 1
                                      Math Curriculum
                                       Fourth Grade
                                                                                                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
                                             Page 2
                                        Math Curriculum
                                         Fourth Grade
       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

                                               Page 3
                                         Math Curriculum
                                          Fourth Grade
                                            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
                                           Make Your Own”
                                            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

                                                Page 4
                                            Math Curriculum
                                             Fourth Grade
                                                                                                     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)


                                                   Page 5
                                                      Math Curriculum
                                                       Fourth Grade
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

                                                             Page 6
                                         Math Curriculum
                                          Fourth Grade
                                                                                                     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
                                                Page 7
                                       Math Curriculum
                                        Fourth Grade
                                                                                                  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
                                              Page 8
                                        Math Curriculum
                                         Fourth Grade
                                           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
                                          Make Your Own”
                                           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

                                               Page 9
                                      Math Curriculum
                                       Fourth Grade
                                        1004                      Modeling                   SG p. 310
                                                                                               selected teacher
                                                                                               homework
                                                                                               questions
                                                                                              URG p. 850
                                                                                              SG p. 320
                                                                                              Teacher
                                                                                               Observation-
                                                                                               demonstration of
                                                                                               task. Explanation
                                                                                               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
                                                                   Answer                      Activities
                                                                  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
                                             Page 10
                                         Math Curriculum
                                          Fourth Grade
                                                                       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

                                               Page 11
                                     Math Curriculum
                                      Fourth Grade
                                       Unit 15, “Using Patterns
                                       Make Your Own”
                                        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
                                       Lab Activities               Answer
                                       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.

                                            Page 12
                                            Math Curriculum
                                             Fourth Grade
                                               1186
                                              Unit 15, “Using Patterns
                                              Make Your Own”
                                               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)


                                                   Page 13
                                                     Math Curriculum
                                                      Fourth Grade
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
                                                           Page 14
                                          Math Curriculum
                                           Fourth Grade
                                             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
                                            Make Your Own”
                                             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
                                                 Page 15
                                     Math Curriculum
                                      Fourth Grade
                                       Area Vs. Length
                                       Unit 15, “Using
                                        Patterns”
                                       Make Your Own: Plant
                                        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
                                                       Fourth Grade
                                                        Unit 16, “Assessing Our
                                                         Learning” Lesson 3 p.
                                                         1186
                                                        Unit 15, “Using Patterns
                                                        Make Your Own”
                                                         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
       Shadows (projections) of
                                                                                      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 &
                                                             Page 17
                                          Math Curriculum
                                           Fourth Grade
       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
                                                     Fourth Grade
                                                                                                             Using Angle
                                                                                                              Circles
                                                                                                             Unit 9
                                                                                                             SG p. 242 #5-8
                                                                                                              SG p. 238-240 ,
                                                                                                              Map Skills
                                                                                                              activity page
                                                                                                             Teacher
                                                                                                              Observation
                                                                                                              measuring angles
                                                                                                             Teacher made
                                                                                                              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
                                                                                 Answer                       Observation:
                                                                                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

                                                          Page 19
                                       Math Curriculum
                                        Fourth Grade
                                                                     Reasonableness of           Teacher
                                                                      Answer                       Observation:
                                                                     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
                                                                      Answer                       Observation:
                                                                     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

                                              Page 20
                                                     Math Curriculum
                                                      Fourth Grade
                                                                                                               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
                                                                                   Answer                      Observation:
                                                                                  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
                                                                                   Answer                      Observation:
                                                                                  Modeling                    Small group
                                                                                  Practice                    activities
                                                                                  Games
                                                                                  Use of Manipulatives
                                                                                  Small Group Instruction
                                                                                  Teacher Observation
                                                            Page 21
                                                        Math Curriculum
                                                         Fourth Grade
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
                                           Fourth Grade
                                            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

                                                Page 23
                                                    Math Curriculum
                                                     Fourth Grade
                                                       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
                                                                                 Sign In and Out Sheet       discussion
                                                                                 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
                                                      Fourth Grade
                                                       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
                                                     Fourth Grade
       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
                                                     Fourth Grade
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
                                                        Fourth Grade
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
                                         Fourth Grade
       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
                                                                                                made by teacher
                                                                                               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
                                                        Fourth Grade
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
                                        Fourth Grade
                                                                                                    Activities- refer to
                                                                                                    rubrics in Unit
                                                                                                    Resource Guides
                                                                                                    and teacher Made
                                                                                                    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
                                                      Fourth Grade
                                                                                                                  Telling
                                                                                                                 SG p. 419-421 #
                                                                                                                  13-15
                                                                                                                 Unit 16
                                                                                                                 URG p. 1206-
                                                                                                                  1209
                                                                                                                 TIMS LAB
                                                                                                                  Activities- refer to
                                                                                                                  rubrics in Unit
                                                                                                                  Resource Guides
                                                                                                                  and teacher Made
                                                                                                                  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
                                                            Page 32
                                                        Math Curriculum
                                                         Fourth Grade
       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
                                                                                                                     and teacher Made
                                                                                                                     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
                                                                  Page 33
                                           Math Curriculum
                                            Fourth Grade
                                                                                                      why they have
                                                                                                      grouped items
                                                                                                     TIMS LAB
                                                                                                      Activities- refer to
                                                                                                      rubrics in Unit
                                                                                                      Resource Guides
                                                                                                      and teacher Made
                                                                                                      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
       conclusions from this                 Unit 1, “Data About         Answer                     Teacher
       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
                                                 Page 34
                                                      Math Curriculum
                                                       Fourth Grade
                                                         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
                                                          Make Your Own”
                                                          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

                                                             Page 35
                                         Math Curriculum
                                          Fourth Grade
                                                                                                   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

                                               Page 36
                                                    Math Curriculum
                                                     Fourth Grade
                                                                                                              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
                                                      Unit 1, “Data About         Answer                      demonstrates
                                                       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

                                                          Page 37
                                        Math Curriculum
                                         Fourth Grade
                                          Make Your Own”
                                           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
       readiness standard 8.3).           Unit 1, “Data About         Answer                      demonstrates
       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
                                           249                                                     and teacher Made
                                          Unit 5, “Using Data to                                  rubrics.

                                              Page 38
                                          Math Curriculum
                                           Fourth Grade
                                             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
                                            Make Your Own”
                                             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
       problem” or “make a                   About Us” Lesson 1 -5        Answer                      demonstrates
       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

                                                 Page 39
                                        Math Curriculum
                                         Fourth Grade
                                          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
                                          Make Your Own”
                                           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
                                          Unit 1, “Data About          Answer                      demonstrates
                                           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
                                          Fourth Grade
                                            Lesson 1-6 pp.201-244                                   Resource Guides
                                            249                                                     and teacher Made
                                           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
                                           Make Your Own”
                                            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
                                           Unit 1, “Data About          Answer                      demonstrates
                                            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

                                                Page 41
                                                 Math Curriculum
                                                  Fourth Grade
                                                   Unit 3, “Numbers and                                Activities- refer to
                                                    Number Operations”                                  rubrics in Unit
                                                    Lesson 1-6 pp.201-244                               Resource Guides
                                                    249                                                 and teacher Made
                                                   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
                                                   Make Your Own”
                                                    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
       Reading and writing                         Units 1-16                    Answer                 demonstrates
       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
                                           Fourth Grade
                                            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
                                            Make Your Own”
                                             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
       teachers, and others, both           Unit 1, “Data About          Answer                      demonstrates
       orally and in writing.
                                                 Page 43
                                   Math Curriculum
                                    Fourth Grade
                                      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
                                      Baseline Assessment                                      and teacher Made
                                      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
                                     Make Your Own”
                                      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
 Fourth Grade
  Units 1-16                  Reasonableness of           discussion
  Unit 1, “Data About          Answer                     Teacher
   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
  Make Your Own”
   Lesson 1 p. 1106
  Unit 10, “Using
   Decimals” Lesson 4
   p.777
  Unit 13, “Division”
   Lesson 5 p.1008

       Page 45
                                       Math Curriculum
                                        Fourth Grade
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:
                                         Unit 1, “Data About          Answer                      Students explain
                                          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
                                         Make Your Own”
                                          Lesson 1 p. 1106
                                         Unit 10, “Using
                                          Decimals” Lesson 4
                                          p.777

                                              Page 46
                                                  Math Curriculum
                                                   Fourth Grade
                                                    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
                                          Fourth Grade
                                            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
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
                                            Fourth Grade
                                              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
                                             Make Your Own”
                                              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
                                          Fourth Grade
                                            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
                                           Make Your Own”
                                            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
       coherent whole.                     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
                                                Page 50
                                          Math Curriculum
                                           Fourth Grade
                                             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
                                            Make Your Own”
                                             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
                                                 Page 51
                                       Math Curriculum
                                        Fourth Grade
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
                                          Us” Lesson 1 -5 pp. 28-      Answer                      task
                                          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
                                         Make Your Own”
                                          Lesson 1 p. 1106
                                         Unit 10, “Using
                                          Decimals” Lesson 4
                                          p.777
                                         Unit 13, “Division”

                                              Page 52
                                        Math Curriculum
                                         Fourth Grade
                                           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
                                           Lab p.128                                                and teacher Made
                                          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
                                          Make Your Own”
                                           Lesson 1 p. 1106
                                          Unit 10, “Using
                                           Decimals” Lesson 4
                                           p.777

                                               Page 53
                                         Math Curriculum
                                          Fourth Grade
                                           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
                                            73                          Games                       task
                                           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
                                           Make Your Own”
                                            Lesson 1 p. 1106

                                                Page 54
                                         Math Curriculum
                                          Fourth Grade
                                           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
                                        Fourth Grade
                                         Make Your Own”
                                          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
                                     Fourth Grade
                                       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
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
       valid.                         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

                                           Page 57
                                                     Math Curriculum
                                                      Fourth Grade
                                                       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
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
       diagrams, charts, or tables)                                                                               task
                                                        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
                                       Fourth Grade
                                        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
                                        Make Your Own”
                                         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
       problems.                        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”

                                             Page 59
                                         Math Curriculum
                                          Fourth Grade
                                            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
                                           Make Your Own”
                                            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
                                           Unit 1, “Data About          Answer                      Teacher
                                            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
                                                                                                      task by explaining
                                                Page 60
                                                Math Curriculum
                                                 Fourth Grade
                                                   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
                                                  Make Your Own”
                                                   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
                                                                                                                tasks/activities
                                                       Page 61
                                           Math Curriculum
                                            Fourth Grade
                                                                          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
       quantitative information.                                                                       tasks/activities
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
                                             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

                                                  Page 62
                                       Math Curriculum
                                        Fourth Grade
                                          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
                                                                                                tasks/activities
F. 6   Use computer-based laboratory     Teacher created            Computer Software to     Teacher
       technology for mathematical        enrichment math             enhance mathematical      Observation of
       applications in the sciences.      activities                  applications in the       student
                                                                      sciences                  tasks/activities




                                             Page 63

								
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