Standard:

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



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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