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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