correlated to the archdiocese of philadelphia -...

SADLIER‐OXFORD Progress in Mathematics Grade 4 Correlated to the Archdiocese of Philadelphia Mathematics Standards for Grade 4

CATEGORY: Operations and Algebraic Thinking Standard M.4.A. Use the four operations with whole numbers to solve problems. 2 Standard M.4.B. Gain familiarity with factors and multiples. 14 Standard M.4.C. Generate and analyze patterns. 20 CATEGORY: Numbers and Operations in Base Ten Standard M.4.D. Generalize place value understanding for multi‐digit whole numbers. 26 Standard M.4.E. Use place value understanding and properties of operations to perform multi‐digit arithmetic. 32 CATEGORY: Numbers and Operations – Fractions Standard M.4.F. Extend understanding of fraction equivalence and ordering. 42 Standard M.4.G. Build fractions from unit fractions by applying and extending previous understandings of operations on

whole numbers. 47

Standard M.4.H. Understand decimal notation for fractions, and compare decimal fractions. 53 CATEGORY: Measurement and Data Standard M.4.I. Solve problems involving measurement and conversion of measurements from a larger unit to a smaller

unit. 58

Standard M.4.J. Represent and interpret data. 66 Standard M.4.K. Geometric measurement: understand concepts of angle and measure angles. 71 CATEGORY: Geometry Standard M.4.L. Draw and identify lines and angles, and classify shapes by properties of their lines and angels. 77

Sadlier Progress in Mathematics Grade 4 Correlated to the Archdiocese of Philadelphia Mathematics Standards for Grade 4 8/3/11 of 81

CATEGORY: Operations and Algebraic Thinking Standard M.4.A. Use the four operations with whole numbers to solve problems.

Sadlier Progress in Mathematics, Grade 4

Essential Questions What should I be able to answer? What guides my thinking?

How will knowledge of problems solving help me function in everyday life?

Introduction to Problem Solving Introduction to Problem Solving: Problem‐Solving Model—pp. 28‐29

*See also Background, Presentation, and Steps and Strategies—TE pp. 28—29.

How do I choose which operation to use to solve a word problem?

Introduction to Problem Solving Introduction to Problem Solving: Choose the Operation—p. 30

Chapter 3 Addition and Subtraction Lesson 11: Problem Solving Strategy: Choose the Operation—pp. 116–117

* See additional Choose the Operation activities—pp. 34, 60, 61, 82–3, 88–89, 115, 118, 119, 156, 157, 198, 199, 211, 221, 223, 225, 232–233, 258–259, 302–303, 304–305, 310–311, 318–319, 350–351, 391, 404–405, 429, 434, 442–443

What strategies can I use to help me solve word problems?

Problem Solving Strategies Choose the Operation—pp. 30, 34, 60, 61, 82–3, 88–89, 115, 118, 119, 156, 157, 198, 199, 211, 221, 223, 225, 232–233, 258–259, 302–303, 304–305, 310–311, 318–319, 350–351, 391, 404–405, 429, 434, 442–443

Draw a Picture—pp. 314–315, 325, 335, 337, 339, 341, 351

Find a Pattern—pp. 58–59, 61, 171, 348–349, 350–351, 375, 405, 435

Guess and Test—pp. 31, 34, 57, 61, 105, 118, 119, 157, 233, 259, 289, 319, 375, 445, 454–455, 456–457

Interpret the Remainder—pp. 174–175, 179, 180–181, 183, 184–185, 196–197, 199, 233, 385, 388–389, 390–391, 393, 395, 397, 401, 404, 405




Logical Reasoning—pp. 86–87, 88, 89, 118, 119, 156, 157, 198, 199, 209, 233, 259, 286–287, 288–289, 319, 350–351, 352–353, 375, 435, 457

Make an Organized List—pp. 51, 57, 59, 61, 118–9, 250–1, 255, 257, 327

Make a Table, 25(S U), 31, 58–9, 60, 61, 68–69, 89, 118, 119, 171, 209, 289, 404–405, 449

More Than One Way—pp. 454–455 Use a Drawing/Model—pp. 49, 53, 56–57, 60, 125, 128–129, 219, 228–229, 283, 285, 288, 314–315, 348–349, 350–351, 359, 360, 362–363, 371, 372–373, 374–375, 407, 434–435

Use a Diagram/Graph—pp. 25(SU), 26(SU), 118, 157, 198, 229, 235, 240–241, 242–243, 244–245, 246–247, 248–249, 253, 254–255, 256–257, 258–259, 261, 288–289, 296, 298–299, 319, 350–351, 405, 435, 456, 459

Use More Than One Step—pp. 32, 34, 60, 71, 85, 89, 95, 99, 101, 109, 111, 113, 117, 118–119, 131, 135, 139, 141, 153, 154, 156–157, 165, 189, 195, 198, 209, 213, 215, 217, 219, 221, 223, 225, 230–231, 232–233, 241, 249, 259, 261, 289, 315, 316–317, 318–319, 350, 374–375, 397, 402–403, 404–405, 429, 432–433, 434–435, 454, 455, 456–457

Use Simpler Numbers—pp. 316–317, 318–319 Work Backward—pp. 154–155, 156, 157, 229, 319, 434–435, 457

Write a Number Sentence—pp. 8–9(SU), 33, 34, 60, 61, 67, 72–73, 76–77, 82–83, 85, 88–89, 97, 99, 101, 102–103, 104–105, 106–107, 108–109, 110–111, 112–113, 115, 116–117, 118–119, 129, 131, 132–133, 134–135, 136–137, 138–




139, 140–141, 142–143, 146–147, 148–149, 150–151, 152–153, 156–157, 159, 164–165, 167, 168–169, 174–175, 178–79, 180–181, 183, 184–185, 186, 189, 190, 198–199, 209, 210–211, 213, 221, 223, 225, 232, 241, 247, 249, 258–259, 261, 296–297, 298–299, 301, 302–303, 304–305, 308, 310–311, 318, 339, 374–375, 383, 387, 388–389, 390–391, 393, 395, 397, 399, 401, 404, 425, 426–427, 428–429, 430, 434, 442–443, 454–455, 456–457

Assessment What will I be expected to know, understand, and be able to do in order to demonstrate my learning?

Formative

3‐2‐1 summarizer/ 3‐list strategies,2‐give important things to look for when solving problem,1‐solution to the problem

Chapter 4 Multiplication by One and Two Digits Check Your Progress: Lessons 1–6A—on‐line

Chapter 5 Divide by One Digit Check Your Progress: Lessons 1–6—on‐line Check Your Progress: Lessons 1–18—on‐line

Chapter 12 Divide by Two Digits Check Your Progress: Lessons 1–12—on‐line

Chapter 14 Get Ready for Algebra Check Your Progress: Lessons 1–2—on‐line

www.progressinmathematics.com Teacher Center: Planning Blackline Masters (Centimeter Grid Paper) * Also provided on TE p. T57

Teacher Center: Common Core Check Your Progress (with Item Analysis) * See also the Lesson Plan in the TE for Write About It/Math Journal activities and Step 4: Summarize/Assess.

Summative

Chapter Test, quiz, performance assessment Chapter Tests




Chapter Test, on‐line Performance Assessment (part of Chapter Test), 92, 122, 160, 202, 408, 460

Chapter Post Test, TE 67L, 95L, 125L, 163L, 381L, 441L

www.progressinmathematics.com Teacher Center: Common Core Chapter Tests (with Item Analysis) * See "Problem Solving," "Tell About It," and "Performance Assessment" on the chapter test.

Post Tests (with Item Analysis) * See "Problem Solving" and "Tell About It" on the chapter post test.

Skills What skills do I need to have in order to answer the essential questions?

M.4.A.1. Interpret a multiplication equation as a comparison, e.g. interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Chapter 4 Multiplication by One and Two Digits Lesson 1B: Use Multiplication to Compare Numbers—on‐line

M.4.A.2. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Chapter 4 Multiplication by One and Two Digits Lesson 1B: Use Multiplication to Compare Numbers—on‐line

Chapter 5 Divide by One Digit Lesson 4A: Use Bar Diagrams—on‐line Lesson 17: Problem Solving Strategy: Interpret the Remainder—pp. 196–197

Lesson 18: Problem Solving Applications: Mixed Review—pp. 198–199

Chapter 12 Divide by Two Digits Lesson 11: Problem Solving Strategy: Use More Than One Step—pp. 402–403





Chapter 14 Get Ready for Algebra Lesson 1: Equations—pp. 442–443

M.4.A.3. Solve multistep word problems posed with whole numbers and having whole‐number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding

Chapter 4 Multiplication by One and Two Digits Lesson 4: Multiply by One‐Digit Numbers—pp. 132–133

Lesson 7: Multiply Three‐Digit Numbers—pp. 138–139

Lesson 11: Products: Rounding to Estimate—pp. 146–147

Chapter 5 Divide by One Digit Lesson 5: Estimate in Division—pp. 172–173 Lesson 6: One‐Digit Quotients—pp. 174–175 Lesson 8: Two‐Digit Quotients—pp. 178–179 Lesson 9: More Two‐Digit Quotients—pp. 180–181

Lesson 10: Three‐Digit Quotients—pp. 182–183 Lesson 11: More Quotients—pp. 184–185 Lesson 12: Zeros in the Quotient—pp. 186–187 Lesson 13: Larger Numbers in Division—pp. 188–189

Lesson 13A: Multistep Problems & Bar Diagrams—on‐line

Lesson 17: Problem Solving Strategy: Interpret the Remainder—pp. 196–197


Chapter 6 Measurement Lesson 13: Problem Solving Strategy: Use More Than One Step—pp. 230–231

Chapter 12 Divide by Two Digits Lesson 2: Divisors: Multiples of Ten—pp. 384–385




Lesson 3: Estimate Quotients—pp. 386–387 Lesson 4: Two‐Digit Dividends—pp. 388–389 Lesson 5: Three‐Digit Dividends—pp. 390–391 Lesson 6: Trial Quotients—pp. 392–393 Lesson 7: Greater Quotients—pp. 394–395 Lesson 8: Four‐Digit Dividends—pp. 396–397 Lesson 10: Greater Dividends—pp. 400–401 Lesson 11: Problem Solving Strategy: Use More Than One Step—pp. 402–403


Chapter 14 Get Ready for Algebra Lesson 1: Equations—pp. 442–443

Content What content do I need to know in order to answer the essential questions?

Fluency in the multiplication facts 1 – 10, including visual and verbal representation e.g. If 3 boys go to the store and buy 7 baseball cards and 7 boys go the store and buy 3 baseball cards. Did they buy the same amount? Justify your answer.

Skills Update—Review of Grade 3 Skills Meaning of Multiplication—p. 7 Multiplication Facts—p. 8 Multiply with 10, 11, and 12—p. 9 * See additional multiplication facts, 11(SU), 12(SU), 126–7, 274–5, 277, 306, 444–5, 449, 452–3

Missing factors e.g. 45 chairs were arranged in 5 rows. How many in each row? 5 x __ = 45

Skills Update—Review of Grade 3 Skills Division Facts—p. 11 Relate Multiplication and Division—p. 12

Chapter 5 Divide by One Digit Lesson 3: Missing Numbers—pp. 168–169

Chapter 14 Get Ready for Algebra Lesson 2: Find Missing Numbers—pp. 444–445 * See additional missing factors, 127, 131, 275, 443, 449

Strategies and Steps in Problem solving – draw a picture or model, make a table, diagram or list, write an equation

Strategies and Steps in Problem Solving Draw a Picture—pp. 314–315, 325, 335, 337, 339, 341, 351




Make an Organized List—pp. 51, 57, 59, 61, 118–9, 250–1, 255, 257, 327

Make a Table, 25(S U), 31, 58–9, 60, 61, 68–69, 89, 118, 119, 171, 209, 289, 404–405, 449

More Than One Way—pp. 454–455 Use a Drawing/Model—pp. 49, 53, 56–57, 60, 125, 128–129, 219, 228–229, 283, 285, 288, 314–315, 348–349, 350–351, 359, 360, 362–363, 371, 372–373, 374–375, 407, 434–435

Use a Diagram/Graph—pp. 25(SU), 26(SU), 118, 157, 198, 229, 235, 240–241, 242–243, 244–245, 246–247, 248–249, 253, 254–255, 256–257, 258–259, 261, 288–289, 296, 298–299, 319, 350–351, 405, 435, 456, 459

Write a Number Sentence—pp. 8–9(SU), 33, 34, 60, 61, 67, 72–73, 76–77, 82–83, 85, 88–89, 97, 99, 101, 102–103, 104–105, 106–107, 108–109, 110–111, 112–113, 115, 116–117, 118–119, 129, 131, 132–133, 134–135, 136–137, 138–139, 140–141, 142–143, 146–147, 148–149, 150–151, 152–153, 156–157, 159, 164–165, 167, 168–169, 174–175, 178–79, 180–181, 183, 184–185, 186, 189, 190, 198–199, 209, 210–211, 213, 221, 223, 225, 232, 241, 247, 249, 258–259, 261, 296–297, 298–299, 301, 302–303, 304–305, 308, 310–311, 318, 339, 374–375, 383, 387, 388–389, 390–391, 393, 395, 397, 399, 401, 404, 425, 426–427, 428–429, 430, 434, 442–443, 454–455, 456–457

Inverse operations Skills Update—Review of Grade 3 Skills Related Facts—p. 5 Division Facts—p. 11 Relate Multiplication and Division—p. 12




Chapter 2 Addition and Subtraction Concepts Lesson 5: Addition and Subtraction Sentences—pp. 76–77

Chapter 5 Divide by One Digit Lesson 2: Relate Multiplication and Division—pp. 166–167

* See also inverse operation—pp. 30, 33, 78, 84, 106, 108, 110, 113, 116, 154–155, 157, 168–169, 174, 178, 180, 182–183, 184, 187, 188, 190, 196–197, 444–445

Estimation strategies – front end/clustering/rounding/rounding and adjusting/compatible numbers

Chapter 2 Addition and Subtraction Concepts English Language Learners: Estimate Sums and Differences—TE pp. 67H‐67I

Lesson 7: Estimate Sums and Differences—pp. 80–81

Chapter 3 Addition and Subtraction Strategic Intervention: 1. Estimate by rounding to the nearest hundred—TE p. 95F

English Language Learners: Front‐End Estimation—TE p. 99I

Lesson 1: Front‐End Estimation—pp. 96–97 Chapter 4 Multiplication by One and Two Digits Lesson 5: Products: Front‐End Estimation—pp. 134–135

Lesson 11: Products: Rounding to Estimate—pp. 146–147

Enrichment: Clustering—p. 159 Chapter 5 Divide by One Digit Lesson 5: Estimate in Division—pp. 172–173

Chapter 12 Divide by Two Digits Lesson 3: Estimate Quotients—pp. 386–387 Lesson 4: Two‐Digit Dividends: Critical Thinking—p. 389




Lesson 5: Three‐Digit Dividends: Mental Math—p. 391

Integration of Learning How does this learning connect to my other areas (subjects) of learning?

Economics – money Chapter 1 Place Value Lesson 8: Make Change—pp. 50–51 Lesson 9: Compare and Order Money—pp. 52–53 Lesson 11: Work with Money—pp. 56–57

Chapter 2 Addition and Subtraction Concepts Lesson 8: Add and Subtract Money—pp. 82–83

Chapter 3 Addition and Subtraction Lesson 1: Front‐End Estimation (money)—pp. 96–97

Lesson 2: Add with Regrouping (money)—pp. 98–99

Lesson 3: Four‐Digit Addition (money)—pp. 100–101

Lesson 4: Add Larger Numbers (money)—p. 103 Lesson 5: Three or More Addends (money)—pp. 104–105

Lesson 6: Subtract with Regrouping (money)—pp. 106–107

Lesson 7: Subtraction: Regroup Twice (money)—pp. 108–109

Lesson 8: Subtract Larger Numbers (money)—pp. 110–111

Lesson 9: Zeros in Subtraction (money)—pp. 112–113

Lesson 10: Addition and Subtraction Practice (money)—pp. 114–115

Chapter 4 Multiplication by One and Two Digits Lesson 5: Products: Front‐End Estimation—pp. 134–135

Lesson 8: Multiply Money—pp. 140–141 Lesson 9: Multiply Four‐Digit Numbers—pp. 142–




143 Lesson 11: Products: Rounding to Estimate—pp. 146–147

Lesson 12: Multiply by Two‐Digit Numbers: Multiply Money—p. 149

Lesson 14: Multiply with Three‐Digit Numbers—pp. 152–153

Chapter 5 Divide by One Digit Lesson 14: Divide Money—pp. 190–191

Science – weights and measurements Chapter 6 Measurement Lesson 3: Compute Customary Units—pp. 210–211

Lesson 7: Work with Metric Units—pp. 218–219

Tools for Learning Which tools will I use that will assist me in my learning?

KWL Flash cards Dry Erase Board Games –Acting Out www.ixl.com/math/grade‐4 The King’s Chessboard – David Birch

* To access online resources, go to— www.progressinmathematics.com GRADE 4 TEACHER CENTER 1 PLANNING Scope and Sequence Road Maps Priority Lessons Table of Contents Pacing Guides Model Lessons for English Learners Blackline Masters Chapter Support Research Base Math Study Take‐Home Activities Chapter Records

2 PRACTICE Skills Update Math Minutes




Problem of the Day Practice Activities Vocabulary Activities Manipulatives Flash Activities Tutorials

3 ASSESSMENT Benchmark Tests Chapter Pretests with Analyses Check Your Progress with Analyses Lessons for Priority Lessons Assessments

4 COMMON CORE Correlations Chapter Pacing Guides Teacher Lesson Plans Student Lessons Check Your Progress with Analyses Chapter Tests with Analyses Cumulative Reviews with Analyses Post Test with Analyses

5 RESOURCES AUDIO GLOSSARY From A to Z (Grade 4 Glossary—English) De la A a la Z (Grade 4 Glossary—Spanish)

Authors National Mathematics Advisory Board

STUDENT CENTER / FAMILY CENTER Skills Update Math Minutes Problem of the Day Practice Activities Vocabulary Activities Alternative Teaching Models




Virtual Manipulatives Audio Glossary From A to Z (Grade 4 Glossary—English) De la A a la Z (Grade 4 Glossary—Spanish)

Enrichment Math Alive at Home: Take‐Home Activities Symbols, Measures, and More


CATEGORY: Operations and Algebraic Thinking Standard M.4.B. Gain familiarity with factors and multiples.



What are the different ways I count? Why is it important for me to skip count?

Chapter 1 Place Value Lesson 4: Place Value (count by 10, 100, 1000)—pp. 42–43

Chapter 6 Measurement Lesson 12: Elapsed Time (count by 1s and 5s)—pp. 228–229

What are prime and composite numbers? Chapter 9 Fractions: Addition and Subtraction Lesson 6B: Prime and Composite Numbers—on‐line

How are factors and multiples related? Chapter 9 Fractions: Addition and Subtraction Lesson 6: Multiples—pp. 306–307Lesson 6A: Factor Pairs—on‐line

Lesson 6B: Prime and Composite Numbers—on‐line


Formative

Board work www.progressinmathematics.com Teacher Center: Common Core Check Your Progress (with Item Analysis) * See also the Lesson Plan in the TE for Write About It/Math Journal activities and Step 4: Summarize/Assess.

Making a factor rainbow for 12 – connecting 1 and 12, 2 and 6, 3and 4

Quick write: list different factor pairs

Mad Minute drill www.progressinmathematics.com STUDENT CENTER 1 PRACTICE Math Minutes

Summative

Chapter Test, quiz, performance assessment www.progressinmathematics.com Teacher Center: Common Core Chapter Tests (with Item Analysis)




* See "Problem Solving," "Tell About It," and "Performance Assessment" on the chapter test.



M.4.B.1. Find all factor pairs for a whole number in the range 1‐100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1‐100 is a multiple of a given one‐digit number. Determine whether a given whole number in the range 1‐100 is prime or composite.

Chapter 8 Fraction Concepts Lesson 6: Factors—pp. 276–277 Chapter 9 Fractions: Addition and Subtraction Lesson 6A: Factor Pairs—on‐line Lesson 6B: Prime and Composite Numbers—on‐line


Multiplication facts Skills Update—Review of Grade 3 Skills Meaning of Multiplication—p. 7 Multiplication Facts—p. 8 Multiply with 10, 11, and 12—p. 9 Understand Division—p. 10 Division Facts—p. 11 Relate Multiplication and Division—p. 12

Chapter 4 Multiplication by One and Two Digits Lesson 1: Multiplication Properties—pp. 126–127

Chapter 8 Fraction Concepts Lesson 5: Write Equivalent Fractions—pp. 274–275

Lesson 6: Factors—p. 277 Chapter 9 Fractions: Addition and Subtraction Lesson 6: Multiples—pp. 306–307

Chapter 14 Get Ready for Algebra Lesson 2: Find Missing Numbers—pp. 444–445

Vocabulary: prime, composite, factor x factor = * New vocabulary is highlighted in yellow and




product, product factor = factor, multiple defined in context in each lesson, also highlighted in yellow and presented in the Lesson Plan in the Teacher's Edition.

* See also — Student Glossary (with definitions and page references to where many terms are introduced)—pp. 486–490

Teacher Glossary (for enrichment: an extension of the Glossary in the Student Edition; defined terms listed alphabetically and grouped by topic)—TE pp. T47–T48

www.progressinmathematics.com Teacher Center Planning: Model Lessons for English Learners Planning: Take‐Home Activities (Vocabulary) Practice: Vocabulary Activities

Student Center/Family Center Vocabulary Activities Audio Glossary Math Alive at Home (Vocabulary)

Multiple vs. Product Skills Update—Review of Grade 3 Skills Meaning of Multiplication (product)—p. 7

Chapter 4 Multiplication by One and Two Digits Lesson 1: Multiplication Properties (factors, products)—pp. 126–127

Lesson 3: Special Factors (factors, products)—pp. 130–131

Lesson 4: Multiply by One‐Digit Numbers (products)—pp. 132–133

Chapter 9 Fractions: Addition and Subtraction Lesson 6: Multiples (common multiples)—pp.




306–307 Chapter 12 Divide by Two Digits Lesson 1: Division Patterns (multiples of 10)—pp. 382–383

Lesson 2: Divisors: Multiples of Ten—pp. 384–385

Sieve of Eratosthenes www.progressinmathematics.com STUDENT CENTER 3 VIRTUAL MANIPULATIVES Manipulatives: Sieve of Eratosthenes (explore patterns and relationships involving multiples)

Odds, evens and squares Chapter 5 Divide by One Digit Lesson 4: Number Patterns: Challenge—p. 171

Area – build rectangles (arrays) with a given area can be 2 ways ex. 6 = 1x6 or x3x2: prime numbers have only 1 rectangle

Chapter 11 Perimeter, Area, and Volume Lesson 2: Use Area Formulas—pp. 360–361 Lesson 3: Perimeter and Area—pp. 362–363 Lesson 3A: Perimeter and Area Formulas—on‐line

Ex. An ice cream truck visits a neighborhood every 4 days. She missed the truck today. When can she expect it again.


Calendar – every 3rd day you cut the lawn Chapter 6 Measurement Lesson 12: Elapsed Time—p. 229

Science ‐ measurement Chapter 6 Measurement Lesson 6: Measure with Metric Units—pp. 216–217

Lesson 7: Work with Metric Units—pp. 218–219 Lesson 8: Metric Units of Capacity—pp. 220–221 Lesson 9: Metric Units of Mass—pp. 222–223





Multiplication Table 100 Chart


2 PRACTICE Skills Update Math Minutes Problem of the Day Practice Activities Vocabulary Activities Manipulatives Flash Activities Tutorials


4 COMMON CORE Correlations




Chapter Pacing Guides Teacher Lesson Plans Student Lessons Check Your Progress with Analyses Chapter Tests with Analyses Cumulative Reviews with Analyses Post Test with Analyses



STUDENT CENTER / FAMILY CENTER Skills Update Math Minutes Problem of the Day Practice Activities Vocabulary Activities Alternative Teaching Models Virtual Manipulatives Audio Glossary From A to Z (Grade 4 Glossary—English) De la A a la Z (Grade 4 Glossary—Spanish)



CATEGORY: Operations and Algebraic Thinking Standard M.4.C. Generate and analyze patterns.



Can I describe change mathematically?

Chapter 7 Statistics and Probability Lesson 3: Line Graphs—pp. 244–245

Can I describe numbers or objects that repeat mathematically?

* See patterns—pp. 39, 58, 61, 85, 129, 130, 137, 144–145, 151, 170–171, 176–177, 208, 213–214, 218, 220, 222–223, 227, 273, 275, 306–307, 342–343, 345, 348–349, 375, 382, 385


Formative

Explore pattern problems Chapter test, quiz, Performance Assessment:

www.progressinmathematics.com Teacher Center: Planning Blackline Masters (Centimeter Grid Paper) * Also provided on TE p. T57


Summative

Every Beat of Your Heart‐ The heart of a child below the age of twelve beats about 100 times a minute. Have the children find their pulse at rest for 1 minute. Then have them do some form of exercise, find their pulse for 1 minute. Then, have them run in place for 1 minute. Ask follow up questions that predict what could happen for longer time or different activities.




M.4.C.1. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were no explicit in the rule itself.

Chapter 4 Multiplication by One and Two Digits Lesson 1A: Number Patterns—on‐line

Chapter 5 Divide by One Digit




For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers why the numbers will continue to alternate in this way.

Lesson 4: Number Patterns—pp. 170–171 Chapter 10 Geometry Lesson 12: Problem Solving Strategy: Find a Pattern—pp. 348–349

Chapter 14 Get Ready for Algebra Lesson 3: Functions—pp. 446–447


Vocabulary: skip counting, multiple counting, sequences ex. Rule start with 2 and multiple by 3

* New vocabulary is highlighted in yellow and defined in context in each lesson, also highlighted in yellow and presented in the Lesson Plan in the Teacher's Edition.





Model situations that the 4 operations of whole numbers as patterns.

Chapter 2 Addition and Subtraction Concepts Lesson 6: Mental Math—pp. 78–79




Chapter 4 Multiplication by One and Two Digits Lesson 1A: Number Patterns—on‐line Lesson 2: Multiplication Models—pp. 128–129 Lesson 3: Special Factors—pp. 130–131 Lesson 6: Multiply with Regrouping—pp. 136–137 Lesson 10: Patterns in Multiplication—pp. 144–145

Lesson 13: More Multiplying by Two‐Digit Numbers (patterns)—pp. 150–151

Chapter 5 Divide by One Digit Lesson 4: Number Patterns—pp. 170–171 Lesson 7: Divisibility—pp. 176–177

An operation can be “undone” by its inverse. * See inverse operations—pp. 30, 33, 78, 84, 106, 108, 110, 113, 116, 154–155, 157, 168–169, 174, 178, 180, 182–183, 184, 187, 188, 190, 196–197, 444–445

Represent a variable as an unknown quantity using a letter or symbol.

Chapter 14 Get Ready for Algebra Lesson 1: Equations—pp. 442–443 Lesson 2: Find Missing Numbers—pp. 444–445

Develop an understanding of the Commutative and Associative Property ex. 3 x 2 = 2 x 3

Chapter 2 Addition and Subtraction Concepts Lesson 1: Addition Properties—pp. 68–69

IN/OUT Tables Chapter 6 Measurement Lesson 2:: Rename Units of Length (function tables)—pp. 208‐209

Lesson 4: Customary Units of Capacity (function tables)—p. 213

Lesson 5: Customary Units of Weight (function table)—p. 214

Lesson 8: Metric Units of Capacity (function table)—p. 220




Lesson 9: Metric Units of Mass (function table)—p. 222

Lesson 11: Time (function tables)—p. 227 Chapter 14 Get Ready for Algebra Lesson 3: Functions—pp. 446–447


Growth in tables and graphs using real world events

Chapter 7 Statistics and Probability Lesson 3: Line Graphs—pp. 244–245 Enrichment: Double Bar Graphs—p. 261

How change is related to time (time tables) Chapter 7 Statistics and Probability Lesson 3: Line Graphs—pp. 244–245

Observing geometric patterns Skills Update—Review of Grade 3 Skills Congruent Figures (patterns)—p. 21

Chapter 10 Geometry Lesson 8: Similar Figures (patterns)—pp. 340–341 Lesson 9: Transformations: Slides and Flips (patterns)—pp. 342–343

Lesson 12: Problem Solving Strategy: Find a Pattern—pp. 348–349

Patterns in science


Pattern Blocks, or Tiles Hundreds chart Calendar Number line The Patchwork Quilt – Valorie Flournoy Performance assessment example: www.rda.aps.edu/mathtaskbank/starthtm. Skip the Movie or Betty’s Miniature Birdhouses

* To access online resources, go to— www.progressinmathematics.com GRADE 4 TEACHER CENTER 1 PLANNING Scope and Sequence Road Maps Priority Lessons Table of Contents Pacing Guides Model Lessons for English Learners Blackline Masters




Chapter Support Research Base Math Study Take‐Home Activities Chapter Records






CATEGORY: Numbers and Operations in Base Ten Standard M.4.D. Generalize place value understanding for multi-digit whole numbers.



Can I express order and compare numbers? Skills Update—Review of Grade 3 Skills Compare Whole Numbers—p. 2

Chapter 1 Place Value Lesson 6: Compare and Order Whole Numbers—pp. 46–47

Do I know the position of a digit in a number affects its value?

Skills Update—Review of Grade 3 Skills Hundreds—p. 1

Chapter 1 Place Value Lesson 1: Thousands—pp. 36‐37 Lesson 2: What is One Million?—pp. 38–39 Lesson 3: Millions—pp. 40–41 Lesson 4: Place Value—pp. 42–43


Formative

Board work www.progressinmathematics.com Teacher Center: Planning Blackline Masters (Centimeter Grid Paper) * Also provided on TE p. T57


Exit cards with solved problems

Homework

Summative

Chapter test, quiz, performance assessment www.progressinmathematics.com Teacher Center: Common Core Chapter Tests (with Item Analysis) * See "Problem Solving," "Tell About It," and "Performance Assessment" on the chapter test.

Post Tests (with Item Analysis)




* See "Problem Solving" and "Tell About It" on the chapter post test.


M.4.D.1. Recognize that in a multi‐digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 70 = 10 by applying concepts of place value and division.

Chapter 1 Place Value Lesson 1: Thousands—pp. 36‐37 Lesson 2: What is One Million?—pp. 38–39 Lesson 3: Millions—pp. 40–41 Lesson 4: Place Value—pp. 42–43

M.4.D.2. Read and write multi‐digit whole numbers using base‐ten numerals, number names, and expanded form. Compare two multi‐digit numbers based on meanings of the digits in each place, using >, =, < symbols to record the results of comparisons.

Chapter 1 Place Value Lesson 1: Thousands—pp. 36‐37 Lesson 3: Millions—pp. 40–41 Lesson 4: Place Value—pp. 42–43 Lesson 6: Compare and Order Whole Numbers—pp. 46–47


M.4.D.3. Use place value understanding to round multi‐digit whole numbers to any place.

Chapter 1 Place Value Lesson 10: Rounding—pp. 54–55

Chapter 2 Addition and Subtraction Concepts Lesson 7: Estimate Sums and Differences—pp. 80–81


Vocabulary: Place value names, period names, expanded form, rounding



Teacher Glossary (for enrichment: an extension of




the Glossary in the Student Edition; defined terms listed alphabetically and grouped by topic)—TE pp. T47–T48



Discover patterns in place value Chapter 1 Place Value Lesson 2: What is One Million? (patterns)—pp. 38–39

Lesson 4: Place Value (patterns)—pp. 42–43 Lesson 12: Problem Solving Strategy: Make a Table or List (patterns)—pp. 58–59

Lesson 13: Problem Solving Applications: Mixed Review (patterns)—pp. 60–61

Compare numbers using place value Skills Update—Review of Grade 3 Skills Compare Whole Numbers—p. 2

Chapter 1 Place Value Lesson 6: Compare and Order Whole Numbers—pp. 46–47

Using rounding to the nearest dollar to estimate costs

Chapter 1 Place Value Lesson 10: Rounding—pp. 54–55

Inverse operations Skills Update—Review of Grade 3 Skills Addition and Subtraction Facts—p. 4 Related Facts—p. 5




Relate Multiplication and Division—p. 12 Chapter 2 Addition and Subtraction Concepts Lesson 9: Check Addition and Subtraction—pp. 84–85

* See inverse operations—pp. 11–13(SU), 30, 33, 76–77, 78, 84, 106, 108, 110, 113, 116, 154–155, 157, 166–167, 168–169, 174, 178, 180, 182–183, 184, 187, 188, 190, 196–197, 444–445


Social Studies ‐Population and Area Chapter 1 Place Value Lesson 3: Millions (area and population in Brazil)—pp. 40–41

Almanac Data ‐ e.g. Tallest Buildings

Other number systems – Roman numerals, Chinese abacus

Chapter 2 Addition and Subtraction Concepts Enrichment: The Abacus—p. 91

Chapter 3 Addition and Subtraction Enrichment: Roman Numerals—p. 121

Newspaper or magazine scavenger hunt for large numbers

Chapter 1 Place Value Lesson 3: Millions: Real‐World Connections (search social studies or science books for numerical facts with large numbers)—TE p. 41

Consumer topics ‐ estimating money Chapter 1 Place Value Lesson 10: Rounding (with money)—pp. 54–55

Chapter 4 Multiplication by One and Two Digits Lesson 11: Products: Rounding to Estimate (money)—pp. 146–147


Place Value Chart Number Line Base Ten Blocks Calculator

* To access online resources, go to— www.progressinmathematics.com GRADE 4 TEACHER CENTER




Napier Bones Literature – How Much is Million? – David Schwartz Anno’s Counting Book – Mitsumasa Anno

1 PLANNING Scope and Sequence Road Maps Priority Lessons Table of Contents Pacing Guides Model Lessons for English Learners Blackline Masters Chapter Support Research Base Math Study Take‐Home Activities Chapter Records



4 COMMON CORE Correlations Chapter Pacing Guides Teacher Lesson Plans Student Lessons Check Your Progress with Analyses




Chapter Tests with Analyses Cumulative Reviews with Analyses Post Test with Analyses






CATEGORY: Numbers and Operations in Base Ten Standard M.4.E. Use place value understanding and properties of operations to perform multi-digit arithmetic.



Do I know efficient methods for finding sums, differences, products and quotients?

Skills Update—Review of Grade 3 Skills Addition and Subtraction Facts—p. 4 Related Facts—p. 5 Add and Subtract without Regrouping—p. 6 Meaning of Multiplication—p. 7 Multiplication Facts—p. 8 Multiply with 10, 11, and 12—p. 9 Understand Division—p. 10 Division Facts—p. 11 Relate Multiplication and Division—p. 12

Chapter 2 Addition and Subtraction Concepts Lesson 1—Lesson 11—pp. 68–89

Chapter 3 Addition and Subtraction Lesson 1—Lesson 12—pp. 96–119

Chapter 4 Multiplication by One and Two Digits Lesson 1–Lesson 16—pp. 126–157

Chapter 5 Divide by One Digit Lesson 1—Lesson 18—pp. 164–199

Do I know what makes a strategy both effective and efficient? * See Tell About It—pp. 64, 92, 122, 160, 238, 262, 264, 292, 294, 322, 324, 354, 356, 378, 380, 408, 410, 438, 440, 460 (also on Chapter Test and Chapter Post Test)

Are my answers reasonable? * See evaluating reasonableness of solution in context—pp. 21(SU), 30–31, 32–33, 34, 44–45, 57, 58–59, 60–61, 78–79, 80–81, 83–84, 88–89, 96–97, 99, 100–101, 102–103, 104–105, 106–107, 108–109, 110–111, 112–113, 114–115, 116–117, 118–119, 126, 131, 133, 134–135, 136–137,




138–139, 140–141, 142–143, 146–147, 148–149, 150–151, 152–153, 154–155, 156–157, 159, 174, 176–177, 178–179, 180–181, 182–183, 184–185, 187, 188–189, 190, 196–197, 198–199, 230–231, 232–233, 256–257, 258–259, 267, 270–271, 273, 276–277,285, 286–287, 289, 298, 302–303, 315, 316–317, 318–319, 335, 337, 339, 345, 348–349, 350–351, 384, 388–389, 390–391, 392, 394–395, 396–397, 398–399, 400, 402–403, 404–405, 421, 424, 426, 428–429, 430–431, 432–433, 434–435, 443, 444–445, 454–455, 456–457


Formative

board work www.progressinmathematics.com Teacher Center: Common Core Check Your Progress (with Item Analysis) * See also the Lesson Plan in the TE for Write About It/Math Journal activities and Step 4: Summarize/Assess.

exit cards with problems

math journal writing

homework

Summative

chapter test, quiz, performance assessments www.progressinmathematics.com Teacher Center: Common Core Chapter Tests (with Item Analysis) * See "Problem Solving," "Tell About It," and "Performance Assessment" on the chapter test.

Post Tests (with Item Analysis) * See "Problem Solving" and "Tell About




It" on the chapter post test.


M.4.E.1. Fluently add and subtract multi‐digit whole numbers using the standard algorithm.

Chapter 2 Addition and Subtraction Concepts Lesson 9: Check Addition and Subtraction—pp. 84–85


Chapter 3 Addition and Subtraction Lesson 2: Add with Regrouping—pp. 98–99 Lesson 3: Four‐Digit Addition—pp. 100–101 Lesson 4: Add Larger Numbers—pp. 102–103

Lesson 5: Three or More Addends—pp. 104–105

Lesson 6: Subtract with Regrouping—pp. 106–107

Lesson 7: Subtraction: Regroup Twice—pp. 108–109

Lesson 8: Subtract Larger Numbers—pp. 110–111

Lesson 9: Zeros in Subtraction—pp. 112–113

Lesson 10: Addition and Subtraction Practice—pp. 114–115


M.4.E.2. Multiply a whole number of up to four digits by a one‐digit whole number, and multiply two two‐digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.


Lesson 2: Multiplication Models—pp. 128–




129 Lesson 3: Special Factors—pp. 130–131 Lesson 4: Multiply by One‐Digit Numbers—pp. 132–133

Lesson 5A: Multiply with Models—on‐line Lesson 6: Multiply with Regrouping—pp. 136–137

Lesson 6A: Use Mental Math to Multiply—on‐line

Lesson 7: Multiply Three‐Digit Numbers—pp. 138–139

Lesson 9: Multiply Four‐Digit Numbers—pp. 142–143

Lesson 10: Patterns in Multiplication—pp. 144–145

Lesson 11A: Multiply with Area Models—on‐line

Lesson 11B: Break Apart Numbers to Multiply—on‐line

Lesson 12: Multiply by Two‐Digit Numbers—pp. 148–149

Lesson 13: More Multiplying by Two‐Digit Numbers—pp. 150–151

Chapter 5 Divide by One Digit Lesson 13A: Multistep Problems & Bar Diagrams—on‐line

M.4.E.3. Find whole‐number quotients and remainders with up to four‐digit dividends and one‐digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models.

Chapter 5 Divide by One Digit Lesson 2: Relate Multiplication and Division—pp. 166–167

Lesson 5A: Use Models to Divide—on‐line Lesson 6: One‐Digit Quotients—pp. 174–175




Lesson 8: Two‐Digit Quotients—pp. 178–179

Lesson 9: More Two‐Digit Quotients—pp. 180–181

Lesson 10: Three‐Digit Quotients—pp. 182–183

Lesson 11: More Quotients—pp. 184–185 Lesson 12: Zeros in the Quotient—pp. 186–187

Lesson 13: Larger Numbers in Division—pp. 188–189

Lesson 13A: Multistep Problems & Bar Diagrams—on‐line


Properties –commutative, associative and distributive Chapter 2 Addition and Subtraction Concepts Lesson 1: Addition Properties—pp. 68–69


Model multiplication using patterns (multiples of 10, 100 and 1,000), graph paper

Skills Update—Review of Grade 3 Skills Meaning of Multiplication—p. 7 Multiply with 10, 11, and 12—p. 9

Chapter 4 Multiplication by One and Two Digits Lesson 2: Multiplication Models—pp. 128–129

Lesson 3: Special Factors—pp. 130–131 Lesson 5A: Multiply with Models—on‐line

Model division with base ten blocks and/or graph paper Skills Update—Review of Grade 3 Skills Understand Division—p. 10




Division Facts—p. 11 Chapter 5 Divide by One Digit Lesson 5: Estimate in Division (base ten blocks, grid paper)—TE pp. 172–173

Lesson 6: One‐Digit Quotients (base ten blocks, grid paper)—TE pp. 174–175

Lesson 8: Two‐Digit Quotients (base ten blocks, grid paper)—TE pp. 178–179

Lesson 9: More Two‐Digit Quotients (base ten blocks, grid paper)—TE pp. 180–181

Lesson 10: Three‐Digit Quotients (overhead base ten blocks)—TE pp. 182–183

Lesson 11: More Quotients (overhead base ten blocks, grid paper)—TE pp. 184–185

Lesson 12: Zeros in the Quotient (base ten blocks)—pp. 186–187

www.progressinmathematics.com TEACHER CENTER 1 PLANNING LESSON PLANNING Blackline Masters: Centimeter Grid Paper—T61

Vocabulary: factors, product, partial products, divisor, dividend, quotient, remainder, compatible numbers


* See also — Student Glossary (with definitions and page references to where many terms are




introduced)—pp. 486–490 Teacher Glossary (for enrichment: an extension of the Glossary in the Student Edition; defined terms listed alphabetically and grouped by topic)—TE pp. T47–T48

www.progressinmathematics.com Teacher Center Planning: Model Lessons for English Learners

Planning: Take‐Home Activities (Vocabulary)

Practice: Vocabulary Activities Student Center/Family Center Vocabulary Activities Audio Glossary Math Alive at Home (Vocabulary)

Using estimation to check reasonable answers * Use estimation to check for reasonableness—pp. 81, 116

Break apart strategy ex. 3,456 3,000 + 400 + 50 + 6 + 1,357 1,000 + 300 + 50 + 7 260 4 = 200 4 + 60 4

Chapter 2 Addition and Subtraction Concepts Lesson 2: Addition Strategies—pp. 70–71


Consumer topics – money, shopping using advertisements, catalogue order forms, seating arrangements, compare shopping prices

Introduction to Problem Solving Problem‐Solving Applications: Mixed Review (sale prices)—p. 34

Chapter 3 Addition and Subtraction Lesson 11: Problem Solving Strategy: Choose the Operation (sale prices)—p. 117

Averages (mean) Chapter 5 Divide by One Digit




Lesson 16: Find the Mean—pp. 194–195

Lattice multiplication as enrichment


Calculators – show how multiplication is repeated addition and division is repeated subtraction

Base ten blocks used as area models Literature – Anno’s Mysterious Multiplying Jar – Anno A Remainder of One – Pinczes http://mason.gmu.edu/~mmankus/whole/base10/asmdb10.htm



3 ASSESSMENT Benchmark Tests Chapter Pretests with Analyses Check Your Progress with Analyses




Lessons for Priority Lessons Assessments


5 RESOURCES AUDIO GLOSSARY From A to Z (Grade 4 Glossary—English)

De la A a la Z (Grade 4 Glossary—Spanish)



Enrichment




Math Alive at Home: Take‐Home Activities

Symbols, Measures, and More


CATEGORY: Numbers and Operations – Fractions Standard M.4.F. Extend understanding of fraction equivalence and ordering.



Do I know when fractions and whole numbers are used together in real life?

Chapter 8 Fraction Concepts Lesson 8: Mixed Numbers—pp. 280–281 Lesson 8A: Compare Fractions Using Benchmarks—on‐line

Can I model, compare and order fractions? Chapter 8 Fraction Concepts Lesson 2: Fractions on a Number Line—pp. 268–269

Lesson 3A: Model Equivalent Fractions—on‐line Lesson 8A: Compare Fractions Using Benchmarks—on‐line

Lesson 9: Compare Fractions—pp. 282–283

Do I know how are fractions alike and different?


Formative

Quick Write/Quick Draw – on the right draw a picture of the fraction and on the right explain what it means.

Chapter 8 Fraction Concepts Check Your Progress: Lessons 1–5—on‐line Check Your Progress: Lessons 6–8A—on‐line

www.progressinmathematics.com Teacher Center: Common Core Check Your Progress (with Item Analysis) * See also the Lesson Plan in the TE for Write About It/Math Journal activities and Step 4: Summarize/Assess.

Model ‐ 1/2 is the same as 2/4, 3/6 and 4/8 in arrays and on the number line

Chapter 8 Fraction Concepts Lesson 2: Fractions on a Number Line—pp. 268–269

Lesson 3: Estimate Fractions—pp. 270–271 Lesson 3A: Model Equivalent Fractions—on‐line Lesson 4: Equivalent Fractions—pp. 272–273 Lesson 5: Write Equivalent Fractions—pp. 274–275

Students fold paper rectangles into thirds, shading 2/3 of the rectangles. Students refold the papers

Chapter 8 Fraction Concepts Lesson 1: Write Fractions: Lesson Readiness—TE




into thirds and then in halves opening the rectangles to see that 4/6 are now shaded. Students look at the displayed fractions as 2/3, (2x2)(2x3), and 4/6 and reason that when the denominator and numerator are multiplied by the same number the resulting fraction is equivalent to the original as shown by the shaded rectangles.

pp. 266–267 Lesson 3: Estimate Fractions—TE pp. 270–271 Lesson 3A: Model Equivalent Fractions—on‐line Lesson 4: Equivalent Fractions—pp. 272–273 Lesson 5: Write Equivalent Fractions—pp. 274–275

Summative




M.4.F.1. Explain why fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Chapter 8 Fraction Concepts Lesson 3A: Model Equivalent Fractions—on‐line Lesson 4: Equivalent Fractions—pp. 272–273 Lesson 5: Write Equivalent Fractions—pp. 274–275

Lesson 7: Fractions: Lowest Terms—pp. 278–279 Lesson 12: Problem Solving Applications: Mixed Review—pp. 288–289

M.4.F.2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same whole.


Lesson 3: Estimate Fractions—pp. 270–271 Lesson 4: Equivalent Fractions—pp. 272–273 Lesson 8A: Compare Fractions Using




Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Benchmarks—on‐line Lesson 9: Compare Fractions—pp. 282–283 Lesson 10: Order Fractions—pp. 284–285 Lesson 12: Problem Solving Applications: Mixed Review—pp. 288–289


Fractions are limited with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Chapter 8 Fraction Concepts Lesson 1: Write Fractions—pp. 266–267 Lesson 2: Fractions on a Number Line—pp. 268–269

Lesson 3: Estimate Fractions—pp. 270–271

Compare fractions with like denominators by comparing the numerators.


Lesson 3: Estimate Fractions—pp. 270–271 Lesson 8A: Compare Fractions Using Benchmarks—on‐line

Lesson 9: Compare Fractions—pp. 282–283

Compare fractions with different denominators by multiplying the numerator and denominator by 1 renaming as 2/2, 3/3 etc.

Example: Is 5/6 > 1/2 ? 3/6 = ½ than 5/6 > 3/6 therefore 5/6 > 1/2

Chapter 8 Fraction Concepts Lesson 8A: Compare Fractions Using Benchmarks—on‐line

Visual pictures of 2 fractions that make a whole. e.g. ½ + ½ = 1 and ¼ + ¾ = 1

Example: If each person at a party will eat 3/8 of a pound of turkey and there are 5 people at the party, how many pounds of turkey will be needed? Between what 2 whole numbers does your answer lie?

Chapter 8 Fraction Concepts Lesson 4: Equivalent Fractions—pp. 272–273

Integration of Learning Recipes Chapter 9 Fractions: Addition and Subtraction Lesson 12: Problem Solving Applications: Mixed




How does this learning connect to my other areas (subjects) of learning?

Review—pp. 318–319

Carpentry Chapter 9 Fractions: Addition and Subtraction Lesson 3: Improper Fractions—p. 301


Fraction bars to compare Number lines, ruler Pattern blocks Legos Quilts visual fractions. com Literature – Fraction Action by Leedy Fraction Fun by Adler







Lessons for Priority Lessons Assessments 4 COMMON CORE Correlations Chapter Pacing Guides Teacher Lesson Plans Student Lessons Check Your Progress with Analyses Chapter Tests with Analyses Cumulative Reviews with Analyses Post Test with Analyses






CATEGORY: Numbers and Operations – Fractions Standard M.4.G. Build fractions from unit fractions by applying and extending previous understandings of

operations on whole numbers.



Do I know how fractions are represented in everyday life?

* See lesson introduction and problem solving exercises with fractions—pp. 296–299, 301–305, 308–311, 316–319

Do I know if the computation with fractions and whole numbers the same or different?

Chapter 2 Addition and Subtraction Concepts Lesson 2: Addition Strategies—pp. 70–71 Lesson 3: Subtraction Concepts—pp. 72–73

Chapter 9 Fractions: Addition and Subtraction Lesson 1: Add Fractions: Like Denominators—pp. 296–297

Lesson 2: Subtract Fractions: Like Denominators—pp. 298–299


Formative

Modeling on white boards: have the children draw a variety of fractions as the sum of unit fractions

Exit cards


Summative

Chapter tests, quiz performance assessment www.progressinmathematics.com Teacher Center: Common Core Chapter Tests (with Item Analysis) * See "Problem Solving," "Tell About It," and "Performance Assessment" on the chapter test.


Skills M.4.G.1. Understand a fraction a/b with a > 1 as a





What skills do I need to have in order to answer the essential questions?

sum of fractions 1/b.

a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Chapter 9 Fractions: Addition and Subtraction Lesson 1A: Use Models to Add Fractions—on‐line Lesson 1C: Use Models to Subtract Fractions—on‐line

b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 +1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

Chapter 9 Fractions: Addition and Subtraction Lesson 1B: Decompose Fractions—on‐line

c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Chapter 9 Fractions: Addition and Subtraction Lesson 4A: Add Mixed Numbers—on‐line Lesson 4B: Subtract Mixed Numbers—on‐line Lesson 5: Add and Subtract Mixed Numbers—pp. 304–305

d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.



Lesson 2A: Word Problems Involving Fractions—on‐line


M.4.G.2. Apply and extend previous understanding of multiplication to multiply a fraction by a whole





number.

a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x ¼, recording the conclusion by the equation 5/4 = 5 x ¼ .

Chapter 9 Fractions: Addition and Subtraction Lesson 8A: Multiply with Fractions—on‐line

b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b.)

Chapter 9 Fractions: Addition and Subtraction Lesson 8A: Multiply with Fractions—on‐line

c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Chapter 9 Fractions: Addition and Subtraction Lesson 8A: Multiply with Fractions—on‐line Lesson 10: Find Part of a Number—pp. 314–315 Lesson 12: Problem Solving Applications: Mixed Review—pp. 318–319


Unit fractions * Unit fractions are represented but not defined at this level.


Lesson 3: Estimate Fractions—pp. 270–271 Lesson 3A: Model Equivalent Fractions—on‐line





Lesson 4: Equivalent Fractions—p. 273 Lesson 5: Write Equivalent Fractions—pp. 274–275

Add and subtract fractional numbers with like denominators, using equivalent fractions.

Example: 1 ¼ ‐ ¾



Lesson 6C: Add Fractions with Denominators of 10 and 100—on‐line

If 4/4 + ¼ = 5/4 then 5/4 – ¾ = 2/4 = 1/2 Chapter 9 Fractions: Addition and Subtraction Lesson 3: Improper Fractions—pp. 300–301 Lesson 4: Estimate with Mixed Numbers—pp. 302–303

Lesson 4A: Add Mixed Numbers—on‐line Lesson 4B: Subtract Mixed Numbers—on‐line Lesson 5: Add and Subtract Mixed Numbers—pp. 304–305

Find fractional part of a given set or area. Model this example: 3 x 2/5 is the same as 6 x 1/5 = 6/5

Chapter 9 Fractions: Addition and Subtraction Lesson 8A: Multiply with Fractions—on‐line Lesson 10: Find Part of a Number—pp. 314–315


Recipes Chapter 9 Fractions: Addition and Subtraction Lesson 12: Problem Solving Applications: Mixed Review—pp. 318–319

Carpentry Chapter 9 Fractions: Addition and Subtraction Lesson 3: Improper Fractions—p. 301

Money

Probability Chapter 9 Fractions: Addition and Subtraction





Lesson 9: Compute Probability—pp. 312–313


Graph paper, place value charts with decimals, number line

Fractions in Action Teacher Web Home Page Smart Boards Technology





CATEGORY: Numbers and Operations – Fractions Standard M.4.H. Understand decimal notation for fractions, and compare decimal fractions.



How can I numbers be expressed in multiple ways? How are fractions and decimals related?

Chapter 9 Fractions: Addition and Subtraction Lesson 6C: Add Fractions with Denominators of 10 and 100—on‐line

Chapter 13 Decimals Lesson 1: Tenths and Hundredths—pp. 412–413 Lesson 2: Decimals Greater Than One—pp. 414–415

Lesson 3: Decimal Place Value—pp. 416–417


Formative

Whiteboard work showing fractions above a number line and decimal equivalent below the line.

“I have, Who has”

www.progressinmathematics.com Teacher Center: Planning Blackline Masters (Fraction Number Lines) * Also provided on TE p. T68


Summative



Skills M.4.H.1. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and

Chapter 9 Fractions: Addition and Subtraction Lesson 6C: Add Fractions with Denominators of




What skills do I need to have in order to answer the essential questions?

use this technique to add two fractions with respective denominators 10 and 100.

[Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.]

For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

10 and 100—on‐line

M.4.H.2. Use decimal notation for fractions with denominators 10 or 100. For examples, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

Chapter 13 Decimals Lesson 1: Tenths and Hundredths—pp. 412–413 Lesson 2: Decimals Greater Than One—pp. 414–415

Lesson 3: Decimal Place Value—pp. 416–417

M.4.H.3. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Chapter 13 Decimals Lesson 3A: Compare Decimals with Models and Symbols—on‐line

Lesson 4: Compare Decimals—pp. 418–419 Lesson 5: Order Decimals—pp. 420–421


Compare fractions and decimals using models of hundred squares and base ten blocks

Chapter 13 Decimals Lesson 3A: Compare Decimals with Models and Symbols—on‐line

Lesson 4: Compare Decimals—pp. 418–419

Identify and understand the relationship between fractions and decimals

Chapter 13 Decimals Lesson 1: Tenths and Hundredths (number line)—pp. 412–413 Use number line to connect fractions and decimals.

Use base ten blocks to connect 3/10 or 3 longs is Chapter 13 Decimals




the same as 30/100 Lesson 1: Tenths and Hundredths (model with base ten blocks)—pp. 412–413


Money Chapter 13 Decimals Lesson 4: Compare Decimals (compare money)—pp. 418–419

Batting averages Chapter 7 Statistics and Probability Chapter Opener (batting averages)—p. 239

Use the computer to draw circle graphs – and the web site create a graph

www.progressinmathematics.com STUDENT CENTER 3 VIRTUAL MANIPULATIVES Manipulatives: Pie Chart (make circle graphs)


Physical models, pictures, number lines, use both customary and centimeter rulers, coins

Base ten blocks Graph paper Nlvm.usu.edu


2 PRACTICE Skills Update Math Minutes




Problem of the Day Practice Activities Vocabulary Activities Manipulatives Flash Activities Tutorials





STUDENT CENTER / FAMILY CENTER Skills Update Math Minutes Problem of the Day Practice Activities Vocabulary Activities




Alternative Teaching Models Virtual Manipulatives Audio Glossary From A to Z (Grade 4 Glossary—English) De la A a la Z (Grade 4 Glossary—Spanish)



CATEGORY: Measurement and Data Standard M.4.I. Solve problems involving measurement and conversion of measurements from a larger unit

to a smaller unit.



How do I use measurements on a daily basis? Skills Update—Review of Grade 3 Skills Customary Units of Length—p. 14 Cup—p. 15 Pound—p. 16 Centimeter and Meter—p. 17 Liter—p. 18 Kilogram—p. 19

Chapter 6 Measurement Lesson 1: Measure with Inches—pp. 206–207 Lesson 2: Rename Units of Length—pp. 208–209 Lesson 3: Compute Customary Units—pp. 210–211

Lesson 4: Customary Units of Capacity—pp. 212–213

Lesson 5: Customary Units of Weight—pp. 214–215

Lesson 6: Measure with Metric Units—pp. 216–217

Lesson 7: Work with Metric Units—pp. 218–219 Lesson 8: Metric Units of Capacity—pp. 220–221 Lesson 9: Metric Units of Mass—pp. 222–223 Lesson 9A: Represent Measures on a Number Line—on‐line

Tables of Measures Time, Metric Units, Customary Units—p. 500

Are there different systems for measuring things?

Can I relate smaller units of measurement to larger ones?


Formative

Use a dry erase board to have the students display answers to equivalent measurements. Example: How many inches = 1 foot? Can 3 feet be equivalent to another unit of measurement? Have

www.progressinmathematics.com Teacher Center: Common Core Check Your Progress (with Item Analysis) * See also the Lesson Plan in the TE for Write



to a smaller unit.


students model units of measurement. About It/Math Journal activities and Step 4: Summarize/Assess.

Summative

Have students design a real life situation problem using finding the perimeter or area of a rectangle. For example: fencing a yard, buying the correct amount of carpet for a room. Design a blueprint for the first floor of a house. For instance, door size, window size, and room size.




M.4.I.1. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two‐column table.

For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

Chapter 6 Measurement Lesson 2: Rename Units of Length—pp. 208–209 Lesson 3: Compute Customary Units—pp. 210–211




Lesson 7: Work with Metric Units—pp. 218–219 Lesson 8: Metric Units of Capacity—pp. 220–221 Lesson 9: Metric Units of Mass—pp. 222–223 Lesson 11: Time—pp. 226–227 Lesson 11A: Rename Measures—on‐line Lesson 12: Elapsed Time—pp. 228–229

M.4.I.2. Use the four operations to solve word Chapter 2 Addition and Subtraction Concepts



to a smaller unit.


problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Lesson 8: Add and Subtract Money—pp. 82–83 Chapter 4 Multiplication by One and Two Digits Lesson 8: Multiply Money—pp. 140–141 Lesson 12: Multiply by Two‐Digit Numbers—pp. 148–149

Chapter 5 Divide by One Digit Lesson 14: Divide Money—pp. 190–191





Lesson 7: Work with Metric Units—pp. 218–219 Lesson 8: Metric Units of Capacity—pp. 220–221 Lesson 9: Metric Units of Mass—pp. 222–223 Lesson 9A: Represent Measures on a Number Line—on‐line

Lesson 12: Elapsed Time—pp. 228–229 Lesson 13: Problem Solving Strategy: Use More Than One Step—pp. 230–231


Chapter 13 Decimals Lesson 10: Divide with Money—pp. 430–431

M.4.I.3. Apply the area and perimeter formulas for rectangles in real world and mathematical

Skills Update—Review of Grade 3 Skills Perimeter—p. 20



to a smaller unit.


problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Chapter 11 Perimeter, Area, and Volume Lesson 1: Use Perimeter Formulas—pp. 358–359 Lesson 2: Use Area Formulas—pp. 360–361 Lesson 3: Perimeter and Area—pp. 362–363 Lesson 3A: Perimeter and Area Formulas—on‐line



Knowledge of customary and metric systems for length, time, volume, and mass.






Tables of Measures Time, Metric Units, Customary Units—p. 500

Relationship between smaller and larger units of measure.

Example: 1 ft is 12 times as long as 1 in.

Skills Update—Review of Grade 3 Skills Customary Units of Length—p. 14 Cup—p. 15




to a smaller unit.






Tables of Measures Metric Units, Customary Units—p. 500

How to apply the formula for area and perimeter of rectangles in real life situations. Example: Determining the amount of flooring for a room, or fencing for a yard.

Chapter 11 Perimeter, Area, and Volume Lesson 1: Use Perimeter Formulas—pp. 358–359 Lesson 2: Use Area Formulas—pp. 360–361 Lesson 3: Perimeter and Area—pp. 362–363 Lesson 3A: Perimeter and Area Formulas—on‐line


Make a conversion table for comparing related smaller and larger units.





Lesson 7: Work with Metric Units—pp. 218–219



to a smaller unit.


Lesson 8: Metric Units of Capacity—pp. 220–221 Lesson 9: Metric Units of Mass—pp. 222–223


Vocabulary: metric, convert, conversion table, perimeter, area, mass, volume.







Science‐ measuring and finding the mass of objects. Comparing measurements such as 16 ounces = 1 lb. 48 ounces = 3 lb. (3x16). Analyzing and interpreting data from experiments.

Chapter 6 Measurement Lesson 5: Customary Units of Weight—pp. 214–215

Lesson 9: Metric Units of Mass—pp. 222–223



to a smaller unit.




Conversion tables, metric stick, yardstick, websites, assorted books, manipulative, Scholastic printable resources. Teacher created.com, AIMS






to a smaller unit.


Lessons for Priority Lessons Assessments 4 COMMON CORE Correlations Chapter Pacing Guides Teacher Lesson Plans Student Lessons Check Your Progress with Analyses Chapter Tests with Analyses Cumulative Reviews with Analyses Post Test with Analyses






CATEGORY: Measurement and Data Standard M.4.J. Represent and interpret data.



What Is a line plot? How can I use a line plot diagram to show data?

Chapter 7 Statistics and Probability English Language Learners: Surveys and Line Plots—TE p. 239I

Differentiated Instruction: Inclusion: Surveys and Line Plots—TE p. 239J

Lesson 4: Surveys and Line Plots—pp. 246–247

Do I know how to add and subtract fractions? Chapter 9 Fractions: Addition and Subtraction Lesson 1A: Use Models to Add Fractions—on‐line Lesson 1: Add Fractions: Like Denominators—pp. 296–297

Lesson 1C: Use Models to Subtract Fractions—on‐line


Lesson 2A: Word Problems Involving Fractions—on‐line

Lesson 3: Improper Fractions—pp. 300–301 Lesson 4: Estimate with Mixed Numbers—pp. 302–303

Lesson 4A: Add Mixed Numbers—on‐line Lesson 4B: Subtract Mixed Numbers—on‐line Lesson 5: Add and Subtract Mixed Numbers—pp. 304–305

What does a fraction represent? Skills Update—Review of Grade 3 Skills Identify Fractions—p. 13


Assessment Formative




What will I be expected to know, understand, and be able to do in order to demonstrate my learning?

Use a dry erase board to display a set of measurements in fractions of a unit. For example: ½, ¼, 1/8.


Solve problems involving adding and subtraction fraction by using information presented in line plots.


Differentiated Instruction: Inclusion: Surveys and Line Plots—TE p. 239J

Lesson 4: Surveys and Line Plots—pp. 246–247

Summative

Project: Design a line plot to solve a word problem. For example: Find and interpret the difference in length between the longest and shortest specimens in an insect collection.

Chapter 7 Statistics and Probability Lesson 4: Surveys and Line Plots—pp. 246–247




M.4.J.1. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).

Solve problems involving addition and subtraction of fractions by using information presented

in line plots.


Chapter 9 Fractions: Addition and Subtraction Lesson 5A: Organize Measurement Data—on‐line




For example, from a line plot find and interpret the difference in length between

the longest and shortest specimens in an insect collection.


Vocabulary: line plot, fraction, data set







Science‐interpreting data and representing it by a line plot.


Differentiated Instruction: Inclusion: Surveys and Social Studies‐ Representing with a line plot how many years lapsed between two historical events




located on the same time line? Line Plots—TE p. 239J Lesson 4: Surveys and Line Plots—pp. 246–247


Websites, AIMS * To access online resources, go to— www.progressinmathematics.com GRADE 4 TEACHER CENTER 1 PLANNING Scope and Sequence Road Maps Priority Lessons Table of Contents Pacing Guides Model Lessons for English Learners Blackline Masters Chapter Support Research Base Math Study Take‐Home Activities Chapter Records




CATEGORY: Measurement and Data Standard M.4.K. Geometric measurement: understand concepts of angle and measure angles.



What geometric shapes do I know? Where do I see geometric shapes every day?

Chapter 10 Geometry Lesson 4: Circles—pp. 332–333 Lesson 5: Polygons—pp. 334–335 Lesson 6: Quadrilaterals—pp. 336–337 Lesson 7: Triangles—pp. 338–339

What is an angle? How do I form an angle? Can I see angles in my daily life?

Chapter 10 Geometry Lesson 1A: Angle Measure—on‐line Lesson 2: Rays and Angles—pp. 328–329 Lesson 2A: Measure Angles—on‐line Lesson 2B: Unknown Angle Measures—on‐line


Formative

Be able to identify different types of angles; acute, obtuse, and right angles.

Chapter 10 Geometry Lesson 1A: Angle Measure—on‐line Lesson 2: Rays and Angles: Measuring Angles (identify right, acute, straight, and obtuse angles)—pp. 328–329

Lesson 2A: Measure Angles—on‐line Lesson 2B: Unknown Angle Measures—on‐line Check Your Progress: Lessons 1–4—on‐line


Students should be able to draw and measure various kinds of angles and geometric figures.

Summative

Project: Design a line plot to solve a word problem. For example: Find and interpret the difference in length between the longest and shortest specimens in an insect collection.


www.progressinmathematics.com Teacher Center: Common Core




Chapter Tests (with Item Analysis) * See "Problem Solving," "Tell About It," and "Performance Assessment" on the chapter test.



M.4.K.1. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one‐degree angle,” and can be used to measure angles.

Chapter 10 Geometry Lesson 1A: Angle Measure—on‐line Lesson 2: Rays and Angles—pp. 328–329

b. An angle that turns through n one‐degree angles is said to have an angle measure of n degrees.

Chapter 10 Geometry Lesson 1A: Angle Measure—on‐line

M.4.K.2. Measure angles in whole‐number degrees using a protractor. Sketch angles of specified measure.

Chapter 10 Geometry Lesson 2: Rays and Angles—pp. 328–329 Lesson 2A: Measure Angles—on‐line

M.4.K.3. Recognize angle measure as additive. When an angle is decomposed into non‐overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to

Chapter 10 Geometry Lesson 2B: Unknown Angle Measures—on‐line




find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure


Vocabulary: angle, acute angle, obtuse angle, right angle, rays, protractor.






Knowledge of relationship between an angle being 1/360 of a circle.

Chapter 10 Geometry Lesson 1A: Angle Measure—on‐line Lesson 2: Rays and Angles: Measuring Angles (half‐circle on protractor measures 180°)—p. 329




Knowledge of variables and how to substituting them in solving addition and subtraction problems to find an unknown angle.

Chapter 2 Addition and Subtraction Concepts Lesson 4: Expressions and Variables (variables)—pp. 74–75

Lesson 5: Addition and Subtraction Sentences (variables)—pp. 76–77

Chapter 10 Geometry Lesson 2B: Unknown Angle Measures—on‐line

Chapter 14 Get Ready for Algebra Lesson 1: Equations (variables)—pp. 442–443 Lesson 2: Find Missing Numbers (variables)—pp. 444–445


Science‐interpreting data using circle graphs. Chapter 7 Statistics and Probability Lesson 5: Circle Graphs—pp. 248–249 Lesson 9: Problem Solving Strategy: Use a Diagram/Graph—p. 257


www.progressinmathematics.com TEACHER CENTER 1 PLANNING LESSON PLANNING Blackline Masters: Fraction Circles—T58

Social Studies‐ circle graphs.


Protractors, manipulatives, websites, dry erase boards, AIMS programs

* To access online resources, go to— www.progressinmathematics.com GRADE 4 TEACHER CENTER 1 PLANNING Scope and Sequence Road Maps Priority Lessons Table of Contents Pacing Guides




Model Lessons for English Learners Blackline Masters Chapter Support Research Base Math Study Take‐Home Activities Chapter Records




5 RESOURCES AUDIO GLOSSARY




From A to Z (Grade 4 Glossary—English) De la A a la Z (Grade 4 Glossary—Spanish)





CATEGORY: Geometry Standard M.4.L. Draw and identify lines and angles, and classify shapes by properties of their lines and

angels.



What are lines made of? How can I draw a line? Do I know of different types of lines? Can I identify lines in my world?

Chapter 10 Geometry Lesson 1: Points, Lines, and Line Segments—pp. 326–327

Lesson 2: Rays and Angles—pp. 328–329 Lesson 3: Parallel and Perpendicular Lines—pp. 330–331

Do I know what a line of symmetry is? Skills Update—Review of Grade 3 Skills Lines of Symmetry—p. 22

Chapter 10 Geometry Lesson 10: Turns (half‐turn symmetry)—pp. 344–345

Lesson 12: Problem Solving Strategy: Find a Pattern (line of symmetry)—p. 349


Formative

Use a dry erase board to practice drawing lines points, line segments, angles (right, acute, obtuse), perpendicular and parallel lines. Students should be able to identify and represent two‐dimensional figures.


Lesson 2: Rays and Angles: Measuring Angles (protractor)—pp. 328–329

Lesson 2A: Measure Angles—on‐line Lesson 3: Parallel and Perpendicular Lines—pp. 330–331


STUDENT CENTER 2 ALTERNATIVE TEACHING MODELS

Use models, concrete objects and manipulatives to represent symmetry and lines of symmetry.

Use protractors to draw and measure right angles and triangles.



angels.


Tutorials Grade 5, Chapter 10, Activity 1—Use a protractor to measure angles

Summative

Project‐ Identify lines in the world. Example: train tracks, intersections, and parallel streets.




M.4.L. 1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two‐dimensional figures.


Lesson 2: Rays and Angles—pp. 328–329 Lesson 3: Parallel and Perpendicular Lines—pp. 330–331

Lesson 4: Circles—pp. 332–333 Lesson 11: Coordinate Geometry—pp. 346–347 Lesson 13: Problem Solving Applications: Mixed Review—pp. 350–351

M.4.L. 2. Classify two‐dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

Chapter 10 Geometry Lesson 6: Quadrilaterals—pp. 336–337 Lesson 7: Triangles—pp. 338–339

M.4.L. 3. Recognize a line of symmetry for a two‐ Chapter 10 Geometry



angels.


dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line‐symmetric figures and draw lines of symmetry.

Lesson 7A: Symmetry—on‐line Lesson 12: Problem Solving Strategy: Find a Pattern—pp. 348–349


Vocabulary: point, line, parallel lines, perpendicular lines, symmetry, lines of symmetry, triangle, right triangle, angels.







Science: constructing tables, charts to represent data.

Skills Update—Review of Grade 3 Skills Record and Organize Data—p. 25

Social Studies: identifying borders, rivers, how the states fit with each other.



angels.


Art: What’s in a name? Perspective drawing.


Ruler, protractor, commercial websites. * To access online resources, go to— www.progressinmathematics.com GRADE 4 TEACHER CENTER 1 PLANNING Scope and Sequence Road Maps Priority Lessons Table of Contents Pacing Guides Model Lessons for English Learners Blackline Masters Chapter Support Research Base Math Study Take‐Home Activities Chapter Records





angels.







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