Correlated to the Archdiocese of Philadelphia · SADLIER‐OXFORD Progress in Mathematics Grade 5 Correlated to the Archdiocese of Philadelphia Mathematics Standards for Grade 5 CATEGORY:

SADLIER‐OXFORD Progress in Mathematics Grade 5 Correlated to the Archdiocese of Philadelphia Mathematics Standards for Grade 5

CATEGORY: Operations and Algebraic Thinking Standard M.5.A. Write and interpret numerical expressions. 2 Standard M.5.B. Analyze patterns and relationships. 8 CATEGORY: Numbers and Operations in Base Ten Standard M.5.C. Understand the place value system. 15 Standard M.5.D. Perform operations with multi‐digit whole numbers and with decimals to hundredths. 22 CATEGORY: Numbers and Operations – Fractions Standard M.5.E. Use equivalent fractions as a strategy to add and subtract fractions. 30 Standard M.5.F. Apply and extend previous understandings of multiplication and division to multiplication and division of

fractions. 38

CATEGORY: Measurement and Data Standard M.5.G. Convert like measurement units within a given measurement system. 48 Standard M.5.H. Represent and interpret data. 54 Standard M.5.I. Geometric measurement: understand the concepts of volume and relate volume to multiplication and

addition. 59

CATEGORY: Geometry Standard M.5.J. Graph points on the coordinate plane to solve real world and mathematical problems. 65 Standard M.5.K. Classify two‐dimensional figures into categories based on their properties. 70

Sadlier Progress in Mathematics Grade 5 Correlated to the Archdiocese of Philadelphia Mathematics Standards for Grade 5 8/3/11 Page 2 of 74

CATEGORY: Operations and Algebraic Thinking Standard M.5.A. Write and interpret numerical expressions.

Sadlier Progress in Mathematics, Grade 5

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

How do I deal with questions that have multiple math operations?

Chapter 3 Division Lesson 14: Order of Operations—pp. 122–123

Chapter 5 Fractions: Addition and Subtraction Lesson 13: Problem Solving Strategy: Work Backward (use order of operations)—p. 188

Chapter 6 Fractions: Multiplication and Division Lesson 11: Divide Fractions by Fractions: Mental Math—p. 219

Lesson 14: Divide Mixed Numbers: Challenge (compute using order of operations)—p. 225

Chapter 9 Decimals: Multiplication and Division Lesson 5: Zeros in the Product (use order of operations)—p. 303

Chapter 14 More Concepts in Algebra Lesson 11: Multiply Integers: Write About It (use order of operations)—p. 461

Lesson 12: Divide Integers (use order of operations)—p. 463

Lesson 14: Function Tables: Critical Thinking (use order of operations)—p. 467

Why is the strategy of order of operations both effective and efficient for me?

When am I going to see and use this skill?

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

Formative

Students can discuss in small groups what they have learned about numerical expressions and order of operations.

www.progressinmathematics.com Teacher Center: Common Core Check Your Progress with Analyses

* See also — Chapter 3 Division Lesson 14: Order of Operations: Summarize/Assess—TE p. 123

Students can write in math journal, “I used to think I could solve a series of equations by working from left to right. Now I know I have to follow order of operations because…”

Students will answer one or more of the Essential Questions.

Summative




Performance Assessment: In a long‐range activity, student will devise an activity or game (such as Hopscotch) that can use steps that will simulate order of operations. Explanations, illustrations, and game rules will be included.

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.5.A. 1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Chapter 2 Multiplication Lesson 2: Properties of Multiplication—pp. 68–69

Chapter 3 Division Lesson 14: Order of Operations—pp. 122–123 Lesson 14A: Variables and Expressions—on‐line

Chapter 14 More Concepts in Algebra Lesson 1: Algebraic Expressions and Equations—pp. 440–441

Lesson 2: Properties of Equality—pp. 442–443

M.5.A. 2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Chapter 2 Multiplication Lesson 2: Properties of Multiplication—pp. 68–69

Chapter 3 Division Lesson 14A: Variables and Expressions—on‐line


Lesson 2: Properties of Equality—pp. 442–443




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

Simplify Order of Operations through the use of parentheses, braces, or brackets.

Do those operations that are in parentheses, braces, or brackets first.

PEMDASFLTR – Please Excuse My Dear Aunt Sally From Leaving The Room

Parentheses, Exponents, Multiplication OR Division, Addition OR Subtraction, From Left To Right

Chapter 3 Division Lesson 14: Order of Operations—pp. 122–123

Chapter 5 Fractions: Addition and Subtraction Lesson 13: Problem Solving Strategy: Work Backward (use order of operations)—p. 188







Use mathematical representation to solve problems.


Lesson 2: Properties of Equality—pp. 442–443 Lesson 3: Addition and Subtraction Equations—pp. 444–445

Lesson 4: Multiplication and Division Equations—pp. 446–447

Lesson 5: Equations with Fractions—pp. 448–449 * Students use mathematical representations to solve problems throughout the program.

Integration of Learning Science, Computer Programming, and Accounting: Chapter 3 Division




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

Investigate how and why mathematical calculations in these areas need order of operations.

Lesson 14: Order of Operations—pp. 122–123 Chapter 5 Fractions: Addition and Subtraction Lesson 13: Problem Solving Strategy: Work Backward (use order of operations)—p. 188







Technology: Use several different types of calculators, E.G., four function, fraction, etc. Give students a series of equations to be put into each type of calculator. Decide which type of calculator automatically solves the equations using order of operations. Student will write the results and decide why certain types of calculators do/do not automatically use order of operations.

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

Trade books, text books, calculators, computers, interactive boards

NCTM website, C&I website, commercial websites

* To access online resources, go to— www.progressinmathematics.com GRADE 5 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 5 Glossary—English) De la A a la Z (Grade 5 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 5 Glossary—English) De la A a la Z (Grade 5 Glossary—Spanish)

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


CATEGORY: Operations and Algebraic Thinking Standard M.5.B. Analyze patterns and relationships.



How can I relate mathematical patterns to patterns in life?

Chapter 1 Place Value, Addition, and Subtraction 1‐1 What Is a Billion? (patterns)—p. 30 1‐5 Decimals Greater Than One: Challenge (write the pattern rule)—p. 39

Chapter 2 Multiplication 2‐3 Mental Math: Special Factors (patterns: multiplying with 10)—pp. 70‐71

2‐4 Patterns in Multiplication (patterns: multiplying with 100, 1000 or multiples)—pp. 72‐73

Enrichment: Exponents (discover a pattern)—p. 91

Chapter 3 Division 3‐2 Division Patterns (patterns)—pp. 98‐99 3‐15 Problem Solving Strategy: Make a Table/Find a Pattern—pp. 124‐125

3‐16 Problem Solving Applications: Mixed Review (use the pattern to solve the problem)—p. 127

Cumulative Review: Talk About It (using a number pattern)—p. 132

Chapter 5 Fractions: Addition and Subtraction 5‐10 Subtraction with Renaming: Critical Thinking (patterns)—p. 183

5‐14 Problem Solving Applications: Mixed Review (patterns)—p. 191

Chapter 6 Fractions: Multiplication and Division 6‐8 Division of Fractions (look for a pattern)—p. 213

6‐9 Reciprocals: Critical Thinking (discover a pattern)—p. 215

Chapter 6 Test: Performance Assessment (predict rule for pattern)—p. 234

Chapter 8 Decimals: Addition and Subtraction

How do patterns shape my understanding of mathematics?

How can I change patterns in mathematics to rules of mathematics?




8‐6 Subtract Decimals (pattern rule)—p. 279 Chapter 9 Decimals: Multiplication and Division 9‐1 Multiply by 10, 100, and 1000 (look for patterns)—pp. 294‐295

9‐3 Multiply Decimals by Whole Numbers: Critical Thinking (arithmetic sequence/geometric sequence)—p. 299

9‐4 Multiply Decimals by Decimals: Critical Thinking (pattern rule)—p. 301

9‐5 Zeros in the Product: Challenge (discover a pattern)—p. 303

9‐6 Divide by 10, 100, and 1000 (use patterns, describe patterns)—pp. 304‐305

Chapter 10 Geometry 10‐11 Transformations (patterns)—pp. 344‐345 10‐12 Tessellations (patterns)—pp. 346‐347 Enrichment: Triangular and Square Numbers (number sequences of whole numbers)—p. 353

Chapter 11 Measurement Topics 11‐4 Temperature: Do You Remember? (skip count to make patterns)—p. 365

Enrichment: Pascal's Triangle—p. 377 Chapter 12 Metric Measurement, Area, and Volume 12‐1 Metric Measurement: Challenge (discover patterns)—p. 383

Chapter 13 Ratio, Proportion, and Percent 13‐8 Problem Solving Strategy: Combine Strategies (find a pattern)—p. 430

Enrichment: Percent Patterns—p. 435 Chapter 14 More Concepts in Algebra 14‐11 Multiply Integers (patterns, write a number pattern)—p. 460




14‐12 Divide Integers: Challenge (complete patterns)—p. 463

14‐14 Function Tables—pp. 466‐467 14‐15 Functions and Coordinate Graphs—pp. 468‐469


Formative

Students can use physical patterns such as in card games, checkers, chess, skip counting, patterns in nature, etc., and relate them to mathematical number patterns.

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.

In small groups, each student will create number patterns, graph these, then discuss these patterns.

Students can use pattern blocks to create tessellations.

Math Journal: Students will answer one or more of the Essential Questions.

Summative

Performance Assessment: In a long‐range activity, students can create games that use patterns. Explanations will include how the game is played, what patterns are used, how patterns help to solve the game, etc. Illustrations should include the actual game and game pieces. These can be made of cardboard or other simple materials. Graphs can be used to illustrate the game.




M.5.B.1. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered

Chapter 14 More Concepts in Algebra Lesson 13B: Sequences—on‐line Lesson 13C: Compare Sequences—on‐line




pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.

For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

Lesson 14: Function Tables—pp. 466–467


Vocabulary: patterns, ordered pairs, corresponding terms, coordinate plane, sequence.

* 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.

* See also — Student Glossary (with definitions and page references to where many terms are introduced)—pp. 502–506

Teacher Glossary (for enrichment: an extension of the Glossary in the Student Edition; defined terms listed alphabetically and grouped by topic)—TE pp. T45–T46

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)




Compare patterns of one sequence to patterns of another sequence. E.G., 0,3,5,7,9 (add 2 to each number). 0,4,8,12,16 (add 4 to each number).

Chapter 1 Place Value, Addition, and Subtraction Lesson 5: Decimals Greater Than One: Challenge (write the pattern rule)—p. 39

Chapter 9 Decimals: Multiplication and Division Lesson 3: Multiply Decimals by Whole Numbers: Challenge (arithmetic sequences)—p. 299

Lesson 4: Multiply Decimals by Decimals: Critical Thinking (write the pattern rule)—p. 301

Chapter 14 More Concepts in Algebra Lesson 13: The Coordinate Plane—pp. 464–465 Lesson 12: Divide Integers: Challenge (find the pattern rule)—p. 463

Lesson 13B: Sequences—on‐line

Describe the relationship between the “add” numbers in the patterns. E.G., “add” 4 is twice as much as “add” 2. Form ordered pairs, e.g., (2,4), then graph these on a coordinate plane.

Chapter 1 Place Value, Addition, and Subtraction Lesson 5: Decimals Greater Than One: Challenge (write the pattern rule)—p. 39

Chapter 9 Decimals: Multiplication and Division Lesson 3: Multiply Decimals by Whole Numbers: Challenge (arithmetic sequences)—p. 299

Lesson 4: Multiply Decimals by Decimals: Critical Thinking (write the pattern rule)—p. 301

Chapter 14 More Concepts in Algebra Lesson 12: Divide Integers: Challenge (find the pattern rule)—p. 463

Lesson 13: The Coordinate Plane (ordered pairs)—pp. 464–465

Lesson 13A: Using Coordinate Graphs—on‐line Lesson 13B: Sequences—on‐line

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

Social Science: Make numerical and logical predictions for various real world activities.

Chapter 7 Statistics and Probability Lesson 1: Probability (make predictions)—pp. 238–239

History: Discuss patterns in history, such as wars,




diseases, migration, inventions, medical advances, etc.

Science: Discuss patterns in science and nature, such as lunar cycles, scientific inventions, the growth cycle of plants, etc.


text books, trade books, calculators, computers, pattern blocks, graphs, interactive boards

NCTM, C& I, and commercial websites

* To access online resources, go to— www.progressinmathematics.com GRADE 5 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


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






CATEGORY: Numbers and Operations in Base Ten Standard M.5.C. Understand the place value system.



What does zero mean? Skills Update—Review of Grade 4 Skills Place Value to Thousands—p. 1 Round Whole Numbers (round to 0)—p. 3 Add and Subtract Whole Numbers (round to 0)—p. 4

Multiply One Digit (round to 0)—p. 5 Tenths and Hundredths (0 shows no tenths)—p. 11

Chapter 1 Place Value, Addition, and Subtraction Lesson 8: Addition Properties/Subtraction Rules: Identity Property of Addition—pp. 44–45

Lesson 11: Subtraction with Zeros—pp. 50–51 Chapter 2 Multiplication Lesson 2: Properties of Multiplication: Zero Property of Multiplication—pp. 68–69

Lesson 9: Zeros in the Multiplier—pp. 82–83 Chapter 3 Division Lesson 5: Zeros in the Quotient—pp. 104–105

Chapter 9 Decimals: Multiplication and Division Lesson 5: Zeros in the Product—pp. 302–303 Lesson 8: Zeros in Division—pp. 308–309

Where do I see and use zeros?

How do I compare powers of ten to the use of zeros in the place value system?

Chapter 1 Place Value, Addition, and Subtraction Lesson 1: What Is a Billion?—pp. 30–31 Lesson 2: Place Value to Billions—pp. 32–33 Lesson 3: Expanded Form—pp. 34–35 Lesson 3A: Powers of Ten—on‐line

Where will I use decimals in real life situations? * See lesson introduction and problem solving exercises with decimals—pp. 271–287, 295–307, 309–317

How does expanding numbers help me to understand place value?

Chapter 1 Place Value, Addition, and Subtraction Lesson 3: Expanded Form—pp. 34–35





Formative

Students will model whole numbers and decimals using base ten blocks.

www.progressinmathematics.com Teacher Center: Planning Blackline Masters (Centimeter Grid Paper) 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.

Students will use 100 grid paper to demonstrate decimals. Use several colors to show comparison of decimals.

In groups of two, students will write the expansion of whole numbers, decimal numbers, and numbers with exponents. Each student will write a portion of the expansion and will critique her/his partner’s written work.


Summative

Performance Assessment: In a long‐range activity, students will use whole numbers, money, and decimals in comparison shopping. In small groups, students will choose a grocery or dry goods product. Compare the prices of the same item in three different stores. Investigate or deduce why there is a difference in prices. Use store ads or actual trips to the store. Use rounding of decimals and whole numbers.




M.5.C.1. Recognize that in a multi‐digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Chapter 1 Place Value, Addition, and Subtraction Lesson 1: What Is a Billion?—pp. 30–31 Lesson 2: Place Value to Billions—pp. 32–33 Lesson 3: Expanded Form—pp. 34–35 Lesson 4: Thousandths—pp. 36–37 Lesson 4A: Decimals and Expanded Form—on‐line




Lesson 5: Decimals Greater Than One—pp. 38–39 Chapter 8 Decimals: Addition and Subtraction Lesson 2: Decimals and Place Value—pp. 270–271

M.5.C.2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole‐number exponents to denote powers of 10.

Chapter 1 Place Value, Addition, and Subtraction Lesson 3A: Powers of Ten—on‐line

Chapter 2 Multiplication Lesson 3: Mental Math: Special Factors—pp. 70–71

Lesson 4: Patterns in Multiplication—pp. 72–73 Chapter 9 Decimals: Multiplication and Division Lesson 1: Multiply by 10, 100, and 1000—pp. 294–295

Lesson 6: Divide by 10, 100, and 1000—pp. 304–305

M.5.C.3. Read, write, and compare decimals to thousandths.

a. Read and write decimals to thousandths using base‐ten numerals

Chapter 1 Place Value, Addition, and Subtraction Lesson 4: Thousandths—pp. 36–37 Lesson 4A: Decimals and Expanded Form—on‐line

Lesson 5: Decimals Greater Than One—pp. 38–39 Chapter 8 Decimals: Addition and Subtraction Lesson 2: Decimals and Place Value—pp. 270–271

b. Compare two decimals to thousandths based on meanings of the digits in each place

Chapter 1 Place Value, Addition, and Subtraction Lesson 6: Compare and Order Numbers—pp. 40–41

Chapter 8 Decimals: Addition and Subtraction Lesson 1: Decimal Sense—pp. 268–269

M.5.C.4. Use place value understanding to round decimals to any place.

Chapter 1 Place Value, Addition, and Subtraction Lesson 7: Rounding Numbers—pp. 42–43





Vocabulary: decimal, decimal point, exponents, powers of 10, tenths, hundredths, thousandths, expanded form. Stress: The word “and” is used when reading decimals only, not with large whole numbers. Decimals are read as “and,” not as “point.”






1. E.G. Use the number 5327. Show how the 5 is 5x1000, the 3 is 3x100, etc. Show how each decimal digit is 1/10 of the place to the left.

Chapter 8 Decimals: Addition and Subtraction Lesson 1: Decimal Sense—pp. 268–269 Lesson 2: Decimals and Place Value—pp. 270–271

2. Show how multiplying by 102 will result in a product ending in two zeros. E.G. 525 x102 = 52500. Explain how the decimal point is moved to the right when multiplying by powers of 10 and to the left when dividing by powers of 10.

Chapter 1 Place Value, Addition, and Subtraction Lesson 3A: Powers of Ten—on‐line

Chapter 8 Decimals: Addition and Subtraction Enrichment: Scientific Notation—p. 289

Chapter 9 Decimals: Multiplication and Division Lesson 1: Multiply by 10, 100, and 1000—pp. 294–295




Lesson 6: Divide by 10, 100, and 1000—pp. 304–305

3. Expand whole numbers and decimal numbers. a) in tenths, hundredths, thousandths. b) compare decimals to the thousandths place. E.G. 0.123 <0256. c) round decimals to any place.

Chapter 1 Place Value, Addition, and Subtraction Lesson 3: Expanded Form—pp. 34–35 Lesson 3A: Powers of Ten—on‐line Lesson 4: Thousandths—pp. 36–37 Lesson 4A: Decimals and Expanded Form—on‐line

Lesson 6: Compare and Order Numbers—pp. 40–41

Lesson 7: Rounding Numbers: Rounding Decimals and Money—p. 43


Investigate how science formulas, engineering, and computer science use exponents, expanded notation.

Chapter 1 Place Value, Addition, and Subtraction Lesson 3: Expanded Form—pp. 34–35

Chapter 2 Multiplication Enrichment: Exponents—p. 91

Chapter 8 Decimals: Addition and Subtraction Lesson 2: Decimals and Place Value—pp. 270–271 Enrichment: Scientific Notation—p. 289

Health/science: Use labels from cans, boxes that show volume or weight as decimal numbers. Compare these numbers.

Social Studies: Compare the population of several United States cities. Make inferences as to why the population in some cities is larger/smaller than others. Round these numbers.


Investigate how science formulas, engineering, and computer science use exponents and expanded notation.

Health/Science: Use labels from cans, boxes, etc. that show volume or weight as decimal numbers.

* To access online resources, go to— www.progressinmathematics.com GRADE 5 TEACHER CENTER 1 PLANNING




Compare these numbers/ Social Studies: Investigate the populations of several cities. Make inferences as to why populations in some cities are larger/smaller than other cities.

Text books, trade books, calculators, computers, graphs, base ten blocks, grid paper, interactive boards NCTM , C&I, and commercial websites

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





CATEGORY: Numbers and Operations in Base Ten Standard M.5.D. Perform operations with multi-digit whole numbers and with decimals to hundredths.



Where will I use multiplication of whole numbers and decimals in real world situations?

* See problem solving activities—pp. 100–107, 114–121

How do I multiply multi‐digit whole numbers? Chapter 2 Multiplication Lesson 1: Factors and Products—pp. 66–67 Lesson 2: Properties of Multiplication—pp. 68–69 Lesson 3: Mental Math: Special Factors—pp. 70–71

Lesson 4: Patterns in Multiplication—pp. 72–73 Lesson 5: Estimate Products—pp. 74–75 Lesson 6: Zeros in the Multiplicand—pp. 76–77 Lesson 7: Multiply Two Digits—pp. 78–79 Lesson 8: Multiply Three Digits—pp. 80–81 Lesson 9: Zeros in the Multiplier—pp. 82–83

How can I find the relationship between multiplication and division?

Skills Update—Review of Grade 4 Skills One‐Digit Quotients (check by multiplying)—p. 6 Two‐Digit Quotients (check by multiplying)—p. 7

Chapter 14 More Concepts in Algebra Lesson 12: Divide Integers (division is the inverse of multiplication)—pp. 462–463

* See also check division by multiplying—pp. 100–107, 114–121

How can I use concrete models to demonstrate addition, subtraction, multiplication, and division of decimals?

Chapter 8 Decimals: Addition and Subtraction Lesson 2A: Use Models to Add Decimals—on‐line Lesson 3: Add Decimals—pp. 272–273 Lesson 5A: Use Models to Subtract Decimals—on‐line

Lesson 6: Subtract Decimals—pp. 278–279 Chapter 9 Decimals: Multiplication and Division Lesson 3: Multiply Decimals by Whole Numbers—pp. 298–299

Lesson 3A: Model Multiplying Two Decimals—on‐line

How can models help me to understand mathematical concepts?




Lesson 4: Multiply Decimals by Decimals—pp. 300–301

Lesson 6A: Model Dividing a Decimal by a Whole Number—on‐line

Lesson 7: Divide Decimals by Whole Numbers—pp. 306–307

Lesson 8: Zeros in Division—pp. 308–309 Lesson 8A: Model Dividing a Decimal by a Decimal—on‐line

www.progressinmathematics.com Teacher Center: Planning Chapter Support (Professional Development) * Using models to demonstrate operations with decimals.


Formative

Students will use concrete objects, such as base ten blocks to illustrate whole numbers and decimals.


Use grid paper and colored pencils/ crayons to illustrate whole numbers and decimals. Write explanations of these in math journals.

Math Journal: Students will answer one or more of the Essentials Questions.

Summative

Performance Assessment: In a long‐range activity, students will create a school bank, with deposits, loans, and interest, using addition, subtractions, multiplication, and division of whole numbers, money, and decimals. Write an on‐going explanation of what has been done and keep records of each process.


Post Tests (with Item Analysis)




In a long‐range activity, students will make flash cards. The cards will illustrate addition, subtraction, multiplication, and division of multi‐digit whole numbers and decimals. Each card will list the concept and the process for solving the equation, and create pictures of the operations. A word problem should be included on each card. One card can be used for each concept. The flash cards can vary according to teacher specifications.

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


M.5.D.1. Fluently multiply multi‐digit whole numbers using the standard algorithm.

Chapter 2 Multiplication Lesson 6: Zeros in the Multiplicand—pp. 76–77 Lesson 7: Multiply Two Digits—pp. 78–79 Lesson 8: Multiply Three Digits—pp. 80–81 Lesson 9: Zeros in the Multiplier—pp. 82–83 Lesson 12: Problem Solving Applications: Mixed Review—pp. 88–89

M.5.D.2. Find whole‐number quotients of whole numbers with up to four‐digit dividends and two‐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 3 Division Lesson 2: Division Patterns—pp. 98–99 Lesson 3: Three‐Digit Quotients—pp. 100–101 Lesson 5: Zeros in the Quotient—pp. 104–105 Lesson 6: Short Division—pp. 106–107 Lesson 9A: Use Arrays to Divide—on‐line Lesson 10: Teens as Divisors—pp. 114–115 Lesson 10A: Use Strategies to Divide—on‐line Lesson 11: Two‐Digit Divisors—pp. 116–117 Lesson 16: Problem Solving Applications: Mixed Review—pp. 126–127

M.5.D.3. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the

Chapter 2 Multiplication Lesson 10: Multiplication with Money—pp. 84–85

Chapter 3 Division Lesson 13: Divide Money—pp. 120–121

Chapter 8 Decimals: Addition and Subtraction




strategy to a written method and explain the reasoning used.

Lesson 2A: Use Models to Add Decimals—on‐line Lesson 2B: Mental Math: Add Decimals—on‐line Lesson 3: Add Decimals—pp. 272–273 Lesson 4: Estimate Decimal Sums—pp. 274–275 Lesson 5: Add More Decimals—pp. 276–277 Lesson 5A: Use Models to Subtract Decimals—on‐line

Lesson 6: Subtract Decimals—pp. 278–279 Lesson 8: Subtract More Decimals—pp. 282–283 Lesson 10: Problem Solving Applications: Mixed Review—pp. 286–287

Chapter 9 Decimals: Multiplication and Division Lesson 1: Multiply by 10, 100, and 1000—pp. 294–295

Lesson 2A: Multiply Decimals—on‐line Lesson 3: Multiply Decimals by Whole Numbers—pp. 298–299

Lesson 3A: Model Multiplying Two Decimals—on‐line

Lesson 4: Multiply Decimals by Decimals—pp. 300–301

Lesson 5: Zeros in the Product—pp. 302–303 Lesson 6: Divide by 10, 100, and 1000—pp. 304–305

Lesson 6A: Model Dividing a Decimal by a Whole Number—on‐line

Lesson 7: Divide Decimals by Whole Numbers—pp. 306–307

Lesson 8: Zeros in Division—pp. 308–309 Lesson 8A: Model Dividing a Decimal by a Decimal—on‐line

Lesson 8B: Divide Decimals—on‐line Lesson 12: Problem Solving Applications: Mixed




Review—pp. 316–317


Vocabulary: properties, quotient, dividend, divisor, digit, equation, arrays, concrete model algorithm (teacher use). Stress the word “and” not “point” when reading decimal numbers. When reading numbers, the word “and” should be used with decimals only, not with large whole numbers.






Mastery of multi‐digit whole numbers using standard form of multiplication.

Chapter 2 Multiplication Lesson 1–Lesson 12—pp. 66–89

Divide whole numbers with 4‐digit dividends and 2‐digit divisors. Show how division is the inverse (opposite) of multiplication.

Chapter 3 Division Lesson 1: Understanding Division (division is the inverse of multiplication)—pp. 96–97

Lesson 10: Teens as Divisors—pp. 114–115 Lesson 11: Two‐Digit Divisors—pp. 116–117 Lesson 12: Divide Larger Numbers—pp. 118–119 Lesson 13: Divide Money—pp. 120–121




3) Addition, subtraction, multiplication, and division of decimals to the hundredths place using models, drawings, and written explanations to relate this to the use of numbers.

Chapter 8 Decimals: Addition and Subtraction—pp. 268–287

Chapter 9 Decimals: Multiplication and Division—pp. 294–317


Technology: In groups of three students, a series of math problems will be solved to determine the most efficient method. Student 1uses pencil and paper. Student 2 uses mental math. Student 3 uses a calculator.

Choose a computation method—pp. 49, 75, 92, 119, 121, 281

Students can interview people in professions that use decimals, such as engineering, carpentry, plumbing, manufacturing to discover how math is used in those jobs.

Student 1 uses pencil and paper. Student 2 uses mental math. Student 3 uses a calculator

Choose a computation method—pp. 49, 75, 92, 119, 121, 281

Social Science: Students can interview people in professions such as engineering, carpentry, plumbing, and manufacturing, that use decimals to discover how math is used in these jobs.


text books, trade books, calculators, computers, pattern blocks, graphs, interactive board

NCTM, C & I, and commercial websites

* To access online resources, go to— www.progressinmathematics.com GRADE 5 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 — Fractions Standard M.5.E. Use equivalent fractions as a strategy to add and subtract fractions.



Where will I use portions of numbers? Chapter 5 Fractions: Addition and Subtraction Chapter Opener: Critical Thinking/Finding Together—p. 163


Where do I see fractions or portions of objects/numbers used in real world situations?

Where can I use addition and subtraction of fractions in real world situations?

How do I use equivalent fractions used to add and subtract fractions with unlike denominators?

Skills Update—Review of Grade 4 Skills Equivalent Fractions—p. 9

Chapter 5 Fractions: Addition and Subtraction Lesson 1A: Add Fractions with Unlike Denominators—on‐line

Lesson 2: Add Fractions: Unlike Denominators—pp. 166–167

Lesson 6A: Subtract Fractions with Unlike Denominators—on‐line

Lesson 7: Subtract Fractions: Unlike Denominators—pp. 176–177

How can I use benchmark fractions to understand if my answer is logical?

Chapter 5 Fractions: Addition and Subtraction Lesson 9A: Use Benchmark Fractions—on‐line


Formative

Students will use fraction dominoes to create games that add and subtract fractions.


Use fraction strips to compare fractions, E.G., How many eighth strips equal a ¼ strip? Is 2/5 greater or less than 3/8? Use fractions strips to compare mixed numbers to improper fractions. Measure objects to the nearest fraction.


Summative




Performance assessment: In a long‐range activity, students will explore real‐world use of fractions. Obtain newspapers, magazines, TV advertisements to demonstrate sale items with “fraction off.” E.G. The sales is ½ off the regular price. Student will write a report describing this, and will use illustrations, computation, word problems, and written explanations.


Post Tests (with Item Analysis) * See "Problem Solving" and "Tell About It" on the chapter post test. Performance assessment: Students will investigate

and create a report on occupations that use fractions. Demonstrate how the occupation uses addition and subtraction of fractions.


M.5.E.1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)



Lesson 3: Add Three Fractions—pp. 168–169 Lesson 4: Add Mixed Numbers—pp. 170–171 Lesson 5: Rename Mixed Number Sums—pp. 172–173



Lesson 8: More Subtraction of Fractions—pp. 178–179

Lesson 8A: Subtract Fractions and Whole Numbers from Mixed Numbers—on‐line

Lesson 9: Subtract Mixed Numbers—pp. 180–181 Lesson 10: Subtraction with Renaming—pp. 182–183




Lesson 11: More Renaming in Subtraction—pp. 184–185

M.5.E.2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Chapter 4 Number Theory and Fractions Lesson 4: Fraction Sense—pp. 140–141

Chapter 5 Fractions: Addition and Subtraction Lesson 1: Rename Fraction Sums: Like Denominators—pp. 164–165



Lesson 6: Rename Differences: Like Denominators—pp. 174–175



Lesson 9: Subtract Mixed Numbers—pp. 180–181 Lesson 9A: Use Benchmark Fractions—on‐line Lesson 10: Subtraction with Renaming—pp. 182–183


Lesson 12: Estimate Sums and Differences of Mixed Numbers—pp. 186–187

Lesson 13: Problem Solving Strategy: Work Backward—pp. 188–189

Lesson 14: Problem Solving Applications: Mixed Review—p. 191

Chapter 6 Fractions: Multiplication and Division Lesson 10B: Word Problems Involving




Fractions—on‐line


Vocabulary: numerator, denominator, equivalent fractions, mixed numbers, sum, difference, benchmark fractions, visual fraction model






Add and subtract unlike fractions and mixed numbers.










Lesson 8A: Subtract Fractions and Whole Numbers from Mixed Numbers—on‐line

Lesson 9: Subtract Mixed Numbers—pp. 180–181 Lesson 10: Subtraction with Renaming—pp. 182–183


Lesson 12: Estimate Sums and Differences of Mixed Numbers—pp. 186–187

Use the least common denominator to make equivalent fractions.

Chapter 4 Number Theory and Fractions Lesson 7: Multiples: LCM and LCD—pp. 146–147



3) Use representations, diagrams, illustrations, manipulatives and equations to solve word problems. Use bench mark fractions and number line to decide if an answer is reasonable.

Chapter 5 Fractions: Addition and Subtraction Lesson 1: Rename Fraction Sums: Like Denominators (number line)—pp. 164–165

Lesson 4: Add Mixed Numbers (fraction strips)—pp. 170–171

Lesson 6: Rename Differences: Like Denominators (number lines)—pp. 174–175

Lesson 9A: Use Benchmark Fractions—on‐line

Integration of Learning Science: Discuss how science formulas use fractions and decimals.

Chapter 10 Geometry Lesson 7: Perimeter (fractions and decimals in





formulas)—pp. 336–337 Chapter 12 Metric Measurement, Area, and Volume Lesson 6: Areas of Rectangles and Squares (fractions and decimals in formulas)—pp. 392–393

Language: use a Venn diagram to determine if fractions that are greater than, less than, or equal to a designated fractions.

* See related content— Chapter 1 Place Value, Addition, and Subtraction Enrichment: Logic and Venn Diagrams—p. 61

Music – Compare whole, half, quarter, eighth, and sixteenth notes. Decide on various arrangements of real life occupations: carpentry, landscaping, automotive, plumbing, painting, flooring, etc. notes that will make a measure of four beats.

* See related content— Chapter 4 Number Theory and Fractions Lesson 10: Compare and Order Fractions—pp. 152–153

Social Science/ Life Skills: Investigate how people in real life occupations, such as carpentry, landscaping, automotive, flooring, painting, plumbing, etc. that use fractions.

* See problem solving activities—pp. 141–143, 145, 148, 151, 153–157, 164–171, 173–191

* See Follow‐Up: Problem Solving / Real‐World Connections / Research—pp. TE 147, 151, 175


Text books, trade books, calculators, computers, pattern blocks, grid paper, base 10 blocks, interactive boards

NCTM. C & I, and commercial websites

* To access online resources, go to— www.progressinmathematics.com GRADE 5 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






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 5 Glossary—English) De la A a la Z (Grade 5 Glossary—Spanish)



CATEGORY: Numbers and Operations – Fractions Standard M.5.F. Apply and extend previous understandings of multiplication and division to multiplication

and division of fractions.



How can fraction models and drawings help me to understand multiplication and divisions of fractions?

Chapter 6 Fractions: Multiplication and Division Chapter Opener: Critical Thinking/Finding Together (using fraction models)—p. 197

Lesson 1: Multiply Fractions—pp. 198–199 Lesson 2: Multiply Fractions by Fractions—pp. 200–201


Where will I see portions of objects multiplied and divided in real life?

Chapter 6 Fractions: Multiplication and Division * See problem solving exercises—pp. 200–203, 205, 207 –213, 215–225, 227–231

* See also Follow‐Up: Problem Solving—TE pp. 201, 203, 205, 207, 219, 225, 227; Real‐World Connections—TE p. 217

Where in real life will I see fractions multiplied and divided?


Formative

Students will use fraction dominoes to create games that use multiplication and division of fractions. Use fraction strips to demonstrate multiplication and division of fractions.


With small groups of students, use dry erase boards to solve word problems: The first student creates a word problem, and passes the board to the next person who decide which operation is needed. The third student solves the equations. The fourth student describes why this solution is correct or incorrect.

Use grid paper to show multiplication of fractions. Use several colors to show this.






Summative

Performance Assessment: In a long‐range activity, each student will create a flip book. Page 1 shows the word problem. Page 2 shows the steps needed to solve the problem. Page 3 shows an illustrations of the solution. Page 4 shows the equation/s used to solve the problem and the answer. Page 5 is a written explanation of the solution and why this solution was chosen.




M.5.F.1. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50‐pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Chapter 6 Fractions: Multiplication and Division Lesson 7A: Interpret the Remainder—on‐line

M.5.F.2. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.





a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently

Chapter 6 Fractions: Multiplication and Division Lesson 1: Multiply Fractions—pp. 198–199 Lesson 2: Multiply Fractions by Fractions—pp. 200–201

Lesson 2A: Use Properties to Multiply Fractions and Whole Numbers—on‐line

Lesson 3: Multiply Fractions and Whole Numbers—pp. 202–203

b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths

Chapter 6 Fractions: Multiplication and Division Lesson 1: Multiply Fractions—pp. 198–199 Lesson 2: Multiply Fractions by Fractions—pp. 200–201

Lesson 6: Multiply Fractions and Mixed Numbers—pp. 208–209

Chapter 12 Metric Measurement, Area, and Volume Lesson 5A: Find Areas of Rectangles and Squares—on‐line

M.5.F.3. Interpret multiplication as scaling (resizing), by:

a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

Chapter 6 Fractions: Multiplication and Division Lesson 2B: Scaling Fractions—on‐line

b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the






given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.

M.5.F.4. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Chapter 6 Fractions: Multiplication and Division Lesson 2: Multiply Fractions by Fractions—pp. 200–201


Lesson 4: Multiply Fractions Using the GCF—pp. 204–205

Lesson 5: Rename Mixed Numbers as Fractions—pp. 206–207

Lesson 6: Multiply Fractions and Mixed Numbers—pp. 208–209

Lesson 7: Multiply Mixed Numbers—pp. 210–211 Lesson 10B: Word Problems Involving Fractions—on‐line

Lesson 17: Problem Solving Applications: Mixed Review—pp. 230–231

M.5.F.5. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

[Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.]

a. Interpret division of a unit fraction by a non‐zero whole number

Chapter 6 Fractions: Multiplication and Division Lesson 10A: Division with a Unit Fraction—on‐





line Lesson 12: Divide Fractions by Whole Numbers—pp. 220–221

b. Interpret division of a whole number by a unit fraction, and compute such quotients.

For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (1/5) = 4.

Chapter 6 Fractions: Multiplication and Division Lesson 8: Division of Fractions—pp. 212–213 Lesson 10: Divide Whole Numbers by Fractions—pp. 216–217

Lesson 10A: Division with a Unit Fraction—on‐line

c. Solve real world problems involving division of unit fractions by non‐zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.

For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3‐cup servings are in 2 cups of raisins?

Chapter 6 Fractions: Multiplication and Division Lesson 10: Divide Whole Numbers by Fractions—pp. 216–217

Lesson 10A: Division with a Unit Fraction—on‐line

Lesson 10B: Word Problems Involving Fractions—on‐line

Lesson 12: Divide Fractions by Whole Numbers—pp. 220–221


Vocabulary: equivalent fractions, numerators, like and unlike denominators, sum, difference, benchmark, benchmark fractions, visual fraction model



Teacher Glossary (for enrichment: an extension of





the Glossary in the Student Edition; defined terms listed alphabetically and grouped by topic)—TE pp. T45–T46



Use models and equations to understand the meaning of a fraction.

Skills Update—Review of Grade 4 Skills Fractions—p. 8 Equivalent Fractions—p. 9

Chapter 4 Number Theory and Fractions Lesson 4: Fraction Sense (models and equations)—pp. 140–141

Multiply a fraction, or a whole number, by a fraction.

Chapter 6 Fractions: Multiplication and Division Lesson 2: Multiply Fractions by Fractions—pp. 200–201


Use a visual model to show the equation. Find the area of a rectangle whose sides are fractions. Use unit squares.

Chapter 12 Metric Measurement, Area, and Volume Lesson 6: Areas of Rectangles and Squares—pp. 392–393

Visualize the product by the size of the fraction. E.G, 4/3 x 2 =2 2/3, which is greater than 2. 2/3 x 4 = 8/3 = 2 2/3, which is less than 4.






Use models in solving word problems. Chapter 6 Fractions: Multiplication and Division Lesson 1: Multiply Fractions (using models)—pp. 198–199

Lesson 2: Multiply Fractions by Fractions: Problem Solving (use models to check computations)—TE p. 201

Lesson 3: Multiply Fractions and Whole Numbers: Problem Solving (draw a diagram)—TE p. 203

Lesson 8: Division of Fractions (models)—pp. 212–213

Lesson 10: Divide Whole Numbers by Fractions (use a diagram)—pp. 216–217

Lesson 12: Divide Fractions by Whole Numbers: Problem Solving (modeling to show division as sharing)—TE p. 221

5) Divide fractions by whole numbers. Divide whole numbers by fractions. Use visuals and stories to explain division of a fraction by a whole number. Use visuals and stories to explain division of a whole number by a fraction. Use real world word problems in division of fractions

Chapter 6 Fractions: Multiplication and Division Lesson 12: Divide Fractions by Whole Numbers—pp. 220–221


Science: Investigate how and why fractions are used in science formulas.

Chapter 10 Geometry Lesson 7: Perimeter (fractions in formulas)—pp. 336–337

Chapter 12 Metric Measurement, Area, and Volume Lesson 6: Areas of Rectangles and Squares (fractions in formulas)—pp. 392–393

Technology: Investigate the role fractions play in





calculators and computers.

Social Science/ Life Skills: Double or half recipes that make use of fractions in their ingredients.

Chapter 6 Fractions: Multiplication and Division Lesson 7: Multiply Mixed Numbers: Problem Solving (recipe)—p. 211

Lesson 15: Estimate Products and Quotients with Mixed Numbers: Problem Solving (recipe)—p. 227

Lesson 17: Problem Solving Applications: Mixed Review (working with recipes)—pp. 230–231

Social Science/ Life Skills: Obtain newspaper ads showing the cost of products. Figure the sales price of items on sale for ½ off, 1/3 off, ¼ off.

* See related content— Chapter 6 Fractions: Multiplication and Division Lesson 3: Multiply Fractions and Whole Numbers: Fractional Part of a Whole Number—p. 203

Chapter 13 Ratio, Proportion, and Percent Lesson 4: Relate Fractions to Percents—pp. 422–423

Lesson 6: Find the Percent of a Number (write percent as a fraction)—pp. 426–427

Lesson 7: Use Percent (sale price/discount)—pp.428– 429


Text books, trade books, fractions strips, grid paper, dominoes, dry erase boards, calculators, computers, interactive boards

NCTM , C&I, and commercial websites

* To access online resources, go to— www.progressinmathematics.com GRADE 5 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.5.G. Convert like measurement units within a given measurement system.



Where, in daily life and/or occupations, will I find it necessary to convert measurements?

Skills Update—Review of Grade 4 Skills Customary Units of Length—p. 14 Customary Units of Capacity and Weight—p. 15 Metric Units of Length—p. 16 Metric Units of Capacity and Mass—p. 17

Chapter 11 Measurement Topics Chapter Opener—p. 357 Lesson 1: Relate Customary Units of Length—pp. 358–359

Lesson 2: Relate Customary Units of Capacity—pp. 360–361

Lesson 3: Relate Customary Units of Weight—pp. 362–363


Chapter 12 Metric Measurement, Area, and Volume Chapter Opener—p. 381 Lesson 1: Metric Measurement—pp. 382–383 Lesson 2: Relate Metric Units of Length—pp. 384–385

Lesson 3: Relate Metric Units of Capacity—pp. 386–387

Lesson 4: Relate Metric Units of Mass—pp. 388–389


Can I learn different systems, other than customary/standard measurement, for measuring things?

Will I find that metric measurement is needed more in today’s world than standard measurement is?

Where will I see standard measurement and metric measurement used in real life?

Does it make sense to me to measure objects in a variety of ways to find the best method?


Formative

Students will work with partners: “My book is 30 cm long. How many mm is that? “ The partner answers, then makes up her/his own problem.

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




measurement in real life situations. About It/Math Journal activities and Step 4: Summarize/Assess. Math journal: Students will answer one or more of

the essential Questions.

Summative

Performance Assessment: In a long‐range activity, students will make a booklet using a theme, E.G., sports, toys, objects in the home, etc. The student will chose a variety of objects, measure each in several different ways, using both standard and metric measurement. The booklet will have illustrations of each object and its measurement conversion. The student will create word problems and write explanations of the activity.




M.5.G. 1. Convert among different‐sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi‐step, real world problems.

Chapter 11 Measurement Topics Lesson 1: Relate Customary Units of Length—pp. 358–359

Lesson 2: Relate Customary Units of Capacity—pp. 360–361

Lesson 3: Relate Customary Units of Weight—pp. 362–363

Lesson 7: Compute with Customary Units—pp. 370–371

Lesson 8: Problem Solving Strategy: Use More Than Step—pp. 372–373


Chapter 12 Metric Measurement, Area, and Volume Lesson 1: Metric Measurement—pp. 382–383 Lesson 2: Relate Metric Units of Length—pp. 384–




385 Lesson 3: Relate Metric Units of Capacity—pp. 386–387

Lesson 4: Relate Metric Units of Mass—pp. 388–389



Vocabulary: convert, all terms used in standard measurement, all terms used in metric measurement






Convert measurements in multi‐step, real world problems.

* See problem solving exercises—pp. 358–363, 365–367, 369–375; 383–389

Integration of Learning Science: Investigate how measurement is used in * See problem solving exercises—pp. 358–363,





science experiments. 365–367, 369–375; 383–389 www.progressinmathematics.com STUDENT CENTER 3 VIRTUAL MANIPULATIVES Manipulatives

Technology: Investigate how measurement is used in computers, art, and graphic arts. Make measurements using virtual manipulatives.

Social Science/Life Skills: Discover ways in which the conversion of measurement is used in occupations such as carpentry, flooring, plumbing, etc.

Social Science: Discuss what might happen if carpenters building a deck did not use accurate measurements.


Text books, trade books, metric and standard measuring tools, calculators, computers, interactive boards, virtual manipulatives

NCTM, C&I, and commercial websites


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 5 Glossary—English) De la A a la Z (Grade 5 Glossary—Spanish)



CATEGORY: Measurement and Data Standard M.5.H. Represent and interpret data.



How can line plots help me understand various types of information?

Chapter 7 Statistics and Probability Strategic Intervention: 4–5. Use data in a table to make a line plot and identify the range and median of the data—TE pp. 237F‐237G

Differentiated Instruction: Physically Impaired: Line Plots—TE p. 237J

Lesson 7: Line Plots—pp. 250–251 Chapter 12 Metric Measurement, Area, and Volume Lesson 12A: Line Plots—on‐line

Where will I find line plots used in the real world?

Will I be able to use various methods to interpret data?

Chapter 7 Statistics and Probability Lesson 5: Range, Median, Mean and Mode—pp. 246–247

Lesson 6: Graphing Sense—pp. 248–249 Lesson 10: Interpret Circle Graphs—pp. 256–257


Formative

Math journal: Student will draw line plots showing various data, then write an explanation of what the information shows.


Use grid paper to plot fractions. Place the number “one” on the far left, and the number “two” on the far right. Given a specific denominator, the student will fill in as many fractions as possible, placing them in an equidistant manner.


Summative

Performance Assessment: In a long‐range activity, the student will use line plots to represent various fractions in real life situations, such as comparing

www.progressinmathematics.com Teacher Center: Common Core Chapter Tests (with Item Analysis)




measurements of objects. Decide and explain how and why these measurements were chosen, and why precision is necessary in real‐life measurements. Formulate word problems using data from line plots.

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



M.5.H.1. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

Chapter 7 Statistics and Probability Lesson 7: Line Plots—pp. 250–251

Chapter 12 Metric Measurement, Area, and Volume Lesson 12A: Line Plots—on‐line


Vocabulary: line plot, data, represent, interpret * 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.



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)

Make line plots using fractions, then interpret that data through models, written explanations.





Science / Social Science: Observe and count the birds at a bird feeder for five minutes. Distinguish and count the types of birds. Plot these on a line plot. Also, note what kind and how many bird fly away, then return to the feeder. This also can be plotted.




Social studies: Make line plots of the area and population of several cities and compare the results.


Text books, trade books, grid paper, metric and standard measuring tools, calculators, computers, interactive boards, virtual manipulatives

NCTM, C&I, and commercial websites

* To access online resources, go to— www.progressinmathematics.com GRADE 5 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 5 Glossary—English) De la A a la Z (Grade 5 Glossary—Spanish)





CATEGORY: Measurement and Data Standard M.5.I. Geometric measurement: understand the concepts of volume and relate volume to

multiplication and addition.



Where and how is volume used in real life situations?

Chapter 12 Metric Measurement, Area, and Volume Lesson 10: Cubic Measure—pp. 400–401 Lesson 11: Volume—pp. 402–403 Lesson 11A: Find Volume—on‐line Lesson 12: Estimate Volume—pp. 404–405 Lesson 12A: Line Plots—on‐line Lesson 13: Problem Solving Strategy: Draw a Picture—pp. 406–407


When will I use volume?

How can models help me to understand volume?


Formative

Student, with a partner, obtains several square or rectangular boxes. Each person will guess the number of unit cubes needed to fill the containers. Keep score as to which person has the nearest estimate of the correct number of unit cubes.

Chapter 12 Metric Measurement, Area, and Volume Lesson 10: Cubic Measure: Lesson Readiness (predict number of unit cubes each box will hold)—TE p. 400

Lesson 11: Volume—pp. 402–403 Lesson 12: Estimate Volume—pp. 404–405



Summative

Performance Assessment: In a long‐range activity, student will choose four containers of various sizes and shapes and fill each with cubic units. Write a detailed report on the amount of cubic

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





units that are needed to fill each container. Decide which types of containers can or cannot be fully packed with cubic units. Explain why this is so and how this conclusion was reached. Use the mathematical formula for volume where it is applicable. Word problems should be created to show the results of the experiment.

"Performance Assessment" on the chapter test.



M.5.I.1. Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.

Chapter 12 Metric Measurement, Area, and Volume Lesson 11: Volume—pp. 402–403 Lesson 12: Estimate Volume—pp. 404–405

b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

Chapter 12 Metric Measurement, Area, and Volume Lesson 11: Volume—pp. 402–403 Lesson 12: Estimate Volume—pp. 404–405

M.5.I.2. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Chapter 12 Metric Measurement, Area, and Volume Lesson 10: Cubic Measure—pp. 400–401 Lesson 11: Volume—pp. 402–403

M.5.I.3. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

a. Find the volume of a right rectangular prism with whole‐number side lengths by packing it with unit cubes and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying

Chapter 12 Metric Measurement, Area, and Volume Lesson 11: Volume—pp. 402–403 Lesson 11A: Find Volume—on‐line Lesson 12: Estimate Volume—pp. 404–405





the height by the area of the base. Represent threefold whole‐number products as volumes, e.g., to represent the associative property of multiplication.

b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems.

Chapter 12 Metric Measurement, Area, and Volume Lesson 11: Volume—pp. 402–403 Lesson 11A: Find Volume—on‐line

c. Recognize volume as additive. Find volumes of solid figures composed of two non‐overlapping right rectangular prisms by adding the volumes of the non‐overlapping parts, applying this technique to solve real world problems.

Chapter 12 Metric Measurement, Area, and Volume Lesson 11B: Separate Solid Figures—on‐line


Vocabulary: volume, solid figures, unit cubes, cubic cm, cubic in, cubic ft, base, rectangular prism, right rectangular prism




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





Planning: Take‐Home Activities (Vocabulary) Practice: Vocabulary Activities


Volume and volume measurement. Use unit cubes to measure volume. If a solid figure is packed with 15 unit cubes, the volume is 15 unit cubes.

Chapter 12 Metric Measurement, Area, and Volume Lesson 10: Cubic Measure—pp. 400–401 Lesson 11: Volume—pp. 402–403

2) Use standard measures as well as non‐standard measures.

3) Use real world word problems involving volume. Compare the measuring of volume using unit cubes to the measuring of volume by multiplying the three side lengths. Use formulas for volume using real world word problems.

Add the volumes of two right rectangular prisms. Real world: Find a way to ship two boxes which will fit into one box. Stack equal‐sized boxes.

Chapter 12 Metric Measurement, Area, and Volume Lesson 10: Cubic Measure—pp. 400–401 Lesson 11: Volume—pp. 402–403 Lesson 12: Estimate Volume—pp. 404–405


Science / Life Skills: Given specific measurements (length, width, and height), calculate how much concrete will be needed to make a patio.

Chapter 12 Metric Measurement, Area, and Volume Lesson 11: Volume—pp. 402–403 Lesson 12: Estimate Volume—pp. 404–405 Science / Life Skills: Given specific measurements

(length, width, height), calculate how much soil will be needed to make a raised garden bed.

Technology: Use virtual manipulatives to calculate the unit cubes needed to fill various types and sizes of containers.

www.progressinmathematics.com On‐line Resources for Student, Family, Teacher Virtual Manipulatives: How High?






Text book, trade books, metric and standard measurement tools, calculators, computers, virtual manipulatives, interactive boards, NCTM, C & I, and commercial websites




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: Geometry Standard M.5.J. Graph points on the coordinate plane to solve real world and mathematical problems.



Where will I see graphs used in the real world, and how are they used?

Chapter 14 More Concepts in Algebra Lesson 13: The Coordinate Plane—pp. 464–465 Lesson 13A: Using Coordinate Graphs—on‐line Lesson 13B: Sequences—on‐line Lesson 13C: Compare Sequences—on‐line Lesson 14: Function Tables—pp. 466–467 Lesson 15: Functions and Coordinate Graphs—pp. 468–469


How will graphing in mathematics help me in understand graphs in other situations and other subject areas?

Why is graphing important to me in solving mathematical problems?


Formative

In small groups, list as many real‐life situations in which graphs are useful.

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.

Use grid paper to plot a given table of ordered pairs. This can be done with partners – one person plots the X axis, the other plots the Y axis. Or one partner plots the ordered pair and the other person checks for correctness.


Summative

Performance Assessment: In a long‐range activity, the student will choose a real‐life political, economic, historical, or geographic situation and graph this. Make inferences as to why the graph is representative of the situation, and explain these inferences. Make predictions based on the graph as to the future of the situation. E.G. Will a drop in the stock market over a period of time cause a slow‐down in other areas, such as






jobs?


M.5.J.1. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x‐axis and x‐coordinate, y‐axis and y‐coordinate).

Chapter 14 More Concepts in Algebra Lesson 13: The Coordinate Plane—pp. 464–465

M.5.J.2. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Chapter 14 More Concepts in Algebra Lesson 13A: Using Coordinate Graphs—on‐line Lesson 15: Functions and Coordinate Graphs—pp. 468–469


Vocabulary: perpendicular, axes, ordered pair, coordinates, coordinate plane, quadrant




www.progressinmathematics.com




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


Graph X and Y axes on a coordinate plane. Chapter 14 More Concepts in Algebra Lesson 13: The Coordinate Plane—pp. 464–465 Lesson 13A: Using Coordinate Graphs—on‐line

Use real world problems involving graphing on a coordinate plane.


Science: Set up an experiment testing the life of certain batteries. Graph the results.

Social Studies: Obtain and graph historical data on rain or snowfall in a series of years.

Social Studies: Trace family histories of the students in the class and graph the number of students from various countries.

Technology: Use spreadsheets to predict the direction and placement of lines on a coordinate plane. Write an explanation that hypothesizes about the direction and placement of these lines.

science, history, geography, economics, art, technology


Text books, trade books, calculators, computers, graphs, interactive boards, virtual manipulatives, NCTM, C&I, and commercial websites

* To access online resources, go to— www.progressinmathematics.com GRADE 5 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: Geometry Standard M.5.K. Classify two-dimensional figures into categories based on their properties.



Where will I find two‐dimensional figures used in the real world?

Chapter 10 Geometry Chapter Opener: Books to Read—TE p. 323 Lesson 3: Polygons—pp. 328–329 Lesson 4: Congruent and Similar Figures—pp. 330–331

Lesson 5: Triangles—pp. 332–333 Lesson 6: Quadrilaterals—pp. 334–335 Lesson 8: Circles—pp. 338–339

Where, in the real world, do I see shapes that use two‐dimensional figures?

How can using models help me understand two‐dimensional figures?


Formative

The student will make a tree diagram of two‐dimensional figures based on their properties. Make a chart, similar to a computer flow chart, of two‐dimensional figures based on their properties. Students can discuss why engineers must study two‐dimensional figures as well as the computation of numbers used in these figures.

Chapter 10 Geometry Lesson 3: Polygons—pp. 328–329 Lesson 5: Triangles—pp. 332–333 Lesson 6: Quadrilaterals—pp. 334–335 Lesson 6A: Classify Quadrilaterals—on‐line Lesson 8: Circles—pp. 338–339

Chapter 7 Statistics and Probability Lesson 2: Tree Diagrams—pp. 240–241


Summative

Performance Assessment: In a long‐range activity, the student will design and build a replica of a building which makes use of several types of two‐dimensional figures. The building can be made of cardboard or some similar easily obtainable material. A written explanation of the process of designing and the types of figures used will be


Post Tests (with Item Analysis)




included. In order to observe examples needed to study the use of various types of figures in buildings, students can observe the variety of buildings in a large city, such as Philadelphia.

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


M.5.K.1. Understand that attributes belonging to a category of two‐dimensional figures also belong to all subcategories of that category.

For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

Chapter 10 Geometry Lesson 5: Triangles—pp. 332–333 Lesson 6: Quadrilaterals—pp. 334–335 Lesson 6A: Classify Quadrilaterals—on‐line

M.5.K.2+. Classify two‐dimensional figures in a hierarchy based on properties.

Chapter 10 Geometry Lesson 6A: Classify Quadrilaterals—on‐line


Vocabulary: angle: acute, right, obtuse; two‐dimensional figures, polygon, triangle: scalene, isosceles, equilateral; quadrilateral, parallelogram, trapezoid, rectangle, rhombus, square, pentagon, hexagon, heptagon, octagon, nonagon, hexagon





Student Center/Family Center




Vocabulary Activities Audio Glossary Math Alive at Home (Vocabulary)

List attributes of two‐dimensional figures. Chapter 10 Geometry Lesson 3: Polygons—pp. 328–329 Lesson 5: Triangles—pp. 332–333 Lesson 6: Quadrilaterals—pp. 334–335 Lesson 6A: Classify Quadrilaterals—on‐line Lesson 8: Circles—pp. 338–339

Classify figures according to angles, sides, and shapes.

Chapter 10 Geometry Lesson 3: Polygons—pp. 328–329 Lesson 5: Triangles—pp. 332–333 Lesson 6: Quadrilaterals—pp. 334–335 Lesson 6A: Classify Quadrilaterals—on‐line


Art/Architecture: Use pattern blocks, or attribute blocks to create designs or tessellations of two‐dimensional figures.

Chapter 10 Geometry Lesson 11: Transformations—pp. 344–345 Lesson 12: Tessellations—pp. 346–347

Technology: Use virtual manipulatives to create designs of two‐dimensional figures.

www.progressinmathematics.com STUDENT CENTER 3 VIRTUAL MANIPULATIVES Manipulatives Geoboard‐Circular (draw and compare two‐dimensional shapes using a circular geoboard)

Art: Draw a chart showing hierarchy of figures, using colors to show comparison/contrast of those figures. This can also be done using a computer.

Chapter 10 Geometry Lesson 3: Polygons—pp. 328–329 Lesson 5: Triangles—pp. 332–333 Lesson 6: Quadrilaterals—pp. 334–335 Lesson 6A: Classify Quadrilaterals—on‐line Lesson 8: Circles—pp. 338–339





Text books, trade books, calculators, computers, virtual manipulatives, pattern blocks, attribute blocks, interactive boards

MCTM, C&I, and commercial websites




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





Documents

Correlated to the Archdiocese of Philadelphia · SADLIER‐OXFORD Progress in Mathematics Grade 5 Correlated to the Archdiocese of Philadelphia Mathematics Standards for Grade 5 CATEGORY: