Professional

# Mathematics for Elementary School Teachers, 5th Edition

### Overview

Intended for the one- or two-semester course required of Education majors, MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS, 5E, offers future teachers a comprehensive mathematics course designed to foster concept development through examples, investigations, and explorations. Visual icons throughout the main text allow instructors to easily connect content to the hands-on activities in the corresponding Explorations Manual. Bassarear presents real-world problems, problems that require active learning in a method similar to how archaeologists explore an archaeological find: they carefully uncover the site, slowly revealing more and more of the structure. The author demonstrates that there are many paths to solving a problem, and that sometimes, problems have more than one solution. With this exposure, future teachers will be better able to assess student needs using diverse approaches.

### Features and Benefits

• Classroom Connection features examples of actual assignments appropriate for elementary math students, questions included in the exercise sets, and margin boxes throughout the text that include examples of children's thinking and work. An apple icon identifies and ties in all three parts of this feature.
• Multiple strategies occur after many Investigations allowing students to analyze numerous approaches to solving problems.
• Coverage of NCTM (National Council of Teachers of Mathematics) Standards has been integrated throughout the text. Early exposure to these standards helps you ponder future teaching objectives.

1. FOUNDATIONS FOR LEARNING MATHEMATICS.
1.1 Getting Started and Problem Solving.
Investigation 1.1a Pigs and Chickens.
Investigation 1.1b A Coin Problem.
1.2 Patterns and Communication.
Investigation 1.2a Sequences and Patterns.
Investigation 1.2b Patterns in Multiplying by 11.
Investigation 1.2c Pascal''s Triangle.
Investigation 1.2d Communicating Patterns in a Magic Square.
1.3 Reasoning and Proof.
Investigation 1.3b Inductive Thinking With Fractions.
Investigation 1.3c Deductive Reasoning and Venn Diagrams.
Investigation 1.3d Why is the Sum of Two Even Numbers an Even Number.
Investigation 1.3e Darts, Proof, and Communication.
Investigation 1.3f The Nine Dots Problem.
Investigation 1.3g How Many Games in the Tournament?.
1.4 Representation and Connections.
Investigation 1.4a How Long Will it Take the Frog to Get Out of the Well?.
Investigation 1.4b How Many Pieces of Wire?.
Looking Back on Chapter 1.
Chapter 1 Summary.
Chapter 1 Review Exercises.
2. FUNDAMENTAL CONCEPTS.
2.1 Sets.
Investigation 2.1b Describing Sets.
Investigation 2.1c How Many Subsets?.
Investigation 2.1d Translating Among Representations.
Investigation 2.1e Finding Information from Venn Diagrams.
2.2 Algebraic Thinking.
Investigation 2.2a A Variable by Any Other Name is Still a Variable.
Investigation 2.2b Baby-sitting.
Investigation 2.2c Choosing Between Functions.
Investigation 2.2d Matching Graphs to Situations.
Investigation 2.2e Developing “Graph Sense.” .
Investigation 2.2f Looking for Generalizations.
Investigation 2.2g How Many Dots?.
2.3 Numeration.
Investigation 2.3a Relative Magnitude of Numbers.
Investigation 2.3b What if Our System was Based on One Hand?.
Investigation 2.3c How Well do you Understand Base Five?.
Investigation 2.3d Base Sixteen.
Looking Back on Chapter 2.
Chapter 2 Summary.
Chapter 2 Review Exercises.
3. THE FOUR FUNDAMENTAL OPERATIONS OF ARITHMETIC.
Investigation 3.1a Pattern in the Addition Table.
3.1c Children''s Strategirs for Adding Large Numbers.
Investigations 3.1d An Alternative Algorithm.
Investigation 3.1e Addition in Base Five.
Investigation 3.1f Children''s Mistakes.
Investigation 3.1g What Was the Total Attendance?.
Investigation 3.1h Estimating by Making Compatible Numbers.
Investigation 3.1i Number Sense with Addition.
3.2 Understanding Subtraction.
Investigation 3.2a Mental Subtraction.
Investigation 3.2b Children''s Strategies for Subtraction with Large Numbers.
Investigation 3.2c An Alternative Algorithm.
Investigation 3.2d Children''s Mistakes in Subtraction.
Investigation 3.2e Rough and Best Estimations with Subtraction.
Investigation 3.2f Number Sense with Subtraction.
3.3 Understanding Multiplication.
Investigation 3.3a A Pattern in the Multiplication Table.
Investigation 3.3b Mental Multiplication.
Investigation 3.3c An Alternative Algorithm.
Investigation 3.3d Why Does the Trick for Multiplying by 11 Work?.
Investigation 3.3e Multiplication in Base Five.
Investigation 3.3f Children''s Mistakes in Multiplication.
Investigation 3.3g Developing Estimation Strategies for Multiplication.
Investigation 3.3h Using Various Strategies in a Real-life Multiplication Situation.
Investigation 3.3i Number Sense with Multiplication. 3.4 Understanding Division.
Investigation 3.4a Mental Division. Investigation 3.4b Understanding Division Algorithms.
Investigation 3.4c The Scaffolding Algorithm.
Investigation 3.4d Children''s Mistakes in Division.
Investigation 3.4e Estimates with Division.
Investigation 3.4f Number Sense with Division.
Investigation 3.4g Applying Models to a Real-life Situation.
Investigation 3.4h Operation Sense.
Looking Back on Chapter 3.
Chapter 3 Summary.
Chapter 3 Review Exercises.
4. NUMBER THEORY.
4.1 Divisibility and Related Concepts.
Investigation 4.1a Interesting Dates.
Investigation 4.1b Patterns in Odd and Even Numbers.
Investigation 4.1c Understanding Divisibility Relationships.
Investigation 4.1d Determining the Truth of an Inverse Statement.
Investigation 4.1e Understanding Why the Divisibility Rule for 3 Works.
Investigation 4.1f Divisibility by 4 and 8.
Investigation 4.1g Creating a Divisibility Rule for 12.
4.2 Prime and Composite Numbers.
Investigation 4.2a The Sieve of Eratosthenes.
Investigation 4.2b Numbers with Personalities: Perfect and Other Numbers.
4.3 Greatest Common Factor and Least Common Multiple.
Investigation 4.3a Cutting Squares Using Number Theory Concepts.
Investigation 4.3b Methods for Finding the GCF.
Investigation 4.3c Relationships Between the GCF and the LCM.
Investigation 4.3d Going Deeper into the GCF and LCM.
Looking Back on Chapter 4.
Chapter 4 Summary.
Chapter 4 Review Exercises.
5. EXTENDING THE NUMBER SYSTEM.
5.1 Integers. Investigation 5.1a Subtraction with Integers.
Investigation 5.1b The Product of a Positive and a Negative Number.
5.2 Fractions and Rational Numbers.
Investigation 5.2a Rational Number Contexts: What Does 3/4 Mean?.
Investigation 5.2b Wholes and Units: Sharing Brownies.
Investigation 5.2c Unitizing.
Investigation 5.2d Fund-Raising and Thermometers.
Investigation 5.2e Partitioning with Number Line Models.
Investigation 5.2f Partitioning with Area Models.
Investigation 5.2g Partitioning with Discrete Models.
Investigation 5.2h Determining an Appropriate Representation.
Investigation 5.2i Sharing Cooking.
Investigation 5.2j Ordering Rational Numbers.
Investigation 5.2k Estimating with Fractions.
5.3 Understanding Operations with Fractions.
Investigation 5.3a Using Fraction Models to Understand Addition of Fractions.
Investigation 5.3b Connecting Improper Fractions and Mixed Numbers.
Investigation 5.3c Estimation and Mental Arithmetic: Sums and Differences of Fractions.
Investigation 5.3d Estimating sums and Differences with Fractions.
Investigation 5.3e Understanding Multiplication of Rational Numbers.
Investigation 5.3f Division of Rational Numbers.
Investigation 5.3g Estimating Products and Quotients.
Investigation 5.3h When Did He Run Out of Gas?.
Investigation 5.3i They''ve Lost Their Faculty!.
5.4 Beyond Integers and Fractions: Decimals, Exponents, and Real Numbers.
Investigation 5.4a Base 10 Blocks and Decimals.
Investigation 5.4b When Two Decimals Are Equal.
Investigation 5.4c When is the Zero Necessary and When is it Optional?.
Investigation 5.4d Connecting Decimals and Fractions.
Investigation 5.4e Ordering Decimals.
Investigation 5.4f Rounding with Decimals.
Investigation 5.4g Decimals and Language.
Investigation 5.4h Decimal Sense: Grocery Store Estimates.
Investigation 5.4i Decimal Sense: How Much Will the Project Cost?.
Investigation 5.4j How Long Will She Run?.
Investigation 5.4k Exponents and Bacteria.
Investigation 5.4l Scientific Notation: How Far is a Light-Year?.
Investigation 5.4m Square Roots.
Looking Back on Chapter 5.
Chapter 5 Summary.
Chapter 5 Review Exercises.
6. PROPORTIONAL REASONING.
6.1 Ratio and Proportion.
Investigation 6.1a Unit Pricing—Is Bigger Always Cheaper?.
Investigation 6.1b How Many Trees Will be Saved?.
Investigation 6.1c How Much Money Will the Trip Cost?.
Investigation 6.1d Reinterpreting Old Problems.
Investigation 6.1e Using Estimation with Ratios.
Investigation 6.1f Comparing Rates.
Investigation 6.1g Is the School on Target?.
Investigation 6.1h Finding Information from Maps.
Investigation 6.1i From Raw Numbers to Rates.
Investigation 6.1j How Much Does That Extra Light Cost?.
6.2 Percents.
Investigation 6.2a Who''s the Better Free-Throw Shooter?.
Investigation 6.2b Understanding a Newspaper Article.
Investigation 6.2d Sale?.
Investigation 6.2e What is a Fair Reason?.
Investigation 6.2f How Much Money Did the Bookstore Pay for the Textbook?.
Investigation 6.2g The Copying Machine.
Investigation 6.2h 132% Increase.
Investigation 6.2i Saving for College.
Investigation 6.2j How Much Does that Credit Card Cost You?.
Looking Back on Chapter 6.
Chapter 6 Summary.
Chapter 6 Review Exercises.
7. UNCERTAINTY: DATA AND CHANCE.
7.1 The Process of Collecting and Analyzing Data.
Investigation 7.1a What is Your Favorite Sport?.
Investigation 7.1b How Many Siblings do you Have?.
Investigation 7.1c Going Beyond a Computational Sense of Average.
Investigation 7.1d How Many Peanuts Can You Hold in One Hand?.
Investigation 7.1e How Long Does it Take Students to Finish the Final Exam?
Investigation 7.1f Videocassette Recorders.
Investigation 7.1g Fatal Crashes.
Investigation 7.1h Hitting the Books.
7.2 Going Beyond the Basics.
Investigation 7.2a How Many More Peanuts Can Adults Hold Than Children?.
Investigation 7.2b Scores on a Test.
Investigation 7.2c Which Battery do You Buy?.
Investigation 7.2d Understanding Standard Deviation.
Investigation 7.2e Analyzing Standardized Test Scores.
Investigation 7.2f How Long Should the Tire be Guaranteed?.
Investigation 7.2g Comparing Students in Three Countries.
Investigation 7.2i What Does Amy Need to Bring Her GPA up to 2.5?.
7.3 Concepts Related to Chance.
Investigation 7.3a Probability of Having 2 Boys and 2 Girls.
Investigation 7.3b Probability of Having 3 Boys and 2 Girls.
Investigation 7.3c Probability of Having at Least 1 Girl.
Investigation 7.3d 50-50 Chance of Passing.
Investigation 7.3e What is the Probability of Rolling a 7?.
Investigation 7.3f What is the Probability of Rolling a 13 with 3 Dice?.
Investigation 7.3g "The Lady of the Tiger.
Investigation 7.3h Gumballs.
Investigation 7.3i Is this a Fair Game?.
Investigation 7.3k Insurance Rates.
7.4 Counting and Chance.
Investigation 7.4a How Many Ways to Take the Picture?.
Investigation 7.4b How Many Different Election Outcomes?.
Investigation 7.4c How Many Outcomes this Time?.
Investigation 7.4d Pick a Card, Any Card!.
Investigation 7.4e So You Think You''re Going to Win the Lottery?.
Looking Back on Chapter 7.
Chapter 7 Summary.
Chapter 7 Review Exercises.
8. GEOMETRY AS SHAPE.
8.1 Basic Ideas and Building Blocks.
Investigation 8.1a Playing Tetris.
Investigation 8.1b Different Objects and Their Functions.
Investigation 8.1c Point, Line, and Plane.
Investigation 8.1d Measuring Angles.
8.2 Two-Dimensional Figures.
Investigation 8.2a Recreating Shapes from Memory.
Investigation 8.2b All the Attributes.
Investigation 8.2c Classifying Figures.
Investigations 8.2d Why Triangles are so Important.
Investigation 8.2e Classifying Triangles.
Investigation 8.2f Triangles and Venn Diagrams.
Investigation 8.2g Congruence with Triangles.
Investigation 8.2i Challenges.
Investigation 8.2k Sum of Interior Angles of a Polygon.
Investigation 8.2l What are my Coordinates?.
Investigation 8.2m Understanding the Distance Formula.
Investigation 8.2n The Opposite Sides of a Parallelogram are Congruent.
Investigation 8.2o Midpoints of any Quadrilateral.
8.3 Three-Dimensional Figures.
Investigation 8.3a What do you See?.
Investigation 8.3b Connecting Polygons to Polyhedra.
Investigation 8.3c Features of Three-Dimensional Objects.
Investigation 8.3d Prisms and Pyramids.
Investigation 8.3e Different Views of a Building.
Investigation 8.3f Isometric Drawings.
Investigation 8.3g Cross Sections.
Investigation 8.3h Nets.
Looking Back on Chapter 8.
Chapter 8 Summary.
Chapter 8 Review Exercises.
9. GEOMETRY AS TRANSFORMING SHAPES.
9.1 Congruence Transformations.
Investigation 9.1a Understanding Translations.
Investigation 9.1b Understanding Reflections.
Investigation 9.1c Understanding Rotations.
Investigation 9.1d Understanding Translations, Reflections, and Rotations.
Investigation 9.1e Connecting Transformations.
Investigation 9.1f Transformations and Art.
9.2 Symmetry and Tessellations.
Investigation 9.2a Reflection and Rotation Symmetry in Triangles.
Investigation 9.2b Reflection and Rotation Symmetry in Quadrilaterals.
Investigation 9.2c Reflection and Rotation Symmetry in Other Figures.
Investigation 9.2d Letters of the Alphabet and Symmetry.
Investigation 9.2e Patterns.
Investigation 9.2f Symmetries of Strip Patterns.
Investigation 9.2g Analyzing Brick Patterns.
Investigation 9.2h Which Triangles Tessellate?.
Investigation 9.2i Which Regular Polygons Tessellate?.
Investigation 9.2j Tessellating Trapezoids.
Investigation 9.2k More Tessellating Polygons.
Investigation 9.2l Generating Pictures Through Transformations.
9.3 Similarity.
Investigation 9.3a Understanding Similarity.
Investigation 9.3b Similarity Using an Artistic Perspective.
Investigation 9.3c Using Coordinate Geometry to Understand Similarity.
Looking Back on Chapter 9.
Chapter 9 Summary.
Chapter 9 Review Exercises.
10. GEOMETRY AS MEASUREMENT.
10.1 Systems of Measurement.
Investigation 10.1a Developing Metric Sense.
Investigation 10.1b Converting Among Units in the Metric System.
10.2 Perimeter and Area. Investigation 10.2a What is the Length of the Arc?.
Investigation 10.2b Converting Units of Area.
Investigation 10.2c Using the Pythagorean Theorem.
Investigation 10.2d Understanding the Area Formulas for Circles.
Investigation 10.2e A 16-Inch Pizza Versus an 8-Inch Pizza.
Investigation 10.2f How Big in the Footprint?.
Investigation 10.2g Making a Fence with Maximum Area.
10.3 Surface Area and Volume.
Investigation 10.3a Are Their Picture Misleading?.
Investigation 10.3b Finding the Volume of a Hollow Box.
Investigation 10.3c Surface Area and Volume.
Looking Back on Chapter 10.
Chapter 10 Summary.
Chapter 10 Review Exercises.

### What's New

• The new edition features improved visual representations of concepts, adding diagrams and illustrations.
• Updated Instructor Resource Manual! Now with additional answers to the exercises in the Explorations Manual.
• NEW 4-color design. 2-color design upgraded to 4-color to better present the author's approach to teaching.
• NEW chapter openers outline the sections within the chapter and the Investigations that appear within the section.
• NEW Looking Back feature appears before the Chapter Summary in each chapter and includes a brief discussion about problem solving, reasoning, connections and relationships, unit, and equivalence as it applies to each chapter.
• Updated! The 4e content for chapter 1 has been rearranged to reflect 4 sections instead of the 7 found in the 4e.
• NEW component has been added to the Classroom Connection feature in which examples of actual assignments appropriate for elementary math students are illustrated. In addition to this, questions in the exercise sets have been identified as a part of Classroom Connection, along with margin boxes throughout the text. An apple icon identifies and ties in all three parts of this feature.
• NEW exercises have been added to most chapters. NEW sub-categories have been added to the exercises and they have been rearranged breaking these down into these three topics for most chapters: Basic, Deepening Your Understanding, and From Standardized Assessments.
• NEW From Standardized Assessments exercises appear as a subset in the exercise sets in most chapters. Since they are actual questions that appear on standardized assessments, these give students a sense of the high-cognitive level of questions to expect on national assessments.
• NEW Investigations have been added to most chapters and have been renumbered to increase accessibility. Multiple strategies occur after many Investigations allowing students to analyze numerous approaches to solving problems.
• Updated! Coverage of NCTM (National Council of Teachers of Mathematics) Standards has been integrated throughout the text. Early exposure to these standards helps students ponder future teaching objectives.
• NEW Questions in Text icon has been added. Questions that appear within the text to reinforce concepts as they are presented are now identified and include the solutions in Appendix C, as opposed to the end of the chapter.
• NEW Enhanced WebAssign® offers an extensive online program for Liberal Arts Mathematics to encourage the practice that's so critical for concept mastery. The meticulously crafted pedagogy and exercises in our proven texts become even more effective in Enhanced WebAssign, supplemented by multimedia tutorial support and immediate feedback as students complete their assignments. Note that the Enhanced WebAssign problems for this text are highlighted by a “>” symbol.
• Diagnostic quizzing for each chapter identifies concepts that students still need to master, and directs them to the appropriate review material. Students will appreciate the interactive Premium eBook, which offers search, highlighting, and note-taking functionality, as well as links to multimedia resources, all available to students when you choose Enhanced WebAssign.

### Bundle: Text + Student Solutions Manual

ISBN-10: 1111649618  | ISBN-13: 9781111649616

List Price = \$308.95  | CengageBrain Price = \$308.95

### Bundle: Text + Math Manipulatives Kit

ISBN-10:  1111649642  | ISBN-13:  9781111649647

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### Bundle: Text + Explorations Manual

ISBN-10:  1111649634  | ISBN-13:  9781111649630

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### Bundle: Text + Enhanced WebAssign - Start Smart Guide for Students + Enhanced WebAssign Homework with eBook Printed Access Card for One Term Math and Science

ISBN-10:  1111649626  | ISBN-13:  9781111649623

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### Printed Text + Enhanced WebAssign Instant Access for Liberal Arts Math & Teacher Math, Single-Term Courses

ISBN-10:  1305593359 | ISBN-13:  9781305593350

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## Supplements

All supplements have been updated in coordination with the main title. Select the main title's "About" tab, then select "What's New" for updates specific to title's edition.

### Instructor Supplements

#### Explorations  (ISBN-10: 0840062451 | ISBN-13: 9780840062451)

This manual contains open-ended activities for the student to practice and apply the knowledge they learn from the main text. When students begin teaching, they can use the activities as models in their own classrooms.

List Price = \$99.95  | CengageBrain Price = \$99.95  | College Bookstore Wholesale Price = \$75.00

#### Student Solutions Manual  (ISBN-10: 1111569045 | ISBN-13: 9781111569044)

Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.

List Price = \$41.95  | CengageBrain Price = \$41.95  | College Bookstore Wholesale Price = \$31.50

#### Enhanced WebAssign - Start Smart Guide for Students  (ISBN-10: 0495384798 | ISBN-13: 9780495384793)

If your instructor has chosen to package Enhanced WebAssign with your text, this manual will help you get up and running quickly with the Enhanced WebAssign system so you can study smarter and improve your performance in class.

List Price = \$49.95  | CengageBrain Price = \$49.95  | College Bookstore Wholesale Price = \$37.50

#### Enhanced WebAssign Instant Access for Liberal Arts Math & Teacher Math, Single-Term Courses  (ISBN-10: 1285858034 | ISBN-13: 9781285858036)

List Price = \$94.00  | CengageBrain Price = \$94.00  | College Bookstore Wholesale Price = \$94.00

#### Instructor's Manual  (ISBN-10: 1111571589 | ISBN-13: 9781111571580)

The Instructor's Manual provides worked-out solutions to all of the problems in the text. In addition, instructors will find helpful aids such as "Teaching the Course," which will show how to teach in a constructivist manner. "Chapter by Chapter Notes" provides commentary for the Explorations Manual as well as solutions to exercises that appear in the supplement.

#### PowerLecture  (ISBN-10: 1111571732 | ISBN-13: 9781111571733)

This CD-ROM provides the instructor with dynamic media tools for teaching. Create, deliver, and customize tests (both print and online) in minutes with ExamView® Computerized Testing Featuring Algorithmic Equations. Easily build solution sets for homework or exams using Solution Builder's online solutions manual. Microsoft® PowerPoint® lecture slides and figures from the book are also included on this CD-ROM.

### Student Supplements

#### Explorations  (ISBN-10: 0840062451 | ISBN-13: 9780840062451)

This manual contains open-ended activities for the student to practice and apply the knowledge they learn from the main text. When students begin teaching, they can use the activities as models in their own classrooms.

List Price = \$99.95  | CengageBrain Price = \$99.95  | College Bookstore Wholesale Price = \$75.00

#### Student Solutions Manual  (ISBN-10: 1111569045 | ISBN-13: 9781111569044)

Go beyond the answers--see what it takes to get there and improve your grade! This manual provides worked-out, step-by-step solutions to the odd-numbered problems in the text. This gives you the information you need to truly understand how these problems are solved.

List Price = \$41.95  | CengageBrain Price = \$41.95  | College Bookstore Wholesale Price = \$31.50

#### Math Manipulatives Kit  (ISBN-10: 0618190937 | ISBN-13: 9780618190935)

The Manipulative Kits include pattern blocks, pentominos, base ten flats, base ten rods, base ten units, tanagrams, and a geoboard.

List Price = \$25.95  | CengageBrain Price = \$25.95  | College Bookstore Wholesale Price = \$19.50

#### Enhanced WebAssign - Start Smart Guide for Students  (ISBN-10: 0495384798 | ISBN-13: 9780495384793)

If your instructor has chosen to package Enhanced WebAssign with your text, this manual will help you get up and running quickly with the Enhanced WebAssign system so you can study smarter and improve your performance in class.

List Price = \$49.95  | CengageBrain Price = \$49.95  | College Bookstore Wholesale Price = \$37.50