Teaching Student-Centered Mathematics : Grades 5-8

by Van de Walle, John; Lovin, Lou Ann H.

• ISBN13: 9780205417971
• ISBN10: 0205417973
• Edition: 1st
• Format: Paperback
• Copyright: 2005-06-17
• Publisher: Pearson

Summary

The resource math teachers have been waiting for is finally here! #xA0; Volume Three of the Van de Walle Professional Mathematics Series provides practical guidance along with proven strategies for practicing teachers of grades 5 through 8.In addition to many of the popular topics and features from John Van de Walle's market-leading textbook, Elementary and Middle School Mathematics, this volume offers brand-new material specifically written for the middle grades. The expanded grade-specific coverage and unique page design allow readers to quickly and easily locate information to implement in the classroom. Nearly 200 grade-appropriate activities are included. The student-centered, problem-based approach will help students develop real understanding and confidence in mathematics, making this series indispensable for teachers! Big Ideasprovide clear and succinct explanations of the most critical concepts in 5-8 mathematics. Problem-based activitiesin Chapters 2-12 provide numerous engaging tasks to help students develop understanding. Assessment Notesillustrate how assessment can be an integral part of instruction and suggest practical assessment strategies. Expanded Lessonselaborate on one activity in each chapter, providing examples for creating step-by-step lesson plans for classroom implementation. A Companion Website(http://www.ablongman.com/vandewalletscm1e) provides access to more than 50 reproducible blackline mastersto utilize in the classroom. The NCTM Content Standardsare provided in the appendixfor teachers'reference. #xA0; Collect all three volumes in the Van de Walle Professional Mathematics Series! Each volume provides in-depth coverage at specific grade levels. Teaching Student-Centered Mathematics: Volume One, Grades K-3, ISBN: 0-205-40843-5 Teaching Student-Centered Mathematics: Volume Two, Grades 3-5, ISBN: 0-205-40844-3 Teaching Student-Centered Mathematics: Volume Three, Grades 5-8, ISBN: 0-205-41797-3

Author Biography

John Van de Walle is Professor Emeritus at Virginia Commonwealth University.

Table of Contents

Preface	ix
Activities at a Glance	xv
About the Authors	xxi
Foundations of Student-Centered Instruction	1	(36)
How Children Learn and Understand Mathematics	1	(10)
Constructing Ideas	2	(1)
Understanding	2	(2)
Classroom Influences on Learning	4	(4)
Using Models in the Classroom	8	(3)
Teaching with Problems	11	(12)
Problem-Based Tasks	11	(3)
The Value of Teaching with Problems	14	(1)
A Three-Part Format for Problem-Based Lessons	15	(5)
Teachers' Questions About Problem-Based Teaching	20	(3)
Planning in a Problem-Based Classroom	23	(6)
Planning Problem-Based Lessons	23	(3)
Variations of the Three-Part Lesson	26	(1)
Diversity in the Classroom	27	(2)
Assessment in a Problem-Based Classroom	29	(7)
Appropriate Assessment	29	(2)
Rubrics and Their Uses	31	(2)
Diagnostic Interviews	33	(2)
Grading	35	(1)
Get Started	36	(1)
Flexible Strategies for Whole-Number Computation	37	(29)
Toward Computational Fluency	37	(4)
Development of Invented Strategies: A General Approach	41	(3)
Invented Strategies for Addition and Subtraction	44	(6)
Invented Strategies for Multiplication	50	(3)
The Traditional Algorithm for Multiplication	53	(2)
Invented Strategies for Division	55	(4)
The Traditional Algorithm for Division	59	(5)
Expanded Lesson	64	(2)
Fraction Concepts and Computation	66	(41)
Understanding Fraction Symbols	67	(7)
Fraction Number Sense	74	(7)
Equivalent-Fraction Concepts	81	(6)
Number Sense and Fraction Algorithms	87	(2)
Addition and Subtraction	89	(4)
Multiplication	93	(5)
Division	98	(7)
Expanded Lesson	105	(2)
Decimal and Percent Concepts and Decimal Computation	107	(24)
Connecting Two Different Representational Systems	107	(6)
Developing Decimal Number Sense	113	(5)
Percents	118	(6)
Computation with Decimals	124	(5)
Expanded Lesson	129	(2)
Extending the Number System	131	(23)
Large Numbers, Small Numbers, and Exponents	131	(7)
Integer Concepts	138	(1)
Operations with Integers	139	(2)
A Problem-Solving Approach for Integers	141	(6)
Rational Numbers	147	(3)
Real Numbers	150	(2)
Expanded Lesson	152	(2)
Developing Concepts of Ratio and Proportion	154	(25)
Proportional Reasoning	154	(2)
Proportional Reasoning and Children	156	(1)
Informal Activities to Develop Proportional Reasoning	157	(12)
Solving Proportions and Percent Problems	169	(8)
Expanded Lesson	177	(2)
Geometric Thinking and Geometric Concepts	179	(51)
Geometry Goals for Your Students	179	(2)
Geometric Thought: Reasoning About Shapes and Relationships	181	(6)
Shapes and Properties Activities	187	(22)
Transformation Activities	209	(6)
Location Activities	215	(7)
Visualization Activities	222	(6)
Expanded Lesson	228	(2)
Developing Measurement Concepts and Formulas	230	(35)
Developing Measurement Concepts and Skills	230	(7)
Measuring Angles	237	(3)
Measuring Area	240	(4)
Measuring Volume	244	(2)
Standard Units of Measure	246	(5)
Developing Formulas	251	(12)
Expanded Lesson	263	(2)
Algebraic Reasoning	265	(19)
Growing Patterns	266	(5)
Other Patterns to Explore	271	(3)
Variables and Equations	274	(8)
Expanded Lesson	282	(2)
Exploring Functions	284	(24)
Function Concepts and Representations	284	(6)
Developing Function Concepts in the Classroom	290	(1)
Functions from Patterns	291	(2)
Functions from the Real World	293	(13)
Expanded Lesson	306	(2)
Exploring Data Analysis	308	(25)
Gathering Data to Answer Questions	309	(2)
Descriptive Statistics	311	(8)
Graphical Representations	319	(7)
Scatter Plots and Relationships	326	(5)
Expanded Lesson	331	(2)
Exploring Concepts of Probability	333	(19)
Theoretical Versus Experimental Probability	334	(7)
Sample Space and Determining Probabilities	341	(4)
Simulations	345	(5)
Expanded Lesson	350	(2)
Appendix A. Principles and Standards for School Mathematics	352	(11)
Appendix B. A Guide to the Blackline Masters	363	(5)
References	368	(4)
Index	372