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Teachers! Prepare Your Students for the Mathematics for SAT* I: Methods and Problem-Solving Strategies

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Overview

Crammed with strategies, ideas, and techniques to help you boost your students’ math SAT I scores.

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Product Details

  • ISBN-13: 9780803964167
  • Publisher: SAGE Publications
  • Publication date: 4/18/1996
  • Series: Teacher Support and Retention Series
  • Edition description: Teacher's Edition, Instructor's Manual,
  • Pages: 128
  • Product dimensions: 8.50 (w) x 10.90 (h) x 0.40 (d)

Meet the Author

Alfred S. Posamentier is professor of mathematics education and dean of the School of Education at the City College of the City University of New York. He has authored and co-authored several resource books in mathematics education for Corwin Press.

Stephen Krulik is professor of mathematics education at Temple University in Philadelphia, where he is responsible for the undergraduate and graduate preparation of mathematics teachers for Grades K-12, as well as in the inservice training of mathematics teachers at the graduate level. He teaches a wide variety of courses, among them the History of Mathematics, Methods of Teaching Mathematics, and the Teaching of Problem Solving. Before coming to Temple University, he taught mathematics in the New York City public schools for 15 years, where he created and implemented several courses designed to prepare students for the SAT examination. Nationally, Krulik has served as a member of the committee responsible for preparing the Professional Standards for Teaching Mathematics of the National Council of Teacher of Mathematics (NCTM). He was also the editor of the NCTM’s 1980 yearbook Problem Solving in School Mathematics. He is the author or co-author of more than 20 books for teachers of mathematics, including Assessing Reasoning and Problem Solving: A Sourcebook for Elementary School Teachers. He has served as a consultant to and has conducted many workshops for school district throughout the United States and Canada, as well as delivering major presentations in Austria, Hungary, Australia, and international professional meetings, where his major focus is on preparing all students to reason and problem-solve in their mathematics classroom, as well as in their lives. Krulik received his BA degree in mathematics from Brooklyn College of the City University of New York, and his MA and EdD in mathematics education from Columbia University’s Teachers College.

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Table of Contents

Preface
About the Authors
Introduction 1
I About the SAT I 4
Format of the SAT I 4
The Mathematics Section of the SAT I 5
Calculator Use on the SAT I - Reasoning Test 6
Student-Produced Response Questions 7
II Advising Students on Test Taking 8
Preparation 8
Test-Taking Procedures 8
To Guess or Not to Guess 9
III Nonroutine Mathematics Topics to Strengthen Students' Problem-Solving Abilities 11
Using Proportional Relationships to Solve Problems 12
Simplifying the Procedure to Solve an Equation 13
Comparing Areas of Similar Figures 13
Work Problems 14
Averaging Rates 15
Finding Areas of "Nameless" Geometric Figures 17
Likelihood Problems 18
Successive Discounts 19
Clock Problems 20
Sequence Problems 22
Counting Problems 24
Comparing Fractions 25
IV Specific Problem-Solving Strategies 27
Strategy 1: Working Backwards 27
Strategy 2: Finding a Pattern 30
Strategy 3: Adopting a Different Point of View 38
Strategy 4: Solve a Simpler, Analogous Problem 48
Strategy 5: Using Extreme Cases 54
Strategy 6: Visual Representation 57
Strategy 7: Intelligent Guessing and Testing 61
Strategy 8: Accounting for All Possibilities 67
Strategy 9: Organizing Data 72
Strategy 10: Deductive Reasoning 78
Appendix: Review of Mathematical Principles 85
Rules for Divisibility 85
Order of Operations 87
A Brief Review of Fractions, Decimal Fractions, and Percents 88
Percentage Problems 92
A Brief Review of Some Essentials of Algebra 93
A Brief Review of Some Essentials of Probability 107
A Brief Review of Some Essentials of Geometry 109
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