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MATH OLYMPIAD CONTEST PROBLEMS for Elementary and Middle Schools (Volume 1) by Dr. G. Lenchner.

Mathematics Teaching in the Middle School
The National Council of Teachers of Mathematics
Volume 2, Number 6 May, 1997

Math Olympiad Contest Problems for Elementary and Middle Schools by George Lenchner. Glenwood Publications (now MOEMS), 2154 Bellmore Avenue, Bellmore, NY 11710, (516) 781-2400

Many readers of this journal have had their students participate in various mathematics contests over the years. The Math Olympiad, an interschool competition that is held five times during the school year at monthly intervals beginning in November, is one of the better-known competitions. In this book Lenchner provides 400 challenging problems, puzzles, and mathematics topics from sixteen years of Math Olympiads.

Intended for use in elementary and middle schools, this volume is not just another book of brain teasers. The introduction concisely reviews many problem-solving strategies. The appendixes are a resource of mathematics concepts, including fractions, factors, and exponents. For teachers looking for certain types of problems to supplement their lessons, a guide breaks down the book into problem types from “addition patterns” and “algebra” to “volume” and “work backward.”

The main body of the book contains eighty Olympiads of five questions each, hints for each question, answers, and detailed solutions. The book includes a glossary and an index.

Many books are available that offer problems, brain teasers, and puzzles for your students, but this one is so complete, concise, and well done that it really should be part of your professional library.

Jeff Hoyle, Dartmouth Middle School, Dartmouth, MA 02747

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MATH OLYMPIAD CONTEST PROBLEMS Volume 2 edited by Richard Kalman.

The California Mathematics Council published the following review of our book, Math Olympiad Contest Problems, Volume 2, in its December 2008 journal, ComMuniCator, combined with those of two other books.

A third book, filled with powerful problems, is Math Olympiad Contest Problems, Volume 2.The introduction to this book contains valuable information about why we study problem solving, characteristics of good problems, what every young mathlete should know, common strategies for problem problems, and suggestions for starting a team for mathematics competitions.

The problems are divided into two parts- division E for elementary school students and division M for middle school students- with sets of 25 problems in each division. There are 250 elementary problems and 175 middle school problems. Following the problems are separate sets of hints, answers, and solutions for all problems. Here are some examples of the middle school problems:

When the six-digit number 3456n7 is divided by 8, the remainder is 5. List both possible values of the digit n. Maxie lies on Fridays, Saturdays, and Sundays, while he tells the truth on all other days. Minnie lies on Tuesdays, Wednesdays, and Thursdays, but she is truthful on all other days. On what day of the week could they both say, "Tomorrow I will lie?" In lowest terms, how much greater is 2003/25 + 25 than (2003 + 25) /25?

A final comment: Many of the problems in these books are also valuable for senior high school students. The problems for elementary students in the third book discussed are appropriate for middle school students, as well.

Beth Schleninger, San Diego

Mathematics Teaching In the Middle School. Vol. 14, No. 5, December 2008/January 2009

If you are looking for a single book to help start a math club or prepare for a competition, Math Olympiad Contest Problems, volume 2, may end your search. The target audiences for this book are teachers, math club sponsors, and students wanting to participate in clubs and competitions. The book contains 425 past Math Olympiad problems that are designed to promote higher-order thinking skills in both upper elementary and middle school students.

The thorough introduction includes a wealth of information for both students and club leaders. For students, the book contains a vocabulary section, review of eleven problem-solving strategies, and suggestions for solving problems in contest settings. For leaders, the book reminds us of the value of developing problem-solving skills.Tips for building mathematics programs, organizing practice sessions,and ideas for end-of-the-year activities are also included.

The heart of the book is the Olympiad problems. For elementary school teams, the book contains ten sets of 5 problems from five previous Math Olympiads (a total of 250 questions). The middle school section contains seven sets of 5 problems from five previous Math Olympiads (a total of 175). The book also contains "Solutions" and "Hints" sections. Navigating among the various sections is hampered by the book's lack of cross-referencing. Despite this weakness, the book would serve as a fine resource of extension activities or as a tool to prepare for mathematics competitions.

Roy Lander, Sophia Academy, Atlanta, GA

Like the MOEMS program itself, this book is an excellent resource for beginning problem solvers in grades 4-8. Teachers, parents, and homeschoolers will find this an excellent resource for finding challenging problems that inspire students to develop a more innovative and thoughtful approach to solving problems. This book contains 425 challenging problems and ingenious solutions for the problems of the popular Mathematics Olympiads in the Elementary and Middle Schools (MOEMS) program.

Richard Rusczyk, pres. AoPS( the world's largest online math contest Web site)

Congratulations ... on your recent publication, "Math Olympiad Contest Problems, Volume 2! As a PICO for over 20 years, I applaud your efforts and look forward to using the book as a resource in both my classroom as I prepare students for Olympiad contests and as a resource as a trainer of teachers.

As I peruse this book, I am extremely impressed with several features that make this user friendly in promoting problem solving.

  • For the PICO....Having all the problems of the last 10 years in one resource, including suggestions for helping to build your school program
  • For the student....Vocabulary and language every mathlete should know, fostering the growth of mathematical communication
  • For any reader....Challenge yourself with 10 years of engaging problems and the variety of strategies you can use to solve these problems
  • For classroom teachers....Suggestions for solving these problems in a variety of ways, allowing for rich discourse in the mathematical
    community of your classroom. You will be amazed at the elegance of the strategies your own students come up with. And problems
    are categorized for easy inclusion with any unit.

This is one resource that won't collect dust on my bookcase. Thank you for sharing these challenging problems in this well-developed resource!

Marshalyn Baker Grade 8 Mathematics Teacher and Mathematics Content Leader Messalonskee Middle School, Me.



CREATIVE PROBLEM SOLVING in School Mathematics 2nd Edition by Dr. George Lenchner.

The Arithmetic Teacher
The National Council of Teachers of Mathematics
March 1984

Creative Problem Solving in School Mathematics. George Lenchner. Houghton Mifflin Co.. One Beacon St.. Boston, MA 02108

This is an excellent professional resource book for teachers of elementary school mathematics. The organization and quality of materials are outstanding! Problem solving is initially defined and characterized via Polya’s How to Solve It. An excellent description of the standard heuristics for problem solving is provided with accompanying mathematical examples.

     A large portion of the text is devoted to seven common curricular themes of elementary school mathematics. Each theme has from four to eight categories of problems for investigation by students. Arriving at solutions to these problems will truly necessitate your students’ use of their problem-solving skills.

     The last section of this important book provides very complete and clearly stated solutions to the problems. This book is an excellent resource from stem to stem.

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CURRICULUM REVIEW 
FEBRUARY 1984

Creative Problem Solving In School Mathematics

George Lenchner

Creative Problem Solving in School Mathematics helps elementary and middle school teachers improve each student’s ability to solve problems. Its emphasis is on teachers “learning by doing” — trying out new approaches and techniques. Through these experiences, mathematics teachers should gain fresh insights and ideas for their classroom teaching.

     The content falls into three major sections on teaching techniques, problem-solving strategies, and relating problem solving to standard topics of the school mathematics curriculum. A special section on resource problems follows.

     The resource problems consist of 20 problem sets (100 problems) written by the author for use in Mathematics Olympiads for Elementary Schools (MOES). These Olympiads are interschool mathematical competitions instituted by the author and held five times during each school year. The 20 problem sets may be used by teachers wishing to conduct an Olympiad Competition in their schools.

     While problem solving has received considerable attention recently, George Lenchner points out that the “ultimate goal of school mathematics at all times has been to develop students’ abilities to solve problems.”

     He distinguishes between an exercise, where the procedure is known, and a problem, where the solution strategy is unknown, thereby requiring some creativity on the part of the problem solver. He discusses in considerable detail the four-step method advocated by George Polya: understanding the problem, planning how to solve the problem, carrying out the problem, and looking back. In addition, he devotes considerable attention to planning how to solve a problem through such strategies as drawing a picture or diagram, finding a pattern, making an organized list, making a table, solving a simpler problem, trial and error, experimenting, acting out the problem, working backwards, writing an equation, and using deduction.

     The topics in the problem solving section cover number patterns, factors and multiples, divisibility, fractions, geometry and measurement, clocks and things, and logic. The topics are presented as examples for teachers to experiment with and to use in preparing their own problem sets for pupils. Numerous line drawing, diagrams, illustrations, tables, and pictures reinforce the activities. The solutions to these problems are more than routine answers, they give detailed explanations and helpful suggestions for each problem set.

     Creative Problem Solving in School Mathematics should be an excellent resource book for elementary and middle school teachers. Some sections also have applications for the secondary school level. Moreover, the book would be helpful in inservice courses.

     This carefully prepared and mathematically sound resource book should stimulate teachers’ interest in problem solving and encourage them to approach problem solving as a creative aspect of mathematics teaching. The book will make a significant contribution to the available literature dealing with elementary school mathematics teaching.

Wilbur H. Dutton, Ed.D.— Professor Emeritus of Elementary Mathematics, University of California, Los Angeles.

Letters to Dr. Lenchner:

“Your book, Creative Problem Solving in School Mathematics, is the best I’ve seen for upper elementary grades.”Rachel C. Hopkins, Norfolk Academy VA

“The layout, content, and problems are all really terrific. I’m teaching a 4 session course on problem solving … and I included your book as number 1 on my bibliography. I have recommended it highly to those people taking the course.”Sandy Cohen, Oceanside NY 

During Math Olympiad practice sessions, I used Creative Problem Solving in School Mathematics as a source book for problems. The students found the problems both challenging and interesting. I have also used many of the problems in the undergraduate course, which I teach for prospective elementary teachers. I am interested in providing inservice instruction for other teachers who are teaching problem solving in their classrooms.Margaret Bangs, Fullerton CA

“Your enthusiasm and love for mathematics jump out of every page. … Not only are all my students deriving special benefits from your book but I too have improved my ability to solve math problems. Your method of working out challenging problems through an organized approach has enabled all of us to confront mathematics without fear. In the past you have inspired me to teach mathematics in a creative and thoughtful way. Your new book serves to reinforce your previous insights into the learning process.”Florence Shapiro, Valley Stream N