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**Randy Evans **was born in Connecticut and raised in Pittsburgh, Pennsylvania. His love affair with games started early in childhood and grew into a lifetime passion. He graduated from Duke University with a BA in Philosophy in 1988 and also received a J.D. from the University of Denver, College of Law in 1992. He teaches middle school and high school math at two Waldorf schools in Atlanta where he works with his wife Jenny. His two daughters, Miranda and Tash, can often be found trying to outwit their dad around the dinner table at a board game.

**Mick Follari** graduated from the Green Meadow Waldorf School and went on to study Engineering at Brown University. His world travels include an assignment for National Geographic on an expedition to Africa, and mountaineering/climbing and photography expeditions to South America, Asia, New Zealand and across the US. Mick is a Waldorf science and math teacher, having taught in several schools around the US, is a web design and development consultant, and is involved in green design/build real estate projects. He lives in Boulder, CO.

**Jamie York**, before discovering Waldorf education, worked in the computer industry, ran a tennis camp for children, served as a Peace Corps volunteer in Nepal, and taught at a boarding school. A native of New England, his search for meaningful education led him to Shining Mountain Waldorf School (in Boulder, Colorado), where he started teaching math in 1994. In addition to teaching middle and high school math, Jamie consults at Waldorf schools and teaches math workshops across North America. He also trains Waldorf math teachers at the Center for Anthroposophy in Wilton, NH. Currently, he is working on getting the new high school math curriculum ready for publication.

**The Purpose of this Book**

This book is intended as a resource for middle school and high school math teachers, in part, to supplement the normal daily homework and classroom material (such as the Making Math Meaningful middle school and high school workbooks).

There may be times when things seem to get dull and the students begin to lose their spark. It is then that the teacher knows it is time to do something different. This book provides ideas for that “something different.”

What’s New in the Third Edition?

· Now includes easier puzzles for 4th and 5th graders

· Additional puzzles for grades 6 – 12

· More than 100 new puzzles in this edition

**What Makes This Book Unique?**

There are many math puzzle books available today. However, it can be daunting for a teacher (especially a teacher in the lower grades for whom math is not a specialty) to pick up a math puzzle book that consists of a couple hundred puzzles, and find a good one that would work well for a math class tomorrow.

This book is specifically geared toward the teacher who needs to find an excellent puzzle or game for tomorrow’s math class. We have tried to limit the number of puzzles and games to just a few excellent ones. We have categorized the puzzles according to grade level. For example, in order to find a puzzle, the teacher needs only to consider the 20 puzzles listed under that grade.

**Skills and Thrills**

Unfortunately, today there is an over-emphasis on the mastery of skills in mathematics curricula. Even for students who appear to be successful, their experience with math amounts to a long list of procedures to be followed in order to solve problems, many of which may seem to be quite meaningless. All too often the repetition and drill of solving endless problems from a textbook or workbook can kill the students’ natural enthusiasm for learning. Students rarely have the opportunity to experience the thrill of mathematics.

What is this thrill of mathematics? It is perhaps best experienced when students encounter a challenge – often a challenge that at first seemed formidable – and they persevere and emerge successful. A good math puzzle or game provides an excellent opportunity for such a thrill.

This is not to say that skills aren’t important; they are. But, it is equally important for students to experience meaningful math, and to have enthusiasm for learning math.

The art of teaching math is, at least partly, how to balance all of the above.

**The Art of Problem Solving**

There’s a difference between solving problems (e.g., doing a problem on a homework sheet) and problem solving. To some degree, real problem solving should receive a greater emphasis in the later high school years, but there should be elements of problem solving in the earlier years as well.

Usually solving a problem (e.g., as given as part of a homework assignment) amounts to following a procedure that the student has been previously shown how to do. Often, this aspect of math teaching is essential and effective. However, even a typical word problem isn’t true problem solving.

So what is true problem solving? There are shades of gray here, but true problem solving must include an experience of uncertainty. The student might say to himself, “I have never seen this before. I have no idea what to do.” Thus begins the experience of problem solving.

These kinds of problem solving experiences may occasionally be encountered through a daily homework assignment, but often the teacher needs to carefully plan these experiences. A good puzzle or game is one way to give the students a genuine problem solving experience.

**Guidelines for Using This Book**

This book is divided into the following sections:

- Puzzles.
- There are puzzles for each of the middle school years and for the high school years.
- The level of difficulty gets greater for the older grades, but that is not to say that difficult puzzles don’t appear for the sixth and seventh graders.
- It is intended that all puzzles listed under the middle school years ought to be solved without the use of algebra. Several of the high school puzzles use some algebra.
- Any puzzle may also be used for grades older than what it is listed for.
- Solutions to the puzzles appear at the end of the book. Of course, it may be best for the teacher to try solving the puzzle (before looking at the solution!) in order to fully experience what the students will go through.
- With some puzzles, there may be several possible solutions. In those cases, the solution key usually gives only one of the solutions. Even for puzzles where there is only one possible solution, a different approach to that solution (from what is given in the solution key) may be possible.
- Games. The intention in this book is to have just a few excellent games for the teacher to choose from. Even for the teacher who loves playing games with his class, it may be that introducing just a couple of new games over the course of the year is adequate. A puzzle is a one-time experience; a good math game can be played again and again, each time providing new benefits.
- Math Magic Tricks. These great attention-grabbers help to develop a sense of wonder for numbers. They are especially effective in grades 5-7, but can also be used in the higher grades as an interesting algebra exercise to show why a given math magic trick works. Additionally, there are around 30 math tricks (for calculating quickly in your head) that are found at the back of the 6th grade and 7th grade Making Math Meaningful workbooks.
- Classroom Activities. This is a modest collection of activities that could possibly turn out to be the highlight of the year for a math class.

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