Publications
Michael’s love of mathematical discovery and puzzles is illuminated in his published works. Please feel free to explore the titles below and visit the Articles and Handouts and Videos pages for supplementary materials. Click the images for purchasing information for printed material. Downloadable PDFs are also available for most products at Michael’s Teachers Pay Teachers store.
Don’t Just Cover Geometry, Discover Geometry!
Discovering Geometry began in Michael's classroom over 35 years ago when he created his own daily lesson plans. Michael believes students learn with a greater depth of understanding when they are actively engaged in the process of discovering concepts and investigating mathematics themselves.
Discovering Geometry is now in its fifth edition and published by Kendall Hunt. The textbook package includes the student textbook, and online and teacher resources.
Please see our Discovering Geometry page for more information about this book and Michael’s supplements. The Discovering Geometry® Video Series, published by Playing It Smart, enhances our vision of the ideal geometry class.
What Do Hamburgers Have to Do with Geometry?
Nothing! But the translucent squares of paper used to separate hamburger patties have a lot to do with it. Michael Serra invites geometry discovery through paper-folding activities with his exciting book Patty Paper® Geometry. Use Patty Paper® Geometry as a supplement to your geometry program or even as a major course of study.
These explorations helps students with:
Transformational geometry (reflections, rotations, and translations)
Performing constructions more accurately
Discovering many of the properties of geometric figures studied in high school geometry courses
For video demonstrations using patty paper or for home-school use, see our Discovering Geometry® Video Series.
Please see here for Patty Paper® Geometry errata.
Make a Smart Move and Discover How Much Fun Math Can Be!
Smart Moves: Developing Mathematical Reasoning With Games and Puzzles is designed to improve your sequential reasoning skills, explore some mathematics, and have fun along the way. The games and puzzles were created to encourage perseverance and logical thinking, while the Mathematical Connections highlight key math concepts.
Some of the games you will find inside include:
The Game of Racetrack
Tour Puzzles
Euler Paths
Magic Squares
Please see here for Smart Moves errata.
Ahoy Matey! Fear Not Mathematics.
Build ye thinking skills, learn ye coordinates, and a smarter pirate ye will be! Pirate Math: Developing Mathematical Reasoning with Games and Puzzles teaches students transformational geometry, Euclidean construction, and cryptography through pirate games and treasure hunts.
Students will:
Use their problem-solving skills to find polyominoes in rectangular, polar, and spherical coordinate systems
Learn about transformational geometry (rotations, reflections, and rigid transformations)
Decipher secret pirate messages
Employ Euclidean constructions to locate buried treasure
Teachers: since 2002, September 19th is International Talk Like A Pirate Day, a fun way to show your playful side while teaching mathematics.
Please see here for Pirate Math errata.
Can You Spot the Error?
Students love to spot errors and What's Wrong with This Picture? uses that enthusiasm to exercise basic geometry skills. Perfect for grades 8–10, this book contains a set of 50 black-line masters that can be used as warm-up exercises, homework, or group activities.
Each page has up to four problems with at least one worked correctly, and at least one containing an error, optical illusion, or conflicting information. Students reason through the problems to determine which are correct and which are not.
Looking out for errors and discussing them as a class:
Deepens students' understanding of the concepts
Improves their powers of observation
Improves their mastery and retention of the material
Exercise Your Mathematical Muscles!
Warmup for your math class with a 10-15 minute Mathercise™ activity. Each lesson includes one reasoning exercise, one solving exercise, one sketching or graphing exercise, and space for a review exercise of your own design. The solving exercises involve percentages, algebra, equations, averages, proportions, probability, and functions and analytic geometry (Books D and E).
This resource includes 50 black-line masters plus teaching tips, sample problems, answer keys, and reproducible answer sheets.
Mathercise™ Book A: Pre-Algebra (Grades 7–8) is for students not yet taking algebra.
Mathercise™ Book B: Pre-Algebra and Algebra (Grades 8–9) is for students taking pre-algebra, algebra, or a first-year high school math course.
Mathercise™ Book C: Algebra and Geometry (Grades 9–10) is for students taking algebra, geometry, or a second-year high school math course.
Mathercise™ Book D: Geometry and Advanced Algebra (Grades 10–11) is for students who have taken a year of algebra and are taking geometry, advanced algebra, or a second- or third-year high school math course. Some sketching exercises involve graphing functions.
Mathercise™ Book E: Advanced Algebra and Pre-Calculus (Grades 11–12) is for students who are taking advanced algebra, precalculus, or a third- or fourth-year high school math course. Some sketching exercises involve graphing functions, including sine and cosine functions.