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## Fractal Patterns and Chaos Games

One of the most wonderful ways to introduce students in middle school or secondary school to the beauty and excitement of contemporary mathematics is to involve them in the many variations of the “chaos game” which produces such intriguing fractal patterns as the Sierpinski triangle and the Koch curve.

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## Corner Reflector Mathematics

Students investigate the geometrical properties used to design reflective safety garments and road signs.

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## Creating a Hybrid Immersive Mathematics Experience

With this professional development program, teachers work with colleagues and experience a manner of teaching that embeds habits of mind.

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## Activities For Students: The Geometry of Tetris

When it was released in the mid-1980s, Tetris jump-started the video game craze, but many students of the current generation have never even seen this game, much less played it. Now, with the flood of mobile device applications, Tetris has made a comeback, and today's students have a chance to use it, too. We have found Tetris to be an engaging tool for high school geometry students to apply an isometry in context and to learn the composition of isometries. The game allows a player to rotate and translate moving pieces to create full rows anywhere on the screen.

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## Mathematical Lens: Transformational Geometry at Guilin Garden, Shanghai

The walls along the walkway leading to Shanghai's Guilin Garden are lined with geometric panels. The following questions refer to the wall panels shown in photographs 1–8. When answering these questions, assume that the patterns continue in all directions.

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## Not So Complex: Iteration in the Complex Plane

Graphing orbits using linear iteration rules inspires enjoyment and artistry.

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## Delving Deeper: Deepening Understanding of Transformation through Proof

In the introductory geometry courses that we teach, students spend significant time proving geometric results. Students who conclude that angles are congruent because “they look that way” are reminded that visual information fails to provide conclusive mathematical evidence. Likewise, numerous examples suggesting a particular result should be viewed with skepticism. After all, unfore–seen counterexamples render seemingly valid conclusions false. Inductive reasoning, although useful for generating conjectures, does not replace proof as a means of verification.

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## Speaking Elliptically about an Ellipse

Ellipses are the focus of photographs and mathematical equations.

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## Can We Use a Mirror to Find Height?

My favorite lesson is based on a problem my geometry students encounter. When we study similar triangles, students use indirect measurement to determine the height of an object.

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## Enhancing Understanding of Transformation Matrices

With the Common Core State Standards' emphasis on transformations, teachers need a variety of approaches to increase student understanding.