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September 2011, Volume 17, Issue 2

 FEATURES Mathematics, Anyone?Robert Reys and Rustin ReysGet your students to rally around the connections between mathematics and tennis. Navigating Classroom ChangeLindsay M. UmbeckA renegotiated classroom culture results in students learning to participate in new ways. Estimation’s Role in Calculations with FractionsDebra I. JohanningSee how students use number sense and also algorithm sense as tools to develop their understanding of fraction operations. Turning Students into Symmetry DetectivesRichard Wilders and Lawrence VanOyenStudents will flip when they are given the opportunity to learn about art and transformations in math class. Second Look:Symmetry Mathematics Teachers Circle around Problem SolvingAnthony Fernandes, Jacob Koehler, and Harold ReiterBy meeting regularly, a group of teachers from different schools promote a culture of problem solving and engagement.

 Departments Solve It!Solve It! Student Thinking: Composites and Primes Cartoon CornerCartoon Corner: Guess What? Palette of Problems/Menu of ProblemsPalette of Problems - September 2011 Mathematical ExplorationMathematical Explorations: What a Pip! Probability and Efron’s Dice Window on ResourcesWindow on Resources: Books - September 2011 Math for RealMath for Real: Packaging Golf Balls

 Second Look - Symmetry Short Takes: Another Good Idea: Pasta SymmetryAuthentic assessment. Article discusses students creating and using representations to communicate mathematical situations, namely, symmetry. Quick Reads provides readers with activities or ideas for the middle school classroom that are quick and applicable. Teaching Mathematics through the Art of KolamThe mathematics of kolam, a traditional art form of southern India. Article discusses simple graph theory, Euler paths and circuits, numerical patterns, symmetry, and growing patterns. Includes student work samples and suggestions for organizing data. Irrational Numbers Can In-Spiral YouAn instructional process to help students visualize irrational numbers. Article discusses creating a spiral, called The Wheel of Theodorus, to construct and compare irrational and rational lengths. Includes student work to help the reader appreciate the possibilities. Just Five Does It: Using Five Numbers to Make Patterned SquaresCreating mathematical art based on number patterns. Article discusses a process that integrates numbers and geometry resulting in attractive patterned squares. Activity may be done with paper and pencil or using computer software. Includes directions for creating patterns using Geometer's Sketchpad. Illuminations Lesson: Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive FiguresRotations; translations, or slides; and reflections, or flips, are geometric transformations that change an object’s position or orientation but not its shape or size. The interactive figures in this four-part example allow a user to manipulate a shape and observe its behavior under a particular transformation or composition of transformations. Principles and Standards: Geometry Standard for Grades 6-8Apply transformations and use symmetry to analyze mathematical situations