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September 2011, Volume 17, Issue 2

FEATURES

Mathematics, Anyone?
Robert Reys and Rustin Reys
Get your students to rally around the connections between mathematics and tennis.

Navigating Classroom Change
Lindsay M. Umbeck
A renegotiated classroom culture results in students learning to participate in new ways.

Estimation’s Role in Calculations with Fractions
Debra I. Johanning
See how students use number sense and also algorithm sense as tools to develop their understanding of fraction operations.

Turning Students into Symmetry Detectives
Richard Wilders and Lawrence VanOyen
Students 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 Solving
Anthony Fernandes, Jacob Koehler, and Harold Reiter
By meeting regularly, a group of teachers from different schools promote a culture of problem solving and engagement.

Second Look - Symmetry

Short Takes: Another Good Idea: Pasta Symmetry
Authentic 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 Kolam
The 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 You
An 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 Squares
Creating 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 Figures
Rotations; 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 6-8

Apply transformations and use symmetry to analyze mathematical situations