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August 2011, Volume 17, Issue 1

 FEATURES Canine Conjectures: Using Data for Proportional ReasoningArla Westenskow and Patricia S. Moyer-PackenhamA family dog supplies the measurements for scatter plots and variables so that students can explore relationships among data setsâ€”not to mention paws and tails. Lining Up Arithmetic SequencesCarol J. BellAsk your students to analyze geometric representations of arithmetic sequences for a meaningful problem-solving experience. Representations and RaftsKimberly Sipes HartwegBuilding a rod raft allows students to make mathematical connections among a model, a table, a formula, and a graph. A Geometric Path to the Concept of FunctionScott Steketee and Daniel ScherTransformations using dynamic software can provide a unique perspective on a common topic. Additional InformationExamples from the Geometer's Sketchpad (ZIP file) Second Look:Transformations

 Departments Readers WriteReaders Write - August 2011 Informing PracticeInforming Practice: The Process of Abstracting in Studentsâ€™ Representations Quick ReadsQuick Reads: A Handy Multiplication Mystery Solve It!Solve It! Student Thinking: Change for a Dollar Cartoon CornerCartoon Corner: That's Perfect! Palette of Problems/Menu of ProblemsPalette of Problems - August 2011 Mathematical ExplorationMath Explorations: Hanging in the Balance Window on ResourcesWindow on Resources: Books - August 2011 Math for RealMath for Real: Hurricane Force Math

 Second Look - Transformations Transformations and Technology: What Path to Follow?A technology-based approach for dealing with a misconception that some students hold concerning the equivalency of geometric transformations. Students can begin to conceptualize transformations in terms of the relationship between preimage and image figures rather than focus on the motion of a figure. Teachers will learn how to use technology to implement this activity in the mathematics classroom. It's Friezing in Here: Tessellations through Art, Architecture, and Cultural ArtifactsThe integration of transformational geometry, mathematics, history, art, and cultural studies in a middle-grades mathematics classroom. From Tessellations to Polyhedra: Big PolyhedraStudents explore relationships among polygons to discover which combinations tessellate; which combinations form polyhedra. Activity sheets, and answers, included. Illuminations Activity: Frieze PatternsStudents can experiment with the seven classes of Frieze patterns with this activity. They can explore the transformations that constitute each of the seven categories.