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## Activities for Students: Dealing Cards with Confidence

When understood and applied appropriately, mathematics is both beautiful and powerful. As a result, students are sometimes tempted to extend that power beyond appropriate limits. In teaching statistics at both the high school and college level, I have found that one of students' biggest struggles is applying their understanding of probability to make appropriate inferences.

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## Free online CCSSM Toolbox

Share news about happenings in the field of elementary school math education, views on matters pertaining to teaching and learning mathematics in the early childhood or elementary school years, and reactions to previously published opinion pieces or articles.

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## The Power of Problem Choice

Fourth- and fifth-grade learners can use differentiated number sets within CGI problem structures to add and subtract fractions with unlike denominators.

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## Virtual manipulatives to assess understanding

Three preservice teachers used virtual manipulatives during clinical interviews with students of elementary school age. The technology exposed students' problem-solving strategies and mathematical understanding, promoting just-in-time teaching about the target content. The process of completing and reflecting on the interviews contributed to growth of the preservice teachers' technological pedagogical content knowledge.

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## Pattern-block frenzy

Teachers share success stories and ideas that stimulate thinking about the effective use of technology in K–grade 6 classrooms. This article describes a set of lessons where sixth graders use virtual pattern blocks to develop proportional reasoning. Students' work with the virtual manipulatives reveals a variety of creative solutions and promotes active engagement. The author suggests that technology is most effective when coupled with worthwhile mathematical tasks and rich classroom discussions.

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## Three-Dimensional Printing: A Journey in Visualization

Using simple materials, a Mathematica software application, and their knowledge of function transformations, students design and create real mathematical sculptures.

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## Technology Tips: Exploring the Golden Ratio with The Geometer's Sketchpad

This article shows how to explore the golden ratio using GSP. Golden rectangles, spirals, triangles, and pentagons are also discussed.

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## The Popcorn Box Activity and Reasoning about Optimization

Investigating rates of change in volume without calculation leads to an enriched sense of the optimization process and encourages reflection and connection among different approaches.

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## Technology Tips: Exploring Three-Dimensional Worlds Using Google SketchUp

Google SketchUp is free, powerful and widely used Computer Aided Design (CAD) software that can have a transformative impact on the teaching of geometry. This article introduces Google SketchUp to readers through lessons that can be integrated into geometry classrooms and also provides additional resources for readers interested in learning more.

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## Sketching Up the Digital Duck

Two preservice teachers describe how using Google SketchUp, Terrapin Logo, and The Geometer's Sketchpad fosters a deeper understanding of measurement concepts.