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## Exploring Sequences Related to Medial Triangles

Sequences are an important topic—not only in mathematics but also in the mathematics curriculum. Exploring sequences related to medial triangles offers learners opportunities to solve problems involving sequences within geometric contexts. Sequences related to medial triangles are also a rich source of beautiful and interesting geometric patterns that can be discovered with the use of dynamic geometry software (DGS) such as GeoGebra or Web Sketchpad. In addition, exploring sequences with DGS allows learners to formulate and test conjectures, an important mathematical process. In this article, I describe how my students used GeoGebra and geometric reasoning to visualize, discover, formulate,

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## Puddle Play!

For the Love of Mathematics

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## Student Engagement with the “Into Math Graph" Tool

We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.

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## Closed Circular Chains

Tangent circles, sequenced to form annular Steiner rings, are photographed in the windows of ancient buildings.

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## Mathematical Modeling with MyMaps and Spreadsheets

Available apps are used to develop and investigate an optimization problem.

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## Calendar and Solutions – August 2014

A set of problems of many types.

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## Triangles from Three Points

Using technology to solve triangle construction problems, students apply their knowledge of points of concurrency, coordinate geometry, and transformational geometry.

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## Calendar and Solutions – May 2014

A set of problems of many types.

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## Connecting Research to Teaching: Evaluating and Writing Dynamic Geometry Tasks

The advent of dynamic geometry software has changed the way students draw, construct, and measure by using virtual tools instead of or along with physical tools. Use of technology in general and of dynamic geometry in particular has gained traction in mathematics education, as evidenced in the Common Core State Standards for Mathematics (CCSSI 2010).

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## Media Clips: Mosquitoes; Pythagorean Baseball

Students analyze items from the media to answer mathematical questions related to the article. This month's clips examine why raindrops do not crush mosquitoes and feature an application of the Pythagorean theorem to baseball. The mathematics involved includes dimensional analysis, ratio and proportion, and the Pythagorean theorem.