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## Defining Supports Geometry

The process of developing definitions is underemphasized in most mathematics instruction. Investing time in constructing meaning is well worth the return in terms of the knowledge it imparts.

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## Coming Full Circle

Teacher candidates develop processes and proficiencies articulated in the Common Core State Standards for Mathematics by investigating connections between and among geometry concepts.

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## Become an Escher Sleuth

Students discover why certain regular polygons tessellate and how M. C. Escher translated and rotated modifications of polygons to create tessellations.

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## If Only Clairaut Had Dynamic Geometry Tools

Using Clairaut's historic-dynamic approach and dynamic geometry tools in middle school can develop students' conceptual understanding before they encounter formal proof in geometry.

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## Angle detectives

This problem scenario presents how a fifth-grade class used logical thinking and spatial reasoning to find the angle measurements of certain polygons without using a protractor. To access the full-size activity sheet, go to http://www.nctm.org/tcm, All Issues. Each month, this section of the Problem Solvers department showcases students' in-depth thinking and discusses the classroom results of using problems presented in previous issues of Teaching Children Mathematics.

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## Photon Translations

“Photon Translations” is a piece of installation art that incorporates all the disciplines of science, technology, engineering, art, and mathematics (STEAM) and is on display at the Stoneleigh-Burnam School in Greenfield, Massachusetts. Installation art is just what it implies: art that is created for the purpose of being installed at a particular location. Sometimes the artwork can be interactive, allowing audience members to participate in the experience in some dynamic way. Terry Marashlian of Northfield, Massachusetts, created this artwork. The author collaborated with Marashlian on creating the musical chimes.

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## August 2016 Problems

A monthly set of problems is aimed at a variety of ability levels.

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## October 2016 Problems

A monthly set of problems is aimed at a variety of ability levels.

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## Palette of Problems

A monthly set of problems is aimed at a variety of ability levels.

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## September Problems

A monthly set of problems is aimed at a variety of ability levels.