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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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## Connecting Slope, Steepness, and Angles

Students must be able to relate many representations of slope to form an integrated understanding of the concept.

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## Activities for Students: Connecting Spatial Reasoning Ideas in Mathematics and Chemistry

Stereochemistry and three-dimensional analysis constitute significant parts of this student activity.

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## Spaghetti Sine Curves: Virtual Environments for Reasoning and Sense Making

The Spaghetti Sine Curves activity, which uses GeoGebra applets to enhance student learning, illustrates how technology supports effective use of physical materials.

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## Is That Square Really a Circle?

Considering circles in taxicab geometry helps students with Euclidean concepts.

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## Visible Thinking in High School Mathematics

Chalk Talk and Claim-Support-Question are two routines for developing students' ability to use multiple representations and encouraging classroom discussion.

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## Exploring Quadrilaterals through Flexible Approaches

Rich mathematical tasks—here, finding and categorizing the quadrilaterals that can be made with vertices on a 4 × 4 grid—can promote adaptability in any classroom.

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## Core Conversations with Educative Dragging

The Measure-Trace-Algebratize (MTA) approach allows students to uncover algebraic relationships within familiar geometric objects.

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## A River Runs through Math Class

Let's go wading! Students connect fundamental mathematics concepts in this real-world, problem-solving field experience.

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## The Back Page: My Favorite Lesson: A Sweet Way to Investigate Volume

This article describes a series of “food labs” designed to help calculus students make sense of abstract volume concepts. The methods include slicing (e.g., disk, washer, cross-section) and shell methods, and the author discusses how to use them in the classroom.