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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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## The Engineering Process in Construction & Design

By implementing high-impact activities, such as designing a school and a skate park, mathematical thinking can be linked to the engineering design process.

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## Quick Reads: Searching for Pythagorean Triples

### a good idea in a small package

This method emphasizes the strong connections between geometric and algebraic representations.

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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.

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## Delving Deeper: Boundaries in Higher Dimensions and Their Kinship with Combinatorics

This is a description of a collaborative investigation by mathematics teachers into the numbers of dimensional boundaries for n > 2. Functions are fit to the patterns observed, and a relationship to Pascal's triangle is noted.

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## Navigating between the Dimensions

Two classroom activities—the Flatland game and sliceforms—are useful vehicles for student exploration of the geometric interplay between the dimensions.