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## Activities for Students: Error Tolerance Formulas Related to Classical Algebra and Geometry

When the diameter of a basketball must be within a certain tolerance, what are the implications for the surface area and volume of the basketball?

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## Geometry + Technology = Proof

Symbolic geometry software, such as Geometry Expressions, can guide students as they develop strategies for proofs.

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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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## Technology Tips: Using the TI-Nspire CAS to Explore Areas of Ellipses

Various methods of determining the area of an ellipse are discussed.

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## The Shape of an Ellipse

Ellipses vary in shape from circular to nearly parabolic. An ellipse's eccentricity indicates the location of its foci, but its aspect ratio is a direct measure of its shape.

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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.

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## Delving Deeper: Teaching the Unthinkable in Introductory Statistics

Most teachers have encountered students who are able to successfully carry out statistical computations but lack a conceptual understanding of the subject. The introduction of technology seems to have had little corrective effect on this problem. This article suggests that the introduction of some modern computer intensive techniques not usually found in introductory courses may redirect students' focus from computational success to conceptual understanding.

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## Technology Tips: Teaching Sampling Distributions Using Autograph

The author uses Autograph, a powerful software program, to illustrate sampling distributions and to demonstrate the central limit theorem.

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## The estimation calculator

Technology from the Classroom is the venue for sharing articles that illustrate the effective use of technology in pre-K—grade 6 mathematics classrooms.