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There are five Transformation manipulatives. Translation, Reflection, and Rotation are all called "Isometries" because they keep the same ("iso-") distances and angles and shape. Each can be explored independently, and then the Transformation - Composition manipulative allows two of the isometries to be performed sequentially. The other available transformation, Dilation, moves every point in the plane away from, or toward, a given Center point by some fixed scaling factor. Dilation retains shape (the images are similar to the original) but changes each length by the same scale factor, so that Dilation is not included as an isometry.

Translation (often called a "slide") moves every point in the plane by a given distance in a particular direction. The distance and direction are shown graphically by a black arrow (or vector), and as new pieces are added to the work space, every piece, single or grouped, is translated in the same way. The user should observe that the image of an object can be moved in two ways, either by dragging and sliding or rotating the original, or by clicking on the tip of the arrow to change its length or direction.

By adding coordinate axes and lattice points to the workspace, it is possible to describe a translation verbally, as "Slide everything 2 units right" or "Translate the given triangle down 3 units and 1 unit left" (which could be described as a <-3,-1> translation. Coupling this kind of exercise with the Transformation - Composition manipulative opens natural questions such as determining the result of two given translations (the addition of vectors) and deciding if order makes a difference. That is, does the <3,-2> translation followed by the <1,1> translation accomplish the same result as performing the <1,1> translation and then the <3,-2> translation? How should the resulting composition be named as a single translation?

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The National Library of Virtual Manipulatives is a three-year NSF supported project to develop a library of uniquely interactive, web-based virtual manipulatives or concept tutorials, mostly in the form of Java applets, for mathematics instruction (K-8 emphasis). The project includes dissemination and extensive internal and external evaluation. For more information, please visit http://nlvm.usu.edu/en/nav/vlibrary.html.

Principal Investigators
Larry Cannon
Jim Dorward
Bob Heal
Leo Edwards

Java Applet Programming
Ethy Cannon
Joel Duffin
David Stowell
Zeke Susman
Richard Wellman
Jennifer Youngberg

Web Site Programming
Joel Duffin