Two math Gizmos highlighted in NCTM article

A recent article in the NCTM magazine Teaching Children Mathematics describes an activity, designed by two professors, that aims to help teachers select clear, effective technology for their classrooms. The article lists five criteria for selecting technology (National Research Council, 2001):

1. Transparency: How easily can the idea be seen through the representation?
2. Efficiency: Does the representation support efficient communication and use?
3. Generality: Does the representation apply to broad classes of objects?
4. Clarity: Is the representation unambiguous and easy to use?
5. Precision: How close is the representation to the exact value?

Based on these, the teachers selected a variety of applets to use in their classes. Among these, they chose two Gizmos that provide nice visuals to help teach number sense with the number line.

The Rounding Numbers (Number Line) Gizmo is noted for its use of "hills" on the number line to help illustrate rounding. In this Gizmo, points can be dragged onto a dynamic number line. When in "hill" mode, the points will slide to the nearest valley (the nearest 10 or 100), helping students to visualize rounding. (By the way, interesting things happen when points are exactly halfway between two valleys – like, for example, 35 when rounding to the nearest 10, or 350 when rounding to the nearest 100. Why don’t these points slide to a valley right away? Thought-provoking discussions about the "round up" convention can ensue!)

Also, the teachers chose Number Line Frog Hop (Addition and Subtraction) Gizmo, in which Fred the Frog hops along a number line to try to catch flies. If Fred hops more than 10 units, he can jump as a "single jump," "tens then ones," or "ones then tens." The latter two modes highlight the "parts" of a number (place value, essentially). In addition, as a teacher points out in the article, you can show repeated addition in this Gizmo as a bridge to multiplication.