Using dynamic geometry software, students can use a Segment tool to draw what looks like a square by eyeballing the locations of the vertices. However, the resulting quadrilateral will not stay a square when its vertices are dragged. Building an “UnMessUpAble” square requires that the quadrilateral stay a square when any of its parts are dragged. This is only possible by baking the geometric properties of a square into the quadrilateral as it’s being built.

Constructing a square requires tools, and Web Sketchpad features a particularly innovative tool interface. When a student taps a tool icon, the entire object to be constructed appears in preview mode. For example, if you tap the Rotate tool in the websketch below (and here), you’ll see a point, a center of rotation, an angle of rotation, and the rotated point . These objects are previews of what you’re about to construct. This overview of the entire tool gives students the opportunity to consider what objects the tool is going to create and plan how to integrate these objects into the existing sketch.

There’s no need for the student to remember or figure out which objects to click, or in what order to do so, to use the tool successfully. One by one, the objects glow (first the center of rotation, then the point to be rotated, and finally the angle of rotation) indicating that they’re ready to be placed in the sketch. This visual information enables less prescriptive and more open-ended student tasks. Students can be encouraged to be self-reliant and self-directed, concentrating on the mathematics of the task rather than following directions from a worksheet or from the teacher.

Furthermore, Web Sketchpad allows a teacher or curriculum developer to create and provide only those tools needed for a particular task. In this manner, we can lead students to think about a problem in targeted ways by limiting them to carefully chosen tools.

Below are five Web Sketchpad construction challenges (one per page) where the goal is to use handpicked sets of tools to build a square. Can you, for example, construct a square with just a Segment and Rotate tool? Or how about starting with Segment, Compass, and Perpendicular tools? Each of the five pages of the websketch offers different tools for building a square.

When you’re done, check out these related construction challenges where the goal is to build a rhombus using 11 different sets of tools.