Tailoring Tools to the Task

In years past, my colleagues and I at Key Curriculum conducted Sketchpad professional development workshops for teachers. One of our favorite activities challenged participants to  construct a rhombus in as many different ways as possible. This assignment invariably led to great discussions because there are a multitude of ways to build a rhombus, and each method highlights its various mathematical properties.

While the rhombus task worked well, it did expose one of the challenges of using Sketchpad: The software features lots of menu commands and toolbox options and navigating all of the functionality can sometimes distract Sketchpad newcomers from the mathematics at hand.

Web Sketchpad differs from Sketchpad by offering  a more streamlined approach to mathematical construction. It allows a teacher or curriculum developer to create and provide only those tools needed for a particular task. We can use this approach to lead students to think about a problem in new mathematical ways, just by limiting them to carefully chosen tools.

Let’s consider, as we did in our professional development classes,  the challenge of constructing a rhombus. Below are four different toolsets, each of which focuses students on different mathematical properties of a rhombus. Your task is to construct a rhombus with each toolset that stays a rhombus when its vertices are dragged. These are elegant challenges. Each toolset includes a Quadrilateral tool for indicating the four vertices and interior of your rhombus, but it’s really the other tools—the Compass tool, the Parallel Line tool, the Reflect Point tool, and Perpendicular Bisector tool—that are responsible for ensuring that the quadrilateral you construct is a rhombus.

Try it yourself—use each collection of tools to construct a rhombus that stays a rhombus when you drag any of its vertices. Are some of your rhombi more general than others? How would you compare the behavior of your four rhombi when their vertices are dragged? What characteristics of a rhombus does your construction exploit?

If you need help, watch the movie at the end of this post that demonstrates four rhombus constructions, one for each toolset. And please, let us know if you come up with a different construction in addition to those in the movie.

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