In my Hidden Polygons blog post from 2014, I described children’s difficulties in recognizing polygons when they’re not displayed in their plain-vanilla forms. So if a triangle isn’t equilateral with a side horizontal to the page, children may not identify it as a triangle. Web Sketchpad, with its ability to show us all triangles and all polygons rather than just specific static images, offers the opportunity to expand children’s sense of what it means to be a triangle, quadrilateral, pentagon, or other polygon. But giving children a triangle and asking them to drag its vertices isn’t very engaging, and there’s no guarantee they’ll explore a wide variety of configurations. Placing polygons in the context of a puzzle where dragging is required seems more effective.
In the websketch below (and here) the goal is to fence in either the sheep or the wolves so that the sheep are safely protected from their predators. There are four pages of challenges. You can move from page to page using the page navigation controls in the lower-right corner of the websketch. Here is a description of the challenges:
Page One: Enclose the sheep or the wolves with a triangular fence. Only one vertex of the triangle can be dragged. In some cases, you may not be able to save the sheep! Press New Puzzle for a fresh challenge.
Page Two: Again, your goal is to enclose the sheep or wolves with a triangular fence, but now, all three vertices of the triangle are draggable.
Page Three: Now you have the choice of using a fence with either four or five sides.
Page Four: Make a challenge for a friend! Drag the sheep and wolves to locations of your choice before sharing the puzzle.