Quadratic: manipulating algebraic expressions on an interactive tabletop

This paper introduces Quadratic---a virtual manipulative for two people to explore algebraic expressions on an interactive tabletop. Users assemble rectangles out of fundamental components: 1, x, and x2. As the area of a rectangle is both the product of its sides and the sum of its components, users can explore how the product of two linear expressions (the rectangle's sides) equals a quadratic equation (the rectangle's area). This virtual manipulative adds several important features to the previously existing physical manipulative: 1) negative pieces; 2) multiple palettes; 3) multiple linked representations between the visual elements, the equivalent algebraic expression, and the graph of that expression; 4) the ability to provide feedback on posed challenges.