Connecting Algebra, Geometry and Graphs
Move from words to symbols, to geometric representations, to plotted points and finally to graphs.
Students must convert words such as "square n, then add four" to an algebraic expression. They then match the expressions to a geometric representation––the area of a rectangle with a movable point: as the point is moved, n changes and the area, A, changes too. As the point on the rectangle is moved, the value of A is plotted against n.
Finally students are asked to input an expression representing the area function. They can immediately see if they are correct because the plotted point will move along the displayed graph.
A lesson using this activity is described by Allan Duncan in a booklet entitled Inspired Connections in Maths Lessons. This description makes clear the power of the dynamically linked multiple representations to enhance student understanding. For a pdf version of the entire booklet please click here.