![]() Select these two measurements and choose Number | Tabulate. Plot a quadratic function, place a point on the function, and measure its x- and y-coordinates. In addition to working simultaneously with graphical and symbolic representations, they can also produce tabular representations. Next, students can use the Number and Graph menus to produce their own functions and graphs. You’ll notice that everything “below the line” in the Measure menu is there to do algebra: in addition to slope, equation, and coordinates, the Coordinate Distance command measures distances in coordinate units-rather than physical units like centimeters or inches that accompany geometric distances. Ask them to drag the line in a way that keeps the y-intercept the same this kind of interaction helps develop visual meanings for each of the constants in a linear equation. Now students make connections between the graph of the equation and the values of both the slope and y-intercept. Next, select the line and choose Measure | Equation. ![]() Drag the whole line, and the slope doesn’t change at all! Students can work with slope visually, gaining fluency with the values associated with flat, slightly inclined, and steep slopes. Tilt the line (drag one of its defining points) to see how the value of the slope changes dynamically. Sketchpad will add a coordinate system and give the slope of the line. Draw a line, select it, and choose Measure | Slope. Sketchpad’s Straightedge tool might strike you first as a geometric object, but with the help of the Measure menu, students can quickly start working with algebraic ideas such as slope, linear equations, and intercepts. One of the first topics of algebra is the study of linear equations and graphs. Much of contemporary algebra curriculum has its roots in 17th and 18th century analytic geometry, and Sketchpad can make that historical connection apparent and relevant to present-day students. And geometry-the visualization of mathematical structure-grounds many of our algebraic ideas of graphing and plotting. But at a deeper level, you’ll find that both the "dynamic" and the "geometry" halves of "Dynamic Geometry" offer valuable and distinct contributions to your students’ deep understanding of algebraic concepts.ĭynamism gives students the ability to vary mathematical quantities directly, and thus captures the ideas of variables and variation central to algebraic understanding. In one sense, Sketchpad is a powerful graphing calculator. You’ll find many tools and techniques that relate directly to your algebra curriculum: expressions and variables, plotting points and graphing equations, functions and families of functions, and so on. Sketchpad is an excellent tool for exploring and understanding algebra.
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