Forging Connections

This site supports the NSF project on Technology-Rich Units for Future Secondary Teachers: Forging Dynamic Connections Between Geometry and Functions, which is part of the NSF's program on Improving Undergraduate STEM Education (IUSE).

Unit 5: Advanced Topics

  1. Sine Tracer: In this lesson you’ll animate a point `x` along the `x`-axis while rotating a point around the unit circle. You'll measure the `y` value of the point on the circle, plot the point `(x, y),` and analyze and explain the shape of the resulting graph.
  2. Piecewise Derivatives: In this lesson you’ll explore the relationship between a graph and its derivative by manipulating a piecewise linear derivative function. You’ll predict the shape of the resulting graph to see how well you did, you'll try to create a graph with a particular shape, and you’ll adjust the derivative to make the graph model the motion of a physical object.
  3. Slope of the Sine Function: In this lesson you’ll graph the sine function and measure its slope at various places along the graph. You’ll then figure out how to trace a graph that shows the slope of the sine at each point along the sine curve, and you'll figure out how your traced graph is connected to the behavior of the sine function.
  4. Multiply Complex Numbers: In this lesson you’ll represent the complex product of two numbers on the complex plane, experiment with geometric transformations involving the original numbers, and discover a simple and elegant way to use geometric transformations to perform multiplication of complex numbers.