Chapter 14: Lessons and Activities

Activity Name Activity Description
Slope Slider This activity allows the manipulation of a linear function of the form f(x)=mx+b and encourages the user to explore the relationship between slope and intercept in the cartesian coordinate system.
Simple Plot Students can plot ordered pairs of numbers, either as a scatter plot or with the dots connected.
Graph Sketcher Students can create graphs of functions by entering formulas -- similar to a graphing calculator.
Graphit Students can graph functions and sets of ordered pairs on the same coordinate plane -- similar to a graphing calculator.
General Coordinates Game Students investigate the Cartesian coordinate system through identifying the coordinates of points, or requesting that a particular point be plotted.
Simple Coordinates Game Students investigate the first quadrant of the Cartesian coordinate system through identifying the coordinates of points, or requesting that a particular point be plotted.
Maze Game Students investigate the Cartesian coordinate system by directing a robot through a mine field laid out on the plane.
Simple Maze Game Students investigate the first quardant of the Cartesian coordinate system by directing a robot through a mine field laid out on the plane.
Vertical Line Test Students learn about the vertical line test for functions by trying to connect points in the plane to build a function.
Possible or Not? Drills students on whether a curve satisfies the properties of functions.
Sequencer Students learn about number patterns in sequences and recursions by specifying a starting number, multiplier and add-on.
The Two Variable Function Pump Students enter two complex numbers (z and c) as ordered pairs of real numbers, then click a button to iterate step by step. The iterates are graphed in the x-y plane and printed out in table form. This is an introduction to the idea of prisoners/escapees in iterated functions and the calculation of fractal Julia sets.
Function Machine Students investigate very simple functions by trying to guess the algebraic form from inputs and outputs.
Linear Function Machine Students investigate linear functions by trying to guess the slope and intercept from inputs and outputs.
Triangle Explorer Students learn about areas of triangles and about the Cartesian coordinate system through experimenting with triangles drawn on a grid.

Lesson Name General Lesson Description
Cartesian Coordinate System Introduces students to plotting points on the Cartesian coordinate system -- an alternative to "Graphing and the Coordinate Plane."
Graphs and Functions Demonstrates the connections between formulas and graphs.
Graphing and the Coordinate Plane Students learn basic ideas needed for graphing on the coordinate plane.
Functions and the Vertical Line Test Introduces students to the vertical line test for graphs of functions.
Reading Graphs Demonstrates the connections between formulas, graphs and stories.
Impossible Graphs Students learn to distinguish between possible and impossible graphs of functions, and to study causes of graphical impossibility.
Lines, Rays, Line Segments, and Planes Introduce students to lines, rays, line segments, and planes.