Chapter 10: Lessons and Activities

Activity Name Activity Description
Hilbert Curve Generator Students step through the generation of a Hilbert Curve -- a fractal made from deforming a line by bending it, allowing them to explore number patterns in sequences and geometric properties of fractals.
Another Hilbert Curve Generator Students step through the generation of a different Hilbert-like Curve -- a fractal made from deforming a line by bending it, allowing them to explore number patterns in sequences and geometric properties of fractals.
Koch's Snowflake Students step through the generation of the Koch Snowflake -- a fractal made from deforming the sides of a triangle, allowing them to explore number patterns in sequences and geometric properties of fractals.
Sierpinski's Triangle Students step through the generation of Sierpinski's Triangle -- a fractal made from subdividing a triangle into four smaller triangles and cutting the middle one out, allowing them to explore number patterns in sequences and geometric properties of fractals.
Sierpinski's Carpet Students step through the generation of Sierpinski's Carpet -- a fractal made from subdividing a square into nine smaller squares and cutting the middle one out, allowing them to explore number patterns in sequences and geometric properties of fractals.
Fractal Dimensions Students investigate the fractal dimensions of several line- deformation fractals.
Fractured Pictures Students generate complicated geometric fractals by specifying starting polygon and scale factor.
Flake Maker Students create their own fractals by specifying a "line deformation rule" and stepping through the generation of a geometric fractal. Parameters: Grid type, number of bending points on the line.
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 2 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.

Lesson Name General Lesson Description
Cartesian Coordinate System Introduce 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 basic ideas needed for learning graphing
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 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.
Introduction to Fractals: Infinity, Self-Similarity and Recursion Introduces the ideas and motivates the activities
Geometric Fractals Outlines the approach to building fractals by cutting out portions of plane figures