Chapter 2: Lessons and Activities

Activity Name Activity Description
Venn Diagrams Students learn about classifying numbers into various categories through answering questions about Venn Diagrams.
Coloring Multiples in Pascal's Triangle Students color numbers in Pascal's Triangle by rolling a number and then clicking on all entries that are multiples of the number rolled, thereby practicing multiplication tables investigating number patterns, and investigating fractal patterns.
Coloring Remainders in Pascal's Triangle Students color numbers in Pascal's Triangle by rolling a number and then clicking on all entries that have the same remainder when divided by the number rolled, thereby practicing multiplication tables, investigating number patterns, and investigating fractal patterns.
Caesar Cipher Students practice simple arithmetic skills by encoding and decoding messages using an affine cipher.
Caesar Cipher II Students practice simple arithmetic skills by encoding and decoding messages to determine the form for an affine cipher.
Caesar Cipher III Students practice their reasoning and arithmetic skills by decoding messages to determine the form for an affine cipher.
Function Machine Students investigate very simple functions by trying to guess the algebraic form from inputs and outputs.
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.
Julia Sets Students enter a complex value for c in the form of an ordered pair of real numbers. The applet draws the fractal Julia set for that seed value.
The Mandelbrot Set Students investigate the relationships between the Mandelbrot set and Julia sets by clicking and zooming.
Linear Function Machine Students investigate linear functions by trying to guess the slope and intercept from inputs and outputs.
Positive Linear Function Machine Students investigate linear functions with positive slopes by trying to guess the slope and intercept from inputs and outputs.
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.
Vertical Line Test Students learn about the vertical line test for functions by trying to connect points in the plane to build a function.

Lesson Name Lesson Description
Sets and Venn Diagrams Introduces students to the notions of sets, elements, and Venn diagrams.
Pascal's Triangle Looks at how Pascal's Triangle can be used to generate Sierpinski triangle-like results
The Mandelbrot Set Introduces all of the 2 variable function and prisoner/escapee notions necessary to understand the Mandelbrot set
Introduction to Functions designed to introduce the basic ideas needed for learning functions
Introduction to Linear Functions designed to introduce the basic ideas needed for learning about linear functions
Graphs and Functions demonstrates the connections between formulas and graphs
Functions and the Vertical Line Test introduces students to the vertical line test for graphs of functions
Impossible Graphs learn to distinguish between possible and impossible graphs of functions, and to study causes of graphical impossibility