Chapter 7: Lessons and Activities

Activity Name Activity Description
The Tortoise and Hare Race Students step through the tortoise and hare race, based on Zeno's paradox, to learn about the multiplication of fractions and about convergence of an infinite sequence of numbers.
Cantor's Comb Students learn about fractions between 0 and 1 by repeatedly deleting portions of a line segment, also learning about properties of fractal objects. Parameter: fraction of the segment to be deleted each time.
Fraction Four Students play a generalized version of connect four, gaining the chance to place a piece on the board by simplifying a fraction. Parameters: Level of difficulty of fractions to simplify.
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.
PieChart Students view piecharts. Parameters: Number of sectors, size of sector as a percent.

Lesson Name Lesson Description
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.
Irregular Fractals Looks at how irregular fractals can be generated and how they fit into computer graphics<./TD>
Fraction Facts Introduces students to fractions and explores basic mathematical operations with fractions, comparing fractions, and converting fractions into decimals or percents.