This unit was designed for middle school students who have had no prior experience with fractal geometry. It should lead them through the definition of a fractal, multiple examples of fractals, where fractals can be found, and how to compose a simple fractal from scratch. It can be used as an individual tutorial, or as the basis for classroom lessons. When used for classroom lessons, the unit provides opportunities for individual work, pair inquiry, as well as group research. Here I will outline how the unit addresses the NCTM Standards, activities that provide opportunities for student assessment, and relevant references and links that can be explored.
#2 Mathematics as communication: develop common understandings of mathematical ideas, including the role of definitions.
#8 Patterns & functions: describe, extend, analyze, and create a wide variety of patterns.
#12 Geometry: identify, describe, compare, and classify geometric figures.
#1 Mathematics as problem solving: generalize solutions and strategies to new problem situations.
#2 Mathematics as communication: use the skills of reading, listening, and viewing to interpret and evaluate mathematical ideas.
#3 Mathematics as reasoning: recognize and apply deductive and inductive reasoning.
#4 Mathematical connections: see mathematics as an integrated whole.
#8 Patterns and functions: describe, extend, analyze, and create a variety of patterns.
#12 Geometry: develop an appreciation of geometry as a means of describing the physical world.
#1 Problem solving: use problem-solving approaches to investigate and understand mathematical content.
#2 Mathematics as communication: develop common understandings of mathematical ideas, including the role of definitions.
#3 Mathematics as reasoning: make and evaluate mathematical conjectures and arguments.
#4 Mathematical connections: use a mathematical idea to further their understanding of other mathematical ideas.
#8 Patterns and functions: describe and represent relationships with tables, graphs, and rules.
#9 Algebra: analyze tables and graphs to identify properties and relationships.
#10 Statistics: make inferences and convincing arguments that are based on data analysis.
#12 Geometry: explore transformations of geometric figures.
#2 Mathematics as communication: reflect on and clarify their own thinking about mathematical ideas and situations.
#3 Mathematics as reasoning: validate their own thinking.
#5 Number and number relationships: understand and apply ratios, proportions, and percents in a wide variety of situations.
#8 Patterns and functions: describe, extend, analyze, and create a wide variety of patterns.
#12 Geometry:
visualize and represent geometric figures with special attention
to developing spatial sense;
understand and apply geometric properties and
relationships;
explore transformations of geometric figures.
There are several activities throughout the unit that lend themselves to formal student assessment. They include:
Informal assessment can be made by observations of how students work in cooperative pairs and groups, how proficient they become using web browsers, and how they communicate ideas verbally to their peers.
I believe that each teacher needs to decide for themselves which activities will carry the most weight or what additional activities are necessary to conclude assessment to decide grades for the unit. Each class may have distinct goals or areas of focus. I feel the end of the unit fractal lesson is a strong alternative to a test to see if students have assimilated the main ideas of the unit.
Return to Table of Contents.
Please send me any comments or suggestions you have about the unit.