| MIT BLOSSOMS - Fabulous Fractals and Difference Equations : | This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of difference equations. |
| MIT BLOSSOMS - Guess the Last Ball: An Exercise in Mathematical Modeling: | This video lesson uses the technique of induction to show students how
to analyze a seemingly random occurrence in order to understand it
through the development of a mathematical model. Using the medium of a
simple game, Dr. Lodhi demonstrates how students can first apply the
'rules' to small examples of the game and then, through careful
observation, can begin to see the emergence of a possible pattern.
Students will learn that they can move from observing a pattern to
proving that their observation is correct by the development of a
mathematical model. Dr. Lodhi provides a second game for students in
the Teacher Guide downloadable on this page. There are no prerequisites
for this lesson and needed materials include only a blackboard and
objects of two different varieties - such as plain and striped balls,
apples and oranges, etc. The lesson can be completed in a 50-minute
class period. |
