Content Area: Math

 

Index: 4.2B Grade 8 CPI 2

 

Standard: 4.2 - Geometry and Measurement

 

Strand: B - Transforming Shapes

 

Cumulative Progress Indicator: 2 -  The student will use iterative procedures to generate geometric patterns.

·        Fractals (e.g., the Koch Snowflake)

·        Self-similarity

·        Construction of initial stages

·        Patterns in successive stages (e.g., number of triangles in each stage of Sierpinski’s Triangle)

 

Grade: 8

 

Sample Activities:

 

·        Students investigate the natural shapes that are produced by growth. They look at how nature produces complex structures in which basic shapes occur over and over. For example, spider webs, honeycombs, pineapples, pinecones, nautilus shells, and snowflakes grow larger in a systematic way (iteration).

 

·        Students learn about the natural shapes that are produced by growth. They investigate how nature produces complex structures in which basic shapes occur over and over. For example, spider webs, honeycombs, and snowflakes grow larger in a systematic way (iteration). Students measure the age of a tree by looking at its rings; this illustrates approximation. Students produce geometric designs that illustrate these principles, as well as fractals, where miniature versions of the entire design are evident within a small portion of the design.

 

·        Students view the slides which accompany the activity book, Fractals for the Classroom, Vol. 1, and determine why each picture might have been included in a book about fractals.

 

·        Additional Framework Activities