Activity Description Learn about fractions between 0 and 1 by repeatedly deleting portions of a line segment, and also learn about properties of fractals. Parameter: fraction of the segment to be deleted each time.

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Cantor's Comb

Place in mathematics curriculum:

This activity can be used to:

• practice students' fraction manipulation skills
• practice students' pattern finding skills
• demonstrate the complexity of infinity
• motivate the ideas of self-similarity and recursion
• demonstrate fractal objects
• motivate the idea of a limit

This activity allows the user to work step by step through the process of building Cantor's comb. This activity would work well in mixed ability groups of two or three for about thirty to forty-five minutes if you use the exploration questions and ten minutes otherwise.

Preparations for this activity:

• work through the first table on the exploration questions with the students
• discuss the concepts of infinity and limit
• review fraction multiplication