Precalculus: Perfect Shuffles

Objectives

• Students will create a piecewise linear function to model a method for shuffling a deck of cards.
• Students will apply composite functions to represent two or more shuffles of a deck.

Vocabulary

• perfect out-shuffle
• perfect in-shuffle
• piecewise linear function
• composition of functions

About the Lesson

This lesson involves creating and using a composite function to describe certain ways of shuffling a deck of cards.
As a result, students will:

• Create a piecewise linear function to represent shuffling a deck of cards in a certain way.
• Compose a piecewise function with itself several times.
• Use a piecewise function and its composites to determine the number of shuffles needed to return a deck of cards to its original order.