Education Technology

Precalculus: Perfect Shuffles

by Texas Instruments


  • 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.


  • 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.