Illuminations: To Fret or Not To Fret

To Fret or Not To Fret
Students explore geometric sequences and exponential functions by considering the placement of frets on stringed instruments.

Math Content

  • Geometric sequences
  • Exponential curves
  • Measurement, precision, and accuracy
  • Ratio

Prerequisite Knowledge

  • Reading metric and U.S. measuring tapes
  • Adding, subtracting, multiplying and dividing fractions
  • Using the Stats Plot and curve-fitting features of a graphing calculator
  • Basic understanding of discrete and continuous functions

Individual Lessons

Lesson 1 - Exploring Measurement, Sequences, and Curves with Stringed Instruments

Students will measure lengths on stringed musical instruments, and discuss how the placement of frets on a fretted instrument is determined by a geometric sequence.

Lesson 2 - Fretting

In the second lesson of this unit, students will use their discoveries from the first lesson to place frets on a fretless instrument. They will then compare geometric sequences with exponential functions.

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