MATH
Lesson 7
Lesson Title: Probability and Chance Music
Synopsis: This lesson will have students learn about theoretical and experimental probabilities by rolling a set of dice and recording the results. The results will then be converted to pitches and rhythms to create "chance music".
Authors: J. Frankel & K. O’Malley
Interdisciplinary Pairing: Mathematics & Music
Objectives:
- Students will understand the differences between experimental and theoretical probabilities and conversions to decimals / percents
- Students will create melodies based on probability learning.
Prior Knowledge & Skills:
- Converting fractions to decimals and to percentages
Equipment:
- Computer lab with notation software such as Sibelius, Finale, Finale NotePad.
- Internet access
- USB keyboard controller/MIDI Lab
- Enough sets of dice for each group to have their own set
Duration:
This lesson takes place over four 45-minute class periods.
Materials:
- Chance Music Website
- PROBABILITY & CHANCE MUSIC HANDOUT (Lesson 7 Handout 1)
- DICE RECORD HANDOUT (Lesson 7 Handout 2)
- Sibelius, Finale, Finale NotePad
Procedure:
Day 1:
- Students will complete both of the Lesson 7 Handouts
- Students will roll their dice 100 times. Record results.
- Students will convert results to decimal/percents
- Students will divide their results into two groups of 50 rolls. Students will record stats for first 50 rolls, stats for next 50 rolls, stats for total 100 rolls.
- How do the results compare??
- Class discussion to highlight the most frequently rolled number and the most infrequently rolled number (for each of the 50 rolls)
Day 2:
- Students will convert first 50 rolls to pitches on the pentatonic scale based on HANDOUT
- Students will convert second 50 rolls to rhythms based on HANDOUT
- Students will input the notes /melodies they created into notation software such as Sibelius, Finale or Finale NotePad
Day 3:
- Students finish inputting melodies
Day 4:
- Students will share melodies with class
- Class Discussion:
- Did we hear any emerging patterns?
- Certain rhythms or pitches that were predominant?
- Teacher will poll each group for their predominant pitch and predominant rhythm ----- that should correlate to patterns heard
- Teacher will create a chart – out of 10 groups in the class, including the following statistics:
- how many this / that predominant thing
- make fraction, convert to % and look at the percentages in descending order
- which # was rolled most? Least?
- Were they approximately equal?
- How do the class's results of 1000 rolls compare to theoretical probabilities?
Evaluation:
- SCORING RUBRIC - LESSON 7
- Scoring final project
Lesson Extension:
- Students could use chance music techniques employed by composer John Cage - I-Ching to create melodies and rhythms
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