Music and Math: What Are The Chances? –
Grade Five - Interdisciplinary Lesson
Ohio Standards
Connection
Fine Arts - Music
Creative Expression and
Communication
Benchmark B
Improvise or compose a
short melody that includes
key signature and meter
signature with proper
notation in treble or bass
clef.
Indicator 4
Create short melodies
using traditional notation.
Lesson Summary:
In this lesson, students will create their own chance music
(aleatoric music) compositions using standard music
notation. They will use worksheets to compose four
measures of rhythm in common time. Pitches will be added
to the rhythm values as determined by the rolls of a number
cube. Students will play their compositions on tuned
instruments and transcribe them onto staff paper.
Additionally, students will conduct simple probability
experiments using a five-sided number generator or
spinner. Students will answer questions about probability
and express their answers in simple fractions and
percentages.
Estimated Duration: One hour and 30 minutes or three 30minute sessions.
Math
Data Analysis and
Probability
Benchmark I
Describe the probability of
an event using ratios,
including fractional
notation.
Indicator 8
Identify the probability of
events within a simple
experiment, such as three
chances out of eight.
Indicator 9
Use 0, 1 and ratios between
0 and 1 to represent the
probability of outcomes for
an event, and associate the
ratio with the likelihood of
the outcome.
Commentary:
This integrated lesson combines the process of composition
in music and the concept of probability in math. Students
often find it difficult to begin composing original pieces of
music. This lesson gives them a framework for
experimenting with simple music composition and eases
composition anxiety. It also helps students understand and
apply the concept of probability in math.
Pre-Assessment:
 Discuss probability with the students. Use terms like
chance, likelihood, fractions and percentages. Ask
them:
 What does it mean when the weatherman says, “It is
unlikely to rain today?” [It probably will not rain
today.];
 What does “it will most likely rain today” mean? [It is
more likely to rain than not rain today. Informal: It’s
probably going to rain today.];
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Music and Math: What Are The Chances? –
Grade Five - Interdisciplinary Lesson
Benchmark K
Make and justify
predictions based on
experimental and
theoretical probabilities.
Indicator 11
Make predictions based on
experimental and
theoretical probabilities





What does “it is certain to rain today” mean? [It absolutely
will rain today.]
What would it mean if the weatherperson said, “It is
equally likely to rain or snow today?” [It is just as likely
to rain as it is to snow today.]
What fraction is one out of two? [one- half];
What percent is equivalent to one out of ten? [10
percent].
Lead students in a simple rhythmic notation practice
session using quarter, eighth and sixteenth notes in 4/4
time.
Scoring Guidelines:
 Evaluate the students’responses to determine if they are
ready for the lesson based on suggested responses and
accuracy of using quarter, eighth and sixteenth notes in a 4
meter.
Post-Assessment:
 Evaluate responses from Attachment A, Rhythm Writer,
and Attachment B, What Are the Chances?
 Assess compositions based on Attachment D,
Composition Rubric.
Scoring Guidelines:
 Evaluate written work using Attachment B, What Are the
Chances?, to see if students understand the concepts.
 Use Attachment D, Composition Rubric, to assess chance
music compositions.
Instructional Procedures:
Day One
1. Review terms from the pre-assessment discussion: likely,
equally likely, unlikely, certain. Ask students to create
new examples using these terms. Explain how to use tally
marks to record outcomes.
2. Divide students into pairs or groups of three based on your
knowledge of how students work together. Distribute
pencils, worksheets and a number cube or spinner to each
group of students.
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Music and Math: What Are The Chances? –
Grade Five - Interdisciplinary Lesson
3. Have students create four rhythm patterns of four beats each using Attachment A, Rhythm
Writer. Review instructions printed on the worksheet.
4. Have students clap or pat the rhythms they compose.
5. Collect the Rhythm Writer pages and distribute page 1 of Attachment B, What Are the
Chances?
6. Ask each set of students to read the questions carefully and agree on the answers.
Encourage students to use fraction models or draw fraction representations to determine
and support their answers. If math manipulatives are unavailable, students may use
common items such as wooden sticks, buttons, toothpicks or individual tone bars to help
visualize concepts.
7. Close the lesson by reviewing the activities and telling students that in the next lesson
they will use the rhythm patterns they created and the number cubes to randomly select
pitches for their compositions.
Instructional Tip:
 Circulate among the student pairs or groups to observe their methods of cooperative
learning and experimentation with the number cubes or spinners. Guide and encourage
students, as needed.
Day Two
8. Review the activities from Day One. Review terms and procedures used.
9. Introduce the concept of composing music by chance. Cite specific examples (find
resources by entering “chance music” in your favorite search engine) and play
recordings of chance music for the students.
10. Students rejoin their groups from Day One.
11. Give students an overview of the activities found on pages two, three and four of
Attachment B, What Are The Chances?
12. Demonstrate on an overhead projector or chalkboard how to complete the pages. Ask
students if they have any questions.
13. Return the previously completed Attachment A, Rhythm Writer to the groups.
14. Have students complete Attachment B, What Are The Chances?
Day Three
15. Ask student groups to exchange papers (pages two, three and four of Attachment B, What
Are The Chances?) and compare responses to their own.
16. Give student groups time to rehearse the chance pieces composed on Day Two.
17. Invite students to share their compositions by performing them for their peers.
18. Display compositions on a bulletin board.
19. Encourage students to continue musical explorations using extension activities.
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Music and Math: What Are The Chances? –
Grade Five - Interdisciplinary Lesson
Differentiated Instructional Support:
Instruction is differentiated according to learner needs, to help all learners either meet the
intent of the specified indicator(s) or, if the indicator is already met, to advance beyond the
specified indicator(s).





Use knowledge about each student’s learning style to determine groupings of students so
a variety of learning styles is represented in each group.
If students are confined to an area, bring materials and resources to them.
Use teacher or peer intervention methods to help struggling students.
Provide students with manipulatives such as cubes, spinners and musical instruments to
promote hands-on learning.
Challenge students to determine the chances of rolling two notes in sequence, such as D
& G [one out of 25]. Use a tree diagram, array or list to determine and support the
probability.
Extensions:
 Have students extend their compositions by combining their four measures of music with
another group’s four measures and performing the new composition for their classmates.
 Have students use number cubes with varying numbers of sides.
 Have students create chance music using a greater range of pitches.
 Have students add lyrics or titles to their original compositions.
 Have students add accompaniments to their compositions using barred or other classroom
instruments.
 Have students research other chance music by composers such as Mozart or Cage.
 Have students perform their compositions for classmates and use informal peer
evaluation to assess.
Vocabulary:
*Term in the Fine Arts Academic Content Standards Music Glossary.
 aleatoric music – music composed or performed randomly, characterized by chance
 fraction - part of a whole number, expressed as a ratio
 measure - the unit on the staff which subdivides music into equal groups of beats
 pentatonic*
 percentage - part of a whole number expressed as part of a hundred
 pitch*
 prediction – making an educated guess of an outcome based on information available
 probability – the chance of an event occurring
 rhythm*
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Music and Math: What Are The Chances? –
Grade Five - Interdisciplinary Lesson
Technology Connections:
 Students may use computerized music-writing programs to notate their compositions.
 Students may use an electronic keyboard to play their compositions, experimenting with
different timbres of instruments and accompaniments.
Library Connections:
 Students use the dictionary to look up definitions of vocabulary words.
 Students research chance music (aleatoric music).
 Students listen to audio recordings of chance music, if available.
Research Connections:
Bahna-James, Tara “The Relationship Between Mathematics and Music”: Secondary School
Student Perspectives.” The Journal of Negro Education 60:3 (1991): 477-485.
(This study examines the relationship between math and music, cites music composed on the
basis of numerical calculations, and explores math as a creative discipline. Specific reference
is made to Mozart’s chance music.)
Bamberger, Jeanne and diSessa, Andrea “Music as Embodied Mathematics: A Study of a
Mutually Informing Affinity.” International Journal of Computers for Mathematical
Learning 8:2 (September, 2003): 123-160.
Home Connections:
 Using some sort of device they find at home, students can invent their own methods for
determining random pitches in songs they create. Have them predict outcomes based on
the number of possibilities involved. For example, a student might label areas on a
dartboard with pitch names. Then, by throwing darts, he or she records the pitches and
turns them into a song.
 Have students conduct probability research at home by doing experiments involving
likely outcomes. For example, if a ball rolls down the stairs, how often will it go to the
right, to the left or straight? Have them record their predictions and findings on paper.
Materials and Resources:
The inclusion of specific resources and references to particular musicians, composers or
works of music in any lesson developed by the Ohio Department of Education should not be
interpreted as an endorsement of the particular resource, musician, composer or work of
music. The Ohio Department of Education does not endorse any particular resource,
musician, composer or work of music.
The Web addresses listed are for a given site’s main page; therefore, it may be necessary to
search within that site to find the specific information required for the lesson. Please note
that information published on the Internet changes over time and the links provided may no
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Music and Math: What Are The Chances? –
Grade Five - Interdisciplinary Lesson
longer contain the information related to a given lesson. Teachers are advised to preview all
sites before using them with students.
Note: Some Web sites contain material that is protected by copyright. Teachers should
ensure that any use of material from the Web does not infringe upon the content owner’s
copyright.
For the teacher:
classroom instruments of definite pitch such as barred instruments,
tone bells, tuned percussion tubes, keyboard, piano or “tuned” water
glasses or bottles; cube pattern or spinners; band or orchestra
instruments students are learning to play, (see
www.answers.com/topic/aleatoric-music#copyright)
For the student:
pencils, number cubes or spinners, staff paper, instruments with
definite pitch
General Tip:
Make the five-sided cube or spinner out of card stock. Be sure to have five sides to the cube
or slices in the pie, to correspond with the pentatonic scale used for this composition project.
Attachments:
Attachment A, Rhythm Writer
Attachment B, What Are the Chances?
Attachment C, Five-Sided Cube Pattern
Attachment D, Composition Rubric
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Music and Math: What Are The Chances? –
Grade Five - Interdisciplinary Lesson
Attachment A
Rhythm Writer
Student Names: ______________________________________________________
Each horizontal line will contain 4 beats (one beat per box) in 4/4 time. Use quarter,
eighth and sixteenth notes only. Do not use rests.
1
2
3
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Music and Math: What Are The Chances? –
Grade Five - Interdisciplinary Lesson
Attachment B
What Are The Chances?
Student Names:
________________________________________________________________
Figure the probability (how likely something is to happen) of rolling a certain number on a
five-sided cube. Complete the following steps to determine your answers.
1.
How many sides are on the cube?
_______
2.
What is the probability of rolling a “2” with the cube? _____ out of _____
3.
Write the probability as a fraction. For example, if you have a coin, your chances of the
coin landing on the “heads” side would be 1 out of 2 , or 1/2 (one half) My fraction
from #2 is: ______ Circle the word that describes the likelihood:
- impossible
- somewhat likely
- very likely
- certain
4.
Change the probability fraction to a percent. For example, 1 out of 2 is ½. What
percent is equivalent to the fraction from #3? ____percent.
5.
Do you think the cube will land on one side more than any of the others?
__________________________________________________________________Predict
which side will land on the surface most often when rolled. Number ___
6.
Test your prediction by doing an experiment. Roll the cube 30 times. Record on the
table below how many times each number occurs. Use tally marks to record your results.
1
2
3
4
5
7.
Was your prediction correct?
________
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Music and Math: What Are The Chances? –
Grade Five - Interdisciplinary Lesson
Attachment B
What Are the Chances?
Day Two
8.
Today, you are using a musical scale with five different pitches. It is called a
pentatonic scale. A two-dimensional five-sided polygon is a ________________.
What part of the word means “five?” Write your answer on the line:
_______________________
These are the pitches you will use:
1
2
3
4
5
G
A
B
DD
E
Now you are ready to start composing chance music.
10.
Roll the cube. If it lands on a “1,” then write the letter “G” above the first note in
your first rhythm box. Continue this process until you have a pitch name for every
note you drew on the Rhythm Writer page. Be sure to have one letter for each note
head, not one letter for each beat box.
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Music and Math: What Are The Chances? –
Grade Five - Interdisciplinary Lesson
Attachment B (Continued)
What Are the Chances?
Day Two
11.
Practice chanting and clapping your patterns from the Rhythm Writer worksheet.
Then, practice saying the letter names you wrote in the boxes in rhythm to help you
prepare for playing the melody. Touch each pitch bar using the correct rhythm. Then,
try to play your melody on the xylophone or another pitched instrument.
12.
You now have four measures of notes. Roll the cube again to decide which measure
will be first, second, third and fourth. If the cube lands on “5,” roll again until you
get another number.
13.
Record the notes you rolled in the correct order on the lines below. You can use the
same note more than once, even right in a row!
_______
14.
_______
________
________
Notate your composition on the staff below. The staff paper has been divided into
four measures. Copy the notes from the first rhythm box on the correct line or space.
If you aren’t sure of the letter names of the lines and spaces, use the guide to help
you.
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Music and Math: What Are The Chances? –
Grade Five - Interdisciplinary Lesson
Attachment B (Continued)
What Are the Chances?
Day Two
15.
The first time you write your composition can be a rough draft. Once you are
satisfied with the piece, copy your final product onto a fresh piece of staff paper.
CONGRATULATIONS!
You’ve just written your first composition!
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Music and Math: What Are The Chances? –
Grade Five - Interdisciplinary Lesson
Attachment C
Five-Sided Cube Pattern
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Attachment D
Music and Math: What Are The Chances? –
Grade Five - Interdisciplinary Lesson
Attachment D
Composition Project Rubric
Name __________________________________________
4
3
2
1
0
Rhythm
Notation
Length
Correct number of
beats per measure
for all four
measures
Correct number of
beats per measure
for three of four
measures
Correct number of
beats per measure
for two of four
measures
Correct number of
beats per measure
for only one
measure
None of the
measures had the
correct number of
beats.
Student correctly
transcribed notes from
Rhythm Writer worksheet
for four measures.
Student correctly
transcribed notes from
Rhythm Writer worksheet
for most measures.
Student correctly
transcribed notes from
Rhythm Writer worksheet
for some measures.
Student seldom correctly
transcribed notes from
Rhythm Writer worksheet.
Student composed
four full measures
of music.
Student was unable to
transcribe any of the notes
correctly.
Student did not
complete any of
the four measures
Student composed
three full measures
of music.
Student composed
two full measures
of music.
Student composed
only one full
measure of music.
Pitch Names
Student placed notes on
the correct line or space
for the entire
composition.
Student placed notes on
the correct line or space
for the most of the
composition.
Student placed notes on
the correct line or space
for some of the
composition.
Student placed notes on
the correct line or space
for a small part of the
composition.
Student was unable to
correctly place notes on
the lines and spaces.
4 is superior
3 is excellent
2 is proficient
1 is progressing
0 is below standard
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