Learning Probability through Media Arts MEDIA ARTS PROJECT

MEDIA ARTS
PROJECT
Learning Probability through Media Arts
Grade
4
Subject
Mathematics
Topic
Probability
Lesson Description
Students will investigate probability in math by comparing experimental results with predicted results.
By using chance, probability and digital tools they will compose music on the computer.
Materials
• 2 tetrahedral polyhedron construction templates (each has four faces), scissors, tape or glue
• Computer lab with at least one computer per group of three students with appropriate music creation
software eg: Music Ace or Garage Band.
Lesson 1
• Introduce the concept and the vocabulary of probability: probable, improbable, impossible, possible,
certain, likely, unlikely.
• Discuss with the class sharing some examples of probability.
• Pose questions to the students who must place the above answers on a scale between never (zero)
and always (1)
• Sample questions:
1. Will it rain tomorrow?
2. Could you ever see a pig fly?
• Have the students create their own questions that would be answered with never/sometimes/always.
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Share questions and discuss.
Demonstrate for the class how to make a tetrahedral polyhedron.
Demonstrate for the class how to use the tetrahedral polyhedrons (TP) roll and record the results.
Have the students work in groups of 3-4 and create the TPs.
Use the chart provided as an example of how to record the outcome of the rolling of the TP.
Have the groups work to examine the following questions and predict the results using the TP chart
as a tool for predicting results.
- What is the probability of getting odd numbers (when rolling and adding the results of both
polyhedrons)?
- Why?
- What is the probability of getting even numbers ….?
- Why?
- What is the probability of getting a sum under 5?
- Why?
- What is the probability of getting 1, 2, 3 etc?
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MEDIA ARTS
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- Are we more likely or less likely to roll a 3 than a 4?
Even: 8/16=1/2
Odd: 8/16=1/2
Tetrahedral Polyhedron # 1
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5
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• Roll two TPs and record the results
• Discuss their exploration of probability.
• Discuss their findings from the TP use.
Lesson 2
This lesson will take place in the computer lab.
• Lead the class in clapping out a series of rhythms using four claps to get them comfortable clapping
as a group.
• Have some of the students take turns leading a clapping rhythm.
• Introduce chance into the clapping game.
• Clap four beats and have the students decide to clap along for just one of those beats (i.e. 4 beats to
a bar, students can choose to clap on beats 1, 2, 3 or 4.).
• What is the probability that everyone will clap on the same beats?
• Have the students see the http://sunsite.univie.ac.at/Mozart/dice/ website to be exposed to the
Mozart musical dice game.
• Discuss the implications of the program changing the measures.
• Discuss the effect of changing instrumentation.
• Introduce the Music Ace software and explore the first lesson (Intro to the staff) and games to learn
about the staff and pitch.
• Demonstrate the Doodle Pad function of the software and show the steps necessary to create sound
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with it.
Demonstrate how the TP can be used to determine which sound will be made.
Students will then move on to the Doodle Pad function on the software to create a 12 bar chance
composition using only whole notes.
The steps for creation are:
1. roll two TP’s to determine the pitch.
2. repeat until all 12 bars are filled
3. listen to the composition
4. repeat the process again, this time using the bass clef to create harmonies
Discuss the use of the music software.
What is the probability of getting a note on a line? (like even numbers)
What is the probability of getting a note in a space? (like odd numbers)
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MEDIA ARTS
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Lesson 3
• Discuss recording the predictions and the results of their probability exploration.
• What ways has that information been expressed so far? (i.e. number chart, musical composition)
• What are some other ways of representing probability?
• Introduce another way of recording the predictions of probability.
• Show a systematic list with four elements on it. The elements chosen could be fun such as characters
from a book that they are reading or from a TV show.
• Write those elements on a TP (perhaps a larger sized one for easier viewing).
• Show the students how to create a systematic list for these four items.
• Continue to explore probability by creating systematic lists of the number of different arrangements
of sets of 3 and 4 musical notes.
• Allow the students time to work on the computer program to explore creating various combinations
on their own using whole notes.
• Ask the question “How do you know when you have them all?” Allow them to consider this question
and then encourage them to find a systematic list.
Example of a systematic list CDEF
CDEF
CDFE
CEDF
CEFD
CFDE
CFED
DEFC
DECF
DFEC
DFCE
DCEF
DCFE
EFCD
EFDC
ECFD
ECDF
EDFC
EDCF
FCDE
FCED
FDCE
FDEC
FECD
FEDC
Note: there are 24 possible arrangements
• Review the exploration of creating the various combinations of notes for their digital music
composition.
• Discuss the creation of the systematic list for their musical composition.
Lesson 4
This lesson will take place in the computer lab.
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Review the concepts of beats and measures with the class.
Engage the students in a brief group vocal exercise to represent whole, 1/2 and 1/4 notes.
Provide some visual representation of whole, 1/2 and 1/4 notes.
Use the TP to demonstrate how to allow probability to determine the length of the note to be used.
Use this method to engage the class in a vocal exercise.
Students can take turns rolling the TP to determine what the class will vocalize.
Students will continue creating musical compositions involving the use of tetrahedral polyhedrons
this time exploring 1/2 notes for 6 bars sequences.
• Working in small groups they will create their musical composition in the following sequence
1. roll 2 TP’s to determine the pitch of each note for their melody
2. use 1/2 notes only for 6 bars
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MEDIA ARTS
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3. play back the composition and enjoy the creation!
• Repeat the process, this time start with whole notes on the bass clef for six bars, then in the same
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six bars, move on to 1/2 notes and 1/4 notes for the same six bars.
Play back the composition and loop it.
Discussion the compositions with the class.
Which one do you prefer? Why?
Compare the melodies and discuss similarities. What is the probability of having the same
composition as a classmate?
Which note are you most likely to roll? Did the composition reflect that?
Lesson 5
• Demonstrate and engage the class in some activities that further explore probability.
• The four notes in our example bar are CDEF.
• If the four notes were placed in a bag, what is the probability of picking them out in this order –
CDEF?
• Is it possible to ensure that it happens?
• Discuss.
• Demonstrate a large scale spinner for the class to use as another method of predicting and
determining probability.
• Show the class how to make a smaller spinner with eight sections on a piece of paper.
• Each section is coloured in using pencil crayons.
• Use four colours in total with one colour for four sections, one colour for two sections and two colours
for one section each.
• The pointer can be made using a paper clip with one end straightened out and then spun around the
tip of a pencil held in the center.
• Have the students break into groups of 3-4 and create a spinner.
• Have the students predict where the spinner is more likely to land. Where is the spinner less likely
to land?
• Have them record their predictions.
• Have the students test their predictions with their spinner.
• Repeat this until they have the results from 20 trials. Have the students share their results with the
class.
• Discuss the results.
Lesson 6
This lesson will take place in the computer lab.
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Share more examples of chance music with the class as well as music created using the computer.
Ask for responses from the class about what they thought about the music.
What one word would you use to describe the music?
The students will be asked to compose their own piece of music on the computer using the following
structure: the teacher will demonstrate
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MEDIA ARTS
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• Create an original 12 bar orchestration using an eight section spinner (eight sections with four
different colours, each representing a whole, 1/2 or 1/4 note)
1. Spin the spinner to determine the instrument to be used for 12 bars
2. Spin the spinner to determine the length of note (i.e. whole, half, third or quarter note)
3. Spin the spinner to determine the pitch
4. Repeat steps 2-3 until the 12 bars are filled.
5. Repeat the whole process several times using other instruments to create an orchestration.
6. Listen to your composition and adjust the tempo (speed). What tempo sounds best?
Lesson 7
Share examples of chance music with the class as well as stories about how those musicians created
that music.
• Demonstrate for the class the use of the pictograph to represent the frequency of the notes used in
their composition.
• Each student will now consider the melodies he/she composed and create a pictograph with the
frequency of each individual pitch (CDEFGABC+).
• Have the students break into groups of 3-4 and compare their compositions to others in the class.
• Discuss similarities and differences.
• Use the pictograph to record the notes from their compositions individually and then as a group.
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C
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Lead a class discussion about the frequency of the occurrence of notes.
Create a pictograph with the entire class results.
Find the mean.
Ask the students to compare their individual results with the class results.
C+
Lesson 8
This lesson will take place in the computer lab.
• The students will now present their compositions in the format that was agreed upon.
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MEDIA ARTS
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• After each presentation the class can comment on and discuss the composition.
• Lead the class in a discussion about probability and their experience of creating music using chance.
Lesson 9
Create a display of the sound compositions and math components. Invite other classes to view
them and explore.
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