Rhythms : Measuring and Dividing Time (Math component of Rhythms and Sound unit. (For Science component see Tin drums .))

by Susan Boshoven and Carlos Araiza .

Objectives: NCTM standards from the California Mathematics Framework for public schools that these activities satisfy for grade 5 through 8 are:

Standard 4: Mathematical Connections

Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as art, music,...

Value the role of mathematics in our culture and society.

Standard 6: Number Systems and Number Theory

Understand and appreciate the need for numbers beyond whole numbers.

Standard 13: Measurement

Extended understanding of the process of measurement.

Through these activities, students will also have practice in interpreting and representing patterns as well as fractions and will be required to add and convert fractions.

Reasons/philosophy for developing this lesson: Fractions are customarily presented to students in a visual context in relation to the measurement and division into pieces of material objects or substances. Many activities have been written which involve the application of fractions in, for example, cooking or dividing geometrical shapes.The primary purpose of this series of activities is to provide an alternative context for understanding fractions.Through these activities students will see how fractions are employed by composers of music to measure and divide time in writing music. Music of Caribbean and Latin American origins was chosen to demonstrate this for its intricate rhythmic structure and cultural importance.The secondary purpose is to demonstrate how mathematics is essential to culture and is universal among cultures as is music.

References: Musicians and composers of music in the community. In the San Francisco Bay Area, San Francisco Performances has an education department and they send musicians to classrooms, and provide materials. The music department at San Francisco State University also provides resources for teachers.The Exploratorium Museum and Library in San Francisco has many exhibits and resources which relate to music and were our main source of information for this project.

web resources: Rhythm and Science web links , Bongo page

The following musicians were sources of information for this project:

For Comparsa from Cuba- Jose Flores.

For Bomba from Puerto Rico- Ito Carillo.

For Akattá from Jamaica- Tebah Roache.

For Meringue from the Dominican Republic- Gilbert Ross.

John Calloway, a teacher with SFUSD, and an accomplished Bay area musician was also consulted.

Lesson Plan

Length of time : may vary from 4 to 6 hours.

Materials : recording of different rhythms, examples of how the rhythms are written or notated, information on how to read music. Exploratorium publication: Exploring Rhythm has an explanation of time signatures and note duration on pages 16 and 17, vol. 15 , no. 2, summer 91, in the article "The ABC's of Musical Time." and is an excellent tool to instruct students on how to read the rhythms.

Summary of Activities and Objectives:

Part I: Listening to different rhythms and invent a way to represent them visually or with syllables.

Part II: Learning how rhythms are represented in music notation utilizing whole, half, quarter, eighth, sixteenth notes and rests, learn to interpret, and produce rhythms by reading music notation.

Part III: Composing rhythms from whole, half, quarter, eighth, sixteenth notes and rests.

Assessment: presentation of a rhythm composition and a written reflection on the importance of math in the composition of rhythm will serve as the assessment for this activity.

Part one : Listening to rhythms (first hour)

Materials- tape player, recordings of different rhythms: Cumbia , Cuban Comparsa, Puerto Rican Bomba, Jamaican Akattá , Brazilian Bosa Nova, and Meringue from the Dominican Republic, colors, pencils, paper. (Note: the underlined rhythms are provided for you on this site. For a complete tape of the rhythms, see page for Carlos Araiza .)

1. Play recordings of different rhythms and invent a way to visually reprsent the different rhythms. Sounds may be represented with wave forms or shapes, or by using combinations of letters or syllables. Play each rhythm several times.

2. Exchange representations with a classmate, and try to identify or play the rhythm each other was attempting to represent. Discuss ideas on how the representations could be improved and what information is essential so that a rhythm can be identified. A class discussion should follow with ideas being recorded on butcher paper or the chalkboard.

Part two: Reading Rhythms (2nd and 3rd hour)

Materials : recording of different rhythms, examples of how the rhythms are written or notated, information on how to read music. Exploratorium publication: Exploring Rhythm has an explanation of time signatures and note duration on pages 16 and 17, vol. 15, no. 2, summer 91, in the article "The ABC's of Musical Time." and is an excellent reference for beginning level instruction on how to read rhythms.

1. Explain and give examples of how to read music beginning with the time signature. All these rhythms are in four-four time, which means there are 4 beats in a measure, and each quarter note gets one beat. A whole note lasts one measure (four beats), A half note has half the value of the whole note which means half the duration or two beats, a quarter note has exactly one-quarter of the value of the whole note and has one-quarter of the duration, or one beat. An eighth note has one-eighth of the duration of a whole note (two eighth notes per beat), and a sixteenth note has 1/16th of the duration (four sixteenth notes per beat).

A homework assignment is provided to check for understanding of equivalents.

Part three: Writing Rhythms (fourth and fifth hours)

materials: paper, pencils, tin can drums .

Write at a two part rhythm (with two different intruments being played together) of a four or more measures and include at two different types of notes (whole notes, half notes, quarter notes, and eighth or sixteenth notes...). After having completed the composition, give it to a partner to test if the rhythm can be interpreted by another person.