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Jazz and Math: The Beat Goes On
Estimated Time of Completion: Two or more 40minute class periods, depending on depth of exploration desired. The number of examples from the PBS Ken Burns JAZZ documentary and Web site that are used to compare tempos will determine the number of class periods needed.
Objectives
 To collect real data through listening, counting and timing.
 To use ratios, rates, and proportions to report data.
 To demonstrate an understanding of the concepts of rhythm and tempo in music.
Materials Needed
 Stopwatch for each group of students.
 Access to Internet for the PBS JAZZ Web Site.
 A copy of the PBS JAZZ documentary.
 Additional recordings of various styles of jazz music will be helpful for more indepth exploration of tempo.
Standards
This lesson correlates to the following math standards established by the National Council of Teachers of Mathematics at http://www.nctm.org/standards/:
 understand and use ratios and proportions to represent quantitative relationships
 develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios
 formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population
 recognize and apply mathematics in contexts outside of mathematics
Procedures and Activities
 As an introduction the concepts of rhythm and tempo, students may watch a segment from the PBS Ken Burns JAZZ documentary, such as Episode Two (1:39:35  1:40:12) which features Arvell Shaw discussing the fact that jazz music is "like a heartbeat." Do students think this is more true of jazz than for other types of music? For instance, some researchers think that playing baroque classical music to infants and young children is soothing because they identify this type of music as most similar to the human heartbeat. What do students think?
 Choose an activity that students are familiar with that is done to a steady rhythm. If space permits, jumping rope to a childhood rhyme can be an interesting way to see that some things naturally fall into a rhythm. Alternatively, many students may know a handclapping routine to a rhyme that would also be a way to see natural rhythm. Having students march in place, or doing jumping jacks if room permits, will also give an indication of counting along with a steady rhythm.
 Prior to conducting the following experiment, students may also access the PBS JAZZ Web site's Music Theory section for an overview of rhythm and tempo. Are these two concepts identical? If not, what's the difference? Challenge students to defend their answers with examples, and/or to seek alternative definitions of these concepts.
 In small groups, students will use the stopwatch to find their heart rate (in beats per minute). To measure heart rate, place two fingertips on the underside of the wrist of your other hand, just below the base of the thumb. Count the pulsations for ten seconds. It is suggested to measure in ten second intervals. This will give the students the opportunity to use equivalent ratios to calculate beats per minute.
12 beats per ten seconds = 72 beats per 60 seconds (one minute)
If necessary, review equivalent ratios with students prior to collecting data. Each student should complete three trials and average. Groups may then find a group mean (average) heart rate.
 Students in small groups (or as a class if time and VCR usage is limited) should view a section of the PBS JAZZ documentary which features at least one minute of continuous music. This selection should be repeated until students can comfortably clap or tap to the beat of the music.
Suggested samples:
 Episode Two, 1:41:45  1:42:33—Louis Armstrong performance, the band tapping feet to the music.
 Episode Four, 1:49:27  1:52:43—The opening segment for "Can't You Boys Play Any Waltzes?"
 Episode Four, 1:53:48  1:56:06—King Porter Stomp
 Episode Five, 1:04:12  1:05:49—Lionel Hampton playing the vibes (vibraphone)
 Episode Six, 02:38  05:40—Swing
 Episode Ten, 01:20  05:07—Dexter Gordon's bebop tenor sax
 Episode Ten, 09:50  11:30—Hello, Dolly
 Episode Ten, 51:20  53:19—Sly & the Family Stone
 Students should then repeat the measurement of beats per minute. To emphasize ratio (rates) and proportion, a worksheet could be prepared with different lengths of data collection.
Example: Count beats for 15 seconds—find beats per minute.
Count beats for 20 seconds—find beats per minute.
(For more challenging examples, use a number of seconds that is not a factor of 60.)
Count beats for 18 seconds—find beats per minute.
 Choose a minimum of four styles of jazz (ragtime, blues, swing, bebop, etc.)
These may be obtained from the JAZZ documentary, from the JAZZ Web site's Music Theory section, or from audio recordings.
For each sample, repeat the measurement of beats per minute. Have students prepare a bar graph or scatterplot (or another type of graph that will provide a useful visual representation that correlates with your current math topics). After preparing the graph, students should draw conclusions about the various types of jazz in regard to tempo.
Assessment Suggestions
This activity may be used to assess various aspects of data collection (organization, units, accuracy , completion of report, etc.). This activity may also be used to assess cooperative learning interactions (leadership, cooperation, group reporting techniques). Math assessment would focus on demonstration of understanding of concepts of ratio (rates) and proportion as well as accurate calculation.
Extensions/Adaptations
 Tempos of different jazz styles could be correlated to the different decades (or parts of decades) covered in each episode. Can students find a trend in the tempo of the music? Hypotheses could be developed before the collection of data, or theories advanced after the data is represented visually.
 Students could dance (move) to a particular selection after the number of beats per minute (tempo) is determined. Immediately after dancing, students might measure their heart rates.
If this is repeated with musical selections at different tempos, students could go on to look at relationships between tempo of music and increase in heart rate.
(If heart rate is 70 at rest, and tempo of music is quarter note=144 (beats per minute, how much does my heart rate increase if we move to that tempo? Compare to music with tempo of 116 or 176.)
About the Author
Carol Fisher is a veteran teacher within the Chicago Public School system.
Winner of both the prestigious Golden Apple Award for Educators and the
Illinois Presidential Awards for Excellence in Science and Math Teaching, she
has been recognized as an innovative math educator. Her lifelong involvement
in music, currently as principal bass clarinet with the internationally
acclaimed Northshore Concert Band balances her right brain and left brain
energies. Carol enjoys sharing ideas with other educators and welcomed the
opportunity to intertwine two aspects of her life and share these activities
with others.
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