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Triangle Songs
A geometry lesson by Patricia M. Holmes
Grade Level: 7-12
Subject Matter: Geometry
Curricular Uses: Mathematics, music, and creative writing
Students will be able to:
- Classify triangles by sides and angles
- Write and perform a song or poem (similar to "Schoolhouse Rock") conveying the meanings of seven terms (acute, right, obtuse, equiangular, equilateral, isosceles, and scalene); but students may also include other facts about triangles (the angles add up to 180 degrees, the Pythagorean Theorem for right triangles, etc.)
Academic Standards Met
Mathematics (NCTM Standards):
Standard 3: Geometry and spatial sense
Mathematics instructional programs should include attention to geometry and spatial sense so that all students analyze characteristics and properties of two- and three-dimensional geometric objects
Standard 8: Communication
Mathematics instructional programs should use communication to foster understanding of mathematics so that all students-
Organize and consolidate their mathematical thinking to communicate with others;
Express mathematical ideas coherently and clearly to peers, teachers, and others;
Use the language of mathematics as a precise means of mathematical expression
Music (McREL Standards - Mid-continent Research for Education and Learning):
Standard 1: Sings, alone and with others, a varied repertoire of music
Uses ensemble skills (e.g., balance, intonation, rhythmic unity)
Standard 2: Performs on instruments, alone and with others, a varied repertoire of music
Performs with expression (e.g., appropriate dynamics, phrasing, rubato) and technical accuracy a large and varied repertoire of instrumental literature at a moderate level of difficulty (e.g., attends to phrasing and interpretation, performs various meters and rhythms in a variety of keys)
Uses ensemble skills (e.g., balance, intonation, rhythmic unity) when performing as part of a group
Standard 3: Improvises melodies, variations, and accompaniments
Improvises rhythmic and melodic variations on given pentatonic melodies and melodies in major and minor keys (e.g., folk songs, standard pop songs, hymn tunes)
Improvises original melodies over given chord progressions in a consistent style, meter, and tonality
Standard 4: Composes and arranges music within specified guidelines
Composes music in a variety of distinct styles (e.g., classical, folk, pop, jazz, rock)
Composes and arranges music for voices and various acoustic and electronic instruments
Understands the ranges and traditional uses of various sound sources (e.g., voices, acoustic instruments, electronic instruments)
Standard 5: Reads and notates music
Reads an instrumental or vocal score of up to four staves
Reads music that contains moderate technical demands, expanded ranges, and varied interpretive requirements
Standard 6: Knows and applies appropriate criteria to music and music performances
Knows specific criteria that affect the quality and effectiveness of music performances, compositions, arrangements, and improvisations (e.g., considers questions of unity or variety, consistency, appropriate use of resources)
Materials
- Video camera and blank VHS tape
- Compact Disc player
- Audio cassette player
- Amplifier and musical instruments, if necessary
- Geometry textbook to use as a reference for seven terms and other triangle facts
Time Allotment
This lesson takes approximately three partial class periods for preparation, plus one full class period for student presentations.
Steps
- Students may organize into groups that they choose or may decide to work alone.
- Students investigate meanings of seven terms classifying triangles by angles and sides using the text.
- Students may choose to present a poem if they prefer not to sing.
- Students may choose to sing their lyrics to the tune of a popular song or may write original music.
- Students may choose to bring in musical instruments for accompaniment, sing to background music, or sing a cappella.
- Students may stick to guidelines of the minimum seven terms, plus add other triangle facts if desired, otherwise they may be creative and have fun with it!
- Students may brainstorm lyrics, but will eventually write or type a final draft to hand in the day of student presentations.
- Use the last 10-15 minutes of three consecutive class periods for students to prepare their songs with their groups, plus provide a weekend before the presentations so that students can meet on their own time to rehearse.
- Use one full class period to present songs one group at a time.
- Teacher may videotape the presentations to view later for the purpose of grading, and students may view other classes' presentations.
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