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Grade: Elementary
Subject: Mathematics

#859. Music and Fractions

Mathematics, level: Elementary
Posted Sat Feb 27 17:51:33 PST 1999 by Jess Buice (
Math-ties during relay races.
Music Notes, Inc., Riverdale, GA USA
Materials Required: board, colored chalk - for indicating fractions
Activity Time: Varies
Concepts Taught: whole, half, quarter, eighth

If the students have been reading the music in general music, they are already aware of basic divisions, although they associate these divisions with length of sound.

In music sound is measured just as time is measured by the clock. Where the clock is based on division of 1's, 5',s etc., music can be measured in all types of divisions. The most common of these is four beats in each measurement.

Thus, a note representing all four beats would be called a whole note, as it takes up the "whole" measure. A note using two of the beats would be called a half note, as it takes up "half' the measure. This is the same with quarter notes and eighth notes. A measure that receives four beats can be represented, or measured/divided into hundreds of veriations. By a single whole note; two half notes, four quarternotes, two quarters and one half, four eighth notes and a half note, etc., as long as the divisions total the four beats needed in each measure.

At the begining of each song there is a fraction written on the staff. This indicates how the measures are being divided through this portion of the song (the sound measurements can change, but more often the time remains constant). The top number of the fraction indicates how the beats are being divided; 4/4 means four beats, 3/2 means 3 beats in each measure. The bottom number indicates which division will receive a beat. Thus 4/4 means there will be four beats, each beat will be represented by a quarter note (four/quarternotes). 3/2 means there are going to be three beats, with each beat being represented by a half note (three/halfnotes). This example begs the question, why is is called a half note, if there are now three half notes in each measure? The note names are based on the most common division of time, 4/4. Thus the although there are three half notes, each half note still receives two quarters, so the divisions remain consistant. The beats can be divided into smaller divisions/measurements, as long as the divisions total the needed beats indicated in the TIME SIGNATURE-4/4, 3/4, 6/8, 3/2, 5/4, ...

Introducing fractions is now a transfer of this known associations to math associations. Choice of words can be very important for repetition of concepts. Calling out the fraction three fourths (3/4) is more easily introuduced as "three of four", which is consistant with the math concept of division, thus the reverse would be three divided by 4, giving you a transition into dividing fractions for percentages, 3/4=0.75.

Building from the music divisions where four is equal to the whole, transfer to math concepts is a breeze!

For more information on note values, search for note value lessons.