Fibonacci Sequence

• CCSS.MATH.CONTENT.HSF.IF.A.3 – Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.

• be able to list some connections between mathematics and music and describe the Fibonacci number pattern sequence, commonly called the Fibonacci Sequence, as well as explain some ways that it appears in music.

1. Prominently display the Soundtrap keyboard in the classroom.
2. Write six numbers of the Fibonacci Sequence on the chalkboard. Ask students to relate how the numbers are generated. Then, ask them to list the next nine or ten numbers in the sequence. Tell them a little about Leonardo of Pisa.
3. Tell the students that mathematicians have found that an unusual quantity of items have Fibonacci numbers associated with them. (For example, you can mention that in nature, poison ivy has the Fibonacci number 3. Wildflowers often have 5 petals).
4. Ask the students to look around the room and find something that may have a Fibonacci number associated with it. Students should discover that a keyboard has 8 white keys, 5 black keys, and 13 notes all together in each octave. Also, the Pentatonic scale has 5 notes, the Diatonic scale has 8 notes, and the Chromatic scale as 13 notes – all Fibonacci numbers!
5. Have them explore the keyboard, record, reflect and share!

1. For further examples of how the Fibonacci numbers can be related to objects in the designed world, go to the Golden Section in Art, Architecture and Music.  

Additional resource: Fibonacci Sequence Youtube video.