The Fibonacci sequence can be used in many different subject areas and it can be used to teach patterns in math, music, art, language arts and science. The teaching of patterns begins in the early grades where students are required to identify various forms of patterning and continues into the elementary grades. For example, an elementary mathematics course outcome for the Newfoundland and Labrador curriculum is that students will explore, recognize, represent and apply patterns and relationships both formally and informally. When teaching mathematical patterns, teachers can relate the Fibonacci sequence to patterns that can be seen in real life such as those of flower petals.
The sequence can be taught within the music curriculum using the keys on a piano, which as mentioned above, follow the Fibonacci number pattern. Teachers can demonstrate to the students that the piano follows the Fibonacci sequence by having 5 black keys, 8 white keys and 13 notes which comprise one octave. This sequence can also be identified in various music scales such as the pentatonic, diatonic, and the chromatic scales (Math and Music).
The Fibonacci sequence can also be found in the area of science and more specifically, in the areas of space and physics. When teaching a unit on space, teachers can provide children with interesting facts on how the universe is based on the Golden Ratio, as there are many galaxies in the universe that contain the Golden Ratio in their structure (Measure of Beauty). Also, teachers can use the Fibonacci sequence when teaching a unit on light. For example, when light is held over a surface (i.e. glass), one part of the light passes through the surface, one part is absorbed and one part is reflected. Therefore a multiple reflection occurs which means that there are a number of reflections that the ray of light takes inside the glass before it re-emerges. The number of rays that re-emerge reflect the Fibonacci number sequence (Measure of Beauty).
Within the language arts curriculum there are ways to bring in the concept of the Fibonacci sequence and its numbers. For example, in the area of poetry, several of the rhythms used are Fibonacci numbers, such as iambic pentameter. As well, the number of lines in particular forms of poetry are Fibonacci numbers, such as limericks, which have five lines or Haiku poems which have three.
The Fibonacci sequence can also be used in teaching spatial proportions in art education. Teachers can use spirals, concentric circles and repeated rectangles to show how interesting patterns can be formed using these figures when teaching students about proportional preferences (The Fibonacci Sequence, p. 92). Also, when teaching a section on portrait drawing, it is important to inform students of the correct facial and body proportions when drawing a human figure. These proportions enable the students to create a drawing that is lifelike and directly proportional to the subject he/she is drawing.
The Fibonacci sequence does not have to be strictly limited to the mathematics curriculum. Incorporating it into other subject areas will allow students to see how the sequence can be relevant to "real life" which makes the information meaningful and relevant for the student. Above all else, this should be a primary goal of any mathematics curriculum.
