You can hook students' interest at the beginning of a unit on the Fibonacci series by presenting the first few elements of the series without explanation. Challenge students to try to find the next elements or to explain the pattern behind the series. To harness competitive urges, divide the class into teams of about five students each and stage a contest to see which team can be first to find the next three elements of the series.
Bring objects to class whose forms show proportions and shapes derived from the Fibonacci series, such as the Golden Mean. The spiral arrangements of pineapple sections, sunflower seeds (while still in the sunflower) and nautilus shells all reflect the Fibonacci series. Many architectural and artistic works are arranged according to the Golden Mean, which is the ratio approximated by any two adjacent elements of the Fibonacci series. Showing students the many places the series appears may whet their appetite to learn more about it.
You can also use paper cutting crafts to introduce the Fibonacci series to younger children in a concrete way. Give each child a roll of receipt paper and have her cut off one short strip, about 1 inch to 2 inches long. Lay the first strip onto the end of the receipt paper and cut another strip of equal length. Lay both strips onto the paper and cut a strip equal to the sum of their lengths. Continue laying the last two strips onto the paper to cut a series of strips whose lengths will represent the Fibonacci series.
Give students a mathematical exercise by assigning them to calculate the elements of the Fibonacci series. Pick a number of elements appropriate to their grade level. The seventh element is the first two-digit number, the twelfth is the first three-digit number and the lengths of the numbers grow by one digit approximately every five elements thereafter. Another way to help students develop mathematical skills is to have them graph the numbers in the Fibonacci series.