Fibonacci Sequences Lesson Plans

Students integrate the patterns of Fibonacci into music. In this geometry lesson, students apply the concepts of recursion, pattern and Phi or Golden Ratio to composing and playing music on various instruments. They lesson is co-taught with a music teacher.

Students gain an understanding of the value and importance of patterns in mathematics. Through video, interaction and hands-on activities, students identify concrete and abstract patterns incorporating logic and deductive and inductive reasoning.

Students write an article about an artist using math in his work. In this algebra lesson, students apply properties of linear equations and ratios as it relate to shapes and figure. They analyze different architectures for shapes and designs.

Students explore a variety of patterns. They examine the patterns in a flower design made of triangles surrounding a square. Pupils complete a table listing the number of triangles needed to complete various flower designs. Students make tables showing the cost of buying different cut-outs of flowers.

Learners discover the magic (mathematics) in summagic and use the distributive property to add like terms. They also apply the rule for the "summagic" problem by adding like terms and using the distributive property. They will use factoring to uncover the magic and explain the mathematics.

Students study patterns and use inductive reasoning to write a linear or quadratic equation for the sequence. Using a graphing calculator, they enter data into a list and set up a scatter plot. After analyzing the collected data, students find a recursive formula for triangular and pentagonal numbers.

Eleventh graders investigate arithmetic and geometric sequences.  In this Algebra II lesson, 11th graders use a graphing calculator to determine if a sequence is linear or exponential.

Tenth graders explore two number patterns that approach the value of the Golden Ration. In this Golden Ratio lesson, 10th graders work with a partner to find the ratio of their height to the distance from their head to their fingertips. Students construct figures with their dimensions that form the Golden Ratio and define the exact value of the Golden Ratio provided.

Students utilize artwork to help illustrate the major ideas of transformations and tessellations. visually identify transformations including reflections, rotations, and translations. They discuss how artists have used geometry in their artwork.

Learners observe that there are myriad combinations of rhythms to choose from when improvising jazz and blues music, and recognize that while the variations seem infinite, they are in fact finite. They notate a 12 bar blues progression using a different combination of notes and rhythms for each of the 12 bars, and then perform it on a keyboard or virtual piano online.