The Fibonacci Sequence

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

In this lesson, students will:

    • understand the Fibonacci sequence (numerically, algebraically, and geometrically).
    • understand how the Fibonacci sequence is expressed in nature.
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.11

Find patterns in application problems involving series and sequences, and develop recursive and explicit formulas as models to understand and describe sequential change.

UP:MA19.FM.11

Vocabulary

  • Difference equation
  • Recursive process
  • Recursive formula
  • Sequences
  • Series

Knowledge

Students know:

  • How to use inductive counting methods such as lists.

Skills

Students are able to:

  • Use inductive counting methods to collect data for conjecturing.
  • Find recursive formulas from collected data.
  • Develop explicit formulas.

Body

  1. Find patterns in application problems involving series and sequences, and develop recursive and explicit formulas as models to understand and describe sequential change.
    Examples: fractals, population growth
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.12

Determine characteristics of sequences, including the Fibonacci Sequence, the triangular numbers, and pentagonal numbers.

UP:MA19.FM.12

Vocabulary

  • Recursive process
  • Recursive formula
  • Triangular numbers
  • Pentagonal numbers
  • Fibonacci sequence
  • Closed Formula

Knowledge

Students know:

  • How to recognize a pattern.

Skills

Students are able to:

  • Identify the pattern in a sequence.
  • Explain why a pattern occurs.

Understanding

Students understand that:

  • The recursion process can be applied to many situations.
  • A sequence lists the solutions of a set of related problems.
  • Formulas can be hypothesized by identifying how the problems are related.

Body

  1. Determine characteristics of sequences, including the Fibonacci Sequence, the triangular numbers, and pentagonal numbers.
    Example: Write a sequence of the first 10 triangular numbers and hypothesize a formula to find the nth triangular number.

Resource Provider

Other

License Type

CUSTOM

Resource Provider other

Discovery Education
https://streaming.discoveryeducation.com/teacherCenter/lessonPlans/pdfs/9-12_Ma…

Custom License Type (URL)

https://www-media.discoveryeducation.com/wp-content/uploads/2021/07/US-General-…

Owner (Author)

habradley
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