Classroom Resource

The Fibonacci Sequence

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.

Unpacked Content

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.

Unpacked Content

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.
Link to Resource
https://streaming.discoveryeducation.com/teacherCenter/lessonPlans/pdfs/9-12_Ma…

Resource Provider

Other

Resource Provider other

Discovery Education
Accessibility
License

License Type

CUSTOM

Custom License Type (URL)

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