Recursive Formulas: Fibonacci Sequence

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

This interactive activity will challenge students' knowledge of the Fibonacci Sequence using the following scenario:

Recursive formulas describe sequences of numbers governed by a common pattern. Here a recursive pattern can be seen in the increasing side length of each square.

    • Use the two red points on the large orange and green squares to continue the pattern. 
    • Try to determine the recursive pattern that governs the side length of the set of squares.
    • Note that this recursive pattern expands from the smallest value to the largest.

Note: You will need to create a free account to access this resource.

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

CK-12
https://www.ck12.org/assessment/tools/geometry-tool/plix.html?eId=MAT.CAL.500.3…

Custom License Type (URL)

https://www.ck12info.org/terms-of-use/

Comments or Notes

Students must create a free account online to begin the interactive activity.

Owner (Author)

habradley
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