ALEX | Alabama Learning Exchange

Recursive Formulas: Fibonacci Sequence

Classroom Resource Information

Title:

Recursive Formulas: Fibonacci Sequence

URL:

https://www.ck12.org/assessment/tools/geometry-tool/plix.html?eId=MAT.CAL.500.3&questionId=54c2c962da2cfe7bd16cc05a&artifactID=2126993&conceptCollectionHandle=analysis-::-recursive-formulas&collectionCreatorID=3&plix_redirect=1

Content Source:

Other
CK-12

Type:

Interactive/Game

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.

Content Standard(s):

Mathematics
MA2019 (2019)
Grade: 9-12
Applications of Finite Math

11. 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

Unpacked Content

Evidence Of Student Attainment:

Students:

-Use inductive counting methods to find recursive patterns and explicit formulas.

Teacher 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.

Diverse Learning Needs:

Mathematics
MA2019 (2019)
Grade: 9-12
Applications of Finite Math

12. 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.

Unpacked Content

Evidence Of Student Attainment:

Students:

Find the next term in a sequence such as the Fibonacci sequence, the triangular numbers, and pentagonal numbers.
Describe the recursion pattern that builds a sequence.
Hypothesize a formula to find the nth term in a sequence.

Teacher 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.

Diverse Learning Needs:

Tags:

fibonacci sequence, formula, pattern, recursive, sequence, series

License Type:

Custom Permission Type
See Terms: https://www.ck12info.org/terms-of-use/
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses

Accessibility

Comments

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

This resource provided by:

Author:

Hannah Bradley

ALEX Classroom Resource

Recursive Formulas: Fibonacci Sequence