Fibonacci Sequence
The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. The sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. The sequence was first described in the year 1202 by Italian mathematician Fibonacci in his book Liber Abaci.
Formula
The formula to find the nth term of the Fibonacci sequence is:
Fn = Fn-1 + Fn-2
Where Fn is the nth term, Fn-1 is the (n-1)th term, and Fn-2 is the (n-2)th term.
Properties of the Fibonacci Sequence
- The sequence starts with 0 and 1.
- Each subsequent number in the sequence is the sum of the previous two.
- The ratio of two consecutive Fibonacci numbers approaches the golden ratio, approximately 1.618, as the sequence progresses.
- The Fibonacci sequence has connections to various natural phenomena, such as the arrangement of leaves on a stem, the breeding patterns of rabbits, and the shape of galaxies.
Study Guide
To understand the Fibonacci sequence, follow these steps:
- Memorize the first few terms of the sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
- Understand the formula Fn = Fn-1 + Fn-2 and how it generates the sequence.
- Practice finding the nth term of the sequence using the formula.
- Explore the connection between the Fibonacci sequence and the golden ratio.
- Research real-world examples of the Fibonacci sequence in nature and art.
By following this study guide, you will gain a solid understanding of the Fibonacci sequence and its applications.
.◂Math Worksheets and Study Guides Fourth Grade. Problem Solving
Study Guide
Problem Solving 
Activity Lesson
Order of Operations Problem Activity Lesson
Make Change Activity Lesson
Multiplication & Division Problem Activity Lesson
Brainteasers: Make a Table Activity Lesson
Sorting Sneakers Activity Lesson
Fruit Salad Activity Lesson
Fence Frenzy Activity Lesson
Newspaper Route Activity Lesson
Parent Night Activity Lesson
Brainteasers: Guess & Check Worksheet/Answer key
Problem Solving Worksheet/Answer key
Problem Solving Worksheet/Answer key
Problem Solving Worksheet/Answer key
Step It Up
Activity LessonActivity LessonActivity LessonActivity LessonActivity LessonActivity LessonActivity LessonActivity LessonActivity LessonActivity LessonWorksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyThe resources above cover the following skills:
Operations and Algebraic Thinking
Use the four operations with whole numbers to solve problems.
Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (See Appendix A, Table 2.) [4-OA2]
Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4-OA3]