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. Multi-step Word Problems
Study Guide
Multi-step Word Problems 
Worksheet/Answer key
Multi-step Word Problems Worksheet/Answer key
Multi-step Word Problems Worksheet/Answer key
Multi-step Word Problems Worksheet/Answer key
Pumpkin Pictograph - Halloween
Worksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyThe resources above cover the following skills:
Number and Operations (NCTM)
Compute fluently and make reasonable estimates.
Develop fluency in adding, subtracting, multiplying, and dividing whole numbers.
Select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.
Algebra (NCTM)
Represent and analyze mathematical situations and structures using algebraic symbols.
Express mathematical relationships using equations.
Use mathematical models to represent and understand quantitative relationships.
Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.
Grade 4 Curriculum Focal Points (NCTM)
Number and Operations and Algebra: Developing quick recall of multiplication facts and related division facts and fluency with whole number multiplication
Students use understandings of multiplication to develop quick recall of the basic multiplication facts and related division facts. They apply their understanding of models for multiplication (i.e., equal-sized groups, arrays, area models, equal intervals on the number line), place value, and properties of operations (in particular, the distributive property) as they develop, discuss, and use efficient, accurate, and generalizable methods to multiply multi-digit whole numbers. They select appropriate methods and apply them accurately to estimate products or calculate them mentally, depending on the context and numbers involved. They develop fluency with efficient procedures, including the standard algorithm, for multiplying whole numbers, understand why the procedures work (on the basis of place value and properties of operations), and use them to solve problems.