Students will

The class will need the following:


Work on the Classroom Activity Sheet together in class. Help students find the Fibonacci numbers in each illustration. Students may also enjoy working on the TakeHome Activity Sheet as a wholeclass project. 

You can evaluate students using the following threepoint rubric:

Finding Ratios Suggest that students measure the length and width of the following rectangles:
An Algebraic Rule Encourage students to try to develop an algebraic formula that expresses the Fibonacci sequence. The formula is described below. Represent the first and second terms in the sequence with x and y . Then the first few terms would be expressed as follows:
First term = x
Ask the students whether they notice anything familiar about the coefficients. (They're numbers in the Fibonacci sequence.) 
Life By the Numbers Keith Devlin. John Wiley & Sons, 1998. Written as a companion volume to the PBS series of the same name, this book focuses on the role mathematics plays in everyday life. Each chapter examines a different aspect of the world we live in and how mathematics is involved: patterns appearing in nature, the curve of a baseball, the chance of winning in Las Vegas, the technology of the future. Lots of pictures round out this clear and exciting presentation. Designing Tessellations: The Secrets of Interlocking Patterns Jinny Beyer. Contemporary Books, 1999. For generations, people have created designs using repeating, interlocking patterns—tessellations. In this slightly oversized, beautifully illustrated book, the author shows how the combination of pattern and symmetry can result in stunning geometric designs. While this unique book uses quilt making as the focus of the design process, it could easily be applied to other arts as well. 
algorithm Definition: A stepbystep procedure for solving a problem. Context: Thealgorithmfor obtaining the numbers in the Fibonacci sequence is to add the previous two terms together to get the next term in the sequence. logarithmic spiral Definition: A shape that winds around a center and recedes from the center point with exponential growth. Context: The nautilus shell is an example of alogarithmicspiral. sequence Definition: A set of elements ordered in a certain way. Context: The terms of the Fibonaccisequencebecome progressively larger. term Definition: An element in a series or sequence. Context: The mathematician Jacques Binet discovered that he could obtain each of thetermsin the Fibonacci sequence by inserting consecutive numbers into a formula. 
This lesson plan may be used to address the academic standards listed below. These standards are drawn from Content Knowledge: A Compendium of Standards and Benchmarks for K12 Education: 2nd Edition and have been provided courtesy of theMidcontinent Research for Education and Learningin Aurora, Colorado. Grade level: 912 Subject area: Mathematics Standard: Understands and applies basic and advanced properties of the concepts of numbers. Benchmarks: Uses discrete structures (e.g., finite graphs, matrices, or sequences) to represent and to solve problems. Grade level: 912 Subject area: Mathematics Standard: Uses basic and advanced procedures while performing the processes of computation. Benchmarks: Uses recurrence relations (i.e., formulas that express each term as a function of one or more of the previous terms, such as the Fibonacci sequence and the compound interest equation) to model and to solve realworld problems (e.g., home mortgages or annuities). Grade level: 912 Subject area: Mathematics Standard: Uses basic and advanced procedures while performing the processes of computation. Benchmarks: Uses a variety of operations (e.g., finding a reciprocal, raising to a power, taking a root, and taking a logarithm) on expressions containing real numbers. 
Chuck Crabtree, freelance curriculum writer. 
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