Subject Area
Math

Activity Overview
DNA has its own code of bases. You have been hired to crack the code of the Fibonacci Sequence. What is the tenth number in the sequence? 20th? Fifth odd number ?

Objective
Students will calculate the Fibonacci Sequence using different number combinations.

Materials
paper and pencil
calculator
math journal

Online Resources
http://www.ee.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html
http://forum.swarthmore.edu/dr.math/faq/faq.golden.ratio.html
http://www.sciencenews.org/sn_arc99/6_12_99/bob1.htm

Activity Outline
Discuss the concept of patterns. Have students work in small groups.
Have students:
1. Estimate in their journals what the answers will be.
2. Use calculators to arrive at the answers.
3. Write the totals down in the journals.
4. Use their journals to reflect the estimates and actual answers. How close are they?
5. Check with another person and see if their answers are close to one another. Why or why not?
6. Give some examples of the Fibonacci Sequence found in their environment. Justify how they know that their examples represent the sequence.
7. Determine the pattern that creates the Fibonacci Sequence?

Assessment Options
Check for the accuracy of their answers in their journals.

Standards and Benchmarks
Standard 1: Uses a variety of strategies in the problem-solving process
1. Understands how to break a complex problem into simpler parts or use a similar problem type to solve a problem
5. Represents problem situations in and translates among oral, written, concrete, pictorial, and graphical forms
7. Constructs informal logical arguments to justify reasoning processes and methods of solutions to problems (i.e., uses informal deductive methods)
6. Generalizes from a pattern of observations made in particular cases, makes conjectures, and provides supporting arguments for these conjectures (i.e., uses inductive reasoning)

Standard 3: Uses the basic and advanced procedures while performing the processes of computation
3. Selects and uses the appropriate computational methods (e.g., mental, paper and pencil, calculator, computer) for a given situation
7. Knows when an estimate is more appropriate than an exact answer for a variety of problem situations

Standard 4: Understands and applies basic and advanced properties of the concepts of measurement
8. Selects and uses appropriate estimation techniques (e.g., overestimate, underestimate, range of estimates) to solve real world problems

Standard 8: Understands and applies basic and advanced properties of functions and algebra
11. Understands the properties of arithmetic and geometric sequences (i.e., linear and exponential patterns)

Standard 9: Understands the general nature and uses of mathematics
2. Understands that mathematics often represent real things using abstract ideas like numbers or lines; they work with these abstractions to learn about the things they represent