Learning Resources
Lesson
During this Investigation you will explore properties of the Fibonacci sequence to predict the number of ancestors for a male bee. Read the introduction on pages 18 & 19 of your text to gain an understanding of how bees procreate. Do not proceed until you have read this material.
Before beginning the Investigation, it is important that you understand the family tree presented. A box with an M represents a male bee and a box with an F symbolizes a female bee. Notice there is always only one box below a box labeled M, but two boxes under a box labeled F.
- Can you explain the reason for this?
- If another line was added to this family tree, what generation would it describe?
Follow the steps outlined in the Procedure of the Investigation.Please read the notes given below for steps B, D, and E as you prepare to carry out the procedure.
Step B: Generate at least 10 terms of the sequence to ensure you have sufficient values needed later in Step E.
Step D: A graph of the ordered pairs (n,
) can be created by hand or using the list editor feature of the TI-83 graphing calculator. You have had lots of exposure to this feature in the previous Mathematics courses. However if you are unsure how to use this feature, yet want to use it, instructions are provided.
After the Investigation s completed, you may view sample graphs to check your work.
Step E: You can plot these values manually or using graphing technology. After you have created the graph, you may view a hint if you are having trouble with your observations.
Notebook Entry: Make an entry for the Fibonacci sequence in your glossary.
In C.Y.U. questions 31 & 35 you will use a geometric approach to solving probability questions. You should see a link between the concept of a geometric sequence and probability concepts.
Activity
Investigation Questions page 20 #'s 23 & 24
C.Y.U. pages 20 & 21 #'s 25 - 35
In # 26, be prepared to explain how you found the patterns and how convinced you are that your descriptions are appropriate.
When you have completed these questions, ask your on-site teacher to get the solutions for you from the Teacher's Resource Binder and check them against your answers. After you do this, if there is something you had trouble with and still do not understand, contact your on-line teacher for help.
Test Yourself
Define 5 sequences recursively so that the tenth term of each is 55.
Solutions
1. There are many possible answers here. Sample ones are listed below.
