# LESSON PLAN II

### Purpose

Increase students' knowledge of the Fibonacci growth pattern.

### Objectives

Students will be able to find the Fibonacci numbers pattern of population growth from a written description.

### Activities

1. Find the number of Dudeney's cows in each month for a year.
2. Continue the Fibonacci numbers for 5 terms following 144.
3. Ancestors of Honeybees: A colony of honeybees has one special female called the queen. There are many worker bees, these are also female, but unlike the queen bee, they produce no eggs. Male bees are called drones and do no work. Male bees have one parent, the queen. Drones hatch from the queen's unfertilized eggs so they have a mother but no father! Female bees have two parents. They hatch after the queen has mated with a male. Females usually end up as worker bees.

So female bees have 2 parents, a male and a female whereas male bees have just one parent, a female. Below there is a display of drone ancestors in a family tree where parents appear under their children.

Drone Family Tree
drone
mother
grannygrampa
great grannygreat grampagreat granny
great great grannygreat great grampagreat great grannygreat great grannygreat great grampa

Note the numbers of drone ancestors in each generation: 1, 1, 2, 3, 5, .

1. How do these numbers continue? What are the next 5 numbers?
2. Make a similar family tree for a worker bee and write the numbers of worker bee ancestors.
3. Do you recognize these numbers?

4. What if a population had the Fibonacci growth pattern, started with 1 but for some reason had 3 as the second term? The next term would have to be 1+3= 4, followed by 3+4=7 and then 4+7=11. What would the next 5 terms be?

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