Wednesday, October 23, 2013

Agenda•BBC

•Homework Check• Lesson: Those Wascally Wabbits II

BBC 10/23/13Aim: SWBAT provide an example of a recurrence

relation. Homework: Last SlideDo Now: Identify the pattern in the sequences

below. See if you can write a function to define the pattern.

a) 3, 7, 11, 15b) 72, 36, 18, 9c) 4, 8, 12, 20

Recurrence Relations• What is a recurrence relation (or a recursive function)?

• Let’s talk about the Fibonacci sequence…

Here were his conditions:

• A newly born pair of rabbits (one male, one female) are put into a field in January.

• Rabbits are able to mate at the age of one month—in February—and produce a new pair in March

• They would then breed again and produce a new pair in April, another pair in May, and so on…

• Meanwhile, the rabbits born in March would reach maturity in April so they would produce a new pair in May, then in June, and so on…

• HOW MANY PAIRS WILL THERE BE IN ONE YEAR?

Group Task1. Create a diagram of the rabbits for the first 6 months.2. Use the diagram to create a table. What is your input?

What is your output? Complete the chart for one year (12 months)

3. Attempt to find Fibonacci’s “rule”. You may explain the rule in complete sentences if you cannot do it algebraically.

First complete the task in your notebooks, then copy your results (the above 3 components) onto poster paper.

Each group will receive one grade. Remember to write your names on the poster.

Questions about the Fibonacci SequenceDefine a sequence? What is the Fibonacci sequence?

How do you figure out the next number in the Fibonacci sequence?

Define a recurrence relation. What does it have to do with the Fibonacci Sequence?

How does a recursive sequence differ from a geometric and arithmetic sequence?

Homework1. Determine if the graphs tothe right are functions.

2. Determine if sets A and B are functions or non-functions.

A: { (-2, -1) (3,3) (1, 2) (-2, 7) }B: { (-3, 0) (-1, 1) (3,0) (-2, -4)

Pyramids

The Puzzle Posed

• How many pairs will there be in one year?