Patterns and Problem Solving

Fibonacci Numbers
In the first chapter we covered in Math for Elementary Teachers, included Patterns and Problem Solving.  Something that was a reoccurring theme that the teacher Amy DelMedico went over was the patterns in our daily life or living things in nature.  When when we saw a picture of a  a Nautilis shell, or a sunflower, I would have never thought math.. or even patterns.  These patterns that occur naturally in nature are interrelated to Fibonacci numbers. Fibonacci numbers traditionally start with 1 and 1, each successive number can be obtained by adding the two previous numbers. 1,1,2,3,5,8,13,21..and so on. Amy Del Medico showed us a very cool video on Fibonacci numbers in class, the link will be listed below.

http://www.etereaestudios.com/movies/nbyn_movies/nbyn_mov_youtube.htm
(This movie was made by Cristobal Vila)

Some examples of the Fibonacci sequence in nature is a sunflower or a pine cone 

Example of Fibonacci Numbers in nature (Below)

Image: Brewbrooks Found At: http://www.google.com/imgres?imgurl=http://amazingdata.com


>A good Blog About Fibonacci Numbers is: Geometry and Nature
>Fun Game for Fibonacci Numbers (its a little tricky at first) http://www.yourdiscovery.com/games/play/fibonacci/




Pascal's Triangle
Another topic we reviewed in Math for Elementary Teachers is Pascal's Triangle. Pascals Triangle is very interesting and has a lot of different patterns. Pascal's Triangle is a triangular pattern of numbers that starts with 1 (in Row 0) and continues to row 1 with 1 and 1 (example below)

1

1              1

1              2              1

1              3              3              1

1              4              6              4              1

The top Row is 0

The second row is 1 

The third row is 2

and so on

the yellow highlight shows 1+1=2 and that is how that line is formed

the second line has 1 and two listed in blue and in the fourth line 3 listen in blue because 1+2=3.

I have highlighted a few just to show how the numbers in in the next line down are developed.

I never really looked at math in patterns, but when I do it seems to come a lot easier.  If you would have told me to try to figure out the next line in Pascals triangle in the beginning I would never have been able to.  But when breaking a big problem down into a smaller one it is much easier to understand it. It is crazy to think that nature and math is related at all.  

>A couple games to help finding patterns are :
Pattern Cracker
Preschool- Crazy Patterns
What Comes Next

I have found on YouTube a video to help finding sequences


I have learned that making connections with math and the real world make it a lot easier to understand and when you break big problems down in to smaller ones it is much simpler. With Fibonacci numbers and Pascals triangle when broken down you can find the next numbers  or sequence with simple addition.