Numbers Galore

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In this workshop, we have studied a many things like deductive reasoning, analytical writing, logical argument in algebra and geometry, complementary and supplementary angles, combinations, and Pascal's Triangle. Our AP includes both Pascal's Triangle and combinations since Pascal's Triangle are based on combinations! We connected the real world and math by figuring out how many different paths you could take from one place to another. My class learned about mathematical combinations and how we can solve them using factorials, permutations, and combinations. We also learned how we could use the Pascal's Triangle to help find how many routes that are on a map. We used the combination formula, nCr, to help find these ways even faster. It was a unit full of finding different ways we could solve or unlock different mathematical combinations and patterns. For this AP, we had to find a way to present different combinations of objects in a dynamic representation. The purpose of this AP was to understand the applications of mathematical combinations and their larger connection to mathematics.

The Pascal Triangle method is named after French mathematician and philosopher, Blaise Pascal, Pascal's Triangle is a triangle array of numbers which end with the number 1 at each end. The other numbers are the sum of the two closest numbers from the row above. In the 1000's, a Persian mathematician Al-Karaji (953–1029) wrote a now lost book which contained the first description of Pascal's triangle. This leads many historians to believe that Blaise Pascal was not the first mathematician to create the Binomial Theorem, although Blaise Pascal was the first person to receive world wide recognition.

Encyclopædia Britannica. (2018) Binomial Theorem

Combinations for the Pascal Triangle are basically a set of data that is broken up into groups of the variables in the data set.  In order to find the answer, we must use the combination formula: n!/r!(n-r)!
N= Whole group number
R= Number being chosen out of whole number

C.H. (2018) Pascal Triangle

Pascal's Triangle is a triangular path of numbers. Inside of the triangle, you must add the two closest numbers and the adjacent together to write down under the two. You can doing this pattern as long as you like, as it will always equal a triangle. If you want to figure out 10C4, you can create a triangle and look for the 4th number on the 10th row. 

C.H. (2018) How Many Routes?

By finding a pattern and using a number for each intersection. I was able to calculate a total of 16 routes that I could take from LeClaire Courts to my middle school without backtracking. I did not have to use any main streets because I was in a small section of a neighborhood.

In conclusion to this action project, I learned many things from this project. I learned more about how I can relate reflections to Pascal's triangle and I found different patterns in Pascal's triangle. Some challenges for me during this process were coming up with a question and answer about mathematical combinations and creating my own Pascal’s Triangle. I found completing this action project challenging because I had to put a lot of effort into this action project. Overall I enjoyed this action project and unit in the Prove it or Lose it, Geometry class.


Works Cited:
Hosch, William L. “Pascal's Triangle.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., 24 Feb. 2013, www.britannica.com/science/Pascals-triangle.

The Editors of Encyclopædia Britannica. “Binomial Theorem.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., 25 June 2018, www.britannica.com/science/binomial-theorem/media/65749/127359.

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