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Last week the children were introduced to Pascal’s Triangle, its history and its properties.  They created their own Pascal’s Triangle and experimented with different seed numbers (the seed number of a traditional Pascal’s Triangle is 1; 1 is placed on the left and right diagonals of the triangle). You fill each cell with the sum of the two cells above it. 

Pascal's Triangle is created by starting with only 1s in each of the two perimeter diagonals of a triangular array. Fill in this array by adding the two numbers above each cell. The numbers start out small such as 1 2 1 on the second row and 1 3 3 1 on the third row and 1 4 6 4 1 on the fourth row but then they explode.

Prime Pyramid: Compete the pyramid by filling in the missing numbers on each row. Each row must contain the consecutive whole numbers from 1 to the row number but not necessarily in that order. In each row, the numbers from 1 to the row number are arranged such that the sum of any two adjacent numbers (neighboring numbers) is a prime number.

The rules for Kakooma are simple. Greg Tang developed this puzzle; I first heard him speak as a parent of elementary school children in 2002. Mr. Tang had a part in inspiring me to change my career to teach math. Subsequently, I attended one of his teach the teacher workshops. 

The Conway Sequence is a sequence of digits (also called Look-and-Say sequence) where each term is made of the reading of the digits (the number of consecutive digits) of the previous term. Conway created this sequence as a method of decoding called Run-Length Encoding.