Patterning with Pascal's Triangle

Blaise Pascal (1623-1662) is considered to be one of the great mathematicians. Although he didn't discover "Pascal's Triangle"; it was known to Islamic, Indian and Chinese mathematicians many years before; he investigated its properties to a greater extent which is why it is currently named after him.

The number in each cell of Pascal's Triangle is found by adding the two numbers above it, except for the top cell which is assigned a value of 1. For the cells on the edge, only one cell is visible above each one; the other can be assumed to be zero.

Math-Drills.com now includes a printable of Pascal's Triangle both in a filled out form (first 12 rows) and in a blank form. Below is a thumbnail image of the filled out version. You can access it directly by clicking on the link in the caption.

Pascal's Triangle Printable found at Math-Drills.com.

Below are a few ideas for elementary and middle school students.

1. Have students fill out the blank version to practice addition and to notice patterns that develop.
2. Show students the filled out version and have them search for patterns. Some of these patterns are quite easy to find, for example, the second diagonals contain a counting sequence. Other patterns are not so easy to see, for example, the sum of the cells in each row is a power of 2. The fifth row sums as follows: 1 + 4 + 6 + 4 + 1 = 16 which is 2 to the fourth power.
3. Have students color various multiples. For example, coloring the multiples of 2 or even numbers should result in an interesting pattern, especially if the triangle has been extended beyond 12 rows. With an infinite number of rows, you actually end up with a fractal named Sierpinski's triangle.
4. For even more ideas, please see All You Ever Wanted to Know About Pascal's Triangle.

We hope you enjoy our version of the Pascal's Triangle and use it in your home school or classroom.