Pascal’s Triangle Templates

What is Pascal’s Triangle? 

Pascal’s triangle is a triangular array of numbers (specifically positive integers) named after famous French mathematician Blaise Pascal. Pascal’s triangle is used in the areas of algebra, combinatorics, and probability theory. 

The first row of Pascal’s Triangle features a single copy of the number 1. The second row features two copies of the number 1. Each subsequent row of Pascal’s Triangle starts with a 1 and ends with a 1. The numbers in the middle of the row can be generated by adding the two numbers above it. 

​The main use case for Pascal’s Triangle at the high school level and beyond is to calculate the coefficients of binomial expansion. 

Lesson Plans Involving Pascal’s Triangle

​Students are often introduced to Pascal’s Triangle in middle school. At this age level, students will not understand many of the applications of the triangle, but they are at the perfect age to begin exploring the interesting patterns that can be found inside this triangular array of numbers. 

What patterns arise in the triangle if you color only the even numbers or only the odd numbers? 

Spoiler Alert: If you color in the odd numbers on Pascal’s Triangle, you will end up creating a Sierpinski Triangle which could lead into a fun mini-unit on fractals and math art! 

Another coloring activity using Pascal’s Triangle which is worth exploring is coloring in the multiples of different numbers. For example, have one student color only the multiples of 2. Have another student color the multiples of 3. Have yet another student color the multiples of 4. 

Students will soon discover that coloring the multiples of a prime number produce very different results than coloring the multiples of a composite number. 

Other types of numbers that can be explored using Pascal’s triangle include square numbers, triangular numbers, and tetrahedral numbers. You can also do a fun lesson on the Fibonacci Sequence by having students explore of the sums of diagonals on Pascal’s Triangle. 

In the past, I have given students different types of numbers to look for on Pascal’s triangle. They colored their results, and I was able to put the Pascal’s Triangles together to create a fun math art bulletin board featuring Pascal’s Triangle to decorate our classroom. 

Pascal’s Triangle Templates

I created a set of Pascal’s Triangle templates for my own classroom, so I thought I would share them with other teachers to use as well.