Complete Pascal’s triangle and reveal some awesome math patterns with these free Christmas tree Pascal’s Triangle worksheets!

Don’t tell Fibonacci, but I might enjoy working with Pascal’s triangle more! What’s better than patterns during the Christmas season?!

Learn about Pascal’s Triangle with this fun Christmas math activity! Pascal’s Triangle is a pretty cool mathematical concept that is filled with tons of patterns!

We turned Pascal’s Triangle into a Christmas tree to work on some math skills and create some awesome tile art!

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What is Pascal’s Triangle?

Pascal’s Triangle is named after Blaise Pascal, a famous French Mathematician and Philosopher. However, the triangle and concept date back centuries in India, Iran, China, Germany, and Italy.

Pascal’s Triangle is a triangular array of binomial coefficients determined by binomial expansion. What is all of this crazy math talk?! Well, binomials are used in algebra and look like 4x+10 or 5x+2.

Basically, Pascal’s Triangle shows you the probability of any combination like the chances of you rolling heads or tails when flipping a coin!

When you look at the triangle, you’ll see the expansion of powers of a binomial where each number in the triangle is the sum of the two numbers above it.

Patterns, Patterns, Patterns! 

There are so many neat patterns in Pascal’s Triangle. The first diagonal of the triangle just contains “1”s while the next diagonal has numbers in numerical order.

The third diagonal has triangular numbers and the fourth has tetrahedral numbers. If you add up each row of Pascal’s Triangle, you’ll find the powers of 2 since they double each time. If you squish all of the numbers in each row together, you’ll find exponents of 11.

Pascal’s Triangle is also symmetrical! If you were to fold the triangle in half, the numbers on the right side are identical to the numbers on the right side.

The pattern that I think is super cool is the Sierpinski Triangle, which can be found if you color all of the odd numbers in Pascal’s Triangle.

Sierpinski Triangle

If you color all of the odd numbers in Pascal’s Triangle, you’ll see the Sierpinski Triangle, a fractal in the shape of a triangle with four equilateral triangles inside of it. To make your own Sierpinski artwork, use the Christmas tree Pascal’s Triangle worksheet.

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Complete Pascal’s Triangle Free Worksheets

Grab these free Pascal’s Triangle worksheets and use them to calculate the missing numbers. Remember that each number is equal to the sum of the two numbers above.

Create Some Beautiful Math Mosaic Artwork

We love tangrams at our house and have recently started applying our tangram skills to working with glass and ceramic tiles to create some pretty sweet artwork!

Check out our neat Sierpinski triangle art and grab some tiles and make your own. We didn’t glue our triangle together because my girls wanted to make symmetrical snowflakes and we needed some more tiles.

If you want to glue your pieces just use the glue to adhere them to mosaic mesh or onto a surface like the back of a picture frame and use the frame to surround your pieces and display.

Materials Needed:

• Triangle or Diamond shaped glass or ceramic tiles
• Lightboard (optional)
• Weldbond Multi-Purpose Adhesive Glue
• Mosaic Mesh

For our Sierpinski mosaic artwork, we used green and yellow diamonds for the odd numbers and blue and red diamonds for our even numbers.

The diamonds helped us cover the empty spaces on our grid a little easier than using double the triangles.

More Math + Art Activities

• Pi Necklace Coding Unplugged Coding Activity
• Teach the Fibonacci Sequence with this Easy Math & Art Activity!
• Finding Pi with Math Sun Catchers
• Amazing Math Art and Drawing Projects for Kids from Teach Beside Me

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