Pascals Triangle Worksheet Pdf

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! Don’t tell Fibonacci, but I might enjoy working with Pascal’s triangle more! What’s better than patterns during the Christmas season?! We turned Pascal’s Triangle into a Christmas tree to work on some math skills and create some awesome tile art!

• Interactive Pascal's Triangle
• Pascal's Triangle Worksheet Pdf Answers

What is Pascal’s Triangle?

Pascal's Triangle: To access this worksheet please sign in to your Transum subscription account. If you do not yet have an account and you are a teacher or parent you can apply for one here. A Transum subscription also gives you access to the 'Class Admin' student management system, the answers to all of the online activities and opens up ad. Microsoft Word - pascals triangle worksheet 2.docx Author: Trevor Jensen Created Date: 12:44:46 AM.

Pascal’s Triangle Pascal’s Triangle is an in nite triangular array of numbers beginning with a 1 at the top. Pascal’s Triangle can be constructed starting with just the 1 on the top by following one easy rule: suppose you are standing in the triangle and would like to know which number to put in the position you are standing on. About 'Pascal's Triangle and Binomial Expansion Worksheet' Pascal's Triangle and Binomial Expansion Worksheet: Worksheet given in this section will be much useful to the students who would like to practice problems on similar triangles.

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.

Recommended: 12 Days of Christmas Pascal’s Triangle Math Activity

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.

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.

Download: Pascal’s Triangle Christmas Tree Patterns Workbook

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, but 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:

• Lightboard (optional)

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.

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Hey there! I’m Toni of House Johnson, the first of her name. This is my circus and these are my monkeys. I’m an Energy Technologies Market Research Analyst & Business Development Guru that finds my joy in letting my Maker flag fly by creating crafts & exploring STEAM concepts with my fantastic four! I’m powered by coffee and sour candy (and probably a little wine). When I’m not chasing toddlers or making babies, you can find me tearing things up and putting them back together over here at Our Family Code as well as exploring all things Motherhood at Get Moving Mama (coming soon)!

Today’s Wonder of the Day was inspired by Tan. Tan Wonders, “What is Pascal's triangle ” Thanks for WONDERing with us, Tan!

We were walking through the Wonderopolis cafeteria the other day when we saw a square having lunch with a triangle and a circle:

Square: What are you two eating?

Interactive Pascal's Triangle

Circle: A piece of pi.

Triangle: A slice of pizza.

Square: Cool…nothing like a good square meal to get you through the day!

Triangle: Later Circle! I'll see you around! It's getting too hot in here.

Circle: You're right, triangle. I'm 360 degrees!

These punny characters continued for a while, but we were in no shape to continue to listen to so many bad geometry jokes!

All joking aside, today's Wonder of the Day features a very special version of one of those shapes: the triangle. Specifically, we'll be discussing Pascal's triangle.

Farming simulator 2015 download full free. Pascal's triangle is an infinite, equilateral triangle composed of numbers. The numbers that make up Pascal's triangle follow a simple rule: each number is the sum of the two numbers above it.

Looking at Pascal's triangle, you'll notice that the top number of the triangle is one. All of the numbers in each of the sides going down from the top are all ones. The numbers in the middle vary, depending upon the numbers above them.

Since Pascal's triangle is infinite, there's no bottom row. It just keeps going and going. Pascal's triangle is named for Blaise Pascal, a French mathematician who used the triangle as part of his studies in probability theory in the 17^th century.

Pascal's Triangle Worksheet Pdf Answers

Blaise Pascal didn't really 'discover' the triangle named after him, though. It has actually been studied all over the world for thousands of years. For example, historians believe ancient mathematicians in India, China, Persia, Germany, and Italy studied Pascal's triangle long before Pascal was born. Pascal did develop new uses of the triangle's patterns, which he described in detail in his mathematical treatise on the triangle.

The basic pattern of Pascal's triangle is quite simple. Despite its simplicity, though, Pascal's triangle has continued to surprise mathematicians throughout history with its interesting connections to so many other areas of mathematics, such as probability, combinatorics, number theory, algebra, and fractals.

So why is Pascal's triangle so fascinating to mathematicians? The more you study Pascal's triangle, the more interesting patterns you find. This is important in mathematics, because mathematics itself has been called the 'study of patterns' and even the 'science of patterns.'

Many of the mathematical uses of Pascal's triangle are hard to understand unless you're an advanced mathematician. Even young students, however, can recognize a couple of the simpler patterns found within Pascal's triangle.

For example, the left side of Pascal's triangle is all ones. The next set of numbers in, known as the first diagonal, is the set of counting numbers: one, two, three, four, five, etc. You'll also notice an interesting pattern if you add up the numbers in each horizontal row, starting at the top. The sums double each time you descend one row, making them the powers of the number two!