Pascal's Triangle Exploration

Pascal's Triangle Exploration

Follow the instructions for each section to complete the worksheet. Pay close attention to the patterns in Pascal's Triangle.

Pascal's Triangle is a triangular array of the binomial coefficients. It is named after the French mathematician Blaise Pascal. Below is the beginning of Pascal's Triangle.

Row 0: 1

Row 1: 1 1

Row 2: 1 2 1

Row 3: 1 3 3 1

Row 4: 1 4 6 4 1

Fill in the missing numbers to complete the next two rows of Pascal's Triangle.

Row 0: 1

Row 1: 1 1

Row 2: 1 2 1

Row 3: 1 3 3 1

Row 4: 1 4 6 4 1

Row 5: 1         1

Row 6: 1           1

1. What is the sum of the numbers in Row 3 of Pascal's Triangle?

2. What pattern do you notice about the numbers along the second diagonal (the numbers 1, 2, 3, 4, ...)?

1. Describe in your own words how each number in Pascal's Triangle is found from the numbers above it.

2. What is the sum of the numbers in Row 0, Row 1, and Row 2? What pattern do you notice about these sums?

1. Every row of Pascal's Triangle starts and ends with the number 1.

2. The numbers in Pascal's Triangle are always increasing as you move from left to right within a row.