Exploring Pascal || Student Center || Teachers' Place || Student Worksheets

Working with a partner, study the numbers in the balloons. What patterns do you see in the arrangement of the numbers? Describe each pattern using words and symbols. ## Exploring Pascal's Triangle

## Elementary Level

Discussion and Solutions

## As you look for patterns, try to answer the following questions:

- Can you predict the next row of numbers?

1, 6, 15, 20, 15, 6, 1

- Add the numbers in each row. Is there a pattern in the sums of these numbers?

1 + 1 = 2

1 + 2 + 1 = 4

1 + 3 + 3 + 1 = 8

1 + 4 + 6 + 4 + 1 = 16

The numbers in the rows all sum to powers of 2

- Do any numbers repeat?

Yes, the rows read the same from left to right as from right to left.

- Can you find a pattern in the diagonal numbers?

Yes, natural numbers and triangular numbers

For More information read about:

natural numbers

1, 2, 3, 4, ...triangular numbers

1, 3, 6, 10, ...powers of 2

2, 4, 8, 16, ...Fibonacci numbers

1, 1, 2, 3, 5, 8, ...

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