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

Elementary Level

Discussion and Solutions

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.

 

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

  1. Can you predict the next row of numbers?
    1, 6, 15, 20, 15, 6, 1

  2. 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

  3. Do any numbers repeat?
    Yes, the rows read the same from left to right as from right to left.

  4. 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, ...

Questions? Write to the workshop facilitators.

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