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 Write-up

Title
Pascal’s Patterns

Problem Statement

 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1

What is the sum of each row? Find a way to describe the pattern of sums by comparing each row's sum to the corresponding row number.

Problem setup

Find the sum of the rows in Pascal’s triangle and look for a pattern by comparing the sums of each row.

Plans to Solve/Investigate the Problem

I plan to use an Excel Spreadsheet to look for a pattern.

Investigation/Exploration of the Problem

I began by labeling a column with the heading of “Rows” and filled in the numbers 1-17.  I next labeled a column

with the heading of “sum”.  I began adding the numbers in each row and produced the following sequence:  1, 2, 4, 8, 16, 32…  I recognized that these numbers were powers of 2.  Row 1 has a sum of 1 and is 20.  Row 2 had a sum of 2 which is 21.  Row 3 has a sum of 4 which is 22.  Row 4 has a sum of 8 which is 23.  Pattern: 2(n-1) where n is equal to the number of rows.

Extensions of the Problem

How can Pascal’s Triangle be used to discover powers of 11?

Author & Contact
Insert name and contact information.
lparsons@rockdale.k12.ga.us

Link(s) to resources, references, lesson plans, and/or other materials
http://ptri1.tripod.com/ink

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