Math 130

Fall 03

 

 

The Staircase Problem

 

            The staircases below are formed from tiles.  Each row contains one more tile than the row above it. 

 

 

 

 

 

 

 

 

• How many tiles would it take to form a staircase of height 10?  Of height 100?  Of height H?

 

• Look for patterns
  
   numerical and visual.  You can play with rearranging the tiles into a shape where it’s easier to count them.  Using more than one color tile in a systematic way might prove helpful.   You can also look for patterns in the numbers.

 

• Justify as many patterns as possible.  Justifying a pattern means finding an argument that will convince a skeptic that your pattern continues beyond the examples you’ve tried.  Look for meaning.  Try to relate your patterns to the initial problem.

 

• Make up variations of this problem and try to solve them.  You can change the pattern in constructing the staircase, ask a different question, etc.

 

 

Copyright 2005, Debra K. Borkovitz.  You may copy or edit this material for non-profit, educational use only.

 

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