Monday, January 31, 2011

Valentine Problem Solving: Heart Paths

Heart Paths

If students enjoyed the Pascal snow activities, then they'll also enjoy this Valentine's version of Pascal paths.  Heart Paths challenges students to find all the different paths that spell HEART if they can only move from a letter to one of the two letters directly below it. 

The number of possible paths is linked to Pascal's Triangle and older students will be amazed at how this mathematical pattern can be used to help them identify all of the paths.  A recording sheet is included in the packet so that students may easily record paths and identify duplicates.

Download the Heart Paths activity which includes the problem, directions, recording sheet and answer key.

Suggestions for Classroom Use:
  • Make an overhead of the Heart Paths problem or use the PDF on a SmartBoard for presentation.  
  • Demonstrate a legitimate path moving from a letter to one of the two letters directly below it.
  • Demonstrate an illegitimate path by moving from a letter to another letter not directly below it.
  • Do not tell students how many paths there are.  Students need to develop confidence in their own ability to capture all of the paths.
  • Use an overhead of the Heart Paths recording sheet (or the PDF file on a SmartBoard for class discussion.  Have students come to the overhead to draw possible paths.
  • Follow up with a discussion of systematic counting.  If students did not use a systemized approach to this problem, demonstrate finding all of the possible paths for the first E, then move to the second E, etc.  NOTE:  The answer key included in this activity follows a systematic counting system.  Systematic counting is an important concept in discrete math and very applicable to computer programming.  For students, it is a logical approach that almost guarantees that they will consider every option, so it is a strong strategy to add to their problem solving repertoire.

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