How many ways can you spell HEART?

Heart Paths

Students will enjoy this discrete math activity that challenges them to find all of the possible ways to spell heart.  Each path starts on the H and moves down to an E, then an A, then an R, and finally a T.  You may only move to one of the two letters directly below the letter you are on. 

This activity is directly related to Pascal's Triangle, so it would be beneficial if students have previous experience with this famous pattern.  Try Pascal's Hearts which challenges students to try to figure out how to fill in the missing rows.  The downloadable file contains a notated solution which teachers may use to lead a class discussion of the solution and any patterns students can find in Pascal's Triangle. 

The downloadable Heart Paths file contains a student recording sheet so that students can record their paths in an orderly fashion.  This enables students to check that they have not duplicated a previous path.  Classroom teachers might make a transparency of this handout to be used on the overhead.  This way different students can draw paths as the class discusses the possible paths.

Be sure to check out the Mathwire Discrete Math collection for additional discrete math Pascal's path activities.  The SNOW activity download includes a teacher step-by-step orderly solution that relates the rows to the rows of Pascal's Triangle. This same process is easily extended to the 5-letter HEART paths.