 ## Monday, January 24, 2011

### Pascal Paths

How Many Ways Can You Make Snow? encourages students to apply the patterns in Pascal's Triangle.   A teacher instructional plan with mathematical background, answer and challenge is included to explain how to present this problem.   A recording sheet was also included as part of the teacher packet so that students are able to record all different solutions in a "systematic" way, which is a goal of discrete mathematics.

Extension:
Extend this lesson using the word winter to form Pascal paths.  How many possible different paths are there for this word?  How does it relate to Pascal's Triangle?

How Many Winter Paths  involves systematic counting of the different Pascal paths in this arrangement of the word WINTER.   Students will be challenged to relate this activity to Pascal's triangle as they analyze their solutions to see if they have found all of the ways to reach each R in the bottom row.   A teacher instructional plan with mathematical background, answer and this challenge is included to explain how to present the problem.   The recording sheet encourages students to trace one path in each frame, making it easy to see if students use a systematic counting approach to solving the problem.
• Download How many winter paths do you see? problem, recording sheet and Pascal's link.  This PDF also contains instructional suggestions for presenting this problem to students.
Note:  Systematic counting is an important concept in discrete mathematics.  Be sure to model using a systematic approach to finding all of the different paths, as presented in the instructional suggestions for this problem.  Students will benefit from adding this logical and systematic counting approach to their problem-solving repertoire.