Applying...“The Problem Solving Process.”

Purpose: Students will Use The Problem Solving Process While Playing Several Games: "Handshake" & "Fence Post."

The Problem Solving Process:

  1. Understand the problem
    1. What data or information is known?
    2. What data or information is unknown?(This is what I am trying to solve)?
    3. What are the conditions?
  2. Make a plan to solve the problem – (This is known as an Algorithm!)
  3. Carry out the plan.
  4. Review and reflect on how the problem was solved

Handshake Problem #1: (Follow “The Problem Solving Process”)
Assume there are 20 people in a room, including you. You must shake hands with everyone else in the room. How many hands will you shake?
If “N” equals the number of people in the room (where N > 0), write an equation that will determine the number of hands that have been shaken dependent upon a changing number of people in the room. 

Solution!

Fence Post Problem: (Follow “The Problem Solving Process”)
You need to build one side of a fence that is 12 yards long. This fence will be built with fence posts and rails that connect one fence post to another. If each fence post is 1 yard away from the next fence post, how many fence posts will be needed for this side of the fence?
If “N” equals the number of post used to build a fence (where N > 0), write an equation that will determine the number of posts needed 
to build a fence with a continually changing length.
Solution!

Handshake Problem #2: (Follow “The Problem Solving Process")
Assume there are 10 people in a room, including you. Each person in the room must shake hands one time, and only one time, with all the other people in the room. How many handshakes will occur in the room?    
If there are 20 people in the room, how many handshakes will occur?                                      
What about 2 people? You need to look for a pattern…this is how you will be able to write and equation!
If “N” equals the number of people in the room (where N > 0), write an equation that will determine the number of hands that have been shaken in the room, when the number of people changes and it is limited by the people in the room can only shake hands one time with the other people in the room.
Solution!