## What's the Shortest Route?

What’s the Shortest Route?
Goals

1. Students will explore the concepts of circuits and paths as it relates to the shortest route between cities.
2. Students will work in order to arrive at the shortest route solution and be able to explain, and justify, how they arrived at this solution.

Abstract

This activity, which is set in the context of having students find the shortest route between cities is related to graph theory, circuits and paths. Students are asked tocome witha method for traveling between cities in a way that allows them to visit each city using the fewest miles. These methods and solutions are then shared with the instructor.

Problem Statement

Finding the shortest route between cities is an important task for most businesses that require their employees to travel to various cities. Shortest routes usually save time and money and keep the travelers from returning to cities too often. In this activity, the students will be asked to determine the shortest route between several cities. They will also be asked to justify their method for coming up with the shortest route.

Instructions

Suppose a salesperson wishes to travel to each city in the map below exactly once, starting and ending in New York, and using only the roads shown. The numbers onthe roads indicate distances (in miles) between cities. Find the shortest route that the salesperson could use.
Look for a method that will work every time you try a problem like this. Are you convinced that your route is the shortest? Why?

Create a Power Point presentationto trace your route and give supporting evidence of why you think your route is the shortest.