# Guess the Last Ball: An Exercise in Mathematical Modeling

Fakhar Lohdi
Professor
National University of Computer and Emerging Technologies (NUCES)
Lahore, Pakistan

Lesson vetted and approved by CPALMS

This video lesson uses the technique of induction to show students how to analyze a seemingly random occurrence in order to understand it through the development of a mathematical model. Using the medium of a simple game, Dr. Lodhi demonstrates how students can first apply the ‘rules’ to small examples of the game and then, through careful observation, can begin to see the emergence of a possible pattern. Students will learn that they can move from observing a pattern to proving that their observation is correct by the development of a mathematical model. Dr. Lodhi provides a second game for students in the Teacher Guide downloadable on this page. There are no prerequisites for this lesson and needed materials include only a blackboard and objects of two different varieties - such as plain and striped balls, apples and oranges, etc. The lesson can be completed in a 50-minute class period.

Dr. Lodhi is a professor in the Department of Computer Science and head of the Software Engineering Research Center (SERC) at NUCES. He is a co-founder and former director of engineering at Vroom Technologies. His areas of interest include software engineering, software metrics, and object oriented methods.

Dr. Lodhi 是NUCES计算机系的一名教授 和软件工程研究中心（SERC）的负责人。他还是Vroom Technologies 的创始人之一和前工程部主任。他的研究领域包括软件工程，软件度量以及面向对象技术。

This is a lesson on mathematical induction presented by Coolmath.com.
http://www.coolmath.com/algebra/19-sequences-series/09-mathematical-induction-01.htm

This is a module on Proof by Induction from the website of Connexions, a place to view and share educational material made of small knowledge chunks called modules that can be organized as courses, books, reports, etc.
http://cnx.org/content/m19075/latest/

http://www.coolmath.com/algebra/19-sequences-series/09-mathematical-induction-01.htm

http://cnx.org/content/m19075/latest/

#### This is how low carb burns

June 2, 2012 at 11:06 am

This is how low carb burns fat: Your liver gets the protein, but your liver needs fuel in order to corevnt the protein into the glucose your body needs. That fuel is the fat in your body. The body corevnts the protein you eat to glucose and the fat is burned off? with the excess fat being corevnted to Ketones which your body can also use as fuel. Low carb is how man ate for thousands of years until we started making all these foodstuffs with carbs in them. CARBS = FAT ON YOUR BODY

#### At last! Someone who

November 24, 2011 at 4:38 am

At last! Someone who understands! Thanks for piostng!

This Lesson is in the following clusters: Mathematical Induction

#### This is how low carb burns

June 2, 2012 at 11:06 am

This is how low carb burns fat: Your liver gets the protein, but your liver needs fuel in order to corevnt the protein into the glucose your body needs. That fuel is the fat in your body. The body corevnts the protein you eat to glucose and the fat is burned off? with the excess fat being corevnted to Ketones which your body can also use as fuel. Low carb is how man ate for thousands of years until we started making all these foodstuffs with carbs in them. CARBS = FAT ON YOUR BODY

#### At last! Someone who

November 24, 2011 at 4:38 am

At last! Someone who understands! Thanks for piostng!