The Broken Stick Experiment: Triangles, Random Numbers and ProbabilityEnglish

Mathematics

Geometry

Instructors

Richard C. Larson
Mitsui Professor of Engineering Systems
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139 USA

Introduction

This learning video is designed to develop critical thinking in students by encouraging them to work from basic principles to solve a puzzling mathematics problem that contains uncertainty. One class session of approximately 55 minutes is necessary for lesson completion. First-year simple algebra is all that is required for the lesson, and any high school student in a college-preparatory math class should be able to participate in this exercise. Materials for in-class activities include: a yard stick, a meter stick or a straight branch of a tree; a saw or equivalent to cut the stick; and a blackboard or equivalent. In this video lesson, during in-class sessions between video segments, students will learn among other things: 1) how to generate random numbers; 2) how to deal with probability; and 3) how to construct and draw portions of the X-Y plane that satisfy linear inequalities.

View a "BLOSSOMS Extra," a PowerPoint audio lesson on discrete vs. continuous random variables as applied to the Broken Stick Problem. (click here to open page)

Watch three animated experiments (See "For Teachers" tab)

Instructor Biography

Dr. Larson's specialty is Operations Research, an interdisciplinary field that uses mathematics and the scientific method to improve decision making in industry and government.

For Teachers

Urban Operations Research: Urban Operations Research
Web-based animated solution to the Broken Stick Problem

Urban Operations Research: Experiment, Sample Space, and Events
Section 2.1 of the book, Urban Operations Research, available on the web

OpenLearn: Mathematical Ideas
Explores reasons for studying math and practical applications of mathematical ideas

Interactive: Probability and Geometry
An interactive lesson connecting probability and geometry

Wolfram MathWorld: Buffon's Needle Problem
Presents and solves another probability puzzle

Wolfram MathWorld: Probability
Provides extensive resources for the study of Probability

Wolfram MathWorld: Geometry
Provides extensive resources for the study of Geometry