# The Broken Stick Experiment: Triangles, Random Numbers and ProbabilityEnglish Mathematics

Geometry

### CPALMS

This lesson is CPALMS Vetted and Approved

### 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