### Summary

Students learn about probability through a LEGO® MINDSTORMS® NTX-based activity that simulates a game of "rock-paper-scissors." The LEGO robot mimics the outcome of random game scenarios in order to help students gain a better understanding of events that follow real-life random phenomenon, such as bridge failures, weather forecasts and automobile accidents. Students learn to connect keywords such as certainty, probable, unlikely and impossibility to real-world engineering applications.

### Engineering Connection

*bids*(or, formal cost estimates) for projects. Engineers usually bid on a project, such as stadium renovation, building an office building or retail complex, or building a new bridge or highway, on the assumption that their firm has an equal chance of winning the bid. Structural engineers employ probability by assessing the likelihood of a structure, such as a building, bridge, highway or tunnel, to undergo

*failure*. Knowledge of probability is a necessary skill to be an effective engineer and practice engineering because it allows for the creation of failure-resistant structures that better develop our physical surroundings and, ultimately, improve the lives of people in our society.

### Educational Standards

Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the *Achievement Standard Network (ASN)*, a project of *JES & Co. *(www.jesandco.org).

In the ASN, standards are hierarchically structured: first by source; *e.g.*, by state; within source by type; *e.g.*, science or mathematics; within type by subtype, then by grade, *etc*.

Click on the standard groupings to explore this hierarchy as it applies to this document.

### Pre-Req Knowledge

### Learning Objectives

- Define probability.
- List examples of how probability is used in real-world engineering applications.
- Identify and explain possible outcomes and probability associated with each outcome.

### Materials List

- Pre-Assessment Quiz, RPS Probability Worksheet and Post-Assessment Quiz, one per student

- for class demo: 1 quarter (coin)
- LEGO MINDSTORMS NXT robot and software, such as the LEGO MINDSTORMS Education NXT Base Set and Software Pack (5003404) available for $376 at https://shop.education.lego.com/legoed/education/NXT/NXT+Base+Set+and+Software+Pk/5003404&isSimpleSearch=false
- computer, loaded with NXT 2.1 software
- pre-programmed NXT brick (comes in the education base set), loaded with the program rock_paper_scissors.rbt

### Introduction/Motivation

*probability*, we need to understand what is meant by this word. Probability is defined as

*a chance that an event will occur*. We can mathematically represent probability in equation form. (Write Equation 1 on the board).

### Vocabulary/Definitions

certain: |
Event that has 100% probability of happening. |

impossible: |
No chance of happening; 0% probability. |

probability: |
A chance that an event will occur. |

probable : |
A good chance of happening; likely. |

outcome: |
The end result. |

uncertainty: |
Event that is unpredictable. |

unlikely: |
A small chance of happening. |

### Procedure

Before the Activity

- Gather materials and make copies of the Pre-Assessment Quiz, RPS Probability Worksheet and Post-Assessment Quiz, one each per student.
- Build the LEGO "RPS" (rock-paper-scissors) robot provided with the base kit components, following instructions in
*The LEGO MINDSTORMS NXT Idea Book*. See Figure 1 and the additional notes in the next section. - Download the NXT rock_paper_scissors.rbt software onto the classroom computer.
- Charge all NXT battery packs, and test the robot.

The RPS Robot

With the Students

- Before starting the activity, administer the pre-assessment quiz.
- Conduct the quarter flip demo and present students with the Introduction/Motivation information.
- Hand out the worksheets.
- Ask the students: Who is familiar with the game rock-paper-scissors? Who can explain how it works to the rest of the class? (As necessary, review and/or demonstrate how the game is played with a few student volunteers.)
- Familiarize students with the operation of the RPS robot. Demonstrate a few times. (Refer to the details in the section above.)
- Instruct students to fill out the worksheet table while the robot is asked to throw a rock, paper or scissors 10 times. To do this, students simply make tally marks in the appropriate column of the table for each trial event (row) of pressing the robot's touch sensor. Point out to students that the outcomes are random.
- Have students answer the worksheet questions.
- Ask students to state, in ratio form, the outcome of
*rock*. The outcome should be 1/3, since three total possible outcomes and one desired outcome exist. (Refer to Equation 1 and refer to the definition of probability as stated in the Introduction/Motivation section.) - Remind students that when the quarter was flipped at the beginning of the activity, the probability of it landing on tails was the same as the probability of landing on heads; both had a 50% probability (one desired outcome over two total outcomes). Likewise, in this activity, the probability of throwing a rock is the same as the probability of throwing a scissor or paper. The probability is 1/3 for each.
- Note: Typically, 10 trials are not enough to generate an outcome of 1/3 for each event, but 10 trials are performed in this activity in the interest of time. To obtain results closer to 1/3, increase the number of trials (as time permits). Doing 100 would be an ideal number of trials.
- Go over question #4 with students. They are asked to imagine that rock is Firm Rock, scissors is Firm Scissors, and paper is Firm Paper (serving to illustrate that each of the robot motors represents a firm or a company). If the firms are competing (via the bidding process) to obtain a job to build a stadium, for instance, all three companies should have an equal probability of getting the job.
- Review with students what has been accomplished in the activity. Discuss why results were slightly different among groups. (Answer: The robot throws out random numbers.)
- Conclude by administering the post-assessment quiz. Or, as a class ask and discuss the quiz questions.

### Attachments

- Rock_paper_scissors (rbt)
- Pre-Assessment Probability Quiz (docx)
- Pre-Assessment Probability Quiz (pdf)
- Pre-Assessment Probability Quiz Answers (docx)
- Pre-Assessment Probability Quiz Answers (pdf)
- Post-Assessment Probability Quiz (docx)
- Post-Assessment Probability Quiz (pdf)
- Post-Assessment Probability Quiz Answers (docx)
- Post-Assessment Probability Quiz Answers (pdf)
- RPS Probability Worksheet (docx)
- RPS Probability Worksheet (pdf)
- RPS Probability Worksheet – Example Answers (docx)
- RPS Probability Worksheet – Example Answers (pdf)

### Assessment

Pre-Activity Assessment

*Pre-Quiz:*Have students complete the five-question Pre-Assessment Quiz to gauge their base understanding of the subject of probability.

Activity Embedded Assessment

*Worksheet:*Have students complete their own RPS Worksheets while working in their teams. During the activity, monitor students' progress on the worksheet sections. At the end of class, collect the worksheets and evaluate students on their mastery of the subject of probability.

Post-Activity Assessment

*Post-Quiz:*Administer the five-question Post-Assessment Quiz (nearly the same as the pre-quiz) and review students' answers compared to their pre-lesson answers to measure their comprehension of the subject of probability. Alternatively, as a class ask and discuss the quiz questions.

### Contributors

Akim Faisal, Janet Yowell

### Copyright

© 2013 by Regents of the University of Colorado; original © 2011 Polytechnic Institute of New York University

### Supporting Program

AMPS GK-12 Program, Polytechnic Institute of New York University

### Acknowledgements

Last modified: August 28, 2015