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OR in Schools

Louise Orpin and Vincent Knight

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Outline

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  1. "Playing Games"

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  • Some Videos from a past event

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  • The OR in schools project

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What is a Game?

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Guess ⅔ of the average game.

Rules:

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  • Every player must write a whole number between 0 and 100 on the provided sheet.

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  • The winner of the game will be the player whose number is closet to ⅔ of the average of all the numbers written by all the players.

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Guess ⅔ of the average game.

100

0

What's the biggest guess that makes sense?

66

44

29

19

1

...

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Guess ⅔ of the average game.

Rules:

​

  • Every player must write a whole number between 0 and 100 on the provided sheet.

​

  • The winner of the game will be the player whose number is closet to ⅔ of the average of all the numbers written by all the players.

​

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TV show from Feb 2008 to Feb 2009 where a jackpot is to be shared between 2 contestants who secretly choose to "split" or "steal".

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Rules

  1. If both players "split", the jackpot is split equally between them.
  2. If 1 player "splits" and the other "steals", the stealer gets the whole jackpot and the splitter leaves with nothing.
  3. If both players "steal", they both leave with nothing.

Golden Balls

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Golden Balls

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Split

Steal

Split

(50,50)

(0,100)

Steal

(100,0)

(0,0)

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Prisoner's Dilemma

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C

D

C

(2,2)

(5,0)

D

(0,5)

(4,4)

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A past event

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A past event

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Prisoner's Dilemma Tournament

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Exam - Revision Game

You must revise for an exam and the curriculm covers 2 subjects: Algebra & Geometry.

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  • The exam can be set on only 1 of the 2 subjects.

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  • You can revise for either or both subjects.

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Exam - Revision Game

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Algebra

Geometry

Revise Algebra

(10,10)

(0,0)

Revise Geometry

(0,0)

(10,10)

Revise Both

(9,15)

(9,15)

?

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?

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R

P

S

R

(0,0)

(-1,1)

(1,-1)

P

(1,-1)

(0,0)

(-1,1)

S

(-1,1)

(1,1)

(0,0)

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Rock Paper Scissor

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R

P

S

R

(0,0)

(-1,1)

(1,-1)

P

(1,-1)

(0,0)

(-1,1)

S

(-1,1)

(1,1)

(0,0)

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Game of Chicken

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Swerve

Straight

Swerve

(0,0)

(-1,1)

Straight

(1,-1)

(-10,-10)

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We use probabilities to calculate the expected outcomes:

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Let's say that the first player "swerves" with probability x and the second player "swerves" with probability y.

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The expected score to the first player is given by:

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Game of Chicken

-10(y-1)(x-1)+(y-1)x-(x-1)y

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Game of Chicken

Here's a 3D plot of that equation:

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Game of Chicken

Looking a bit more closely at the expected outcomes of the first player:

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Probability of second player swerving.

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Game of Chicken

With a little bit more work, we can show that the players should "swerve" almost all the time (90% of the time).

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Game Theory - Conclusions

  • Fun! (Because you get to play games)

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  • Lots of Applications:

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    • Business
    • Biology
    • Politics

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  • Useful and applicable every single day.

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Guess ⅔ of the average game.

Rules:

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  • Every player must write a whole number between 0 and 100 on the provided sheet.

​

  • The winner of the game will be the player whose number is closet to ⅔ of the average of all the numbers written by all the players.

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The OR in Schools Project

  • A review on the future of OR education highlighted a lack of awareness of OR in schools

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  • The Society created the OR in Schools Taskforce

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  • Stretch target - ‘Every school child knows what OR is’

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  • ‘What is OR?’ DVD

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  • Dedicated website aimed at teachers and young people

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www.LearnAboutOR.co.uk

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How are we currently getting OR in Schools

  • School visits by OR Society members

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  • Teaching resources

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  • Workshops at teacher conferences

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  • Networks with maths community

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  • Advertising the LearnAboutOR website

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Decision Maths

  • Decision Mathematics is part of the much wider area of Discrete Mathematics

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  • Decision Maths is an optional module in A Level Maths

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  • Many of the techniques learnt in Decision Maths are OR techniques
    • Critical Path Analysis
    • Linear Programming
    • Network Analysis
    • Game Theory

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Example resource

Linear Programming modelling exercise using Lego

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11 year olds doing graphical LP with the Lego exercise

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Volunteer for OR in Schools

  • Go into a class and run an activity
  • Approach interested schools
  • Support links between schools/colleges and OR Society

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The Benefits:

  • Networking
  • Develop new skills and confidence
  • Counts towards OR Society accreditation

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Support for volunteers

  • Hands on exercises
  • Case studies
  • Presentations

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STEM Ambassadors

  • Support people going into schools
  • Induction training with other ambassadors
  • Enhanced CRB check

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How to get involved

Contact a local school to offer your services

Your university or employer may have outreach links already

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Register as a volunteer with The OR Society

email: louise.orpin@theorsociety.com