Can you help the school plan the perfect guest list? Use linear programming to decide how many prefects and students to maximise social media likes without running out of time or goodie bag supplies. Learning/curriculum areas: • GCSE o Algebra notation, vocabulary and manipulation o Solving algebraic equations and inequalities o Calculations with integers o Graphs of equations and functions, interpreting graphs • A Level o Algebra and functions of inequalities • A Level: Decision/Discrete maths o Linear programming o Use graphical methods to solve constrained optimisation problems and/or two variable problems where integer solutions are required o (optional) Excel Solver

Workshop 5 - Cooking Bolognese (Critical Path Analysis) Have you got time to cook, wash up and eat before meeting your friends at the cinema? What time do you need to start cooking and how long will each step take? This workshop uses critical path analysis to solve problems. Curriculum areas covered: GCSE: apply the four operations to integers use standard units of time, using decimal quantities where appropriate A Level: Interpret and communicate solutions in the context of the original problem. Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics. A Level: Decision/Discrete maths Completion of the precedence table for a given activity network. Construct, represent and interpret a precedence (activity) network. Use critical path analysis and be able to interpret outcomes, including implications for criticality. Determine earliest and latest start and finish times for an activity network. Identify critical activities, critical paths and the float of non-critical activities. This pack includes:  Cover Sheet  Student Worksheet  Presentation  Teacher Notes  Diagram cards The OR technique featured in this workshop is critical path analysis. Critical path analysis is a popular project management tool, it shows the shortest time needed to complete a project and factors in which tasks are dependent on others. For more information visit our website: theorsociety .com

Game #5 - Theme Park (Travelling Salesman Problem) More Information Soon

Workshop 1 - Lego Furniture Factory (Linear Programming) Can you help furniture company SWEDEBUILD design a new furniture range and maximise their profit? Use Lego to model the furniture and work out which combination of tables and chairs is the most profitable, and then see if you can use algebra to reach the same answer. Curriculum areas covered: GCSE: Algebra notation, vocabulary and manipulation Solving algebraic equations and inequalities Calculations with integers Graphs of equations and functions, interpreting graphs A Level: Algebra and functions of inequalities A Level: Decision/Discrete maths: Linear programming Use graphical methods to solve constrained optimisation problems and/or two variable problems where integer solutions are required This pack includes:  Cover Sheet  Presentation  Teacher Notes  Student worksheet  Answer Sheet The OR technique behind this is optimization (minimum cost / maximum profit etc.). Linear programming is a commonly used OR technique and is also a major component of the Discrete/Decision module of Maths A Levels. For more information visit our website: theorsociety .com

Worksheet 4 - Prim’s/Kruskal’s algorithms A Prim’s/Kruskal’s algorithms based worksheet. Ideal for use an introductory task/homework. Curriculum areas covered: • Understand the language of networks including node, arc and weight • Solve network optimisation problems using spanning trees • Minimum spanning tree/minimum connector problem • Least weight route/set of arcs • Prim’s algorithm • Kruskal’s algorithm This pack includes:  Cover Sheet  Student worksheet  Answer Sheet Network problems and algorithms are common elements of Operational Research (OR). For more information visit our website: theorsociety .com

Game #7 - Sports Matching You’re the sports captain of your school and you’ve got to allocate students to different teams. They all have their favourite sports and some of them are very good at certain sports. Can you allocate them in the best way to ensure your school wins the sports day? Session Duration Guide  For Year 10-11 / Average ability groups: Allow 45-50 minutes  For Year 12-13 / High ability groups: Allow 30-45 minutes

Worksheet 5 - Save Earth (Critical Path Analysis) A critical path analysis based around scheduling a rocket launch to prevent a meteor strike. Ideal for use as an introductory task/homework, this worksheet is a fun example of critical path analysis. Curriculum areas covered: • A Level o Interpret and communicate solutions in the context of the original problem. o Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics. • A Level: Decision/Discrete maths o Completion of the precedence table for a given activity network. o Construct, represent and interpret a precedence (activity) network. o Use critical path analysis and be able to interpret outcomes, including implications for criticality. o Determine earliest and latest start and finish times for an activity network. o Identify critical activities, critical paths and the float of non-critical activities. o Refine models and understand the implications of possible changes in the context of critical path analysis. This pack includes:  Cover Sheet  Student worksheet  Answer Sheet Critical path analysis is a technique frequently used in Operational Research (OR). For more information visit our website: theorsociety .com

Algorithm information pack - a handy resource for revision or moments where students need reminding how to apply certain algorithms. Algorithms are frequently used in Operational Research (OR). For more information visit our website: theorsociety .com

Game #2 - Playing Snakes and Ladders - Climbing the Career Ladder (Algorithms) The aim of this pack is to introduce students to one of the topics of O.R. in a fun and engaging way. It uses a specially designed board game to engage students by moving around the board, and exploring the different careers and opportunities available to maths students. Perhaps you become a mathematical comedian and move forwards 4 spaces, or perhaps you buy the wrong plane for B.A. and move back 2 spaces! This then leads onto how a board game is designed, flow charts and the algorithms behind it. Aimed at: Secondary school  For Year 7-9 / Low ability groups: Allow 90 minutes  For Year 10-11 / Average ability groups: Allow 60 - 90 minutes  For Year 12-13 / High ability groups: Allow 60 minutes The material uses: Counting, Flow charts, Algorithms This pack includes:  Board game  Career profiles  Work experience cards  Cover sheet  Presentation  Video Q&A sheet  Teacher Notes Not included but provided on a school visit:  Counters  Dice The O.R. technique behind this is Algorithms. This information is also available online to download

Game #4 - Making Paper Cups - Paper Cup Challenge (Improving Processes) The aim of this pack is to introduce students to one of the topics of O.R. in a fun and engaging way. Firstly, we get students folding paper up, down and across to make paper cups. Then the challenge gets technical (and competitive!) - teams are timed building paper cups, and must organise the task into sub-tasks - such as folding or designing. This leads onto thinking about efficiency and process improvement. What worked? What didn’t? Lets time it and do it again! The students have a chance to make changes to their process before comparing the means, standard deviations and variances. Aimed at: Secondary school  For Year 7-9 / Low ability groups: Allow 90 - 120 minutes  For Year 10-11 / Average ability groups: Allow 60 - 90 minutes  For Year 12-13 / High ability groups: Allow 45 – 60 minutes The material uses: Mean, Variance, Standard Deviation, addition, subtraction This pack includes:  Student worksheet  Teacher notes  Presentation  Cover Sheet The O.R. technique behind this is simulation and improving processes (looking at the most efficient way of doing something). This information is also available online to download.

Worksheet 2 - Paper Rounds (Network Problems) A network problems worksheet including a paper round problem. Ideal for use an introductory task/homework, this worksheet demonstrates a real world example of network problems. Curriculum areas: • Understand the language of networks including node, arc and weight • Use networks to model the connections between objects This pack includes:  Cover Sheet  Student worksheet  Answer Sheet Network Problems are frequently solved using Operational Research (OR). For more information visit our website: theorsociety .com

 For Year 10-11 / Average ability groups: Allow 45-60 minutes  For Year 12-13 / High ability groups: Allow 45 minutes

Worksheet 1 - Staff Costs (Linear Programming) A linear programming problem based around staff costs for a shop. Ideal for use an introductory task/homework, this worksheet demonstrates a real world use of linear programming. Curriculum areas covered: • Formulate o constrained optimisation problems o problems as linear programs • Use graphical methods o to solve constrained optimisation problems o to solve two variable problems where integer solutions are required • Discuss the effect of changing one or two of the coefficients and how this will impact the solution • Investigate constraints and objectives in numerical cases using algebra and ad hoc methods This pack includes:  Cover Sheet  Student worksheet  Answer Sheet Linear Programming is a technique frequently used in Operational Research (OR). For more information visit our website: theorsociety .com

What resources have we uploaded? What are they about? Who are we? What is OR? This summarises our free resources and explains why we are passionate about ensuring every student knows what OR is. You can find more information about OR, OR in Education and our resources at theorsociety . com

Have you got time to bake a pie, wash up and eat before meeting your friends at the cinema? What time do you need to start cooking and how long will each step take? This workshop uses critical path analysis to solve problems. Curriculum areas covered: GCSE: apply the four operations to integers use standard units of time, using decimal quantities where appropriate A Level: Interpret and communicate solutions in the context of the original problem. Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics. A Level: Decision/Discrete maths Completion of the precedence table for a given activity network. Construct, represent and interpret a precedence (activity) network. Use critical path analysis and be able to interpret outcomes, including implications for criticality. Determine earliest and latest start and finish times for an activity network. Identify critical activities, critical paths and the float of non-critical activities. This pack includes:  Cover Sheet  Student Worksheet  Presentation  Teacher Notes  Diagram cards The OR technique featured in this workshop is critical path analysis. Critical path analysis is a popular project management tool, it shows the shortest time needed to complete a project and factors in which tasks are dependent on others. For more information visit our website: theorsociety . com

Workshop 3 - Theatre Bookings (Bin-Packing) You’re in charge of organising bookings and seating for a theatre company. You have to decide who sits where, if anyone sits by themselves, and what to do with people who book in a group. What’s the most efficient way to seat people? How do you take into account audience preferences? Did you know that there are bin-packing algorithms that can help? Curriculum areas covered: GCSE: whole number theory structure & calculation A-Level; Decision/Discrete maths: definition of an algorithm working with & implementing algorithms awareness of uses and limitations of algorithms bin packing algorithms This pack includes:  Cover Sheet  Theatre Modelling Pack (theatre seating grid and booking groups)  Presentation  Pros and Cons of Algorithms Sheet  Teacher Notes  Student worksheet  Answer Sheet The OR technique behind this is algorithm is more formally known as a bin packing algorithm because one is packing different groups sizes and seeing how many “bins” (i.e. rows, in this case) the group sizes fit in, in order to use up the minimum amount of space possible. For more information visit our website: theorsociety .com

Worksheet 3 - Courier Service (Travelling Salesperson) A travelling salesperson problem based around a courier service. Ideal for use an introductory task/homework, this worksheet demonstrates a real world example of the travelling salesperson problem. Curriculum areas covered: • Travelling salesperson problem • Determination and interpretation of upper bounds • Determination and interpretation of lower bounds • Real world factors that may influence the problem This pack includes:  Cover Sheet  Student worksheet  Answer Sheet Network problems are frequently encountered in Operational Research (OR). For more information visit our website: theorsociety .com