# The OR Society's Shop

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OR is all about using maths and analytics to solve problems and make better decisions. We want all students to be aware of OR, it is a fascinating area and leads to many rewarding careers. These resources are available to help teachers introduce OR to their students. They are suitable for all high school students. Each resource includes an overview of the curriculum areas it covers.

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OR is all about using maths and analytics to solve problems and make better decisions. We want all students to be aware of OR, it is a fascinating area and leads to many rewarding careers. These resources are available to help teachers introduce OR to their students. They are suitable for all high school students. Each resource includes an overview of the curriculum areas it covers.

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#### Worksheet 4: Prim's/Kruskal's Algorithms

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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: https://www.theorsociety.com/what-we-do/or-in-schools/for-teachers/

#### Worksheet 5: Critical Path Analysis: Save Earth

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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: https://www.theorsociety.com/what-we-do/or-in-schools/for-teachers/

#### Workshop 5 - Cooking Bolognese (Critical Path Analysis)

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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: https://www.theorsociety.com/what-we-do/or-in-schools/for-teachers/

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#### Worksheet 3: Travelling Salesperson: Courier Service

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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: https://www.theorsociety.com/what-we-do/or-in-schools/for-teachers/

#### Algorithm Info Pack

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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: https://www.theorsociety.com/what-we-do/or-in-schools/for-teachers/

#### Workshop 1 - Lego Furniture Factory (Linear Programming)

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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: https://www.theorsociety.com/what-we-do/or-in-schools/for-teachers/

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#### Worksheet 1: Linear Programming: Staff Costs

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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: https://www.theorsociety.com/what-we-do/or-in-schools/for-teachers/

#### Worksheet 2: Network Problems: Paper Round

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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: https://www.theorsociety.com/what-we-do/or-in-schools/for-teachers/

#### Outline and Overview of Resources Available

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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 www.theorsociety.com

#### Workshop 3 - Theatre Bookings (Bin-Packing)

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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 &amp; calculation A-Level; Decision/Discrete maths: definition of an algorithm working with &amp; 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: https://www.theorsociety.com/what-we-do/or-in-schools/for-teachers/

#### Workshop 5b - Pi Day Pie (Critical Path Analysis)

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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: https://www.theorsociety.com/what-we-do/or-in-schools/for-teachers/

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