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HoDoMS www.mathscareers.org.uk Careers Strand - Working with Employers

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HoDoMS www.mathscareers.org.uk Over 30 clips Hosted on NCETM Website Sorted by GCSE topic www.ncetm.org.uk/resources/11329 Maths in Work

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HoDoMS www.mathscareers.org.uk Clips include: Scientific Instrument Designer (logs, loci, speed distance time, area, angles) Sports Engineer (projectiles, speed distance time, rate) Freelance Costume Designer (fractions, enlargement, multiplication) Environmental Officer (data handling skills, percentages, rates) Finance Officer (currency conversion, rounding, percentage change) Navigational Officer, P&O Ferries (Pythagoras, circle theorems, trig.)

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HoDoMS www.mathscareers.org.uk Maths in Navigation http://www.ncetm.org.uk/resources/12669

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HoDoMS www.mathscareers.org.uk Nuffield Bursaries Yr 12 students 4-6 week placement in July-August Nuffield foundation (www.nuffieldfoundation.org)www.nuffieldfoundation.org Cummins Turbo Technologies, Coventry University, Unipart, Rolls Royce, Women Business development Agency, Qinetiq, NHS, National Grid, Warwick Castle

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HoDoMS www.mathscareers.org.uk Applications of mathematics in real world context Problem based learning Learning outside the classroom Diversity in learning Mathematics BRIDGING THE GAP Contribution To Practice:

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HoDoMS www.mathscareers.org.uk 100 Pupils 4 Employers Year 10 and Year 12 days Maths at Work Days

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HoDoMS www.mathscareers.org.uk

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HoDoMS www.mathscareers.org.uk A “Fractional Factorial” Experiment

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Welcome

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(2) Project Resource Allocation Problem Your team is currently working on two different projects, both of which are important, but there is limited time in which to complete them You need to decide how to allocate our team’s time in order to maximise our payback Decisions, Decisions

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Every hour spent on Project 1 generates £40 payback; whereas every hour spent on Project 2 generates £30 payback Decisions, Decisions If the team spends 3 hours on Project 1 and 5 hours on Project 2, what will be the total payback? If the team spends X 1 hours on Project 1 and X 2 hours on Project 2, what will be the total payback? The formula for the total payback is.…………………………… Payback = (3 x £40) + (5 x £30) = £270 40 X 1 + 30 X 2

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Your team can spend a maximum of 250 hours on Project 1 due to the available expertise in the team Your team works for a maximum total of 500 hours per week on any projects Decisions, Decisions Write an inequality to represent this constraint using X 1, where X 1 is the number of hours spent on Project 1 Write an inequality to represent this constraint using and, where and are the total number of hours spent on Projects 1 and 2 respectively X 1 ≤ 250 X 1 + X 2 ≤ 500

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Plotting the Feasible Region Decisions, Decisions 100 200 300 400 500 500 400 300 200 100 0 X2X2 X1X1

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Finding the Optimal Solution Decisions, Decisions Optimum Direction Payback = 40 X 1 + 30 X 2 Optimum Solution X1 = 250 and X2 = 250 Payback = 40 X 1 + 30 X 2 = £17500

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(4) Asset Renewal Problem Purchasing a new piece of hardware costs £12,000 The cost of maintaining the hardware depends on the age of the hardware at the beginning of the year To avoid maintenance cost associated with older hardware, we can trade it in for newer kit at the end of the year Decisions, Decisions

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Objective: MINIMISE the TOTAL COST incurred over four years (Cost = Purchasing Costs + Maintenance Costs – Money Received from Trade-Ins) Decisions, Decisions Age of hardware at beginning of year Annual Maintenance Cost Trade in Price at the end of the period 0£2000£7000 1£4000£6000 2£5000£2000 3£9000£1000

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Examples (a) Purchase hardware and trade it in every year and purchase new hardware Decisions, Decisions 01234 Cost = £28000 £7000 Cost of Hardware £12000 Maintenance Costs £2000 Less Trade In - £7000 TOTAL COST £7000

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Examples (b) Purchase hardware, trading it in at the end of year 1 and then purchasing new hardware which is kept for the next 3 years Decisions, Decisions 01234 £7000 £21000 Cost = £28000 Cost of Hardware £12000 Maintenance Costs £2000 Less Trade In - £7000 TOTAL COST £7000 Cost of Hardware £12000 Maintenance Costs £2000 + £4000 + £5000 Less Trade In - £2000 TOTAL COST £21000

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All Possible Options In order to work out which the cheapest option would be out of all options we must first calculate the different options Decisions, Decisions 01234 £7000 £12000 £21000 £31000

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Finding the Optimum Solution Decisions, Decisions 01234 £7000 £12000 £21000 £31000

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Finding the Optimum Solution Decisions, Decisions 01234 £7000 £12000 £21000 £31000

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Finding the Optimum Solution Decisions, Decisions 01234 £7000 £12000 £21000 £31000

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Finding the Optimum Solution Decisions, Decisions 01234 £7000 £12000 £21000 £31000 Optimal Solution = Purchase new hardware after every 2 years

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Today we have touched on some of the maths we use in Project Management, but this is just one area of the business If you have enjoyed it, lots of what we have done today falls under the Operational Research Branch of Mathematics Operational Research includes: Mathematical Programming, Simulation, Forecasting, Game Theory, Decision Analysis Any Questions? Summary

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HoDoMS www.mathscareers.org.uk Other Maths at Work sessions included KPMG – Forensic accounting of a chocolate factory Barclays – Would you Give Banana inc a business loan? Cummins Turbo Technologies – Maths behind engineering problems

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HoDoMS www.mathscareers.org.uk What’s the Point of Maths ? Development Day around maths related careers For Mathematics Teachers and Careers Advisers Up to date information on jobs and new and emerging sectors Chance to speak to people currently employed in industry In association with CRAC

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HoDoMS www.mathscareers.org.uk Employers

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HoDoMS www.mathscareers.org.uk Posters and Resources All available in MMG in a Box Career Profiles www.mathscareers.org.uk

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HoDoMS www.mathscareers.org.uk Summary Maths in Work clips Maths at Work days STEM/IMA ambassadors do visit schools ACCA / RAF have dedicated teams which visit schools Nuffield Placements Showing how maths is used in the real world can be really inspiring and motivating to young people

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HoDoMS www.mathscareers.org.uk “ I’ve realised that maths is used in all types of work and it can be interesting” “I’ve realised it’s used every day” “I’ve realised that maths is used for a lot more things than I first thought” Finishing with some quotes…

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