hodoms careers strand - working with employers

HoDoMS

www.mathscareers.org.uk

Careers Strand - Working with Employers

HoDoMS


• Over 30 clips• Hosted on NCETM Website• Sorted by GCSE topic• www.ncetm.org.uk/resources/11329

Maths in Work

http://www.ncetm.org.uk/resources/11329

HoDoMS


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.)

HoDoMS


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

http://www.ncetm.org.uk/resources/12669

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Nuffield Bursaries

• Yr 12 students

• 4-6 week placement in July-August

• Nuffield foundation (www.nuffieldfoundation.org)

• Cummins Turbo Technologies, Coventry University, Unipart, Rolls Royce, Women Business development Agency, Qinetiq, NHS, National Grid, Warwick Castle

http://www.nuffieldfoundation.org/

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• 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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100 Pupils 4 EmployersYear 10 and Year 12 days

Maths at Work Days

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HoDoMS


A “Fractional Factorial” Experiment

Welcome

(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

Every hour spent on Project 1 generates £40 payback; whereas every hour spent on Project 2 generates £30 payback


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 X1 hours on Project 1 and X2 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 X1 + 30 X2

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


Write an inequality to represent this constraint using X1 , where X1 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

X1 ≤ 250

X1 + X2 ≤ 500

Plotting the Feasible Region


100 200 300 400 500

500

400

300

200

100

0

X2

X1

Finding the Optimal Solution


100 200 300 400 500

500

400

300

200

100

0

X2

X1

Optimum Direction

Payback = 40 X1 + 30 X2

Optimum SolutionX1 = 250 and X2 = 250Payback = 40 X1 + 30 X2 = £17500

(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


Objective: MINIMISE the TOTAL COST incurred over four years

(Cost = Purchasing Costs + Maintenance Costs – Money Received from Trade-Ins)


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

Examples

(a) Purchase hardware and trade it in every year and purchase new hardware


0 1 2 3 4

Cost = £28000£7000 £7000 £7000 £7000

Cost of Hardware £12000Maintenance Costs £2000Less Trade In - £7000

TOTAL COST £7000

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


0 1 2 3 4

£7000

£21000 Cost = £28000

Cost of Hardware £12000Maintenance Costs £2000Less Trade In - £7000

TOTAL COST £7000

Cost of Hardware £12000Maintenance Costs £2000 + £4000 + £5000Less Trade In - £2000

TOTAL COST £21000

All Possible OptionsIn order to work out which the cheapest option would be out of all

options we must first calculate the different options


0 1 2 3 4£7000 £7000 £7000 £7000

£12000 £12000 £12000

£21000 £21000

£31000

Finding the Optimum Solution


0 1 2 3 4£7000 £7000 £7000 £7000

£12000 £12000 £12000

£21000 £21000

£31000



0 1 2 3 4£7000 £7000

£12000 £12000 £12000

£21000 £21000

£31000



0 1 2 3 4£7000 £7000

£12000 £12000

£21000

£31000

Optimal Solution = Purchase new hardware after every 2 years

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

HoDoMS


Other Maths at Worksessions 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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www.mathscareers.org.ukWhat’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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Employers

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www.mathscareers.org.ukPosters and Resources

• All available in MMG in a Box

Career Profiles

• www.mathscareers.org.uk

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www.mathscareers.org.ukSummary

• 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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“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…

hodoms careers strand - working with employers

Documents

decisions slide

payback decisions

year decisions

years decisions

projects decisions

new hardware decisions

tradeins decisions

decisions age of hardware