Engineering Maths Skills ProgrammeCurriculum map · planning document
GCSE Maths in Engineering · Scheme of work
The whole
curriculum
Every content area of GCSE Mathematics mapped to an engineering job that needs it. Twenty-three modules in total: five already built, eighteen proposed, each with a scenario and a suggested interaction. Nothing here is a topic wearing a hard hat — each scenario is a job where the maths genuinely decides the outcome.
Modules23
Built5 · 60 marks
Proposed18
Full programme276 marks
01
Coverage by domain
The six DfE content areasN
Number
2 built · 5 proposed| Curriculum content | Module | Engineering scenario | Status |
|---|---|---|---|
| Place value, four operations, factors, multiples, primes, HCF and LCM | Gear TrainsModule 08 | A gearbox with a hunting tooth: how many turns before the same two teeth meet again?Drag gears together to mesh them | Proposed |
| Fractions, decimals, ordering, converting between systems | The Spanner DrawerModule 07 | Imperial and metric fasteners in one toolbox — which spanner actually fits?Drag spanners onto bolts, sort a drawer into order | Proposed |
| Indices, roots and index laws | The Spanner DrawerModule 07 | Unit prefixes and index laws: why kN·m and N·mm are the same quantity.Tile-matching pairs | Proposed |
| Standard form | Sizing a Cable RunModule 03 | Resistivity of copper at 1.72×10⁻⁸ Ω m in a volt drop calculation.Drag the machine along the floor | Built |
| Percentages, including reverse and repeated change | Quoting the JobModule 09 | Build a customer quotation: markup, trade discount, VAT, then work backwards from the price paid.Assemble a quote from draggable line items | Proposed |
| Rounding, estimation, error intervals and bounds | Limits & FitsModule 06 | A shaft machined to Ø25.00 ±0.02 into a hole at +0.05/−0.00. Will every pair assemble?Virtual micrometer — turn the thimble to measure | Proposed |
| Exact calculation and degree of accuracy | Batching a Concrete BaseModule 02 | Cement by mass, then rounded up to whole 25 kg bags.Drag sacks into the mixer drum | Built |
A
Algebra
1 built · 5 proposed| Curriculum content | Module | Engineering scenario | Status |
|---|---|---|---|
| Notation, substitution, expanding and factorising | The Guard EnclosureModule 12 | Fixed length of mesh guarding around a robot cell — write the area as an expression.Drag the enclosure corners | Proposed |
| Rearranging formulae and changing the subject | Sizing a Cable RunModule 03 | Make length the subject to find the longest run a cable will stand.Isolator switch bank | Built |
| Linear equations, straight-line graphs, gradient and intercept | Sensor CalibrationModule 10 | A pressure transducer’s output plotted against true pressure: gradient is sensitivity, intercept is offset.Tap the graph to plot readings, drag the best-fit line | Proposed |
| Simultaneous equations, algebraic and graphical | Two Pumps, One TankModule 11 | Two pumps of unknown flow rate. Two timed fills give two equations.Drag two lines to their intersection | Proposed |
| Quadratics: solving, graphs and turning points | The Guard EnclosureModule 12 | Maximum floor area from a fixed perimeter — the turning point is the answer.Live parabola beside the plan view | Proposed |
| Inequalities and regions | The Guard EnclosureModule 12 | Minimum clearance and maximum footprint expressed as a feasible region.Shaded region updates as corners move | Proposed |
| Reciprocal and exponential graphs | Setting CNC Cutting SpeedsModule 04 | Spindle speed against cutter diameter — a reciprocal curve with a machine ceiling across it.Rotary speed dial | Built |
| Real-life graphs and rate of change | The Cooling CurveModule 13 | A casting cooling overnight: exponential decay, and the rate read off a tangent.Tap a timeline to take temperature samples | Proposed |
| Sequences, nth term, arithmetic and geometric | Production Ramp-UpModule 14 | Output rises by a fixed number of units each shift — when does the line hit target?Step through shifts and build the sequence | Proposed |
R
Ratio, proportion and rates of change
3 built · 3 proposed| Curriculum content | Module | Engineering scenario | Status |
|---|---|---|---|
| Units, compound units and scale drawings | Bearings & the PipelineModule 17 | A site plan at 1:2500 — convert drawn lengths to real ones.Place waypoints on a scaled site plan | Proposed |
| Ratio, sharing and equivalent ratios | Batching a Concrete BaseModule 02 | 1:2:4 by mass — and why 2:4:8 is the same concrete.Drag-and-drop materials | Built |
| Percentage change, growth and decay | The Cooling CurveModule 13 | Temperature falling by a fixed percentage each interval.Sampling taps on a timeline | Proposed |
| Compound measures: speed, density, pressure, flow | The Hydraulic JackModule 21 | Pascal’s law: a small force on a small piston lifts a car. Pressure is the constant.Pump the handle, watch pressure and force | Proposed |
| Direct and inverse proportion | Setting CNC Cutting SpeedsModule 04 | Halve the cutter diameter and the spindle speed doubles.Tool rack picker | Built |
| Density and mass | Sizing a Hydraulic TankModule 05 | Steel plate and hydraulic oil, by volume and by mass.Corner resize grip | Built |
G
Geometry and measures
2 built · 7 proposed| Curriculum content | Module | Engineering scenario | Status |
|---|---|---|---|
| Angles, parallel lines and polygon properties | Plans & ElevationsModule 16 | Reading angles off a folded sheet-metal bracket.Orbit the isometric part by dragging | Proposed |
| Congruence, similarity and scale factors for area and volume | Scaling the PrototypeModule 15 | A half-scale model weighs an eighth as much. The square-cube law, and why it bites.Drag a scale factor, models side by side | Proposed |
| Constructions, loci and bearings | The Robot CellModule 23 | Safe working envelope of a robot arm: loci, exclusion zones and bisected walkways.Construct arcs and bisectors by clicking | Proposed |
| Pythagoras and right-angled trigonometry, including exact values | Sizing a Footbridge TrussModule 01 | Diagonal length and angle of a truss member.Drag the top chord grip | Built |
| Sine rule, cosine rule and area = ½ab sin C | The Crane JibModule 19 | A jib, a tie and a mast form a non-right-angled triangle. Find the reach.Swing the jib through its arc | Proposed |
| Circles: arcs, sectors, tangents and circle theorems | Belt Drives & PulleysModule 18 | Belt length round two pulleys — tangents, radii and wrap angle.Drag pulley centres apart | Proposed |
| Perimeter, area, volume and surface area of prisms, cylinders, cones and spheres | Sizing a Hydraulic TankModule 05 | A reservoir sized three ways: capacity, plate area, plate mass.Corner resize grip | Built |
| 3D representation, plans and elevations | Plans & ElevationsModule 16 | Match a machined part to its correct front, side and plan views.Rotate the part, drag views to match | Proposed |
| Transformations and vectors | Bracket ForcesModule 20 | Two forces on a bracket resolved into a resultant — vector addition made physical.Drag arrowheads to set each force | Proposed |
P
Probability
0 built · 1 proposed| Curriculum content | Module | Engineering scenario | Status |
|---|---|---|---|
| Probability scale, relative frequency, expected outcomes | Reliability & RedundancyModule 22 | A conveyor with three motors. What is the chance the line stops this month?Build a system by wiring components | Proposed |
| Tree diagrams, Venn diagrams, independent and conditional events | Reliability & RedundancyModule 22 | Series and parallel reliability: why a backup pump changes everything.Drag components into series or parallel | Proposed |
S
Statistics
0 built · 1 proposed| Curriculum content | Module | Engineering scenario | Status |
|---|---|---|---|
| Sampling, averages, range and spread | Process ControlModule 23 | Sample five parts an hour off a running line and plot the mean.Tap the line to take a sample | Proposed |
| Charts: histograms, box plots, cumulative frequency | Process ControlModule 23 | Batch variation shown three ways — and which chart an inspector actually uses.Switch chart type, same data | Proposed |
| Scatter graphs, correlation and lines of best fit | Sensor CalibrationModule 10 | Does the sensor drift with temperature? Plot it and see.Drag the best-fit line | Proposed |
02
Suggested delivery order
Four blocksBlock A
Measurement and number
Foundations. Everything downstream assumes these.
- 07 The Spanner Drawer
- 06 Limits & Fits
- 02 Batching a Concrete Base
- 09 Quoting the Job
- 08 Gear Trains
Block B
Shape, space and structure
The geometry strand, built around things that get fabricated.
- 01 Sizing a Footbridge Truss
- 05 Sizing a Hydraulic Tank
- 16 Plans & Elevations
- 15 Scaling the Prototype
- 18 Belt Drives & Pulleys
- 19 The Crane Jib
- 17 Bearings & the Pipeline
Block C
Formulae, graphs and modelling
Algebra in the form engineers actually meet it.
- 03 Sizing a Cable Run
- 04 Setting CNC Cutting Speeds
- 10 Sensor Calibration
- 11 Two Pumps, One Tank
- 12 The Guard Enclosure
- 13 The Cooling Curve
- 14 Production Ramp-Up
- 21 The Hydraulic Jack
Block D
Uncertainty and control
The strand engineering courses skip most often, and industry relies on most.
- 20 Bracket Forces
- 23 The Robot Cell
- 22 Reliability & Redundancy
- 23 Process Control
03
Gaps and judgement calls
Read before commissioningSpec references need checking
The five built modules carry codes in the style of a single awarding body. Boards number their content differently, so before publication these should be re-mapped against whichever specification your centres actually deliver. This map deliberately uses topic names rather than codes for that reason.
Probability and statistics are the real gap
Two of the six domains have no built module at all, and they are the two that engineering teaching most often skips. Reliability, tolerance distributions and process control are the daily bread of quality engineering, and they map almost perfectly onto tree diagrams, histograms and scatter graphs. If you commission only two more modules, make them 22 and 23.
Some topics resist an honest engineering setting
Circle theorems, surds and algebraic proof are hard to place in a real workshop without inventing a contrivance. Modules 18 and 07 get partway there through belt geometry and unit algebra, but a learner needing full Higher coverage of these will still need conventional teaching alongside. Better to say so than to bolt a fake context onto a page of pure algebra.
Foundation and Higher are not separated here
Each module currently spans grades 4 to 9 by stretching within one context. That works up to a point, but a Foundation-only cohort will find modules 12, 19, 20 and 22 heavy going. A tiered variant of each — same scenario, different question ladder — would be a cheaper route to full coverage than writing separate modules.
Produced for EAL engineering learners.
Planning document — module scenarios and interactions are proposals, not commitments.