Maths and science in design and technology
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Para educadores: diapositivas de la lección, apuntes de repaso listos para usar sobre Maths and science in design and technology (Design and Technology, Maths and Evaluation) — úsalos en tu lección, o presenta el tema como una actividad interactiva de clase que tus aprendices juegan como un juego en vivo.
Apuntes de la lección
Maths in design
- State ratio order and use compatible units. At drawing:real = 1:5, multiply a drawn length by 5 to obtain the corresponding real length. A resized screen image may no longer be measurable at its nominal scale; written dimensions state intended real sizes.
- Percentages need a base. If only 0.8 m² of a 1.0 m² sheet is useful and all remaining material is unusable, waste is (1.0 − 0.8)/1.0 × 100 = 20%. Do not call reusable offcuts waste without that assumption.
- Area uses squared units and volume cubic units. For the illustrated 2 × 3 × 4 cm cuboid, volume is 24 cm³. Circle area is πr² and circumference 2πr; identify radius versus diameter before substituting.
- A tolerance of 50.0 ± 0.5 mm permits dimensional limits of 49.5–50.5 mm, under the specified inspection procedure. It describes an acceptance range, not zero measurement uncertainty or an instruction that all tolerances must be small.
State ratio order and percentage base
Science in design
- Common loading modes include tension, compression, bending, torsion and shear. Torsion is a twisting effect associated with torque, and shear tends to make adjacent material slide. Magnetism can exert forces; it is a different kind of description rather than something that cannot load a material.
- Triangular bracing can reduce racking of a jointed framework. Actual stiffness, strength and stability depend on geometry, members, joints, loads and supports, so the presence of a triangle does not certify a structure.
- For a suitable constant-resistance model, V = IR. With R = 6 Ω, I = V/6 gives 1 A at 6 V and 2 A at 12 V. The plotted straight line is computed from this ideal model rather than a measured dataset. In a stated DC model P = VI; at 12 V and 2 A power is 24 W.
- For an ideal meshing pair, driven speed = driver speed × driver teeth/driven teeth. With 20 driving 60 teeth at 90 rpm, driven speed is 30 rpm. An external pair reverses direction; losses affect available power, and this is not a torque or strength specification.
- Efficiency compares useful output with total input on a consistent basis. For 60 J useful from 80 J input, efficiency is 75%; the other energy is transferred to less useful outputs rather than destroyed.
Ideal resistor model: R = 6 Ω
Using formulae
- Choose the formula, identify each quantity and convert units before substitution. Then calculate, state the relevant units and check scale and meaning. Carry adequate precision through working before final rounding.
- Shelf example: 800 mm = 80 cm, 200 mm = 20 cm and 18 mm = 1.8 cm. Volume = 80 × 20 × 1.8 = 2,880 cm³. Equivalently 2,880,000 mm³ ÷ 1,000 = 2,880 cm³. Geometric volume alone does not determine mass without a suitable density.
- Conversion factors apply to the dimension: 1 cm² = 100 mm² and 1 cm³ = 1,000 mm³. Similarly 600 × 400 mm = 240,000 mm² = 0.24 m². Applying only the linear factor to area or volume produces an incorrect result.
Volume uses three lengths
Costing and estimation
- Material cost = stated quantity × compatible price per unit. Add relevant labour and allocated overheads using a consistent costing method. Identify waste allowance, delivery, tax or other exclusions rather than calling a material-only total the complete project cost.
- Invented example: £12 materials + £8 labour = £20 stated cost, with all other costs and taxes excluded. A 25% mark-up on cost adds £5 and gives £25 selling price. Profit as a share of price is £5/£25 = 20%, showing why margin and mark-up are different.
- Use estimates to check a result and plan, then refine with measurements and justified allowances. Arithmetic accuracy does not establish actual demand, material performance or safe design; numerical models depend on their assumptions.
Invented price calculation
Connect the model to the decision
- Ask what the result means: an area estimates a sheet requirement, volume can inform a material quantity, a circuit model predicts one operating point, and a price example uses a chosen percentage base. State the assumptions that make the result applicable.
- Use measurements and appropriate tests to check a design prediction. A graph derived from an ideal formula is useful teaching evidence but is not an experimental validation or a complete product assessment.
Loading modes describe effects
Diapositivas
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Preguntas de práctica
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1.What is a ratio?
Easy- Aa comparison of two quantities
- Ba tool
- Ca joint
- Da finish
2.What is scale?
Easy- Aa type of material
- Ba joint
- Ca finish
- Dthe ratio of drawing size to real size
3.What is 25% of 80?
Easy- A40
- B8
- C20
- D25
4.What is the volume of a rectangular cuboid with length 2 cm, width 3 cm and height 4 cm?
Easy- A48 cm³
- B24 cm³
- C9 cm³
- D12 cm³
5.What is the area of a circle formula?
Easy- Aπr²
- B2πr
- Cπd
- Dr²
6.What is the circumference formula?
Easy- Aπr²
- Br²
- C4πr
- D2πr
7.A drawing at scale 1:2 shows 30 mm. What is the real length?
Easy- A32 mm
- B28 mm
- C60 mm
- D15 mm
8.A material costs £4 per metre. What is the cost of 3.5 m?
Easy- A£15
- B£14
- C£7.50
- D£12
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