Sec 3 G3 Maths Bukit Timah | Parcel Delivery Rates

Secondary 3 G3 Mathematics Tutor Bukit Timah | Parcel Delivery Mathematics: Weight Bands, Flat Fees and Cost Comparisons — Did you know? A parcel weighing 1.01 kg can be charged as two kilograms in a fictional ‘per started kilogram’ pricing model. Yet under a different model charging exactly for measured mass, the bill changes smoothly rather than jumping at a boundary. This contrast helps Secondary 3 G3 Mathematics students understand unit conversion, inequalities, piecewise pricing and whole-number rounding. Read the charging rule first; the same parcel can have several different mathematically correct prices under different rules.

Quick answer: Convert every parcel mass to kilograms first (1 kg = 1,000 g). A linear charge might be fixed fee + rate per kg × mass. A per-started-kilogram charge uses ceil(mass in kg) units. A flat weight band charges the named band price, while marginal bands charge the amounts within each tier. These are different structures. All rates and services in the examples are invented and are not live courier quotations or shipping rules.

The 2027 SEC G3 Mathematics K310 syllabus includes rates, proportional reasoning, inequalities, algebraic modelling, unit conversion and contextual problem-solving. Parcel delivery is an original application of those tools, not a prediction of a particular examination story or a guide to real shipping regulations. Follow the current school chapter schedule and the terms explicitly provided in each exercise.

Quick reference: the meaning of each delivery-rate model

Mass conversion: 1 kg = 1,000 g; divide grams by 1,000 to obtain kilograms.
Exact per-kilogram rate: price = base fee + kg × stated dollars/kg.
Per started kilogram: billable units = smallest whole integer at least as large as measured kg.
Per started 500 g: billable units = ceil(mass in g/500), if the question explicitly defines that interval.
Flat weight band: choose the one price for the interval containing the measured mass.
Marginal weight tiers: divide the mass among the priced bands and add each band’s charge.
Weight limit: a parcel outside the stated limit may be disallowed, not merely charged more.
Multiple parcels: add individually priced totals or price a combined shipment only if consolidation is expressly allowed.
Volume: length × width × height for a rectangular parcel; a real carrier’s chargeable-weight formula cannot be assumed without its rule.
Budget and comparisons: include all stated fixed fees and use the same parcel mass for competing options.

How to read and model a fictional delivery price

A weight conversion comes before a rate calculation

An imaginary parcel labelled 1,250 grams has mass 1.25 kilograms. If a price is quoted in dollars per kilogram, using the number 1,250 instead of 1.25 would multiply the result by a thousand. The conversion 1 kg=1,000 g is a simple but decisive first step.

Write the unit beside the number before substituting into the equation. If a mass in grams is smaller than one thousand, its kilogram value must be less than one. An independent reverse check multiplies the converted kilogram value by one thousand to reproduce the printed grams.

Some charges rise continuously with the mass

In a model charging S$3 for every kilogram used without any upward weight rounding, a 1.5 kg parcel costs S$4.50 before fixed fees. A parcel of 1.6 kg costs S$4.80. The cost is directly proportional to mass when there is no base fee and the rate is fixed.

This continuous model is deliberately simplified. A student should not automatically round the mass to two kilograms unless the question says ‘per started kilogram’ or gives a tiered billing rule. Pricing the same package under two different models is a useful method-selection test.

A fixed fee gives a linear expression with a nonzero intercept

If a fictional courier charges S$4 base handling and S$3 per exact kilogram, then C=4+3m for mass m in kg. At zero measured mass, the mathematical expression would still be S$4, though a real delivery might not accept a zero-weight parcel.

The fixed charge belongs once per delivery under this stated model. In a graph of cost against mass, it is the y-intercept, while the three-dollar-per-kilogram rate is the slope. This connects everyday pricing to N6 straight-line relationships.

Per-started-kilogram pricing is a staircase

Suppose the model charges S$5 per started kilogram. A 1.00 kg parcel incurs one S$5 unit, while a 1.01 kg parcel incurs two S$5 units. The billed count is ceil(m), where m is the weight in kilograms. The price has jumps at whole-kilogram boundaries.

When the measured mass is exactly an integer, do not add an extra unit. The condition ‘every started kilogram’ treats 2.00 kg as two units and any amount greater than two, up to three, as three units. A number-line sketch makes the boundary rule clearer.

A flat band is not the same as a per-kilogram price

A hypothetical schedule might say up to 2 kg: S$6; above 2 kg to 5 kg: S$10; above 5 kg: S$15. A 4 kg parcel pays S$10 under that schedule, not four times a rate inferred from the first band.

The interval definitions matter. The words ‘up to’ normally include the boundary; ‘above’ excludes it. A correct answer identifies the single matching band and states the chosen price. Do not invent fractional band charges when the model gives flat prices.

Marginal tiers charge separate portions

An invented tariff might charge the first 2 kg at S$4/kg and every kilogram beyond that at S$3/kg. A 5 kg parcel costs 2×4+3×3=S$17. It is wrong to multiply all 5 kg by S$3 or all 5 by S$4.

Make a short two-row table listing weight in each tier and its rate. The total weight in the rows should add back to the parcel mass. This is the same mathematical structure as tiered utility pricing and piecewise data tables.

A minimum or maximum can create a constraint

Suppose an exercise states that a service permits parcels of at most 10 kg. A 10.1 kg item lies outside the allowed domain and cannot be assigned a valid price without another given rule. The problem has not said the courier will simply accept it at the next band.

Mathematical modelling includes knowing when a proposed input fails the stated conditions. A calculation outside the permissible interval can produce a number but not a valid answer to the delivery question. Label the inequality before pricing the parcel.

The word ‘per parcel’ matters with multiple items

If a fixed S$3 handling fee applies to each separately shipped parcel, sending four parcels incurs four handling fees. If the question instead offers one consolidated shipment with a single handling fee, the total can differ even when combined measured weight is unchanged.

The two models are not automatically interchangeable. Consolidating parcels may be prohibited or permitted under the question; only the given conditions decide. A learner should identify how many times each fixed fee is charged before computing the variable amount.

Consolidation may save billable units when rounding applies

Consider three parcels of 0.6 kg each and a model priced per started kilogram. Separate parcels each count as one kilogram, so three billable units result. If consolidation into one parcel is expressly allowed, total mass is 1.8 kg, giving two billable units.

This is a mathematical example of rounding before versus after addition. The result depends on actual pricing terms and packaging restrictions, which are not modelled here unless stated. It is an excellent opportunity to compare two valid calculation orders.

A parcel’s box volume is separate from its mass

A rectangular package 20 cm by 15 cm by 10 cm has volume 3,000 cm³, or three litres. Nothing in those dimensions alone determines its mass. A light item and a dense item could occupy the same box while weighing differently.

Some real logistics companies use dimensional-weight pricing, but the conversion rule varies. In a classroom problem, never guess a chargeable-weight factor. Use a dimensional weight only when the question expressly supplies the formula and relevant dimensions.

Choosing a cost comparison needs the full total

Two hypothetical options might be A: S$8 handling plus S$3/kg, and B: S$5/kg without handling. For 2 kg, A costs S$14 and B costs S$10. For 6 kg, A costs S$26 and B costs S$30. Neither is cheaper across every positive weight.

Equating 8+3m=5m gives a break-even weight of 4 kg in this model. This is a straight-line intersection problem; an honest conclusion states the mass and the applicable assumptions rather than declaring one company always cheaper.

Piecewise tariffs can have discontinuities

A flat band can jump from S$6 to S$10 as mass passes 2 kg even when the mass changes only slightly. A simple linear rate changes smoothly. Graphing price against mass reveals why two schedules that look similar in a table can behave differently at boundaries.

A tutor can draw a small number line with 2 kg and 5 kg marked. Ask pupils whether 2.00, 2.01 and 5.00 kg belong in the same interval. Reading the inequality accurately is often the key skill, not complex calculation.

Whole-pack and carton capacity uses a ceiling

If an imaginary shipping batch needs eleven one-kilogram packages and each carton holds at most five of them, three cartons are required. Two hold only ten. This is the same integer interpretation used for coach seats and material packs.

The ceiling depends on a countable unit. Do not round a monetary cost to the next whole dollar unless the question requests it. Rounding rules follow the object or pricing contract, not the student’s preference.

A weight-based quote is not automatically a delivery promise

The examples do not include real customs, volumetric weight thresholds, insurance, prohibited goods, geography, service speed, taxes or carrier terms. Those may materially change an actual quote. This article is designed to teach the Mathematics of stated schedules.

The learning goal is to identify the fee structure and apply its quantities correctly. Students should avoid inferring a live price, delivery availability or permitted shipment from fictional classroom numbers.

Unit cancellation makes a checking route

Dollars per kilogram multiplied by kilograms gives dollars. Kilograms divided by kilograms per parcel would give a count under a suitable model. If an attempted calculation leaves kg² or dollars per kg when a dollar total is requested, review the operation.

Writing units explicitly helps with longer word problems that mix grams, kilograms, box volumes and fixed charges. The final sentence should state whether the result is billable kilograms, parcel count or currency amount.

The simplest correct answer can include ‘insufficient data’

If a question gives only the rate of S$5 per kilogram but no parcel mass, one cannot calculate a total cost. Similarly, knowing a box’s dimensions without the relevant pricing rule is not enough for a delivery quote.

Recognising which variable is missing is an important reasoning skill under the SEC Mathematics objectives. The point is not to invent extra data simply because the question resembles a previous worksheet.

A tutor should teach the price structure first

Give students three schedules for the same 2.4 kg parcel: exact-mass rate, per-started-kilogram rate and one flat band. Ask them to circle which rounding rule applies, then work the arithmetic independently. Different answers may all be correct under different given contracts.

A follow-up with weight exactly on a boundary can expose whether the student understood ‘up to’ and ‘above’. A later problem with a different mass and the labels removed helps test genuine method selection.

K310 application does not promise a shipping-topic exam

The 2027 G3 Mathematics syllabus includes rates, percentages, equations, inequalities and real-world modelling. Parcel delivery is one original way to join those skills, not a claim that courier regulations are a required syllabus chapter.

The classroom standard remains the same: define the quantity, match units, choose the correct mathematical rule, justify any whole-number step and check the answer against the original conditions.

50 worked examples: weights, bands and prices

These are original teaching examples using completely invented weight bands and fees. They are not current courier prices, real service terms or official SEC exam questions. Ten distinct models appear in five numerical variations each. Before calculating, identify whether the price is exact per kilogram, rounded per started kilogram, flat per band or a marginal tier. Then check the selected model at its boundary.

Convert parcel grams into kilograms

This group practises convert parcel grams into kilograms. State the weight unit and pricing convention before multiplying or rounding. Five numerical variations test whether a learner can recognise the same rule even when the boundary changes.

Worked example 1. Question: A fictional parcel has measured mass 750 g. Express it in kilograms. Method: Divide by 1,000: 750/1000=0.75 kg. Independent check: Multiplying 0.75 kg by 1,000 returns 750 g. Watch for: A gram number cannot be inserted directly into a rate stated per kilogram.

Independent extension: Convert grams to kilograms before applying any quoted dollars-per-kilogram rate. Change parcel mass by a small amount across a band boundary and predict whether the charge jumps. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 2. Question: A fictional parcel has measured mass 1000 g. Express it in kilograms. Method: Divide by 1,000: 1000/1000=1 kg. Independent check: Multiplying 1 kg by 1,000 returns 1000 g. Watch for: A gram number cannot be inserted directly into a rate stated per kilogram.

Independent extension: Name whether the price includes a fixed fee once or for each parcel. Draw a small graph of cost against mass for the particular pricing rule. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 3. Question: A fictional parcel has measured mass 1250 g. Express it in kilograms. Method: Divide by 1,000: 1250/1000=1.25 kg. Independent check: Multiplying 1.25 kg by 1,000 returns 1250 g. Watch for: A gram number cannot be inserted directly into a rate stated per kilogram.

Independent extension: Do not apply a ceiling unless the fictional schedule expressly uses started units. Compare a second fictional price plan using the same parcel mass. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 4. Question: A fictional parcel has measured mass 1500 g. Express it in kilograms. Method: Divide by 1,000: 1500/1000=1.5 kg. Independent check: Multiplying 1.5 kg by 1,000 returns 1500 g. Watch for: A gram number cannot be inserted directly into a rate stated per kilogram.

Independent extension: At an exact kilogram boundary, check whether an extra billed unit really begins. Explain why the rule would give a different price if the item were sent separately. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 5. Question: A fictional parcel has measured mass 1750 g. Express it in kilograms. Method: Divide by 1,000: 1750/1000=1.75 kg. Independent check: Multiplying 1.75 kg by 1,000 returns 1750 g. Watch for: A gram number cannot be inserted directly into a rate stated per kilogram.

Independent extension: Keep flat band schedules separate from marginal weight tiers. Construct a reverse calculation to find which mass produced the given variable charge. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Price an exact-kilogram-rate model

This group practises price an exact-kilogram-rate model. State the weight unit and pricing convention before multiplying or rounding. Five numerical variations test whether a learner can recognise the same rule even when the boundary changes.

Worked example 6. Question: An invented service charges S$4 per exact kilogram with no fixed fee or upward rounding. Find charge for 1 kg. Method: Cost=1 kg×S$4/kg=S$4.00. Independent check: Dividing cost S$4.00 by 1 kg recovers the given S$4/kg rate. Watch for: Do not round the mass upward when the pricing model explicitly says exact mass.

Independent extension: Read interval wording such as ‘at most’ and ‘above’ before choosing a tariff. State which additional real-world carrier conditions would be needed for an actual quotation. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 7. Question: An invented service charges S$4 per exact kilogram with no fixed fee or upward rounding. Find charge for 1.25 kg. Method: Cost=1.25 kg×S$4/kg=S$5.00. Independent check: Dividing cost S$5.00 by 1.25 kg recovers the given S$4/kg rate. Watch for: Do not round the mass upward when the pricing model explicitly says exact mass.

Independent extension: If consolidation is allowed, compare rounding before and after combining measured mass. Change parcel mass by a small amount across a band boundary and predict whether the charge jumps. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 8. Question: An invented service charges S$4 per exact kilogram with no fixed fee or upward rounding. Find charge for 1.5 kg. Method: Cost=1.5 kg×S$4/kg=S$6.00. Independent check: Dividing cost S$6.00 by 1.5 kg recovers the given S$4/kg rate. Watch for: Do not round the mass upward when the pricing model explicitly says exact mass.

Independent extension: Use a rate × mass calculation to reconstruct the variable cost for a linear schedule. Draw a small graph of cost against mass for the particular pricing rule. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 9. Question: An invented service charges S$4 per exact kilogram with no fixed fee or upward rounding. Find charge for 1.75 kg. Method: Cost=1.75 kg×S$4/kg=S$7.00. Independent check: Dividing cost S$7.00 by 1.75 kg recovers the given S$4/kg rate. Watch for: Do not round the mass upward when the pricing model explicitly says exact mass.

Independent extension: Label currency and weight in every step rather than writing only numbers. Compare a second fictional price plan using the same parcel mass. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 10. Question: An invented service charges S$4 per exact kilogram with no fixed fee or upward rounding. Find charge for 2 kg. Method: Cost=2 kg×S$4/kg=S$8.00. Independent check: Dividing cost S$8.00 by 2 kg recovers the given S$4/kg rate. Watch for: Do not round the mass upward when the pricing model explicitly says exact mass.

Independent extension: Check that a proposed parcel satisfies any permitted maximum or stated minimum. Explain why the rule would give a different price if the item were sent separately. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Price per started whole kilogram

This group practises price per started whole kilogram. State the weight unit and pricing convention before multiplying or rounding. Five numerical variations test whether a learner can recognise the same rule even when the boundary changes.

Worked example 11. Question: A fictional tariff charges S$5 per started kilogram, with no base fee. What is the price for 1 kg? Method: Billable units=ceil(1)=1. Price=1×S$5=S$5.00. Independent check: The quantity fits within 1 full kilogram billing units; 0 units would not fit it unless the mass lies at that exact lower bound. Watch for: A noninteger weight is rounded up only because the stated pricing rule requires it.

Independent extension: Revisit a changed tariff after two days, with the worked model hidden. Construct a reverse calculation to find which mass produced the given variable charge. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 12. Question: A fictional tariff charges S$5 per started kilogram, with no base fee. What is the price for 1.25 kg? Method: Billable units=ceil(1.25)=2. Price=2×S$5=S$10.00. Independent check: The quantity fits within 2 full kilogram billing units; 1 units would not fit it unless the mass lies at that exact lower bound. Watch for: A noninteger weight is rounded up only because the stated pricing rule requires it.

Independent extension: Convert grams to kilograms before applying any quoted dollars-per-kilogram rate. State which additional real-world carrier conditions would be needed for an actual quotation. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 13. Question: A fictional tariff charges S$5 per started kilogram, with no base fee. What is the price for 1.5 kg? Method: Billable units=ceil(1.5)=2. Price=2×S$5=S$10.00. Independent check: The quantity fits within 2 full kilogram billing units; 1 units would not fit it unless the mass lies at that exact lower bound. Watch for: A noninteger weight is rounded up only because the stated pricing rule requires it.

Independent extension: Name whether the price includes a fixed fee once or for each parcel. Change parcel mass by a small amount across a band boundary and predict whether the charge jumps. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 14. Question: A fictional tariff charges S$5 per started kilogram, with no base fee. What is the price for 1.75 kg? Method: Billable units=ceil(1.75)=2. Price=2×S$5=S$10.00. Independent check: The quantity fits within 2 full kilogram billing units; 1 units would not fit it unless the mass lies at that exact lower bound. Watch for: A noninteger weight is rounded up only because the stated pricing rule requires it.

Independent extension: Do not apply a ceiling unless the fictional schedule expressly uses started units. Draw a small graph of cost against mass for the particular pricing rule. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 15. Question: A fictional tariff charges S$5 per started kilogram, with no base fee. What is the price for 2 kg? Method: Billable units=ceil(2)=2. Price=2×S$5=S$10.00. Independent check: The quantity fits within 2 full kilogram billing units; 1 units would not fit it unless the mass lies at that exact lower bound. Watch for: A noninteger weight is rounded up only because the stated pricing rule requires it.

Independent extension: At an exact kilogram boundary, check whether an extra billed unit really begins. Compare a second fictional price plan using the same parcel mass. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Price per started five hundred grams

This group practises price per started five hundred grams. State the weight unit and pricing convention before multiplying or rounding. Five numerical variations test whether a learner can recognise the same rule even when the boundary changes.

Worked example 16. Question: A hypothetical parcel of 600 g is charged S$2 per started 500 g, with no other fees. Find its charge. Method: Billable units=ceil(600/500)=ceil(1.2)=2. Price=2×S$2=S$4.00. Independent check: The 2 units cover 1000 g, which is at least 600 g; one fewer unit would be insufficient. Watch for: Do not confuse 500 g intervals with 500 kg intervals or exact proportional billing.

Independent extension: Keep flat band schedules separate from marginal weight tiers. Explain why the rule would give a different price if the item were sent separately. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 17. Question: A hypothetical parcel of 830 g is charged S$2 per started 500 g, with no other fees. Find its charge. Method: Billable units=ceil(830/500)=ceil(1.66)=2. Price=2×S$2=S$4.00. Independent check: The 2 units cover 1000 g, which is at least 830 g; one fewer unit would be insufficient. Watch for: Do not confuse 500 g intervals with 500 kg intervals or exact proportional billing.

Independent extension: Read interval wording such as ‘at most’ and ‘above’ before choosing a tariff. Construct a reverse calculation to find which mass produced the given variable charge. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 18. Question: A hypothetical parcel of 1060 g is charged S$2 per started 500 g, with no other fees. Find its charge. Method: Billable units=ceil(1060/500)=ceil(2.12)=3. Price=3×S$2=S$6.00. Independent check: The 3 units cover 1500 g, which is at least 1060 g; one fewer unit would be insufficient. Watch for: Do not confuse 500 g intervals with 500 kg intervals or exact proportional billing.

Independent extension: If consolidation is allowed, compare rounding before and after combining measured mass. State which additional real-world carrier conditions would be needed for an actual quotation. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 19. Question: A hypothetical parcel of 1290 g is charged S$2 per started 500 g, with no other fees. Find its charge. Method: Billable units=ceil(1290/500)=ceil(2.58)=3. Price=3×S$2=S$6.00. Independent check: The 3 units cover 1500 g, which is at least 1290 g; one fewer unit would be insufficient. Watch for: Do not confuse 500 g intervals with 500 kg intervals or exact proportional billing.

Independent extension: Use a rate × mass calculation to reconstruct the variable cost for a linear schedule. Change parcel mass by a small amount across a band boundary and predict whether the charge jumps. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 20. Question: A hypothetical parcel of 1520 g is charged S$2 per started 500 g, with no other fees. Find its charge. Method: Billable units=ceil(1520/500)=ceil(3.04)=4. Price=4×S$2=S$8.00. Independent check: The 4 units cover 2000 g, which is at least 1520 g; one fewer unit would be insufficient. Watch for: Do not confuse 500 g intervals with 500 kg intervals or exact proportional billing.

Independent extension: Label currency and weight in every step rather than writing only numbers. Draw a small graph of cost against mass for the particular pricing rule. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Read a flat weight-band charge

This group practises read a flat weight-band charge. State the weight unit and pricing convention before multiplying or rounding. Five numerical variations test whether a learner can recognise the same rule even when the boundary changes.

Worked example 21. Question: An invented schedule charges S$6 for 0–2 kg inclusive, S$10 for above 2 through 5 kg, and S$15 for above 5 kg. Find the charge for 1.5 kg. Method: The mass 1.5 kg belongs to the up-to-2-kg band, so the flat charge is S$6.00. Independent check: The chosen interval contains the measured weight and is disjoint from the other stated bands. Watch for: A flat band price is not multiplied by every kilogram in the package.

Independent extension: Check that a proposed parcel satisfies any permitted maximum or stated minimum. Compare a second fictional price plan using the same parcel mass. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 22. Question: An invented schedule charges S$6 for 0–2 kg inclusive, S$10 for above 2 through 5 kg, and S$15 for above 5 kg. Find the charge for 2.75 kg. Method: The mass 2.75 kg belongs to the above-2-to-5-kg band, so the flat charge is S$10.00. Independent check: The chosen interval contains the measured weight and is disjoint from the other stated bands. Watch for: A flat band price is not multiplied by every kilogram in the package.

Independent extension: Revisit a changed tariff after two days, with the worked model hidden. Explain why the rule would give a different price if the item were sent separately. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 23. Question: An invented schedule charges S$6 for 0–2 kg inclusive, S$10 for above 2 through 5 kg, and S$15 for above 5 kg. Find the charge for 4 kg. Method: The mass 4 kg belongs to the above-2-to-5-kg band, so the flat charge is S$10.00. Independent check: The chosen interval contains the measured weight and is disjoint from the other stated bands. Watch for: A flat band price is not multiplied by every kilogram in the package.

Independent extension: Convert grams to kilograms before applying any quoted dollars-per-kilogram rate. Construct a reverse calculation to find which mass produced the given variable charge. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 24. Question: An invented schedule charges S$6 for 0–2 kg inclusive, S$10 for above 2 through 5 kg, and S$15 for above 5 kg. Find the charge for 5.25 kg. Method: The mass 5.25 kg belongs to the above-5-kg band, so the flat charge is S$15.00. Independent check: The chosen interval contains the measured weight and is disjoint from the other stated bands. Watch for: A flat band price is not multiplied by every kilogram in the package.

Independent extension: Name whether the price includes a fixed fee once or for each parcel. State which additional real-world carrier conditions would be needed for an actual quotation. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 25. Question: An invented schedule charges S$6 for 0–2 kg inclusive, S$10 for above 2 through 5 kg, and S$15 for above 5 kg. Find the charge for 6.5 kg. Method: The mass 6.5 kg belongs to the above-5-kg band, so the flat charge is S$15.00. Independent check: The chosen interval contains the measured weight and is disjoint from the other stated bands. Watch for: A flat band price is not multiplied by every kilogram in the package.

Independent extension: Do not apply a ceiling unless the fictional schedule expressly uses started units. Change parcel mass by a small amount across a band boundary and predict whether the charge jumps. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Calculate a marginal two-band charge

This group practises calculate a marginal two-band charge. State the weight unit and pricing convention before multiplying or rounding. Five numerical variations test whether a learner can recognise the same rule even when the boundary changes.

Worked example 26. Question: An imaginary tariff charges the first 2 kg at S$4/kg and each additional kilogram at S$3/kg. Price 3 kg, with exact rates and no fixed fees. Method: First-band charge=2×4=S$8. Extra mass=3−2=1 kg, priced at 1×3=S$3.00. Total=S$11.00. Independent check: Band masses 2+1=3 kg; the costs add to S$11.00. Watch for: Do not charge all 3 kg at the cheaper marginal rate.

Independent extension: At an exact kilogram boundary, check whether an extra billed unit really begins. Draw a small graph of cost against mass for the particular pricing rule. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 27. Question: An imaginary tariff charges the first 2 kg at S$4/kg and each additional kilogram at S$3/kg. Price 4 kg, with exact rates and no fixed fees. Method: First-band charge=2×4=S$8. Extra mass=4−2=2 kg, priced at 2×3=S$6.00. Total=S$14.00. Independent check: Band masses 2+2=4 kg; the costs add to S$14.00. Watch for: Do not charge all 4 kg at the cheaper marginal rate.

Independent extension: Keep flat band schedules separate from marginal weight tiers. Compare a second fictional price plan using the same parcel mass. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 28. Question: An imaginary tariff charges the first 2 kg at S$4/kg and each additional kilogram at S$3/kg. Price 5 kg, with exact rates and no fixed fees. Method: First-band charge=2×4=S$8. Extra mass=5−2=3 kg, priced at 3×3=S$9.00. Total=S$17.00. Independent check: Band masses 2+3=5 kg; the costs add to S$17.00. Watch for: Do not charge all 5 kg at the cheaper marginal rate.

Independent extension: Read interval wording such as ‘at most’ and ‘above’ before choosing a tariff. Explain why the rule would give a different price if the item were sent separately. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 29. Question: An imaginary tariff charges the first 2 kg at S$4/kg and each additional kilogram at S$3/kg. Price 6 kg, with exact rates and no fixed fees. Method: First-band charge=2×4=S$8. Extra mass=6−2=4 kg, priced at 4×3=S$12.00. Total=S$20.00. Independent check: Band masses 2+4=6 kg; the costs add to S$20.00. Watch for: Do not charge all 6 kg at the cheaper marginal rate.

Independent extension: If consolidation is allowed, compare rounding before and after combining measured mass. Construct a reverse calculation to find which mass produced the given variable charge. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 30. Question: An imaginary tariff charges the first 2 kg at S$4/kg and each additional kilogram at S$3/kg. Price 7 kg, with exact rates and no fixed fees. Method: First-band charge=2×4=S$8. Extra mass=7−2=5 kg, priced at 5×3=S$15.00. Total=S$23.00. Independent check: Band masses 2+5=7 kg; the costs add to S$23.00. Watch for: Do not charge all 7 kg at the cheaper marginal rate.

Independent extension: Use a rate × mass calculation to reconstruct the variable cost for a linear schedule. State which additional real-world carrier conditions would be needed for an actual quotation. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Add a single fixed charge to exact-weight pricing

This group practises add a single fixed charge to exact-weight pricing. State the weight unit and pricing convention before multiplying or rounding. Five numerical variations test whether a learner can recognise the same rule even when the boundary changes.

Worked example 31. Question: A fictional courier quotes one S$4 handling fee plus S$3 per exact kilogram. Find total for 2 kg. Method: Total=S$4+2×S$3=S$10.00. Independent check: Removing the fixed fee leaves S$6.00, which divided by 2 kg gives S$3/kg. Watch for: The one-time handling fee is not repeated for every kilogram.

Independent extension: Label currency and weight in every step rather than writing only numbers. Change parcel mass by a small amount across a band boundary and predict whether the charge jumps. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 32. Question: A fictional courier quotes one S$4 handling fee plus S$3 per exact kilogram. Find total for 3 kg. Method: Total=S$4+3×S$3=S$13.00. Independent check: Removing the fixed fee leaves S$9.00, which divided by 3 kg gives S$3/kg. Watch for: The one-time handling fee is not repeated for every kilogram.

Independent extension: Check that a proposed parcel satisfies any permitted maximum or stated minimum. Draw a small graph of cost against mass for the particular pricing rule. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 33. Question: A fictional courier quotes one S$4 handling fee plus S$3 per exact kilogram. Find total for 4 kg. Method: Total=S$4+4×S$3=S$16.00. Independent check: Removing the fixed fee leaves S$12.00, which divided by 4 kg gives S$3/kg. Watch for: The one-time handling fee is not repeated for every kilogram.

Independent extension: Revisit a changed tariff after two days, with the worked model hidden. Compare a second fictional price plan using the same parcel mass. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 34. Question: A fictional courier quotes one S$4 handling fee plus S$3 per exact kilogram. Find total for 5 kg. Method: Total=S$4+5×S$3=S$19.00. Independent check: Removing the fixed fee leaves S$15.00, which divided by 5 kg gives S$3/kg. Watch for: The one-time handling fee is not repeated for every kilogram.

Independent extension: Convert grams to kilograms before applying any quoted dollars-per-kilogram rate. Explain why the rule would give a different price if the item were sent separately. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 35. Question: A fictional courier quotes one S$4 handling fee plus S$3 per exact kilogram. Find total for 6 kg. Method: Total=S$4+6×S$3=S$22.00. Independent check: Removing the fixed fee leaves S$18.00, which divided by 6 kg gives S$3/kg. Watch for: The one-time handling fee is not repeated for every kilogram.

Independent extension: Name whether the price includes a fixed fee once or for each parcel. Construct a reverse calculation to find which mass produced the given variable charge. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Compare two complete pricing options

This group practises compare two complete pricing options. State the weight unit and pricing convention before multiplying or rounding. Five numerical variations test whether a learner can recognise the same rule even when the boundary changes.

Worked example 36. Question: Offer A has S$8 base fee plus S$3/kg, and Offer B charges S$5/kg without a base fee. For 2 kg, compare full prices. Method: Offer A=S$14.00, Offer B=S$10.00. Offer B is cheaper by S$4.00. Independent check: Equating 8+3m=5m gives m=4 kg; the choice for 2 kg is consistent with that crossover. Watch for: Comparing only S$3 and S$5 per kg ignores the base fee and can choose the wrong offer.

Independent extension: Do not apply a ceiling unless the fictional schedule expressly uses started units. State which additional real-world carrier conditions would be needed for an actual quotation. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 37. Question: Offer A has S$8 base fee plus S$3/kg, and Offer B charges S$5/kg without a base fee. For 3 kg, compare full prices. Method: Offer A=S$17.00, Offer B=S$15.00. Offer B is cheaper by S$2.00. Independent check: Equating 8+3m=5m gives m=4 kg; the choice for 3 kg is consistent with that crossover. Watch for: Comparing only S$3 and S$5 per kg ignores the base fee and can choose the wrong offer.

Independent extension: At an exact kilogram boundary, check whether an extra billed unit really begins. Change parcel mass by a small amount across a band boundary and predict whether the charge jumps. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 38. Question: Offer A has S$8 base fee plus S$3/kg, and Offer B charges S$5/kg without a base fee. For 4 kg, compare full prices. Method: Offer A=S$20.00, Offer B=S$20.00. Both offers tie. Independent check: Equating 8+3m=5m gives m=4 kg; the choice for 4 kg is consistent with that crossover. Watch for: Comparing only S$3 and S$5 per kg ignores the base fee and can choose the wrong offer.

Independent extension: Keep flat band schedules separate from marginal weight tiers. Draw a small graph of cost against mass for the particular pricing rule. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 39. Question: Offer A has S$8 base fee plus S$3/kg, and Offer B charges S$5/kg without a base fee. For 5 kg, compare full prices. Method: Offer A=S$23.00, Offer B=S$25.00. Offer A is cheaper by S$2.00. Independent check: Equating 8+3m=5m gives m=4 kg; the choice for 5 kg is consistent with that crossover. Watch for: Comparing only S$3 and S$5 per kg ignores the base fee and can choose the wrong offer.

Independent extension: Read interval wording such as ‘at most’ and ‘above’ before choosing a tariff. Compare a second fictional price plan using the same parcel mass. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 40. Question: Offer A has S$8 base fee plus S$3/kg, and Offer B charges S$5/kg without a base fee. For 6 kg, compare full prices. Method: Offer A=S$26.00, Offer B=S$30.00. Offer A is cheaper by S$4.00. Independent check: Equating 8+3m=5m gives m=4 kg; the choice for 6 kg is consistent with that crossover. Watch for: Comparing only S$3 and S$5 per kg ignores the base fee and can choose the wrong offer.

Independent extension: If consolidation is allowed, compare rounding before and after combining measured mass. Explain why the rule would give a different price if the item were sent separately. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Compare separate and consolidated started-kilogram billing

This group practises compare separate and consolidated started-kilogram billing. State the weight unit and pricing convention before multiplying or rounding. Five numerical variations test whether a learner can recognise the same rule even when the boundary changes.

Worked example 41. Question: A fictional service permits merging 3 identical 0.6 kg parcels into one shipment. It bills S$5 per started kg and no other fees. Compare separate and consolidated cost. Method: Separately each 0.6 kg parcel uses one billed kg, costing S$15.00 total. Combined mass=1.8 kg, billed as 2 units, costing S$10.00; saving=S$5.00. Independent check: The merged shipment has the same measured mass but may require fewer whole billed units. The example expressly allows consolidation. Watch for: Do not assume real couriers permit combining parcels or have this invented price structure.

Independent extension: Use a rate × mass calculation to reconstruct the variable cost for a linear schedule. Construct a reverse calculation to find which mass produced the given variable charge. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 42. Question: A fictional service permits merging 4 identical 0.6 kg parcels into one shipment. It bills S$5 per started kg and no other fees. Compare separate and consolidated cost. Method: Separately each 0.6 kg parcel uses one billed kg, costing S$20.00 total. Combined mass=2.4 kg, billed as 3 units, costing S$15.00; saving=S$5.00. Independent check: The merged shipment has the same measured mass but may require fewer whole billed units. The example expressly allows consolidation. Watch for: Do not assume real couriers permit combining parcels or have this invented price structure.

Independent extension: Label currency and weight in every step rather than writing only numbers. State which additional real-world carrier conditions would be needed for an actual quotation. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 43. Question: A fictional service permits merging 5 identical 0.6 kg parcels into one shipment. It bills S$5 per started kg and no other fees. Compare separate and consolidated cost. Method: Separately each 0.6 kg parcel uses one billed kg, costing S$25.00 total. Combined mass=3 kg, billed as 3 units, costing S$15.00; saving=S$10.00. Independent check: The merged shipment has the same measured mass but may require fewer whole billed units. The example expressly allows consolidation. Watch for: Do not assume real couriers permit combining parcels or have this invented price structure.

Independent extension: Check that a proposed parcel satisfies any permitted maximum or stated minimum. Change parcel mass by a small amount across a band boundary and predict whether the charge jumps. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 44. Question: A fictional service permits merging 6 identical 0.6 kg parcels into one shipment. It bills S$5 per started kg and no other fees. Compare separate and consolidated cost. Method: Separately each 0.6 kg parcel uses one billed kg, costing S$30.00 total. Combined mass=3.6 kg, billed as 4 units, costing S$20.00; saving=S$10.00. Independent check: The merged shipment has the same measured mass but may require fewer whole billed units. The example expressly allows consolidation. Watch for: Do not assume real couriers permit combining parcels or have this invented price structure.

Independent extension: Revisit a changed tariff after two days, with the worked model hidden. Draw a small graph of cost against mass for the particular pricing rule. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 45. Question: A fictional service permits merging 7 identical 0.6 kg parcels into one shipment. It bills S$5 per started kg and no other fees. Compare separate and consolidated cost. Method: Separately each 0.6 kg parcel uses one billed kg, costing S$35.00 total. Combined mass=4.2 kg, billed as 5 units, costing S$25.00; saving=S$10.00. Independent check: The merged shipment has the same measured mass but may require fewer whole billed units. The example expressly allows consolidation. Watch for: Do not assume real couriers permit combining parcels or have this invented price structure.

Independent extension: Convert grams to kilograms before applying any quoted dollars-per-kilogram rate. Compare a second fictional price plan using the same parcel mass. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Choose whole cartons under a capacity rule

This group practises choose whole cartons under a capacity rule. State the weight unit and pricing convention before multiplying or rounding. Five numerical variations test whether a learner can recognise the same rule even when the boundary changes.

Worked example 46. Question: A hypothetical batch has 11 identical one-kilogram parcels and each carton may carry at most five of them. Find the fewest cartons. Method: Cartons=ceil(11/5)=3. Total positions=15, enough for 11 parcels. Independent check: One fewer carton provides 10 positions, below the required 11. Watch for: This counts packages, not an unrestricted fractional number of cartons.

Independent extension: Name whether the price includes a fixed fee once or for each parcel. Explain why the rule would give a different price if the item were sent separately. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 47. Question: A hypothetical batch has 15 identical one-kilogram parcels and each carton may carry at most five of them. Find the fewest cartons. Method: Cartons=ceil(15/5)=3. Total positions=15, enough for 15 parcels. Independent check: One fewer carton provides 10 positions, below the required 15. Watch for: This counts packages, not an unrestricted fractional number of cartons.

Independent extension: Do not apply a ceiling unless the fictional schedule expressly uses started units. Construct a reverse calculation to find which mass produced the given variable charge. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 48. Question: A hypothetical batch has 19 identical one-kilogram parcels and each carton may carry at most five of them. Find the fewest cartons. Method: Cartons=ceil(19/5)=4. Total positions=20, enough for 19 parcels. Independent check: One fewer carton provides 15 positions, below the required 19. Watch for: This counts packages, not an unrestricted fractional number of cartons.

Independent extension: At an exact kilogram boundary, check whether an extra billed unit really begins. State which additional real-world carrier conditions would be needed for an actual quotation. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 49. Question: A hypothetical batch has 23 identical one-kilogram parcels and each carton may carry at most five of them. Find the fewest cartons. Method: Cartons=ceil(23/5)=5. Total positions=25, enough for 23 parcels. Independent check: One fewer carton provides 20 positions, below the required 23. Watch for: This counts packages, not an unrestricted fractional number of cartons.

Independent extension: Keep flat band schedules separate from marginal weight tiers. Change parcel mass by a small amount across a band boundary and predict whether the charge jumps. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Worked example 50. Question: A hypothetical batch has 27 identical one-kilogram parcels and each carton may carry at most five of them. Find the fewest cartons. Method: Cartons=ceil(27/5)=6. Total positions=30, enough for 27 parcels. Independent check: One fewer carton provides 25 positions, below the required 27. Watch for: This counts packages, not an unrestricted fractional number of cartons.

Independent extension: Read interval wording such as ‘at most’ and ‘above’ before choosing a tariff. Draw a small graph of cost against mass for the particular pricing rule. Make a new example with a weight just below or just above the relevant boundary and explain whether the bill should change abruptly or continuously. A delayed mixed question tests whether the method can be chosen without its topic label.

Six delivery-pricing mistakes worth diagnosing

Forgetting kilograms when a mass is given in grams

Divide by 1,000 before multiplying by any stated dollars-per-kilogram rate. Locate the first wrong model assumption and test a different weight near a pricing boundary. A correction is useful only if the learner can explain why the formula or rounding rule changed.

Rounding a weight even when exact billing was specified

Use the price convention actually given. A ceiling belongs only in a started-unit or other explicit rounding model. Locate the first wrong model assumption and test a different weight near a pricing boundary. A correction is useful only if the learner can explain why the formula or rounding rule changed.

Confusing flat bands with marginal tiers

Flat bands assign one price for a complete interval; marginal tiers price separate portions at different rates. Locate the first wrong model assumption and test a different weight near a pricing boundary. A correction is useful only if the learner can explain why the formula or rounding rule changed.

Multiplying a fixed base fee by kilograms

A one-off fee is charged once under the stated rule; only the variable mass rate multiplies by kg. Locate the first wrong model assumption and test a different weight near a pricing boundary. A correction is useful only if the learner can explain why the formula or rounding rule changed.

Ignoring permitted weight or carton limits

Check whether the input satisfies its stated domain, and round whole cartons upward when required. Locate the first wrong model assumption and test a different weight near a pricing boundary. A correction is useful only if the learner can explain why the formula or rounding rule changed.

Treating an invented school price table as an actual shipping quote

Real couriers use different geographic, packaging, service and tariff terms. The exercises are only mathematical models. Locate the first wrong model assumption and test a different weight near a pricing boundary. A correction is useful only if the learner can explain why the formula or rounding rule changed.

How a Bukit Timah Maths tutor can teach pricing models

A Secondary 3 G3 Mathematics tutor in Bukit Timah can show pupils three fictional courier schedules for the same 2.5 kg parcel. One charges exact mass, another rounds every started kilogram, and the third uses a flat 2–5 kg band. Pupils compare results and explain why different charges may all be correct for different stated contracts.

The tutor can next change the weight to exactly 2.0 kg and then 2.01 kg. Boundary reading becomes essential. A later unfamiliar comparison removes the pricing-model headings, requiring each pupil to identify whether the rule is linear, flat tier or ceiling-based without prompting.

The unchanged Clementi Secondary 1 Mathematics small-group guide illustrates the foundation-level approach. The Secondary 3 G3 Mathematics tuition Bukit Timah overview gives year-level context. This article does not indicate real delivery availability or current courier rates.

A six-week plan for weights and delivery rates

Week 1 — convert grams and kilograms accurately

Work forwards and backwards in mass units and label dollars-per-kilogram rates. Keep one initial attempt and a later changed tariff. Progress appears when the learner identifies the correct rate structure without being shown a worked line.

Week 2 — recognise exact-weight linear pricing

Apply variable mass charges plus one-time fees, then check by reverse division. Keep one initial attempt and a later changed tariff. Progress appears when the learner identifies the correct rate structure without being shown a worked line.

Week 3 — practise whole-unit charging

Use per-started-kg and per-started-500-g examples, testing exact boundary weights. Keep one initial attempt and a later changed tariff. Progress appears when the learner identifies the correct rate structure without being shown a worked line.

Week 4 — distinguish flat and marginal bands

Mark pricing intervals on number lines and calculate charges using separate tiers. Keep one initial attempt and a later changed tariff. Progress appears when the learner identifies the correct rate structure without being shown a worked line.

Week 5 — compare providers and consolidation rules

Use complete totals and any stated permission to combine packages. Keep one initial attempt and a later changed tariff. Progress appears when the learner identifies the correct rate structure without being shown a worked line.

Week 6 — solve mixed unseen parcel scenarios

Read the model independently, check constraints and explain why its units or rounding fit. Keep one initial attempt and a later changed tariff. Progress appears when the learner identifies the correct rate structure without being shown a worked line.

Frequently asked questions

How do I convert 1,250 g into kg?

Divide by 1,000 to obtain 1.25 kg. A fresh parcel weight or pricing band can test this reasoning independently.

What does per started kilogram mean?

Each commenced one-kilogram billing unit is counted as a whole unit under that stated pricing rule. A fresh parcel weight or pricing band can test this reasoning independently.

Does a weight of 2.00 kg count as three started kilograms?

No. Under the usual mathematical ceil(weight in kg) definition it counts as two; just above 2.00 counts as three. A fresh parcel weight or pricing band can test this reasoning independently.

Is a flat weight band the same as marginal pricing?

No. A flat band assigns one total interval price; marginal rates charge the corresponding weight segments. A fresh parcel weight or pricing band can test this reasoning independently.

Can I combine three parcels into one bill?

Only if the problem permits consolidation and states how the combined shipment is charged. A fresh parcel weight or pricing band can test this reasoning independently.

How do fixed fees change delivery costs?

They create a cost independent of the mass, added to the variable mass charge. A fresh parcel weight or pricing band can test this reasoning independently.

Can box dimensions alone determine its weight?

No. Volume alone does not establish mass or a carrier’s dimensional-weight rule. A fresh parcel weight or pricing band can test this reasoning independently.

What if the package is over the permitted maximum?

The proposed service option may be invalid under the model; do not invent another tariff. A fresh parcel weight or pricing band can test this reasoning independently.

Are these current Singapore courier rates?

No. Every price and band is invented solely for Mathematics instruction. A fresh parcel weight or pricing band can test this reasoning independently.

Which G3 skills does this connect to?

K310 rates, mass unit conversion, inequalities, graphs and contextual mathematical problem-solving. A fresh parcel weight or pricing band can test this reasoning independently.

Official syllabus: 2027 SEC G3 Mathematics K310. These examples are original fictional billing models, not courier advertisements, regulated service instructions or SEC examination questions.

The takeaway

Did you know? The hardest part of a pricing question is often deciding what the rate actually means. Exact mass, started kilograms, flat bands and marginal tiers are not interchangeable. State the unit and rule, calculate the complete fee, and check the weight boundary. That is useful algebraic thinking well beyond shipping examples.

Secondary 3 G3 Mathematics Tutor Bukit Timah | Parcel Delivery Mathematics: Weight Bands, Flat Fees and Cost Comparisons