G3 Mathematics tuition can help your child distinguish direct from inverse proportion by checking what stays constant. For direct proportion y = kx, the ratio y ÷ x is constant. For inverse proportion y = k ÷ x, the product xy is constant, with x non-zero.
For Punggol parents, begin with two pairs of values and ask the student to calculate both the ratio and the product. ‘Both quantities increase’ is not enough to prove direct proportion, and ‘one decreases’ is not enough to prove inverse proportion.
The 2027 SEC G3 Mathematics syllabus is K310 and includes direct and inverse proportion. This guide focuses on choosing the relationship before calculating, so the student can explain the model and check whether an answer fits the situation.
Find your next learning step
Match the learning plan to K310 · Look for a constant, rather than a visual impression · Compare two original sets of values · Read the assumptions in a real-world problem · Check whether the student can reject a wrong model
Match the learning plan to K310
Read the official 2027 K310 Mathematics syllabus with the school’s current teaching programme. The examples below are suggested learning activities, not official questions or a promised examination format.
Use the student’s actual subject level, examination year and recent work when selecting support. PG1, PG2 and PG3 are Posting Groups; they do not replace checking the G level of the individual subject. Confirm the provider’s subject availability before booking.
Look for a constant, rather than a visual impression
In y = 3x, doubling x doubles y, and y ÷ x remains 3. In y = 12 ÷ x, doubling a positive x halves y, and xy remains 12.
A straight line alone does not establish direct proportion. The graph of y = 3x + 2 is straight, but does not pass through the origin and y ÷ x is not constant.
Likewise, a decreasing relationship need not be inverse proportion. For example, y = 12 − x decreases as x increases, but xy changes. Ask what the equation says before choosing a label.
Compare two original sets of values
For Set A, use (x, y) = (2, 6), (4, 12), (6, 18). Each ratio y ÷ x equals 3. The pairs are consistent with y = 3x.
For Set B, use (2, 12), (4, 6), (6, 4). Each product xy equals 24. The pairs are consistent with y = 24 ÷ x.
In Set A, when x = 10, the model gives y = 30. In Set B, the same x gives y = 2.4. The calculation is short once the relationship is chosen correctly.
A finite table supports a proposed model; it does not establish that the same rule holds for every possible value outside the stated context. Use the relationship given in the question and respect its domain.
Read the assumptions in a real-world problem
For a fixed distance d travelled at constant speed v, time t = d ÷ v. Thus vt = d. Increasing speed reduces time according to an inverse-proportion model while distance remains fixed.
By contrast, at a fixed unit price p, cost C = pq is directly proportional to quantity q if there is no fixed charge, discount or other change in price.
Suppose a delivery includes a $5 fixed fee. Then C = pq + 5. Cost rises with quantity, but total cost is no longer directly proportional to quantity.
Try this original check: y is inversely proportional to x, and y = 8 when x = 3. The constant is xy = 24; when x = 6, y = 4. Explain why halving occurs before relying on a calculator.
Check whether the student can reject a wrong model
Give a table that fits neither relationship. Can the student say so rather than forcing every task into one of two categories? That is useful mathematical judgement.
Ask for the constant, equation, substitution, units and a contextual check. A tutor can then distinguish weak arithmetic from a mistaken relationship.
Continue with the existing G3 distance and area scale guide for another proportional-reasoning task.
Choose a focused next step
Use the Primary, PSLE and SEC subject directory to find related questions.
Bring one recent piece of work and the teacher’s feedback to a consultation. Ask which decision needs repair and how the child will demonstrate independent progress on an unfamiliar question. A manageable practice plan can be more useful than adding several new worksheets.
The Clementi Secondary 1 Mathematics guide illustrates diagnosis and focused 3-pax teaching. Close attention to the student’s reasoning is a useful principle when choosing support for the actual subject.
Official syllabus checked 11 October 2026. All worked examples here are original teaching activities, not SEAB questions or official model answers.
