Did you know that a ratio of 2:3 does not automatically mean that the first group is two-thirds of the total? If the ratio compares red counters with blue counters and those are the only two groups, red counters make up two-fifths of all the counters. The first useful tuition step is to name what each number compares.
For Bukit Timah parents helping with Maths homework, ask your child to label both parts of the ratio before calculating. Then ask what the question means by “total”. A child may simplify ratios accurately yet lose the relationship when turning a part-to-part comparison into a fraction.
Bring a labelled drawing and the original wrong answer to the tutor. Ask for a matched pair: one question comparing the two groups and another asking for one group as a fraction of the whole. Keep the numbers simple until your child can explain why the denominator changes.
Find your next learning step
Choose a short teaching check, then bring the first attempt to the tutor.
SECTION 1 OF 5
Name the quantities before using the numbers
Write “red:blue = 2:3”, rather than only “2:3”. The labels preserve the order. Red compared with blue is 2:3; blue compared with red is 3:2. Changing the order without changing the numbers changes the statement.
Next identify the collection called the whole. If green counters also exist, adding only the red and blue parts does not describe all the counters. The familiar “add the ratio parts” step works only when those parts make up the specified total.
SECTION 2 OF 5
See the same collection in three relationships
Take 4 red counters and 6 blue counters. Red:blue is 4:6, which simplifies to 2:3. Red is 4/6, or 2/3, of the number of blue counters. Red is 4/10, or 2/5, of the total number of counters.
The numbers describe the same collection with different comparison bases. Ask the child to complete the sentence “This fraction compares red with ___.” That missing word is often more revealing than another calculation. Draw five equal ratio units, two red and three blue, to make the whole visible.
Contents · Previous section · Next section
SECTION 3 OF 5
Find out whether the difficulty is language or structure
If the child selects the right quantities but calculates incorrectly, practise the numerical step. If they calculate 2 ÷ 3 correctly for a question about the whole, return to what the denominator represents. More division practice alone will not repair that choice.
Ask for a short spoken explanation before a fresh independent question. A parent may help label an example during teaching; make that support clear when reporting the result. An answer obtained after the denominator was supplied does not show that the child chose it independently.
Contents · Previous section · Next section
SECTION 4 OF 5
Extend the relationship without rushing
If red:blue is 2:3 and there are 25 counters altogether, the five ratio units represent 25 counters. One unit represents 5 counters, giving 10 red and 15 blue. Check both the ratio and the total. This is an original teaching illustration, not an examination marking prescription.
A problem involving a difference uses a different relationship: with the same ratio, the difference is one ratio unit. Let the tutor choose when to introduce that variation. The aim is to identify what the known quantity represents before deciding which operation to use.
Contents · Previous section · Next section
SECTION 5 OF 5
Check transfer on a new pair of groups
Change counters to books, keeping a comparable level of difficulty. Ask for the ratio between two categories, then the fraction of the stated total. If the child needs the same prompt again, tell the tutor which phrase caused the difficulty rather than describing the whole ratio topic as weak.
The immutable eduKateSG Mathematics guide emphasises why a method is valid before speed. This is a useful example: once the comparison base is clear, calculation becomes easier to check. Bring one labelled first attempt to a consultation after the starting position is clear.
Contents · Previous section · Series guide
Continue with the closest question
- Choose a useful diagram
- Match numbers to the quantities
- Check understanding beyond a correct answer
- Bukit Timah tuition decision guide
- Bukit Timah tuition hub
- eduKateSG’s 3-pax Mathematics teaching guide
Match the practice to the course
For Primary and PSLE practice, use the child’s actual teaching coverage and task instructions. In secondary school, PG1–PG3 are Posting Groups; G1–G3 are subject levels. Match support to the individual subject and examination year. See MOE’s Posting Groups guide and SEAB’s SEC information.
Reviewed 11 October 2026. Examples are original teaching illustrations. Home checks are suggestions to discuss with the teacher or tutor; they do not prescribe examination marking rules or promise results.
Arrange a parent–student consultation after the starting position is clear. Bring the task, first attempt and the point where help was needed.