Did you know that a bigger denominator names more equal parts of the same whole, so each part is smaller? If two fractions have the same numerator and refer to equal wholes, 1/8 is smaller than 1/6. Eight equal pieces are smaller than six equal pieces.
For Bukit Timah parents checking Primary Maths tuition, draw two equal rectangles. Divide one into six equal parts and the other into eight equal parts, then shade one part in each. Ask the child to point to the denominator, explain what it counts and compare the shaded amounts before using a rule.
Keep the first explanation. If the child says “8 is bigger, so 1/8 is bigger,” teach the meaning of the denominator. If they compare unequal wholes, repair that condition first. Then give a fresh pair such as 1/5 and 1/7 without announcing the answer.
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SECTION 1 OF 5
Make the whole and equal parts visible
A fraction describes a relationship. The denominator tells how many equal parts make the whole, while the numerator tells how many of those parts are selected. Both numbers matter, and the wholes being compared must be equivalent.
Use paper strips or bar diagrams of equal length. Six equal partitions make larger pieces than eight equal partitions. Let the child trace one sixth and one eighth rather than memorising “the bigger bottom number is smaller” without a picture.
Check the word equal. If one strip is physically longer, or the parts inside a strip are unequal, the drawing cannot support the intended comparison.
SECTION 2 OF 5
Use the shortcut only inside its conditions
For unit fractions such as 1/6 and 1/8, a larger denominator gives a smaller part when the whole is the same. The same direction works for fractions with an equal positive numerator, such as 3/7 and 3/10, provided the wholes are equal.
The shortcut is not a rule for every pair. Three eighths is greater than one sixth even though 8 is the larger denominator. A student who watches only the bottom numbers misses the selected number of parts.
Ask the child to say the conditions aloud: same whole, equal numerator, positive fractions. This makes the method usable without turning it into a misleading chant.
SECTION 3 OF 5
Compare one original pair in three ways
Consider 1/6 and 1/8. A bar model shows one sixth occupying more of an equal bar. Equivalent fractions also help: 1/6 = 4/24 and 1/8 = 3/24, so 4/24 is greater.
For a later learner, cross-products give 1 × 8 = 8 and 1 × 6 = 6, confirming 1/6 > 1/8. Teach this after the child understands what is being compared; otherwise the procedure can hide the original misconception.
The three representations should agree. If the diagram, equivalent fractions and calculation appear to conflict, inspect the partition, copied numbers or comparison sign before adding more practice.
SECTION 4 OF 5
Match the explanation to the learning stage
In Primary 3 and Primary 4, concrete and pictorial comparisons can stabilise the denominator’s meaning. Upper-primary work can connect fractions to decimals, percentages, ratios and word problems. Secondary work extends the same magnitude sense into rational numbers and algebraic fractions.
Do not move the student to a later procedure merely because they can repeat a sentence about denominators. Ask them to order a few carefully chosen fractions and explain each decision.
At secondary level, match examples to the student’s actual Mathematics subject level and school sequence. A Posting Group does not by itself state the level of every subject the student takes.
SECTION 5 OF 5
Check whether the idea transfers
After teaching 1/6 and 1/8, try 1/4 and 1/9, then 3/8 and 1/6. The first fresh pair checks the unit-fraction idea; the second checks whether the child knows the shortcut has limits.
Record the first answer, the representation used and the later independent answer. Improvement means the child can choose a valid comparison method, not only repeat the tutor’s example.
If the error persists, separate vocabulary, partitioning, multiplication facts and comparison-sign knowledge. Tuition can then repair the smallest missing connection instead of assigning a large mixed worksheet.
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Bring one useful example to a consultation
Bring the child’s original attempt, the wording of the task and any help already given. Ask which idea or decision needs teaching, how a fresh independent attempt will be checked, and whether a suitable 3-pax placement and subject arrangement are available.
Continue with the closest question
- Why adding the same number does not make an equivalent fraction
- Primary 4 fractions or word problems first?
- Bukit Timah Primary to SEC tuition-help series
Match support to the actual course
The examples are original teaching illustrations. The routines are practical educational guidance, not measured outcomes, grade promises or universal marking rules. Match every task to what has been taught and to the school’s instructions.
Source check: 11 October 2026. The SEC begins in 2027 and records subjects at their respective G1, G2 or G3 subject levels. Posting Groups and individual subject levels are not interchangeable. For examination preparation, confirm the actual subject, level, candidate type, examination year and syllabus before choosing materials.