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A fraction of a whole describes how many equal parts are being considered out of the equal parts that make up that whole. Identify the whole before reading the fraction. In three-quarters, four tells us the number of equal parts in the whole and three tells us how many of those parts are selected.
This Primary 3 Mathematics guide uses one-whole examples to connect diagrams, fraction names and written notation. Its focus is identifying and representing the part-whole relationship. Equivalent fractions, unlike-fraction calculations and fractions of sets belong to related lessons rather than being crowded into this starting task.
Valour Primary's 2026 Mathematics overview includes fractions at P3. MOE's Mathematics syllabus updated October 2025 is the national reference; direct access presented a verification screen during this series. These are original teaching examples, not official assessment questions or a complete syllabus audit. Follow the school's current scope.
Imagine one rectangular sheet of paper divided into four equal strips. The whole is the complete sheet, not only the shaded section. If one strip is shaded, the shaded fraction of the sheet is one-quarter.
Say “one-quarter of this whole sheet”. Naming the whole prevents a child from switching silently between one strip, the complete sheet and several sheets during the explanation.
For a shape's area fraction, the parts must have equal areas. Four regions of visibly different areas do not each represent one-quarter merely because there are four regions.
Parts can have different shapes yet equal areas, but beginners benefit from clear equal strips or matching pieces. Do not use an unscaled sketch's appearance to invent measurements when the question gives no equality information.
The denominator is the number below the fraction bar. In 3/4, it says the whole is considered as four equal parts. Each one of those parts is one-quarter of that whole.
It does not describe only the unshaded parts. If three of the four strips are shaded, the denominator remains four because all four parts still make up the whole sheet.
The numerator is the number above the fraction bar. In 3/4, it counts three selected equal parts. With the same four-part whole, shading two parts gives 2/4 and shading one gives 1/4.
Count selected parts once each. Reading 3/4 as four selected parts out of three reverses the roles. Point to the whole's total parts and the selected parts before recording the fraction.
A strip is divided into five equal sections and two are shaded. The shaded fraction is 2/5 and the unshaded fraction is 3/5. Together they cover all five sections: 5/5, or one whole.
Use the same whole and partition for both fractions. The three in 3/5 counts unshaded equal sections; it is not a new denominator. This is a diagram-based connection, not a requirement to begin formal fraction arithmetic before the child is ready.
Half of a large sheet can have a greater area than half of a small sheet. Both are one-half of their respective wholes, but the actual areas need not be equal.
When comparing fraction diagrams as amounts, check whether the wholes are the same size or whether sizes are specified. “Both show one-half” and “both shaded areas are equal” are different claims.
- A rectangle has six equal sections, with two shaded. Write the shaded fraction.
- A circle has four equal-area sectors, with three shaded. What fraction is unshaded?
- A sheet has three unequal-area pieces. Can each automatically be called one-third of its area?
- In 4/5, what does the five tell us?
- Two differently sized sheets each have half shaded. Must their shaded areas be equal?
Answers: 1. 2/6. 2. 1/4. 3. No; thirds of the whole area require equal-area parts. 4. The whole is considered as five equal parts. 5. No; the wholes have different sizes. The first answer is kept in the given partition form; simplification is a later connection.
Use three checks: identify the whole, count its equal parts and count the selected parts. If a fraction answer is wrong, return to the first check that failed rather than supplying a rule to memorise.
Once that relationship is secure, continue to the existing P4 equivalent-fractions guide through the Mathematics hub. Changing the number of equal parts can preserve an amount, but understanding the original whole comes first.