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Top 200 Vocabulary for Primary 6 Mathematics | PSLE Maths Ratio, Algebra, Circles and Percentage

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by

eduKate Asia

Quick answer: Primary 6 Standard Mathematics prepares pupils to interpret and solve questions involving fraction division, reverse percentage, ratio, simple algebra, circles, composite figures, cuboid dimensions and averages. This guide explains 200 essential words and short phrases, organised by mathematical purpose, with worked PSLE-style examples and strategies for recognising what a question actually asks.

The MOE 2021 Primary Mathematics syllabus, updated October 2025 places these topics in Primary 6 Standard Mathematics, while the SEAB Mathematics (0008) examination format from 2026 assesses factual understanding, application and mathematical reasoning. The glossary below contains syllabus terminology and useful explanation language; it is not an official MOE memorisation list. Students must also retain the foundations from Primary 1–5, because PSLE Mathematics does not test Primary 6 topics in isolation.

Find the answer quickly:

Top 200 Primary 6 Mathematics vocabulary words for PSLE

Use each entry to make decisions rather than to recite a definition. A helpful practice sequence is to identify the term, draw a model or write a relationship, compute carefully, and explain why the result fits the question. Change the story after the first successful attempt to test whether the concept transfers.

1. Fraction division and number relationships (words 1–20)

  1. divide a fraction — Separate a fractional quantity into equal groups or count groups within it.
  2. proper fraction divided by whole — Share a fraction equally among a whole-number count.
  3. whole divided by proper fraction — Find how many small fractional units fit in a whole amount.
  4. fraction divided by fraction — Find how many copies of one fractional amount fit into another.
  5. reciprocal — The fraction formed by swapping a nonzero fraction’s numerator and denominator.
  6. multiplicative inverse — A nonzero number that multiplies with another to give one.
  7. multiply by reciprocal — A method for dividing fractions after the quantities are interpreted.
  8. fraction quotient — The value obtained by division involving fractions.
  9. fractional divisor — A divisor that is a fraction rather than a whole number.
  10. fractional dividend — The fraction being split or measured by division.
  11. unit-fraction groups — Equal portions such as one-fourths used to count how many fit.
  12. division as sharing — Divide an amount among a stated number of equal recipients.
  13. division as measuring — Count how many equal divisor-sized portions fit into the starting amount.
  14. number of pieces — How many pieces of a specified size the quantity contains.
  15. size of each piece — The amount in one equal portion after sharing.
  16. fraction bar model — A bar split into equal portions to show a fraction division.
  17. division reasonableness — Check that dividing by a number below one gives a larger numerical result.
  18. fraction multiplication check — Multiply quotient by divisor to recover the starting dividend.
  19. simplify fractional quotient — Reduce an answer to a simpler equivalent fraction where suitable.
  20. interpret fraction answer — State the number of items, lengths or groups represented by a fraction.

2. Reverse percentages and changes (words 21–40)

  1. percentage of a whole — A share of a total expressed in parts per hundred.
  2. percentage base — The original total from which a stated percent is calculated.
  3. known percentage part — The amount corresponding to a given percentage.
  4. unknown original whole — The starting quantity to recover from a percentage part.
  5. reverse percentage — Find the whole when a part and its percent are known.
  6. one-percent unit — The amount represented by one percent of the whole.
  7. hundred-percent total — The complete original amount.
  8. percentage increase — A rise expressed as a percentage of the starting value.
  9. percentage decrease — A fall expressed as a percentage of the starting value.
  10. original value — The starting amount before the change.
  11. new value — The amount after the change.
  12. change in value — The difference between new and original amounts.
  13. increase amount — The extra value added to reach the new amount.
  14. decrease amount — The value removed from the original amount.
  15. percentage change formula — Change divided by original value, then multiplied by 100%.
  16. original price before discount — The listed price before a percentage reduction.
  17. remaining percentage — The percentage retained after a stated decrease.
  18. growth percentage — A percentage describing an increase relative to the base.
  19. reduction percentage — A percentage describing a decrease relative to the base.
  20. percentage denominator — The reference total against which a proportion is measured.

3. Ratio notation and equivalent ratios (words 41–60)

  1. ratio — A comparison between quantities in the same kinds of units.
  2. ratio a to b — A written comparison of two part quantities.
  3. ratio a to b to c — A written comparison of three part quantities.
  4. ratio colon — The symbol : separating the terms of a ratio.
  5. ratio order — The sequence of quantities named in a ratio.
  6. first ratio term — The quantity represented by the first position in a ratio.
  7. second ratio term — The quantity represented by the second position.
  8. third ratio term — The quantity represented by the third position in a three-part ratio.
  9. ratio unit — A single common part when a ratio is drawn as equal bars.
  10. ratio bar model — Bars made of equal-sized units showing a comparison.
  11. equivalent ratio — A ratio obtained by multiplying or dividing all terms equally.
  12. simplest ratio — A ratio whose whole-number terms have no common factor above one.
  13. ratio scaling — Multiply all terms by the same nonzero whole-number factor.
  14. ratio reduction — Divide all terms by a common whole-number factor.
  15. part-to-part ratio — A comparison of two separate component quantities.
  16. part-to-whole ratio — A comparison of one component with the complete total.
  17. ratio to fraction — Convert a part-to-whole relationship into a fraction of the total.
  18. whole-number ratio terms — The prescribed P6 ratio setting uses whole-number terms.
  19. same-unit comparison — Convert related measurements to compatible units before forming a ratio.
  20. ratio interpretation — Explain what the first and second terms stand for in a story.

4. Ratio distribution and missing quantities (words 61–80)

  1. total ratio parts — The sum of the terms in a ratio used to divide a whole.
  2. one ratio part — The total quantity divided by the number of ratio units.
  3. share in a given ratio — Allocate a quantity according to proportional parts.
  4. two-person sharing ratio — A comparison of amounts received by two people.
  5. three-person sharing ratio — A comparison of allocations among three recipients.
  6. difference in ratio parts — Subtract the smaller term from the larger term.
  7. difference-unit model — Use a known difference to find the value of one ratio unit.
  8. known total — The total amount already supplied in a sharing question.
  9. unknown share — The component quantity the problem asks us to determine.
  10. missing ratio term — An unspecified value in a pair of equivalent ratios.
  11. equivalent ratio equation — A relation between ratios representing the same comparison.
  12. ratio table — A table showing consistent corresponding proportional quantities.
  13. ratio comparison — Decide how two quantities relate multiplicatively.
  14. ratio versus difference — Recognise that 2:3 is a relative comparison, not a gap of one object.
  15. ratio before-and-after — A problem where one quantity changes and the relationship must be updated.
  16. unchanged quantity — A part whose amount remains fixed during a ratio change.
  17. updated ratio — The comparison after a change has occurred.
  18. ratio model label — A note identifying each bar or component.
  19. part-to-whole fraction — One ratio component divided by the sum of all ratio components.
  20. ratio answer check — Reconstruct the given total and comparison from the calculated shares.

5. Letters, expressions and substitution (words 81–100)

  1. algebra — Using symbols and numbers to describe mathematical relationships.
  2. unknown number — A value not yet given and represented by a letter or blank.
  3. letter symbol — A character such as a used in place of a number.
  4. variable — A symbol whose assigned value can vary between examples.
  5. simple expression — A combination of numbers, operations and possibly a letter without an equals sign.
  6. algebraic term — A part of an expression separated by addition or subtraction.
  7. constant term — A number appearing without a letter in an expression.
  8. coefficient — The number multiplying a letter, such as 3 in 3a.
  9. letter coefficient — The multiplying factor associated with a variable.
  10. like terms — Terms with the same letter part and powers.
  11. unlike terms — Terms that cannot be combined by simply adding their coefficients.
  12. combine like terms — Add or subtract coefficients attached to matching letter parts.
  13. linear expression — An expression in which the letter has power one.
  14. three a — The expression 3a, meaning 3 multiplied by a.
  15. a divided by three — The expression a/3, meaning a shared into three equal parts.
  16. expression value — The number obtained after replacing a letter with a given value.
  17. substitution — Replace a letter with the specified number before calculating.
  18. evaluate an expression — Find a numerical value using substitution.
  19. simplify an expression — Write it more compactly without changing its value.
  20. expression versus equation — An equation includes an equals sign, but an expression alone does not.

6. Simple equations and mathematical balance (words 101–120)

  1. equation — A statement that two expressions have the same value.
  2. equals sign — The symbol = showing two sides are equal.
  3. left-hand side — The expression written before the equals sign.
  4. right-hand side — The expression written after the equals sign.
  5. solution of equation — A value making the equality true.
  6. solve for the letter — Find the unknown’s value from the stated equality.
  7. linear equation — An equality with a letter to the first power.
  8. whole-number coefficient — The multiplier of a letter when that multiplier is a whole number.
  9. balance principle — Do the same valid operation to both sides to preserve equality.
  10. undo addition — Subtract the known added value from both sides.
  11. undo subtraction — Add the known removed value to both sides.
  12. undo multiplication — Divide both sides by the nonzero multiplying factor.
  13. undo division — Multiply both sides by the given nonzero divisor.
  14. one-step equation — An equation solved using one inverse operation.
  15. two-step equation — An equation needing two successive inverse operations.
  16. equation from a story — Translate a written relationship into a mathematical equality.
  17. unknown as box — A blank box representing the value to be found.
  18. substitution check — Replace the letter with the proposed solution and test both sides.
  19. expression matching — Show that two differently written expressions have the same value.
  20. equation explanation — Describe why each operation keeps the statement balanced.

7. Circles: radius, diameter, circumference and area (words 121–140)

  1. circle — A plane figure whose boundary is equally distant from its centre.
  2. centre of a circle — The point equally far from all points on the circle.
  3. radius — A line segment from the centre to the circle.
  4. diameter — A line segment through the centre joining two points on the circle.
  5. diameter twice radius — The relationship d = 2r.
  6. radius half diameter — The relationship r = d/2.
  7. circumference — The distance all the way around a circle.
  8. pi — The constant π, the ratio of a circle’s circumference to its diameter.
  9. pi approximation — A convenient approximate value such as 3.14 or 22/7 when specified.
  10. circumference formula — C = πd or C = 2πr.
  11. circle area — The amount of surface within a circle.
  12. circle area formula — A = πr².
  13. radius squared — The radius multiplied by itself.
  14. distance around — Everyday language referring to circumference.
  15. surface inside circle — Everyday language referring to its area.
  16. circular boundary — The curved line forming the circumference.
  17. measured radius — The stated or measured distance from centre to circle.
  18. measured diameter — The stated or measured width through the centre.
  19. circular unit check — A circle’s area needs square units, circumference needs length units.
  20. circle calculation estimate — Check the result against the diameter and overall figure size.

8. Semicircles, quarter circles and composite regions (words 141–160)

  1. semicircle — One half of a circle cut through its diameter.
  2. quarter circle — One fourth of a circle divided by two perpendicular radii.
  3. semicircle curved arc — Half of the full circle’s circumference.
  4. semicircle perimeter — Its half-circular arc plus its straight diameter.
  5. semicircle area — Half the area of the complete circle.
  6. quarter-circle curved arc — One quarter of the full circumference.
  7. quarter-circle perimeter — Its quarter arc plus two straight radii.
  8. quarter-circle area — One quarter of the full circle’s area.
  9. arc length in this setting — The length along a semicircle or quarter-circle boundary.
  10. straight boundary — The diameter or radius segments included in a partial circle’s perimeter.
  11. curved boundary — The circular arc included in a perimeter calculation.
  12. composite shape — A shape combining more than one simple geometric region.
  13. rectangle-and-semicircle region — A composite shape made from a rectangle joined to a half-circle.
  14. square-and-quarter-circle region — A region using a square and a quarter-circle.
  15. triangle-and-semicircle region — A composite shape that includes a triangle and half-circle.
  16. add non-overlapping areas — Sum the areas of parts that do not cover the same surface.
  17. subtract overlapping area — Remove a piece already included when finding the required region.
  18. outer edge only — Include only exposed boundaries when calculating a perimeter.
  19. internal dividing line — A segment within a joined figure that must not be counted as an external edge.
  20. composite-circle answer — A final area or perimeter combining the relevant curved and straight parts.

9. Cuboid unknown dimensions and geometric reasoning (words 161–180)

  1. cuboid volume — The product of its length, width and height.
  2. cube edge length — The common length of all twelve edges of a cube.
  3. cube volume — Edge length multiplied by itself three times.
  4. known volume — A specified total number of cubic units.
  5. unknown cuboid length — A length inferred from volume and other dimensions.
  6. unknown cuboid width — A width inferred from volume and other dimensions.
  7. unknown cuboid height — A height inferred from volume and base area.
  8. cuboid base area — The area of the rectangular face supporting its height.
  9. volume divided by base area — A method for recovering the height.
  10. face area of cuboid — The area of one rectangular face.
  11. volume divided by edge — The area of a perpendicular face when the appropriate length is known.
  12. cube-root interpretation — The equal edge length whose cube equals the stated volume.
  13. geometric dimension — A length, width or height required for a solid.
  14. volume unit consistency — Keep length measurements compatible before calculating cubic units.
  15. composite angle figure — A diagram made from joined polygons with related angles.
  16. triangle angle sum — The three inside angles of a triangle total 180 degrees.
  17. quadrilateral angle relationship — Angle facts obtained from the properties of four-sided figures.
  18. parallelogram angle property — Opposite angles are equal and adjacent angles add to 180 degrees.
  19. rhombus angle property — Opposite interior angles of a rhombus are equal.
  20. trapezium angle relationship — Use its parallel sides and angle properties to infer unknowns.

10. Average, PSLE working and question-language cues (words 181–200)

  1. average — The total of numerical values divided by their count.
  2. mean of a data set — Another name for the arithmetic average.
  3. data total — The sum of the individual values.
  4. number of data values — How many entries are included in the average.
  5. total from average — Average multiplied by the count of values.
  6. unknown entry from average — Find a missing value by subtracting known values from the required total.
  7. new average — The mean after a value or the number of values changes.
  8. original average — The mean before a change to the data set.
  9. equal-share interpretation — A way to understand average as redistributing the total evenly.
  10. data reasonableness — The average lies between the smallest and largest values in a nonempty data set.
  11. multiple-choice question — An item where one answer must be selected from several choices.
  12. short-answer question — An item asking for a result in the provided response space.
  13. structured question — An item containing related parts that require clear working.
  14. non-calculator paper — A paper where calculator use is not allowed.
  15. calculator paper — A paper where an approved calculator may be used.
  16. method mark — Credit that may be awarded for correct method under the published marking rules.
  17. shown working — Steps explaining how a mathematical answer was obtained.
  18. question conditions — All restrictions and facts stated in the problem.
  19. final answer statement — A sentence showing the requested quantity and its unit.
  20. independent verification — A separate calculation or substitution confirming the result.

Seven worked PSLE-style examples with explanations

1. Fraction division: “How many portions?”

Question: A container holds 2 L of juice. Each cup holds 1/4 L. How many full cups can be filled? Calculate 2 ÷ 1/4 = 2 × 4 = 8. The interpretation is eight groups of one quarter. Now ask a different question: “Share 3/4 L among three pupils equally.” That is 3/4 ÷ 3 = 1/4 L each. Both are division, but in the first we count portions of a fixed size; in the second we find the size of each share. Draw a strip to check that the words and arithmetic match.

2. Reverse percentage: “The part is known; what was the whole?”

Question: $36 is 30% of an original amount. What is the whole amount? First, 1% is $36 ÷ 30 = $1.20. Therefore 100% is $120. Check that 30% of $120 equals $36. Students sometimes divide by 100 instead of 30 because they recognise the word “percentage” but do not identify which quantity stands for 100%.

3. Percentage increase: the denominator is the original quantity

Question: A product rises from $50 to $60. The increase is $10. Percentage increase is $10 ÷ $50 × 100% = 20%. The denominator is $50, not $60, because the original price is the reference. A later price of $60 is the new value. Ask the student to label original, change and new on a number line before calculating.

4. Ratio sharing: know which quantities the ratio compares

Question: Kai and Mira share 25 cards in the ratio 2:3. There are 2 + 3 = 5 equal ratio parts, so each part represents 25 ÷ 5 = 5 cards. Kai has 10 cards and Mira has 15. The ratio 2:3 is a part-to-part comparison; the fraction of the total held by Kai is 2/5, not 2/3. Check both the total and the ratio after finding the shares.

5. Simple algebra is a balance relationship

Question: Solve 3a + 5 = 20. Subtract 5 from both sides: 3a = 15. Divide by 3: a = 5. Substitute back: 3 × 5 + 5 = 20. P6 introduces simple linear equations with whole-number coefficients. The aim is not a memorised command to “move the 5 across”; it is recognising that equal changes on both sides preserve the equality.

6. Circles: curved boundary and enclosed area

Question: A circle has radius 7 cm. Using π ≈ 22/7 as directed, its circumference is 2 × 22/7 × 7 = 44 cm and its area is 22/7 × 7 × 7 = 154 cm². A semicircle of that radius has a curved arc of 22 cm, but its perimeter is 22 + 14 = 36 cm because the straight diameter also counts. A quarter circle has an arc of 11 cm and perimeter 11 + 7 + 7 = 25 cm. The most common mistake is finding only an arc and leaving out the straight edges.

7. An average is a total relationship

Question: Four quiz scores average 8 marks. The total is 4 × 8 = 32 marks. Three known scores are 4, 7 and 10. Their sum is 21, so the fourth must be 32 − 21 = 11. Check: (4 + 7 + 10 + 11) ÷ 4 = 8. Do not assume every “average” question asks for a division: when the mean and count are already known, multiplication recovers the total.

What P6 adds to the mathematics learnt earlier

Primary 5 introduces percentages as parts of a whole, rate and triangle/cuboid calculations. Primary 6 builds inverse relationships: find the whole from a percentage part, compare quantities by ratio, recover missing dimensions from volume, and express unknowns through simple algebra. Fractions progress into division, and area extends to circles and selected curved composite shapes. These are connections, not isolated chapters.

Students benefit from recognising a common question beneath different stories. “How many quarters fit in two litres?”, “How many cups of one quarter litre can I pour?” and “How many 1/4-litre servings?” are three descriptions of the same relationship. The object changes; the mathematics stays the same. That is why precise vocabulary and flexible representations often matter more than rushing through large numbers of similar worksheets.

How PSLE Standard Mathematics is assessed

SEAB’s Mathematics (0008) format for examinations from 2026 specifies Paper 1 at 1 hour 10 minutes without calculator and Paper 2 at 1 hour 20 minutes with an approved calculator, for a total of 100 marks across the two papers. The format uses multiple-choice, short-answer and structured or long-answer questions. SEAB explicitly distinguishes recall and computation, application and mathematical reasoning; a pupil who only memorises a formula cannot rely on calculation speed alone.

Use the published examination-year document as the authority for the actual year in which a pupil will sit PSLE; do not rely on old worksheets for a paper duration or question count. In practice, train short no-calculator methods and longer clearly explained problems separately. A calculator can check arithmetic on an allowed paper, but it does not choose the correct model or identify the reference quantity in a reverse-percentage question.

Seven recurring errors and what they mean

  1. Divides fractions without understanding group size: show equal fraction strips and ask how many named pieces fit.
  2. Finds 30% of the given part instead of the whole: label which amount is 30% and use one-percent units to recover 100%.
  3. Reverses a ratio: write the names above each ratio term before creating equal unit bars.
  4. Treats 2:3 as 2/3 of the total: calculate total ratio parts and distinguish part-to-part from part-to-whole.
  5. Combines unlike algebraic terms: use counters for the letter terms and separate numerical constants.
  6. Omits diameters from semicircle perimeters: trace the entire outer boundary with a finger.
  7. Divides the average by the number of values again: start from total = average × count and solve for the unknown.

Four-week plan: vocabulary to independent PSLE reasoning

Week 1 — Fractions, reverse percentages and ratio

Practise two kinds of fraction division with drawn strips. Label 100% on percentage bars and separate original amount from changed amount. Use simple ratio units to divide quantities and compare shares. End each session with one unfamiliar story that uses the same mathematical relationship.

Week 2 — Algebra and equivalent representations

Translate words into simple expressions, combine like terms and solve equations by preserving balance. Draw a bar model for one problem, then use a letter for the same unknown. Ask which representation made the relationship easiest to see.

Week 3 — Circles, composite shapes and cuboid dimensions

Distinguish circumference from area and label every curved and straight part of a semicircle. Recover missing dimensions using the volume relationship. Revisit relevant angle properties with a written reason for each step.

Week 4 — Average and mixed PSLE-style questions

Reconstruct totals from averages, then attempt a balanced set of questions mixing earlier and current topics. Alternate short exact computations with longer reasoned explanations. Track the reason for every error: misunderstood language, wrong representation, inaccurate arithmetic or incomplete final answer.

A practical parent and tutor diagnostic

When reviewing a paper, ask the child to explain the first decision they made, not only the last incorrect step. If the wrong operation was chosen, investigate the words that changed the meaning. If the diagram was sound but the calculation failed, practise arithmetic fluency. If the answer is correct but unexplained, ask for a second representation. Sign up for Mathematics tuition only after the student’s starting position is clear.

Frequently asked questions

Do P6 pupils need to know algebra?

Yes. P6 Standard Mathematics includes simple letter expressions, substitution and simple linear equations with whole-number coefficients. This is not the same scope as full secondary-school algebra.

Does P6 cover ratio and percentage increase?

Yes. Ratio is explicitly introduced in the P6 Standard content list, along with finding a whole from a given percentage part and calculating percentage increase or decrease.

Are circles and their perimeters in Primary 6?

Yes. The official syllabus includes circumference and area of circles, areas and perimeters of semicircles and quarter circles, and specified composite figures containing these shapes.

Is an average the same thing as a middle value?

No. The arithmetic mean in this syllabus is total of the data values divided by their number. It is not the same as the median, which is the middle ordered value and is a different statistical concept.

Should parents begin with hard PSLE problems?

Begin with the child’s actual gaps. A pupil who is still uncertain about the difference between part-to-part and part-to-whole ratios benefits more from clear models than from more complex exam practice.

Official references and the next learning route

Read the MOE Primary 1–6 Mathematics syllabus, updated October 2025 and the SEAB PSLE Mathematics (0008) assessment document for examinations from 2026. The eduKate Primary Mathematics syllabus overview and Primary 5 Mathematics vocabulary companion provide context for how these skills build across years. Check the latest exam-year document again when planning revision for a future cohort.