PSLE Maths Problem-Sum Keywords | Relationship Guide

Problem sums keywords such as altogether, remaining, at first and as many as are relationship clues, not buttons that automatically mean add, subtract, multiply or divide. A strong PSLE Maths reader translates the full sentence into a bar model, equation, table or other representation before choosing an operation.

Parents searching for problem sums keywords, PSLE Maths word problems, model method keywords and problem-sum vocabulary are usually trying to solve one recurring issue: the child can perform the calculation but misreads the relationship. “More than” describes a comparison; “remaining” describes what is left after change; “at first” anchors an earlier state. The actual operation depends on what quantities are known and what the question asks.

Treat every keyword as a hypothesis about structure, then verify it against the whole problem. This page maps the main relationship families and builds a translation routine. Use it with the Singapore Vocabulary Guide and the eduKate Vocabulary Learning System.

Quick Read

Keywords are clues, not automatic operations.
Group words by part-whole, comparison, change, rate, percentage and time.
Translate the whole sentence before calculating.
Watch increase by versus increase to.
Diagnose language interpretation separately from arithmetic.

60 PSLE Maths relationship keywords

Part-whole and totals

1. altogether

altogether signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

2. total

total signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

3. in all

in all signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

4. combined

combined signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

5. sum

sum signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

6. whole

whole signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

7. part

part signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

8. remaining

remaining signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

9. left

left signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

10. used

used signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

Comparison

11. more than

more than signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

12. less than

less than signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

13. fewer than

fewer than signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

14. greater than

greater than signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

15. smaller than

smaller than signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

16. difference

difference signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

17. as many as

as many as signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

18. twice as many

twice as many signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

19. three times as many

three times as many signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

20. compared with

compared with signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

Change

21. increase by

increase by signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

22. increase to

increase to signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

23. decrease by

decrease by signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

24. decrease to

decrease to signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

25. gained

gained signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

26. lost

lost signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

27. added

added signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

28. removed

removed signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

29. at first

at first signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

30. now

now signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

Rate and grouping

31. each

each signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

32. every

every signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

33. per

per signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

34. for every

for every signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

35. equally

equally signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

36. shared

shared signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

37. groups of

groups of signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

38. rate

rate signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

39. average

average signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

40. unit

unit signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

Fractions and percentage

41. fraction of

fraction of signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

42. percentage of

percentage of signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

43. remainder

remainder signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

44. part of

part of signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

45. out of

out of signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

46. discount

discount signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

47. percentage increase

percentage increase signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

48. percentage decrease

percentage decrease signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

49. original amount

original amount signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

50. final amount

final amount signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

Time and sequence

51. before

before signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

52. after

after signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

53. later

later signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

54. earlier

earlier signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

55. duration

duration signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

56. from…to…

from…to… signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

57. elapsed

elapsed signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

58. at the same time

at the same time signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

59. every interval

every interval signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

60. by the time

by the time signals a relationship. Restate the sentence in plain English, identify what is known and unknown, then draw a model or write an equation. Create a second example in which the same phrase appears but the required operation changes. This proves that the language is being interpreted rather than matched mechanically.

The keyword trap

A keyword-first method can fail because the same word appears in different unknown-position problems. “Altogether” may accompany an addition when parts are known, but a part may need subtraction when the total and other part are known. Relationship first, operation second.

Choose three keywords from different groups. Write two word problems for each with different unknown positions. Solve them using a representation and explain why the same keyword can lead to different operations.

Increase by versus increase to

“Increase by 20” means add 20 to the original amount; “increase to 20” means the new amount becomes 20. The same distinction applies to percentages. Small prepositions can change the entire model.

At first and now

These time anchors often signal before-and-after states. Label the earlier quantity and later quantity explicitly. Ask what change connects them and whether the unknown is the original amount, change or final amount.

As many as and times as many

“As many as” can indicate equality; “twice as many” or “three times as many” indicates multiplicative comparison. Do not confuse multiplicative comparison with additive “more than”.

The Fencing Method

Fence near-phrases with contrasting examples: 20 more than versus 20 times as many; decrease by versus decrease to; shared equally versus each receives. Minimal pairs show exactly which word changes the mathematical relationship.

Representation

Translate words into a bar model, number sentence, table or labelled diagram. Then read the representation back into words. Bidirectional translation helps reveal whether the model truly matches the problem.

Error diagnosis

If a student gets the wrong answer, locate the earliest failure: reading, relationship, representation, operation, calculation or checking. A reading error needs language repair; an arithmetic error needs a different intervention.

Checking

Return the answer to the wording. Does it satisfy “remaining”, “at first” or “more than”? Substituting the result back into the relationship catches many plausible-looking wrong answers.

30 translation drills

Drill 1

Choose one keyword, write a one-sentence relationship, draw or describe the bar model, then write the equation. Change which quantity is unknown and solve again. Finish by rewriting the wording without the original keyword while preserving the same mathematical structure.

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Frequently asked questions

Does ‘altogether’ always mean add?

No. It indicates a total; the operation depends on which quantities are known.

Does ‘remaining’ always mean subtract?

It describes a quantity left after change. Sometimes the unknown is the starting amount, so a different operation is needed.

Are keywords useless?

No. They are useful clues when connected to relationships rather than memorised as operation triggers.

How should parents practise?

Ask the child to explain the relationship and draw a model before calculating.

Why does my child calculate correctly but answer wrongly?

The calculation may be correct for a misread model. Diagnose the language stage first.

Should pupils underline keywords?

Yes, if they also connect those words to the full sentence and model.

What is the best checking method?

Substitute the result back into the stated relationship and verify units and reasonableness.

What shows mastery?

The pupil can translate varied wording into the same structure and the same wording into different unknown positions.

Continue through the Singapore Vocabulary Guide.

eduKate SG

PSLE Maths Problem-Sum Keywords: What “Altogether”, “Remaining”, “At First” and “As Many As” Tell You