PRIMARY 5 MATHEMATICS LEARNING GUIDE · BATCH 12 · GUIDE 46
Restating a problem means changing its form without changing its mathematics. A difficult sentence can become a simpler sentence, a bar model, an equation, a table, a timeline or a labelled diagram. The representation changes; the relationship must not.
This heuristic is powerful because many Primary 5 problems are hard at the language layer before they are hard at the calculation layer. Restating removes linguistic clutter, exposes hidden quantities and makes relationships auditable.
This is a problem-solving owner rather than a new syllabus topic. Return to the Primary 5 Mathematics Learning Hub. Related guides: Model Method Language Traps · Mathematical Communication, Working, Notation & Explanation.
1. Restating is not simplifying the numbers
To restate “A has 25% more than B” as “A is 125% of B” changes wording but preserves the same quantities. Replacing B=482 with B=100 would be a different heuristic: simplifying the case.
2. Equivalent statements preserve truth
“A is 20 more than B” is equivalent to “B is 20 less than A” and “A−B=20”. Different forms reveal different aspects of the same relation.
3. Start with the target
Rewrite the question as a short target statement: “Find final amount”, “Find number of groups”, “Find missing height”. A clear target helps remove irrelevant detail.
4. Convert relational language into equations
“Mina has 3 times as many cards as Ravi” becomes M=3R. “Mina has 15 more cards than Ravi” becomes M=R+15.
5. Convert equations into bars when the relationship is easier to see visually
M=3R becomes one bar of three equal units for M and one unit for R. Visual form can reduce symbolic load for Primary 5 learners.
6. Convert bars into equations when the model becomes crowded
If a bar model has many annotations and one unknown, an equation can compress the same structure and make reverse operations clearer.
7. Convert repeated-rate stories into tables
“18 litres each minute” can become columns for minutes and litres. Tables are especially useful when several rate states or comparisons are involved.
8. Convert time stories into timelines
Start time, duration and end time are easier to manage when placed on a line in chronological order. Restating prevents subtraction from the wrong endpoint.
9. Convert geometry prose into labelled diagrams
“A perpendicular height of 8 cm from the opposite vertex to a 15 cm base” should be drawn. The diagram makes the base-height pairing visible.
10. Restate percentage as a multiplier
“After a 20% discount” can become “pay 80% of original” or “multiply original by 0.8”. Choose the form that best matches the target.
11. Restate fraction-of-another as equal units
“A is 3/5 of B” becomes A=3 units, B=5 units. This form is often easier for totals and differences.
12. Restate changing-whole problems as states
Instead of one paragraph, write S0→S1→S2. Attach each fraction or percentage to the state immediately before it.
13. Restate “of the remainder” explicitly
“One third of the remainder” becomes “new whole = remainder; take 1/3 of new whole”. This prevents accidental reuse of the original total.
14. Restate comparison questions around the reference quantity
“A is 25% more than B” becomes “B=100%, A=125%”. This is often safer than beginning with subtraction.
15. Restate reverse percentage problems backward
“After a 20% decrease, amount is 160” becomes “80% of original=160”. The unknown original is now attached to a clear reference.
16. Restate excess-shortage as two equal totals
“24 each leaves 36; 27 each is short 9” becomes 24n+36=27n−9. The hidden fixed total becomes explicit.
17. Restate transfer problems with system boundaries
Write “inside A+B” beside internal transfers and “outside system” beside external transfers. This determines whether total is conserved.
18. Restate group problems with units
“240 books, 20 books per box” becomes 240 books ÷ 20 books/box = 12 boxes. Units reveal the quotient meaning.
19. Restate multi-step questions as subgoals
Ask: what must I know immediately before the final answer? Then what must I know before that? This creates a dependency chain.
20. Restating can reveal unnecessary information
If the target and relationships do not use the colour, date or descriptive background, those details can be ignored. Restating separates mathematical signal from story decoration.
21. Restating can reveal missing information
If the equivalent mathematical statement still has two independent unknowns but only one relationship, the problem may be underdetermined unless another condition exists.
22. Equivalent statements can support checking
If A=3/5 B and B=100, A=60. Restate as B=5/3 A: 5/3×60=100. The reverse form verifies the relation.
23. Representation switching should reduce uncertainty
Do not switch forms merely to make the page look busy. Move from words to bars, bars to equations, or equations to tables only when the new form makes a hidden feature clearer.
24. Some representations preserve different strengths
Bars show relative size well. Equations compress unknown relationships. Tables show repeated states. Timelines preserve order. Diagrams preserve spatial constraints. Choose according to the uncertainty.
25. Representation switching is a metacognitive strategy
If one representation is not helping, deliberately change it. This is not failure. It is strategy control.
26. Error map
| Error | Cause | Repair question |
|---|---|---|
| Restatement changes the numbers or condition | Not equivalent | Would both forms always have the same answer? |
| Bar model drawn before relation understood | Representation chosen too early | Can you state the relation in one sentence first? |
| Equation loses units or meaning | Symbols detached from context | What does each symbol represent? |
| Table used for one static comparison | Representation inefficient | Would bars or one equation be clearer? |
27. Restatement routine
- State the target.
- Name each quantity and unit.
- Rewrite the key relationship in plain mathematical language.
- Choose a representation.
- Check that no condition changed during translation.
28. Practice set A
- Restate “A is 30 more than B” in two equivalent ways.
- Restate “A is 40% more than B” using percentages and a multiplier.
- Restate “A is 2/3 of B” using equal units.
- Restate “20% of the remainder is used” using state language.
- Restate “18 litres per minute for 7 minutes” as an equation.
29. Practice set B
- 24 items per group leaves 18 extra; 27 per group is short 6. Write an equality in n.
- After a 25% discount, price is $90. Restate as a percentage equation for original price.
- A bus holds at most 40 people. There are 173 people. Restate the final decision after division.
- A triangle has base 15 cm and perpendicular height 8 cm. Restate as an area expression.
- A gives 20 counters to B. Restate the invariant for system A+B.
30. Answers
1. A=B+30; B=A−30.
2. B=100%, A=140%; A=1.4B.
3. A=2 units, B=3 units.
4. New whole=remainder; used amount=20%×new whole.
5. Total=18×7=126 litres.
6. 24n+18=27n−6.
7. 75% of original=$90.
8. 173÷40=4 remainder 13; five buses needed if everyone must travel.
9. Area=1/2×15×8.
10. A+B remains constant if the transfer stays inside the two-group system.
31. Full restatement problem
A shop has some pens. It sells 30% of them. Then it gives away one quarter of the remaining pens. Finally 210 pens remain. Find the original number.
Restate by states. After first action, 70% remains. After second action, 3/4 of that remains. Therefore final = original ×0.7×3/4 = original×0.525.
0.525 of original=210, so original=400 pens.
The long story becomes one chain of equivalent state multipliers.
32. Final checkpoint
A strong Primary 5 learner can restate a difficult story without changing its mathematics, translate relational language into equations or units, attach percentages and fractions to the correct reference quantity, switch among bars, tables, timelines and diagrams deliberately, and use equivalent forms to expose hidden relationships or verify a solution.
Continue to Primary 5 Mathematics Learning Guide | Simplify the Problem, Solve a Smaller Case & Rebuild the Original.
