PRIMARY 5 MATHEMATICS LEARNING GUIDE · BATCH 11 · GUIDE 43
Many model-method errors begin before the diagram is drawn. The learner misreads the relationship phrase. “20 more than”, “20% more than”, “3 times as many as”, “3/5 of”, “less than” and “fewer than” can look linguistically similar while encoding different mathematical structures.
This guide isolates those language traps so that bar models and equations begin from the correct relationship. It is not an English lesson. It is a mathematics-reading guide for relational phrases that control quantity structure.
Return to the Primary 5 Mathematics Learning Hub. Related foundations: Word Problems, Bar Models & Multi-Step Reasoning · Comparison Bar Models.
1. “More than” usually signals additive comparison
“A has 20 more than B” means A = B + 20. The extra 20 is a difference segment.
2. “Less than” reverses the reference
“A has 20 less than B” means A = B − 20, or B=A+20. Read who owns the larger amount.
3. “Times as many” is multiplicative, not additive
“A has 3 times as many as B” means A=3×B, not B+3.
4. “Three times more” is ambiguous everyday language
In school mathematics, avoid relying on ambiguous informal wording. Prefer explicit statements such as “three times as many” or “200% more”. When interpreting a question, use the precise relationship provided by the assessment source.
5. “Fraction of” names the reference quantity
“A is 3/5 of B” means B is the whole for that fraction. A=3/5×B.
6. Fraction of another quantity is not fraction of the total
If A=3/5 of B, then A and B together represent 8 equal units, so A is 3/8 of the combined total—not 3/5.
7. “Of the remainder” changes the reference
If one third of the remainder is used, the remainder—not the original—is the active whole for that fraction.
8. “20% more than” is multiplicative comparison
If A is 20% more than B, B=100% and A=120% of B. A=1.2B.
9. “20 more” and “20% more” diverge as the base changes
If B=250, 20 more gives 270; 20% more gives 300. The first is fixed difference, the second scales with B.
10. “20% less than” uses the larger reference as 100%
If A is 20% less than B, A=80% of B. If A=160, B=200.
11. Percentage comparisons are not symmetric
If A is 25% more than B, B is not 25% less than A. Example B=100, A=125. B is 20% less than A.
12. “Difference between” asks for subtraction
If A=84 and B=57, difference=27. It does not ask how many times one quantity is another.
13. “How many times” asks for quotient
If A=84 and B=28, A is 3 times B because 84÷28=3.
14. “Each” often creates a rate or equal-group structure
“8 boxes with 24 each” means total=8×24. “192 items placed 24 each” means groups=192÷24.
15. “Per” identifies a unit rate
“$4 per notebook” means $4 for one notebook. “18 litres per minute” means 18 litres for each minute.
16. “Remaining” creates a new state
The phrase signals that an earlier change has already occurred. A later fraction or percentage may use this new state as its whole.
17. “Altogether” usually creates a total constraint
If A and B altogether are 150, then A+B=150. This can combine with difference or multiplicative comparison to solve both.
18. “Fewer” versus “less” still requires quantity meaning
Natural-language grammar differs for countable and measured quantities, but mathematically both can indicate a smaller amount. Identify the quantities before choosing subtraction.
19. “Increase by” versus “increase to”
Increase 80 by 20 means 100. Increase 80 to 20 is not sensible as an increase because 20 is lower. “By” names change; “to” names final value.
20. “Decrease by 20%” versus “decrease to 20%”
Decrease by 20% leaves 80% of original. Decrease to 20% leaves only 20% of original. The wording controls the multiplier.
21. Bar-model translation table
| Phrase | Structure |
|---|---|
| A is 20 more than B | A=B+20 |
| A is 3 times B | A=3B |
| A is 3/5 of B | A=(3/5)B |
| A is 20% more than B | A=1.2B |
| A and B total 150 | A+B=150 |
22. Read relation before drawing bars
A beautiful bar model built from the wrong relationship is still wrong. Translate the sentence into one equation or verbal relation first.
23. Use contrast pairs
Practise “20 more” beside “20% more”, “3 times” beside “3 more”, and “1/3 of original” beside “1/3 of remainder”. Contrast exposes the exact semantic boundary.
24. Error map
| Error | Language trap | Repair |
|---|---|---|
| A=B+3 for “3 times” | Additive/multiplicative confusion | Ask how many equal copies of B. |
| 3/5 treated as part of total | Reference lost | What follows the word “of”? |
| 20% more solved by +20 | Percentage base ignored | What is 100%? |
| Second fraction applied to original | “Remainder” ignored | What is the active whole now? |
25. Practice laboratory
- B=60. A is 25 more. Find A.
- B=60. A is 25% more. Find A.
- A is 3/5 of B and B=100. Find A and A as fraction of total A+B.
- A is 4 times B; total=150. Find both.
- 500 items: 2/5 used, then 1/3 of remainder used. Find second-stage amount used.
- Price decreases by 20% from $250. Find final. Then compare with “decreases to 20%”.
26. Answers
1. 85.
2. 75.
3. A=60; A is 60/160=3/8 of total.
4. 5 units=150; B=30, A=120.
5. Remainder=300; one third=100.
6. Decrease by 20% → $200. Decrease to 20% → $50.
27. Full language-control problem
Mei has 40% more beads than Ravi. Ravi has 25 fewer beads than Hana. Hana has 175 beads. Find Mei’s beads.
Ravi=175−25=150. Mei=140% of 150=210.
The problem contains an additive comparison first and a multiplicative percentage comparison second.
28. Final checkpoint
A strong Primary 5 learner can translate relational phrases before calculating, distinguish additive from multiplicative comparison, identify the reference quantity after “of” and percentage language, interpret “by” versus “to”, and build models only after the relationship is stable.
Continue to the Primary 5 → Primary 6 Percentage Difference & Change Bridge.
