PRIMARY 5 → PRIMARY 6 MATHEMATICS BRIDGE · BATCH 11 · GUIDE 44
This page is a transition bridge, not a new Primary 5 syllabus owner. Primary 5 already develops percentage as part-whole reasoning, discount and other direct applications. Primary 6 extends that foundation into percentage increase, percentage decrease and more demanding multiplicative-change problems. This bridge prepares the reference-base control needed for that next stage without duplicating the Primary 6 canonical owner.
Receiving owner: Primary 6 Mathematics Learning Guide | Ratio, Percentage and Multiplicative Change.
Return to the Primary 5 Mathematics Learning Hub or review Primary 5 Percentage Applications, Discounts, GST & Money Problems.
1. Percentage always needs a reference base
“20%” is incomplete until we know 20% of what. The reference quantity is treated as 100%.
2. Percentage difference as comparison language
If A=120 and B=100, A is 20% more than B because the difference 20 is measured against B=100.
3. Reverse comparison changes the base
Although A is 20% more than B, B is 20/120=1/6≈16.7% less than A. Percentage comparison is directional.
4. Percentage increase uses the original as 100%
If $200 increases by 15%, increase=30 and final=230. The multiplier is 115%=1.15.
5. Percentage decrease uses the original as 100%
If $200 decreases by 15%, decrease=30 and final=170. The multiplier is 85%=0.85.
6. Increase then decrease are not symmetric
100 increased by 20% becomes 120. Decreasing 120 by 20% gives 96, not 100, because the second 20% uses a different base.
7. Changing reference bases are the central difficulty
Every time the quantity changes and a later percentage is applied to the new amount, the active 100% changes too.
8. Successive percentage changes multiply
Increase by 10% then decrease by 20% gives factor 1.1×0.8=0.88. Final is 88% of original, a net 12% decrease.
9. Do not add successive percentage changes blindly
+10% and −20% do not automatically mean −10% because the bases differ.
10. Reverse percentage prepares Primary 6 change problems
If a value after a 20% decrease is 160, then 80% of original=160, so original=200.
11. Percentage points versus percentage change
If a score rises from 60% to 75%, the increase is 15 percentage points. Relative to 60%, that is a 25% increase. These are different measures.
12. Use percentage points carefully
Percentage points compare two percentages directly. Percentage change compares the difference with the original value.
13. From fraction to percentage change
If a quantity becomes 5/4 of its original, it is now 125% of original: a 25% increase.
14. From percentage change to multiplier
Increase by p% → multiply by 1+p/100. Decrease by p% → multiply by 1−p/100.
15. Comparison and change can look similar
“A is 25% more than B” compares two quantities. “A increases by 25%” compares one quantity across two states. Both use 125% multipliers but the story structure differs.
16. Base control in money contexts
A $300 item discounted 20% becomes $240. If a later 10% charge applies to the sale price, it is 10% of $240, not $300.
17. Base control in population or quantity contexts
A group of 500 increases by 12% to 560. If the new group then decreases by 10%, final=504. The final is still slightly above original.
18. Same numerical difference can create different percentage changes
An increase of 20 from 100 is 20%. An increase of 20 from 200 is 10%. Percentage change depends on the starting base.
19. Readiness diagnostic
A learner is ready for formal Primary 6 percentage-change work if they can identify 100%, calculate direct percentage, reverse a percentage result, distinguish additive from multiplicative comparison, and update the reference base after each state change.
20. Error map
| Error | Cause | Repair question |
|---|---|---|
| Adds successive percentages | Changing bases ignored | What is 100% at each stage? |
| Assumes reverse percentage is same | Direction ignored | Which quantity is the base? |
| Confuses percentage points with percentage change | Two comparison measures mixed | Are we comparing percentages directly or relative to original? |
| Uses final as original base | State labels missing | Which state is the reference? |
21. Bridge practice
- 100 increases by 20%. Find final.
- 120 decreases by 20%. Find final.
- 100 increases 20%, then decreases 20%. Find final and net change.
- A value rises from 80 to 100. Find percentage increase.
- A percentage rises from 60% to 75%. Find percentage-point increase and relative percentage increase.
- After a 20% decrease, a value is 160. Find original.
22. Answers
1. 120.
2. 96.
3. 96; net 4% decrease.
4. Difference 20 / original 80 = 25%.
5. 15 percentage points; 15/60=25% relative increase.
6. 160÷0.8=200.
23. Full bridge problem
A quantity increases by 25%, then the new amount decreases by 20%. What is the final amount compared with the original?
Multiplier=1.25×0.8=1.00. Final equals 100% of the original.
This is a special case where unequal percentage rates cancel because they apply to different bases in just the right proportions.
24. Handoff to Primary 6
Continue to the canonical Primary 6 Mathematics Learning Guide | Ratio, Percentage and Multiplicative Change.
This bridge should remain a prerequisite runway: stable reference-base control first, formal percentage-change ownership in Primary 6.
