Te reo Māori terms
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Learning objective overview
Master Teaching Guide coverage for this objective.
Current NZC (2007)
NA5-5NA6-3
New NZC (2026)
NZC26-P4-NUM-FIN-K-Y9-03NZC26-P4-NUM-FIN-K-Y9-04NZC26-P4-NUM-FIN-P-Y9-01NZC26-P4-NUM-NSO-P-Y9-17NZC26-P4-NUM-NSO-P-Y10-10NZC26-P3-NUM-NSO-P-Y7-31NZC26-P3-NUM-NSO-P-Y8-22
Resources
- Dr Austin Maths - Reverse Percentages Practice GridQuestions PDF · Answers
- CorbettMaths on reverse percentagesQuestions PDF · Answers
Terminology
- Reverse percentage
- Original amount
- Multiplier
- Percentage increase
- Percentage decrease
- Sale price
- Discount
Task goals
- Reverse a single percentage increase or decrease by dividing the new amount by the multiplier (1 plus or minus the rate as a decimal) to find the original amount.
- Read a percentage-change bar diagram where the new amount is known and the original (100%) end is unknown.
- Apply reverse percentage to money and real-world contexts (discounts, GST, pay rises and cuts, population and measurement change).
- Explain why reversing a percentage change means dividing by the multiplier, not subtracting the percentage of the new amount.
- Reverse two successive percentage changes by dividing by both multipliers (in the correct order) to find the original amount.
- Find an unknown constant annual percentage rate from a start and an end value over two equal periods, using a squared multiplier.
- Apply reverse percentage reasoning to a two-variable context (e.g. area after independent percentage changes to two dimensions) and explain why the combined change is not zero.
Where this fits
What leads into this objective, and where it goes next.
Before
Percentage Change: Increase, Decrease and Reverse Percentages
Increasing and decreasing by a given percentage
Relationship between percentages, fractions, and decimals
You are here
Reverse percentage
Know
A percentage increase can be described by the additional percentage or the percentage of the final amount compared to the original amount (e.g. a 20% increase represents 120% of the original amount).
Statement▸
Year 9 · Number · Financial mathematics
NZC26-P4-NUM-FIN-K-Y9-03
Know
A percentage decrease can be described by the percentage lost or the percentage of the final amount compared to the original amount (e.g. a 20% decrease represents 80% of the original amount).
Statement▸
Year 9 · Number · Financial mathematics
NZC26-P4-NUM-FIN-K-Y9-04
Also under NA5-5:
Also under NA6-3:
For teachers
Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.