Reverse percentage

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.