How to Teach Percent Increase and Decrease
"The price went up 20%." "Your grade dropped 15%." Percent change is one of the most practical math skills — and one of the most confusing, because it involves three different numbers: the original, the new, and the percent.
The core idea: change relative to the original
Percent increase or decrease measures how much something changed, relative to where it started.
A shirt was $40, now it is $50. The increase is $10. But $10 out of $40 is a 25% increase.
The same $10 increase on a $200 jacket would only be a 5% increase. The absolute change ($10) is the same, but the percent change depends on the starting value.
Key Insight: Percent change is always relative to the original. The same dollar amount represents different percents depending on the starting value. "Is $10 a lot?" depends entirely on "$10 compared to what?"
The formula
Percent change = (amount of change ÷ original amount) × 100
Or equivalently:
- Percent increase = (new - original) ÷ original × 100
- Percent decrease = (original - new) ÷ original × 100
Percent increase examples
A bike costs $200 and the price increases to $250.
- Change: $250 - $200 = $50
- Percent increase: ($50 ÷ $200) × 100 = 25%
Your test score went from 60 to 75.
- Change: 75 - 60 = 15
- Percent increase: (15 ÷ 60) × 100 = 25%
Percent decrease examples
A jacket originally $80 is on sale for $60.
- Change: $80 - $60 = $20
- Percent decrease: ($20 ÷ $80) × 100 = 25%
A town's population went from 5,000 to 4,500.
- Change: 5,000 - 4,500 = 500
- Percent decrease: (500 ÷ 5,000) × 100 = 10%
Finding the new amount from a percent change
Percent increase: New = original × (1 + percent/100)
A $60 item with a 20% markup: $60 × 1.20 = $72
Percent decrease: New = original × (1 - percent/100)
A $60 item with a 30% discount: $60 × 0.70 = $42
Connection to basic percents
This builds directly on percent skills:
- Finding a percent of a number (the amount of change)
- Understanding what 100% means (the original amount)
- Calculating with decimals and fractions
Common mistakes
Using the new value instead of the original: A price goes from $40 to $50. They compute $10 ÷ $50 = 20% instead of $10 ÷ $40 = 25%. Always divide by the original value.
Thinking percent increase and decrease are reversible: If a price increases 50% from $100 to $150, a 50% decrease from $150 gives $75, not $100. The percents are not symmetric because the base changes.
Confusing percent of with percent change: "20% of 80" is 16. "80 increased by 20%" is 96. Different questions, different answers.
Percent change measures how much something changed relative to where it started. Always divide by the original. Use it for discounts, markups, population changes, grade improvements — any situation where you need to express a change as a proportion of the starting value.
If you want a system that builds percent change on solid percent fundamentals and applies it to real-world contexts — that is what Lumastery does.