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Teacher Guide: Percent Gain and Loss

Learn how to calculate and interpret percentage gains and losses on investments.

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10 questions on Investing Basics. Students join with a name, you see everyone's score.

For Teachers

Learning Objectives
  • Calculate percent gain using the percent change formula
  • Calculate percent loss using the percent change formula
  • Interpret positive and negative percent changes
  • Compare investments using percent returns
  • Understand why losses require larger gains to recover
Prerequisites
  • • Understanding of percentages and decimals
  • • Basic operations with positive and negative numbers
  • • Familiarity with fractions and division
Discussion Starters
  • 1. Why do you think a 50% loss is harder to recover from than a 50% gain is to make?
  • 2. If two investments both made 500 dollars profit, does that mean they performed equally well?
  • 3. How would you explain to a friend why percent change matters more than dollar change?
  • 4. What's worse: losing 20% once or losing 10% twice? Calculate both!
Common Misconceptions

Dollar profit matters more than percent gain

Remediation: Use examples: 100 dollars profit on 200 dollars (50% gain) vs 100 dollars profit on 10000 dollars (1% gain). Which is the better investment?

Gains and losses of equal percentage cancel out

Remediation: Work through 100 dollars + 10% = 110 dollars. Then 110 dollars - 10% = 99 dollars. You're down 1 dollar! Do the same with larger percentages.

Differentiation Ideas

For Struggling Students:

  • • Use simple numbers (100 to 150, etc.) for easier mental math
  • • Create visual bar models showing original and new values
  • • Provide formula reference cards during practice

For On-Level Students:

  • • Calculate percent changes with realistic stock prices
  • • Compare multiple investments to find the best performer
  • • Work backwards: given percent change, find original or new value

For Advanced Students:

  • • Explore compound percent changes (multiple gains/losses in sequence)
  • • Calculate what percent gain is needed to recover from various losses
  • • Analyze real historical stock data and calculate actual returns
Standards Alignment
  • 7.RP.A.3 (CCSS.MATH.CONTENT.7.RP.A.3)

    Use proportional relationships to solve multistep ratio and percent problems

  • 7.EE.B.3 (CCSS.MATH.CONTENT.7.EE.B.3)

    Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers

Lesson Resources
  • visualGain/Loss Comparison Chart

    Interactive chart showing original vs new values

  • activityInvestment Simulator

    Practice calculating returns on mock portfolios

  • worksheetReal Stock Analysis

    Calculate percent changes from actual stock data

Lesson Content

Everything students see: definition, examples, common mistakes, applications. Tap to open.

Definition

Percent gain measures how much an investment has increased as a percentage of its original value. Percent loss measures how much it has decreased.
The formula for percent change is:
Percent Change=New Value−Original ValueOriginal Value×100%\text{Percent Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\%
  • If the result is positive, it's a gain
  • If the result is negative, it's a loss
For example, if a stock goes from 100 dollars to 125 dollars:
125−100100×100%=25% gain\frac{125 - 100}{100} \times 100\% = 25\% \text{ gain}

Worked Examples

You bought shares for 80 dollars and sold them for 100 dollars. What is your percent gain?
1

Identify the values

Original value = 80 dollars, New value = 100 dollars → Values identified
2

Find the change

100−80=20100 - 80 = 20 dollars profit → Change = 20 dollars
3

Divide by original

2080=0.25\frac{20}{80} = 0.25 → Decimal = 0.25
4

Convert to percent

0.25×100%=25%0.25 \times 100\% = 25\% → 25% gain

Common Mistakes

Using the new value as the denominator

Why it's wrong: Percent change is always relative to the ORIGINAL (starting) value, not the new value.

Correct: Always divide by the original value: New−OriginalOriginal\frac{\text{New} - \text{Original}}{\text{Original}}

Thinking a 50% loss and 50% gain cancel out

Why it's wrong: After a 50% loss, you have half your money. A 50% gain on half is only 75% of original.

Correct: 100 dollars - 50% = 50 dollars. Then 50 dollars + 50% = 75 dollars. You still lost 25%!

Forgetting to multiply by 100

Why it's wrong: The formula gives a decimal. You must multiply by 100 to get a percentage.

Correct: 0.250.25 is not 25%. You must write 0.25×100%=25%0.25 \times 100\% = 25\%

Why It Matters

Understanding percent gain and loss is essential for:
  • Evaluating investments: Is your portfolio growing or shrinking?
  • Comparing opportunities: Which investment had better returns?
  • Setting goals: How much do you need to gain to reach your target?
  • Understanding risk: A 50% loss requires a 100% gain to recover!
Every investor, from beginners to professionals, uses these calculations daily to make informed decisions.

Real World Applications

Stock Market Returns

Investors track percent gains and losses to evaluate their portfolio performance.

Example:

If you invested 1000 dollars and your portfolio is now worth 1150 dollars, you have a 1150−10001000×100%=15%\frac{1150-1000}{1000} \times 100\% = 15\% gain.

1Try It Yourself

You bought shares for 200 dollars. They are now worth 250 dollars.

What is your percent gain?

Step 1: Write the mathematical expression

Calculate: 250−200200×100%\frac{250 - 200}{200} \times 100\%

Comparing Investment Options

Percent change helps compare investments of different sizes.

Example:

Investment A: 500 dollars becomes 600 dollars (20% gain). Investment B: 2000 dollars becomes 2300 dollars (15% gain). Investment A performed better even though B earned more dollars.

2Try It Yourself

Fund X went from 40 dollars to 52 dollars per share. Fund Y went from 100 dollars to 120 dollars per share.

Which fund had the better percent return?

Step 1: Write the mathematical expression

Calculate percent change for each fund

Key Takeaways

  • 1Percent change = New−OriginalOriginal×100%\frac{\text{New} - \text{Original}}{\text{Original}} \times 100\%
  • 2Positive result = gain; Negative result = loss
  • 3Always divide by the ORIGINAL value, not the new value
  • 4Losses hurt more than equivalent gains (50% loss needs 100% gain to recover)
  • 5Percent change lets you compare investments of different sizes fairly

Frequently Asked Questions

Why do I divide by the original value and not the new value?

Percent change measures how much the value changed relative to where it started. The original value is your reference point. If you used the new value, you'd be measuring something different.

What's the difference between percent gain and total return?

Percent gain is the percentage increase in value. Total return includes percent gain plus any dividends or interest earned during the holding period.

Can you have more than 100% gain?

Yes! If an investment doubles, that's 100% gain. If it triples, that's 200% gain. There's no upper limit to gains, but losses are capped at 100% (losing everything).

Glossary

Percent gain
The increase in value expressed as a percentage of the original value
Percent loss
The decrease in value expressed as a percentage of the original value
Original value
The starting amount or purchase price of an investment
Break even
When the current value equals the original investment (0% gain or loss)
Return
The profit or loss on an investment, often expressed as a percentage

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