Teacher Guide: Percent Gain and Loss
Learn how to calculate and interpret percentage gains and losses on investments.
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Class quiz
10 questions on Investing Basics. Students join with a name, you see everyone's score.
For Teachers
- 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
- • Understanding of percentages and decimals
- • Basic operations with positive and negative numbers
- • Familiarity with fractions and division
- 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!
Dollar profit matters more than percent gain
Gains and losses of equal percentage cancel out
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
- 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
- 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.
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Definition
- If the result is positive, it's a gain
- If the result is negative, it's a loss
Worked Examples
You bought shares for 80 dollars and sold them for 100 dollars. What is your percent gain?
Identify the values
Original value = 80 dollars, New value = 100 dollars → Values identified
Find the change
dollars profit → Change = 20 dollars
Divide by original
→ Decimal = 0.25
Convert to percent
→ 25% gain
Answer: You made a 25% gain on your investment.
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:
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: is not 25%. You must write
Why It Matters
- 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!
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 gain.
You bought shares for 200 dollars. They are now worth 250 dollars.
What is your percent gain?
Step 1: Write the mathematical expression
Calculate:
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.
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 =
- 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?
What's the difference between percent gain and total return?
Can you have more than 100% gain?
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