Educational material from 
What you will learn
- Calculate changes in money and percentages using the starting value as the base.
- Explain why different starting amounts produce two possible rankings.
- Check successive percentage changes one step at a time.
Session plan: 30 minutes
Allow five minutes for an initial prediction, ten for calculations in pairs, ten for comparison and five for an individual exit question. Copy the table onto paper and give each pair a calculator. All amounts were created for teaching; no app account or real stock prices are needed. Currency amounts remain in Swedish kronor, written as SEK.
Students should already understand percentages as parts of a hundred. Ask them to show the calculation and its unit. This model has no deposits, withdrawals, fees, dividends or currency changes. All starting values refer to the same time, and all ending values to the same later time. These conditions make the results comparable within the task.
Student worksheet: make two rankings
First subtract each starting value from its ending value. Then divide the difference by the starting value and multiply by 100. Rank the accounts from the largest to the smallest change in money, and make a separate ranking by percentage change. State which measure answers each question.
Now replace all starting amounts with SEK 1,000 and keep each account’s percentage change. Calculate the new ending values. Write one sentence explaining why this second experiment helps compare rates of change while also describing different amounts from the original table.
If the table does not fit, scroll it sideways.
| Account | Start | End |
|---|---|---|
| A | SEK 1,000 | SEK 1,120 |
| B | SEK 3,000 | SEK 3,240 |
| C | SEK 2,000 | SEK 1,840 |
Answer key: B leads in money, A in percentage
A gains SEK 120: 120 / 1,000 × 100 = 12%. B gains SEK 240: 240 / 3,000 × 100 = 8%. C loses SEK 160: −160 / 2,000 × 100 = −8%. The ranking by money is B, A, C; by percentage it is A, B, C.
With SEK 1,000 as the common starting base, the ending values become SEK 1,120, SEK 1,080 and SEK 920. A now leads on both measures. Changing the starting amounts changes the comparison in money. Neither ranking tells us which account or company will perform well in a future period.
If the table does not fit, scroll it sideways.
| Account | Change in money | Percentage change |
|---|---|---|
| A | +SEK 120 | +12% |
| B | +SEK 240 | +8% |
| C | −SEK 160 | −8% |
Teacher notes: change the base and follow another period
If a student divides by the ending value, ask which amount existed before the change. If a student compares only 120 and 240, ask whether the question concerns money gained or the rate of change. Have students state both answers in complete sentences so that the measure is explicit.
Add one more step for A alone: after rising by 12%, its value falls by 12%. The new base is SEK 1,120. The ending value is 1,120 × 0.88 = SEK 985.60, which is SEK 14.40 below the original SEK 1,000. The change across both periods together is −1.44%, rather than zero.
Look for a named base, a retained minus sign and an explanation of the next period’s starting value. Students can continue with Investiq’s percentage-return lesson and then follow a simulated holding. The digital follow-up supplements the calculation on the worksheet; it does not supply evidence about future returns.
Student and teacher sheets for printing
The same activity is available as separate sheets: a student worksheet with blank answer spaces and teacher notes with the answers. Open the sheet you need and use your browser’s print function. The sheets have an A4 layout and require no app account.
Give students the student worksheet and keep the teacher sheet for the discussion. The complete session plan, sources and digital follow-up remain on this page.
Try it yourself
One account rises from SEK 500 to SEK 575 and another from SEK 2,000 to SEK 2,200. Which has the larger gain in money, and which in percentage?
Show the solution and explanation
The second account gains more money: SEK 200. The first gains more in percentage terms: 15%, compared with 10%.
75 / 500 × 100 = 15 and 200 / 2,000 × 100 = 10. Two correct measures answer two different questions.
Check your understanding
Can you add +12% and −12% for successive periods?
Not when the changes apply to different bases. Multiply 1.12 by 0.88 first, then compare the ending value with the original base.
Why should the comparison use the same period?
Otherwise one account may have been observed for longer. A common period makes this particular comparison clearer.
Practise with virtual money
Try what you just learned in a practice portfolio with virtual money. You don't deposit any real money.
How the practice portfolio worksKeep learning and practising
More activities on this topic
Calculate, interpret and evaluate sources
- Evaluate stock claims: a classroom activity with three statements
- Read a stock chart in class: three claims and an answer key
- Stock splits and new shares: ownership cards for the classroom
- Inflation and purchasing power: a classroom basket worksheet
- Stock order fees: a classroom worksheet and cash-flow answers
- A paper stock-market game: two rounds, student journal and answers
Sources and examples
The sources support the factual explanations. Calculations and exercises were created for this lesson. Amounts and price changes are invented unless stated otherwise.
This material is educational and does not recommend securities to buy. A simulated result does not guarantee a future result.
