Introduction to Stocks

Learn what stocks are, how they work, and the basic math behind buying and selling shares.

Intermediate25 minLesson
Printable worksheet

Definition

A stock (also called a share) is a small piece of ownership in a company. When you buy a stock, you become a part-owner of that company.
Key Terms:
  • Share: One unit of ownership in a company
  • Stock Price: The current cost of one share (changes constantly)
  • Portfolio: All the investments you own together
Example: If a company has 1,000,000 shares and you own 100 shares:
Your ownership=1001,000,000=0.0001=0.01%\text{Your ownership} = \frac{100}{1{,}000{,}000} = 0.0001 = 0.01\%
You own 0.01% of the company!

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What is a stock?

Worked Examples

Emma wants to buy 15 shares of a tech company. Each share costs 42 dollars. How much will she spend in total?
1

Identify the values

Number of shares = 15, Price per share = 42 dollars → 15 shares at 42 dollars each
2

Multiply shares by price

15×42=63015 \times 42 = 630 → 630 dollars
3

Write the answer

Total investment = 630 dollars → Emma spends 630 dollars

Common Mistakes

Confusing number of shares with total value

Why it's wrong: Owning 100 shares sounds like a lot, but if each share costs 5 dollars, your total investment is only 500 dollars. Someone with 10 shares at 200 dollars each has invested 2000 dollars.

Correct: Always multiply: Total Value = Number of Shares × Price per Share

Calculating percent return using wrong base

Why it's wrong: Return should be based on your initial investment, not your final value.

Correct: Percent Return = (Gain ÷ Initial Investment) × 100, NOT (Gain ÷ Final Value) × 100

Thinking a stock drop of 50% followed by a 50% rise means you break even

Why it's wrong: If you invest 100 dollars and lose 50%, you have 50 dollars. A 50% gain on 50 dollars gives you only 75 dollars!

Correct: Percentages are always calculated on the current value, not the original. You need a 100% gain to recover from a 50% loss.

Interactive Visual

Bar Chart

20 shares: bought at 35, now 48

Purchase cost(700)
Current value(960)
Profit(260)

Bar Chart

Profit or loss

Marcus: 20 × (48 − 35)(260)
James: 50 × (22 − 28)(-300)

Interactive Sandbox

Expression Calculator

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History

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Practice Problems

15 problems
Problem 1 of 15
Easy
What is a stock?

Why It Matters

Understanding stocks is essential for building wealth and financial security:
  • Growing Money: Historically, stocks have grown about 7-10% per year on average over long periods
  • Retirement: Most retirement accounts (like 401(k)s) invest primarily in stocks
  • Financial News: Stock prices are discussed daily in news and affect the economy
  • Career Skills: Many jobs in finance, business, and technology involve understanding stocks
The math skills you learn here will help you make smart decisions about investing your own money someday!

Real World Applications

Building a Portfolio

Investors spread their money across different stocks to reduce risk. This is called diversification.

Example:

A portfolio might include: 10 shares of a tech company at 150 dollars each (1500 dollars), 25 shares of a retail company at 40 dollars each (1000 dollars), and 50 shares of a bank at 30 dollars each (1500 dollars). Total portfolio value: 4000 dollars.

1Try It Yourself

You have 1000 dollars to invest. You buy 20 shares of Company A at 25 dollars each, and spend the rest on Company B at 10 dollars per share.

How many shares of Company B can you buy?

Step 1: Write the mathematical expression

Calculate remaining money, then divide by share price:

Stock Market News

When news says a stock is up 5% or down 3%, this refers to the change in price from the previous day's close.

Example:

If a stock closed at 80 dollars yesterday and is up 5% today, the new price is: 80 × 1.05 = 84 dollars.

2Try It Yourself

A stock closed at 120 dollars yesterday. Today it dropped 8%.

What is the new stock price?

Step 1: Write the mathematical expression

Multiply by (1 - percent decrease):

Dividends

Some companies pay dividends - regular payments to shareholders from company profits.

Example:

If a company pays a 2 dollar dividend per share and you own 100 shares, you receive: 100 × 2 = 200 dollars.

3Try It Yourself

A company pays a quarterly dividend of 0.75 dollars per share. You own 80 shares.

How much do you receive in dividends per year?

Step 1: Write the mathematical expression

Calculate quarterly payment, then multiply by 4:

Key Takeaways

  • 1A stock is a share of ownership in a company
  • 2Total investment = Number of shares × Price per share
  • 3Profit/Loss = Current value - Initial investment
  • 4Percent return = (Gain ÷ Initial investment) × 100
  • 5Diversification means spreading investments across different stocks
  • 6Dividends are payments companies make to shareholders

Frequently Asked Questions

Stock prices change based on supply and demand. If more people want to buy a stock than sell it, the price goes up. If more people want to sell than buy, the price goes down. News, company performance, and economic conditions all affect prices.
Stock prices change based on supply and demand. If more people want to buy a stock than sell it, the price goes up. If more people want to sell than buy, the price goes down. News, company performance, and economic conditions all affect prices.
Yes, if a company goes bankrupt, its stock can become worthless and you lose your entire investment. This is why diversification is important - spreading money across many stocks reduces risk.
A stock is ownership in a company - your returns depend on the company's success. A bond is a loan to a company or government - they promise to pay you back with interest. Stocks are riskier but can grow more; bonds are safer but grow less.

Glossary

Stock
A share of ownership in a company; also called a share or equity
Share
One unit of ownership in a company's stock
Portfolio
All the investments (stocks, bonds, etc.) that a person owns
Dividend
A payment made by a company to its shareholders from its profits
Return
The gain or loss on an investment, often expressed as a percentage
Diversification
Spreading investments across different stocks to reduce risk
Today's challengeOne problem, three tries

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