MathIsimple
Lesson 5-1

Variables & Unknown Numbers

Learn to use letters and symbols to represent unknown numbers in mathematical expressions. Master variables through age problem solving activities.

Learning Scenario: Age Problem Solving

Scenario: You're solving age mysteries! Sarah is 8 years old, and her mom is 25 years older than her. How old is Sarah's mom? Instead of writing "Sarah's mom's age," we can use a letter like 'm' to represent the unknown age. So we write: m = 8 + 25 = 33.

This is your introduction to algebra! Letters and symbols can represent unknown numbers, making math problems easier to solve and understand.

What are Variables?

Variables are letters or symbols that represent unknown numbers. They're like placeholders for numbers we don't know yet.

Examples:

  • • x = unknown number
  • • y = another unknown
  • • n = number of items
  • • a = age
Algebraic Expressions

An algebraic expression combines numbers, variables, and operations (+, -, ×, ÷) without an equals sign.

Examples:

  • • x + 5
  • • 3 × y
  • • n - 2
  • • a + 25
Step-by-Step Learning
1

Identifying Unknown Numbers

Look for words like "how many," "what number," or "unknown" in word problems. These tell you there's a number you need to find.

Example: "How old is Tom?" → Tom's age is unknown, so we can use 't' for Tom's age

2

Choosing Variables

Pick a letter that makes sense for the unknown. Use the first letter of what you're looking for, or common letters like x, y, n.

Example: "How many apples?" → use 'a' for apples, or 'n' for number

3

Writing Expressions

Translate word problems into algebraic expressions using your chosen variables and the given information.

Example: "5 more than a number" → x + 5

Interactive Activities

Activity 1: Variable Selection

Choose a variable for each unknown:

  • • How many books? → ?
  • • What's the temperature? → ?
  • • How old is the dog? → ?
  • • What's the weight? → ?
  • • How many students? → ?

Activity 2: Expression Writing

Write expressions for these phrases:

  • • 3 more than a number
  • • 7 less than a number
  • • Twice a number
  • • Half of a number
  • • A number plus 10
Practice Problems

Problem Set 1: Variable Selection

1. Choose a variable for "how many cookies"

2. Choose a variable for "what's the height"

3. Choose a variable for "how many days"

4. Choose a variable for "what's the price"

Problem Set 2: Expression Writing

5. Write an expression for "5 more than x"

6. Write an expression for "3 times y"

7. Write an expression for "n minus 4"

8. Write an expression for "a divided by 2"

Problem Set 3: Real-World Applications

9. Tom is 12. His sister is 3 years older. Write an expression for his sister's age.

10. A book costs $8. You have $20. Write an expression for how much money you'll have left.

11. You have 15 stickers. You give away some. Write an expression for how many you have left.

12. A rectangle has length 5 and width w. Write an expression for the area.

Common Mistakes to Avoid

❌ Using the same variable for different unknowns

Wrong: Using 'x' for both age and weight in the same problem

Correct: Use 'a' for age and 'w' for weight

❌ Forgetting to include operations

Wrong: "5 more than a number" → 5x

Correct: "5 more than a number" → x + 5

Key Takeaways

Variables represent unknown numbers in math problems

Choose meaningful letters for your variables

Algebraic expressions combine numbers, variables, and operations

Practice translating word problems into algebraic expressions