Key Takeaways
- Variables represent unknown numbers
- Expressions don't have equals signs; equations do
- Combine like terms by adding/subtracting coefficients
- Solve equations by using inverse operations
- Always check your answer by substituting back
Algebra Basics
The ParaPro tests basic algebra skills including working with variables, expressions, and simple equations.
Understanding Variables
A variable is a letter that represents an unknown number.
Example: In the expression 3x + 5, the variable is x.
Algebraic Expressions vs. Equations
| Type | Definition | Example |
|---|---|---|
| Expression | Numbers/variables combined with operations | 3x + 5 |
| Equation | Two expressions set equal | 3x + 5 = 14 |
Evaluating Expressions
To evaluate an expression, substitute a value for the variable.
Example: Evaluate 2x + 3 when x = 4
- 2(4) + 3 = 8 + 3 = 11
Combining Like Terms
Like terms have the same variable raised to the same power.
| Like Terms | Not Like Terms |
|---|---|
| 3x and 5x | 3x and 5y |
| 2x² and 7x² | 2x² and 7x |
| 4 and -9 | 4 and 4x |
Combining: Add or subtract the coefficients
- 3x + 5x = 8x
- 7y - 2y = 5y
Solving One-Step Equations
Goal: Get the variable alone on one side.
Addition/Subtraction:
- x + 5 = 12 → Subtract 5: x = 7
- y - 3 = 10 → Add 3: y = 13
Multiplication/Division:
- 3x = 15 → Divide by 3: x = 5
- x/4 = 8 → Multiply by 4: x = 32
Solving Two-Step Equations
Example: 2x + 5 = 13
Step 1: Undo addition/subtraction
- 2x + 5 = 13
- 2x = 8 (subtract 5)
Step 2: Undo multiplication/division
- 2x = 8
- x = 4 (divide by 2)
Check: 2(4) + 5 = 8 + 5 = 13 ✓
Translating Words to Algebra
| Words | Operation | Example |
|---|---|---|
| Sum, plus, more than | Add | x + 5 |
| Difference, minus, less than | Subtract | x - 3 |
| Product, times, of | Multiply | 4x |
| Quotient, divided by | Divide | x/2 |
| Is, equals | = | x = 7 |
Example Word Problem
"A number increased by 7 equals 15. What is the number?"
Translation: x + 7 = 15 Solution: x = 8
Classroom Application
Help students with algebra by:
- Using concrete objects before abstract symbols
- Creating word problem translation charts
- Teaching "undo" operations step-by-step
- Using balance scales to visualize equations
- Practicing checking answers by substitution
Solve for x: 3x - 7 = 14
Simplify: 4x + 3 + 2x - 1