Section 1.1: Algebraic Thinking
Algebraic thinking involves recognizing patterns, understanding how numbers relate, and using symbols to represent unknowns and generalize mathematical relationships.
Key Idea:
Use letters to represent unknown values in equations and expressions, e.g., \( x + 5 = 12 \) or \( y = 3n + 2 \).
Example 1
Find the value of \( x \) if \( x + 7 = 15 \).
Subtract 7 from both sides: \( x = 15 - 7 \)
So, \( x = 8 \).
Practice Problems
- Write an expression for: "Seven more than a number is 15".
- Solve for \( x \): \( 3x + 4 = 19 \).
- Identify the unknown in: "Twice a number minus 5 equals 9".
- Generalize a pattern: The sum of the first \( n \) odd numbers is ___?
- Translate into algebra: "Three times a number plus 2 is the same as 11".