Teaching Textbooks Algebra 1 Flashcards

Algebra Terminology and Concepts

• Operations: Fundamental arithmetic processes including addition, subtraction, and division.
• Equation: A mathematical statement consisting of two groups of numbers (and possibly variables) separated by an equal sign.
• Expression: A combination of numbers and variables representing a value, but not containing an equal sign.
• Solution: The answer derived from solving an equation, formally recognized as such.

Problem Solving Process

• Five-step Process:
  • Assign a variable (e.g. x) to represent the unknown.
  • Analyze the problem to identify two equatable elements; formulate a word equation.
  • Convert the word equation into an algebraic equation.
  • Calculate the solution to the algebraic equation.
  • Interpret the solution to understand its real-world implications.

Algebraic Principles

• Undoing: A method employed to reverse an operation, commonly by subtracting to eliminate an addition.
• Golden Rule of Algebra: Ensures that any alterations made to one side of an equation must also be made to the other side by the same quantity, maintaining equivalence.
• Inverse Operations: Operations that revert each other; for example, addition and subtraction or multiplication and division.

Expression Manipulation

• Rewriting: The act of altering the presentation of an expression without modifying its overall value.
• Equivalent Expressions: Different expressions that yield the same mathematical value upon evaluation.

Fundamental Mathematical Concepts

• Rate of Change: A measure of how quickly a quantity changes over time, often related to slope in graphing functions.
• Negative Numbers: Values that fall below zero, playing a critical role in various mathematical contexts.
• Positive Numbers: Values that exceed zero, representing quantities above a neutral point.
• Number Line: A visual representation of numbers in sequential order, illustrating the relationships between different values.
• Integers: The set of whole numbers that include positive numbers, negative numbers, and zero.
• Opposite of a Number: The counterpart of a given number that shares the same absolute value but differs in sign.

Operational Rules

• Order of Operations:
  • Perform all multiplications and divisions first, moving from left to right.
  • Follow with all additions and subtractions, also left to right.
  • Use parentheses or fractions to indicate any alterations to the standard order.

Algebraic Components

• Coefficient: A numerical factor that multiplies a variable, indicating the scale of the variable's influence in an expression.
• Reciprocal: The result of flipping a fraction or number, demonstrating its multiplicative inverse; for instance, the reciprocal of 2/3 is 3/2.