Problem Solving Fundamentals

The foundation of math problem-solving is built on several key principles and strategies. Here are the essential elements:

1. Understanding the Problem

  • Read carefully and identify what is being asked.
  • Determine known and unknown values.
  • Identify relevant mathematical concepts.

2. Developing a Plan

  • Choose a strategy (e.g., algebra, geometry, logic).
  • If the problem seems too complicated, break the problem into smaller, manageable steps.
  • Consider similar problems and past experiences. Practicing a variety of problems is essential for this step.

3. Implementing the Plan

  • Carry out calculations carefully. Show all work which is showing your work to yourself.
  • Keep track of steps to avoid errors.
  • Use estimation to check if the answer is reasonable.

4. Reviewing and Checking

  • Verify calculations and logic. Be careful of negatives and applying algebraic rules to expressions/equations.
  • Check the answer against the original problem.
  • Consider alternative methods for efficiency.

5. Building Strong Fundamentals

  • Master basic operations (addition, subtraction, multiplication, division).
  • Understand that variables represent numbers so the rules of numbers apply to variables.
  • Understand key concepts (fractions, algebra, geometry, probability).
  • Develop logical reasoning and pattern recognition.