Math Problem Solving Strategies

Problem Solving

• Involves using mental strategies to overcome obstacles and find solutions
• Requires a combination of skills, including:
  • Critical thinking
  • Analytical thinking
  • Creative thinking
  • Logical reasoning
• Key strategies for problem solving in maths:
  • Breaking down complex problems into simpler parts
  • Identifying patterns and relationships
  • Using visual aids, such as diagrams or charts
  • Working backwards from the solution
  • Checking and verifying answers

Number Sequences

• A sequence is an ordered list of numbers, often following a specific pattern or rule
• Types of number sequences:
  • Arithmetic sequences (e.g. 2, 5, 8, 11, ...)
    • Each term increases or decreases by a fixed constant
  • Geometric sequences (e.g. 2, 6, 18, 34, ...)
    • Each term is obtained by multiplying the previous term by a fixed constant
  • Fibonacci sequences (e.g. 0, 1, 1, 2, 3, 5, 8, ...)
    • Each term is the sum of the two preceding terms
• Skills required for number sequences:
  • Pattern recognition
  • Algebraic manipulation
  • Inductive reasoning
  • Ability to generalize rules and formulas

Logical Reasoning

• Involves using deduction and inference to arrive at a conclusion
• Key aspects of logical reasoning in maths:
  • Identifying and understanding logical operators (e.g. AND, OR, NOT)
  • Recognizing and constructing valid arguments
  • Identifying and avoiding fallacies
  • Using Venn diagrams and other visual aids to represent logical relationships
• Types of logical reasoning problems:
  • Syllogisms (e.g. All A are B, All B are C, therefore All A are C)
  • Number series (e.g. 1, 2, 4, 8, ?)
  • Logic grids (e.g. determining the arrangement of objects based on given clues)

Problem Solving

• Problem solving involves using mental strategies to overcome obstacles and find solutions, requiring a combination of critical thinking, analytical thinking, creative thinking, and logical reasoning.
• Strategies for problem solving in maths include:
  • Breaking down complex problems into simpler parts to understand the problem better
  • Identifying patterns and relationships to find clues to the solution
  • Using visual aids, such as diagrams or charts, to represent the problem and solution
  • Working backwards from the solution to find the initial problem
  • Checking and verifying answers to ensure accuracy

Number Sequences

• A sequence is an ordered list of numbers that follow a specific pattern or rule, with examples including arithmetic, geometric, and Fibonacci sequences.
• Arithmetic sequences involve each term increasing or decreasing by a fixed constant, such as 2, 5, 8, 11, ...
• Geometric sequences involve each term being obtained by multiplying the previous term by a fixed constant, such as 2, 6, 18, 34, ...
• Fibonacci sequences involve each term being the sum of the two preceding terms, such as 0, 1, 1, 2, 3, 5, 8, ...
• Skills required for number sequences include pattern recognition, algebraic manipulation, inductive reasoning, and the ability to generalize rules and formulas.

Logical Reasoning

• Logical reasoning involves using deduction and inference to arrive at a conclusion, with key aspects including:
  • Identifying and understanding logical operators, such as AND, OR, and NOT
  • Recognizing and constructing valid arguments
  • Identifying and avoiding fallacies
  • Using Venn diagrams and other visual aids to represent logical relationships
• Types of logical reasoning problems include:
  • Syllogisms, which involve using logic to arrive at a conclusion, such as All A are B, All B are C, therefore All A are C
  • Number series, which involve identifying the next number in a sequence, such as 1, 2, 4, 8, ?
  • Logic grids, which involve determining the arrangement of objects based on given clues