Problem Solving Strategies in Mathematics

Aug 25, 2024

Mathematics in the Modern World - Day 4 Lecture Notes

Introduction

  • Good morning and welcome to Day 4 of Mathematics in the Modern World.
  • Reminder to take care of your energy – eat well!

Lesson Focus

  • Today's lesson is about strategies and problem solving, particularly:
    • Making a table
    • Finding patterns

Objectives

  1. Understand the make a table and find a pattern strategies.
  2. Apply these strategies in problem solving.

Problem Solving in Mathematics

  • Central theme: mathematics is about problem solving.
  • Discussed different emotional states of students (happy, shocked, etc.).

Mixed Emotions in Problem Solving

  • Introduced the concept of mixed fractions in mathematics and how they relate to real life.

POLYA’s Four Steps in Problem Solving

  1. Understand the problem (U): Identify the given information.
  2. Plan (P): Develop an equation or strategy to solve the problem.
  3. Execute (E): Carry out the plan by performing calculations.
  4. Check (C): Verify the solution by substituting back into the original equation.

Example Problem

  • Problem: The sum of the ages of a father and son is 48 years, with the father being 3 times as old as the son.
    • Let x = son's age.
    • Father's age = 3x.
    • Equation: x + 3x = 48.
    • Solution: x = 12 (son's age), 3x = 36 (father's age).

Additional Example Problems

  1. Perimeter of a Rectangle Problem:
    • Given perimeter and relationships between length and width, solve for dimensions.
  2. Work Problem:
    • John can paint a room in 6 hours; Rudy can do it in 3. How long will it take if both work together?
    • Solution involves using rates of work.

Strategies for Problem Solving

  1. Make a Table: Organize data to visualize solutions.
  2. Find Patterns: Recognize systematic repetitions in data.
    • Example: Triangles needed for bridges and distances swum by relay teams.

Conclusion

  • Importance of understanding math concepts in real-life applications.
  • Encouragement to persist in studies despite challenges.
  • Reminder for students to engage with the material actively.

Class Participation

  • Encouraged raising hands for questions or input.
  • Interactive with students answering questions and sharing observations.

Closing Remarks

  • Reminder of the importance of applying learned strategies in different contexts.
  • End of the session with thanks and encouragement to continue studying.