DEFINE ROUTINE PROBLEMS WITH EXAMPLES.
DEFINE NON-ROUTINE PROBLEMS WITH EXAMPLES.
Answer (1)
Answer:Routine ProblemsDefinition: Routine problems are those that can be solved by applying a known procedure, algorithm, or a series of well-defined steps. They typically have a clear question, provide all necessary facts or numbers, and the method for solving them is familiar and has often been practiced before. The primary task in solving a routine problem is to identify the appropriate operation or procedure and execute it correctly. They often involve basic arithmetic operations and are practical in nature, serving a socially useful function for daily life.Characteristics:* Predictable solutions.* Direct application of previously learned algorithms or formulas.* Often involve a single or a straightforward sequence of arithmetic operations.* The path to the solution is usually clear.Examples:1. Calculating the total cost of groceries: * Problem: You buy a loaf of bread for $3.50, a gallon of milk for $4.00, and a dozen eggs for $2.75. How much do you spend in total?2. Finding the area of a rectangle: * Problem: A rectangular garden is 10 meters long and 5 meters wide. What is its area?3. Determining change from a purchase: * Problem: You buy an item for $12.50 and pay with a $20 bill. How much change should you receive?4. Calculating hourly wages: * Problem: An employee earns $15 per hour and works for 40 hours in a week. How much does the employee earn that week?Non-Routine ProblemsDefinition: Non-routine problems are complex problems that do not have an immediately obvious solution method or a standard algorithm that can be directly applied. They often require creative thinking, strategic planning, and the use of various problem-solving heuristics (strategies that increase the probability of finding a solution but don't guarantee it). The procedure for solving them is unknown, and they may have multiple distinct ways to arrive at a solution or even multiple acceptable solutions. These problems aim to develop higher-order thinking skills, mathematical reasoning, and flexibility in problem-solving.Characteristics:* No readily available formula or step-by-step procedure.* Requires original or creative thinking.* Often involves a search for heuristics or strategies.* May have multiple solution paths or multiple acceptable solutions.* Can be ill-defined or replicate real-life situations without clear keywords for a solution.Examples:1. The "Handshake Problem": * Problem: If there are 10 people in a room and each person shakes hands with every other person exactly once, how many handshakes occur?2. Estimating a large quantity: * Problem: Approximately how many piano tuners are there in the city of Manila?3. The "Magic Triangle" or "Number Puzzle": * Problem: Place the numbers 1 to 9, one in each circle of a triangle diagram, so that the sum of the four numbers along any of the three sides of the triangle is 20.4. Optimizing a route: * Problem: You need to visit five different stores in a city, starting and ending at your home, to minimize the total travel time. How do you plan your route?
