3.1.2 Mathematical problem solving

• Why is understanding the problem and its requirements crucial in problem-solving?

  For successful problem-solving
• Match the aspect of problem understanding with its key question:

  Context ↔️ Where does this problem come from?

  Requirements ↔️ What is the problem asking you to find?

  Key Information ↔️ What are the important details given?
• What should you do with the key information extracted from the problem statement?

  Organize it clearly
• Understanding the problem involves identifying its context
• What does determining the requirements in problem-solving involve?

  Reading the problem statement
• Identifying specific values or equations is part of determining the requirements in problem-solving.

  True
• Outlining specific steps is part of planning the implementation of a solution strategy.


  True
• Verifying the solution ensures it is correct and addresses the problem effectively.


  True
• Applying the formula for the volume of a cylinder is necessary to solve the water tank problem.


  True
• Steps in developing a solution strategy

  1️⃣ Brainstorm possible approaches

  2️⃣ Evaluate the options

  3️⃣ Select a strategy

  4️⃣ Plan the steps
• For finding the area of an irregular polygon, the Shoelace formula is chosen for its directness
• What is the purpose of verifying the solution in mathematical problem-solving?

  Ensure correctness and validity
• Steps in the problem-solving process

  1️⃣ Understand the problem and its requirements

  2️⃣ Identify and extract key information

  3️⃣ Develop a solution strategy

  4️⃣ Implement the solution steps

  5️⃣ Verify the solution and its validity
• Understanding the problem involves reading the statement
• Understanding the context involves identifying relevant concepts from the curriculum
• Steps for developing a solution strategy:

  1️⃣ Brainstorm possible approaches

  2️⃣ Evaluate the options

  3️⃣ Select a strategy

  4️⃣ Plan the steps
• Identifying and extracting key information is a crucial first step in solving mathematical problems
• Identifying the requirements of a problem involves understanding what needs to be found or proven.

  True
• Determining the requirements involves understanding what the problem is asking you to find or prove.

  True
• A well-thought-out solution strategy helps you stay focused and organized during problem-solving.


  True
• Understanding the context involves identifying relevant concepts and theorems from the curriculum.


  True
• Why is understanding the context important in problem-solving?

  To identify relevant concepts
• When evaluating possible approaches, factors like complexity, efficiency, and the likelihood of success
• Methodical implementation is key to successfully solving the problem
• The requirement in the water tank example is to calculate its volume
• What is the critical first step after understanding a problem's requirements in mathematical problem-solving?

  Develop a solution strategy
• What are three possible approaches for finding the area of an irregular polygon?

  Coordinate geometry, decomposition, Shoelace formula
• Maintaining focus and double-checking work is crucial during the implementation phase.

  True
• Understanding the problem includes identifying its context, determining its requirements, and extracting the key information
• Extracting key information involves identifying important facts, figures, conditions, and assumptions
• What is the purpose of organizing key information in a table during problem-solving?

  To keep it clear and concise
• What does implementing the solution steps involve in problem-solving?

  Executing the planned approach
• What are the key parameters of the water tank described in the example?

  Radius and height
• Steps to develop a solution strategy after understanding the problem requirements

  1️⃣ Brainstorm possible approaches

  2️⃣ Evaluate the options

  3️⃣ Analyze the pros and cons

  4️⃣ Select a promising approach
• Developing a solution strategy ensures a focused and organized problem-solving process.


  True
• What is the primary goal of implementing the solution steps in mathematical problem-solving?

  Execute the planned approach
• Match the aspect of solution verification with its key question:

  Checking Requirements ↔️ Does the solution meet the problem statement?

  Logical Reasoning ↔️ Is the solution logically sound and error-free?

  Checking Assumptions ↔️ Are the assumptions valid in context?

  Evaluating Reasonableness ↔️ Does the solution make sense?