Knowt
Problem Solving
Introduction to Problem Solving
Problem solving is the process of finding a solution to a question or a situation. It involves interpreting the problem, choosing the best approach, and applying mathematical concepts to arrive at a solution.
Five Step Process
Step 1: What is asked?
The first step is to understand what the problem is asking. This involves identifying the key question or objective that is needed.
Tips for Identifying What is Asked:
Underline or highlight the key question in the problem statement.
Look for keywords such as "find," "calculate," "determine," or "how many,” as they usually indicate what needs to be solved.
Restate the problem in your own words to ensure understanding.
Examples of identifying What is Asked:
Example 1: "A train travels 120 miles in 2 hours. What is the average speed of the train?"
What is asked? The problem is asking for the average speed of the train.
Example 2: "If 3 apples cost 1.50, how much would 7 apples cost?"
What is asked? The problem is asking for the cost of 7 apples.
Step 2: What is Given?
The second step is to identify the information provided in the problem.
Tips of Identifying What is Given:
List out the information provided in the problem.
Look for numerical values and relationships between them.
Identify any conditions.
Examples:
Example 1: "A train travels 120 miles in 2 hours. What is the average speed of the train?"
What is given? The distance is 120 miles, and the time is 2 hours.
Example 2: "If 3 apples cost 1.50, how much would 7 apples cost?"
What is given? 3 apples cost 1.50.
Step 3: Determine the Operation to be Used
The third step is to determine the appropriate mathematical operation(s) required to solve the problem.
Four Fundamental Operations:
Addition- is the process of finding the total or sum by combining two or more numbers.
Subtraction- is the process of finding the difference between two numbers by taking one number away from another.
Multiplication- is the process of finding the total by combining a number a certain number of times.
Division- the process of splitting a number into equal parts or groups.
Other Important Operations:
Exponent- An exponent indicates how many times a number, called the base, is multiplied by itself.
Square Roots- The square root of a number is a value that, when multiplied by itself, gives the original number.
Order of operations
Brackets first
Indices or exponents
Division and Multiplication
Addition and subtraction
Examples:
Example 1: "A train travels 120 miles in 2 hours. What is the average speed of the train?"
Operation to be used: Division.
Example 2: "If 3 apples cost 1.50, how much would 7 apples cost?"
Operation to be used: Multiplication.
Step 4: Write the Number Sentence
It involves translating the problem into a mathematical equation or expression, known as a number sentence.
Tips for Writing the Number Sentence:
Correct mathematical symbols- use the right symbol. (e.g. plus, minus, multiply, divide)
Correct equation- Write down the equation in a clear and organized manner.
Check your equation- to ensure it reflects the problem accurately.
Examples:
Example 1: "A train travels 120 miles in 2 hours. What is the average speed of the train?"
Number sentence: Speed = 120 ÷ 2.
Example 2: "If 3 apples cost 1.50, how much would 7 apples cost?"
Number sentence: Cost per apple= 1.50 ÷ 3. Total cost for 7 apples= Cost per apple × 7.
Step 5: Perform the Operation and Write the Complete Answer
This step involves calculating the result and ensuring that the answer is presented in the correct units and context.
Performing the Operation:
Perform the calculations- carefully perfom either manually or using a calculator.
Double-check- Always double-check your calculations to ensure accuracy.
Units- include units in your final answer where applicable (e.g., miles per hour, pounds, etc.).
Complete Answer- Write a clear and complete answer that fully addresses the question.
Examples:
Example 1: "A train travels 120 miles in 2 hours. What is the average speed of the train?"
Operation: 120 ÷ 2 = 60.
Complete answer: The average speed of the train is 60 miles per hour.
Example 2: "If 3 apples cost £1.50, how much would 7 apples cost?"
Operation: 1.50 ÷ 3 = 0.50 (Cost per apple). 0.50 × 7 = 3.50.
Complete answer: 7 apples would cost 3.50.
Conclusion
Problem solving is a systematic process that involves understanding the problem, identifying the given information, selecting the appropriate mathematical operations, translating the problem into a mathematical expression, and performing the necessary calculations to arrive at a solution. By following this structured approach, you can efficiently tackle mathematical problems and ensure accuracy in your results. This method not only helps in achieving correct answers but also builds confidence and critical thinking skills essential for both academic and real-world scenarios.
Problem Solving
Introduction to Problem Solving
Problem solving is the process of finding a solution to a question or a situation. It involves interpreting the problem, choosing the best approach, and applying mathematical concepts to arrive at a solution.
Five Step Process
Step 1: What is asked?
The first step is to understand what the problem is asking. This involves identifying the key question or objective that is needed.
Tips for Identifying What is Asked:
Underline or highlight the key question in the problem statement.
Look for keywords such as "find," "calculate," "determine," or "how many,” as they usually indicate what needs to be solved.
Restate the problem in your own words to ensure understanding.
Examples of identifying What is Asked:
Example 1: "A train travels 120 miles in 2 hours. What is the average speed of the train?"
What is asked? The problem is asking for the average speed of the train.
Example 2: "If 3 apples cost 1.50, how much would 7 apples cost?"
What is asked? The problem is asking for the cost of 7 apples.
Step 2: What is Given?
The second step is to identify the information provided in the problem.
Tips of Identifying What is Given:
List out the information provided in the problem.
Look for numerical values and relationships between them.
Identify any conditions.
Examples:
Example 1: "A train travels 120 miles in 2 hours. What is the average speed of the train?"
What is given? The distance is 120 miles, and the time is 2 hours.
Example 2: "If 3 apples cost 1.50, how much would 7 apples cost?"
What is given? 3 apples cost 1.50.
Step 3: Determine the Operation to be Used
The third step is to determine the appropriate mathematical operation(s) required to solve the problem.
Four Fundamental Operations:
Addition- is the process of finding the total or sum by combining two or more numbers.
Subtraction- is the process of finding the difference between two numbers by taking one number away from another.
Multiplication- is the process of finding the total by combining a number a certain number of times.
Division- the process of splitting a number into equal parts or groups.
Other Important Operations:
Exponent- An exponent indicates how many times a number, called the base, is multiplied by itself.
Square Roots- The square root of a number is a value that, when multiplied by itself, gives the original number.
Order of operations
Brackets first
Indices or exponents
Division and Multiplication
Addition and subtraction
Examples:
Example 1: "A train travels 120 miles in 2 hours. What is the average speed of the train?"
Operation to be used: Division.
Example 2: "If 3 apples cost 1.50, how much would 7 apples cost?"
Operation to be used: Multiplication.
Step 4: Write the Number Sentence
It involves translating the problem into a mathematical equation or expression, known as a number sentence.
Tips for Writing the Number Sentence:
Correct mathematical symbols- use the right symbol. (e.g. plus, minus, multiply, divide)
Correct equation- Write down the equation in a clear and organized manner.
Check your equation- to ensure it reflects the problem accurately.
Examples:
Example 1: "A train travels 120 miles in 2 hours. What is the average speed of the train?"
Number sentence: Speed = 120 ÷ 2.
Example 2: "If 3 apples cost 1.50, how much would 7 apples cost?"
Number sentence: Cost per apple= 1.50 ÷ 3. Total cost for 7 apples= Cost per apple × 7.
Step 5: Perform the Operation and Write the Complete Answer
This step involves calculating the result and ensuring that the answer is presented in the correct units and context.
Performing the Operation:
Perform the calculations- carefully perfom either manually or using a calculator.
Double-check- Always double-check your calculations to ensure accuracy.
Units- include units in your final answer where applicable (e.g., miles per hour, pounds, etc.).
Complete Answer- Write a clear and complete answer that fully addresses the question.
Examples:
Example 1: "A train travels 120 miles in 2 hours. What is the average speed of the train?"
Operation: 120 ÷ 2 = 60.
Complete answer: The average speed of the train is 60 miles per hour.
Example 2: "If 3 apples cost £1.50, how much would 7 apples cost?"
Operation: 1.50 ÷ 3 = 0.50 (Cost per apple). 0.50 × 7 = 3.50.
Complete answer: 7 apples would cost 3.50.
Conclusion
Problem solving is a systematic process that involves understanding the problem, identifying the given information, selecting the appropriate mathematical operations, translating the problem into a mathematical expression, and performing the necessary calculations to arrive at a solution. By following this structured approach, you can efficiently tackle mathematical problems and ensure accuracy in your results. This method not only helps in achieving correct answers but also builds confidence and critical thinking skills essential for both academic and real-world scenarios.
