Form 1 Unit 1: Lesson 6 – Introduction To Problem Solving

Objective:

At the end of the lesson, the student should be able to interpret and solve word problems.

Introduction to problem solving

Problem solving is the process of identifying a problem, developing possible solution path and taking the appropriate course of action or steps to solve the problem. The ability to solve problems is a basic skill and is essential to life. All the mathematics discovered so far has come from solving real-life problems. If you try solving a problem and you fail, don’t give up, try again, you may get it right the next time.  Problem solving is an important mathematical skill. To solve a mathematical problem, follow the steps below.

STEPS IN SOLVING PROBLEMS  

Define the problem

Read it right through to get an overview. Read it again, underlining key fact/facts. Ask yourself: What am I given?   What are the unknowns? Can I state the problem in my own words? What information if any is missing or not needed?

Generate alternatives strategy

Guess check and refine; estimate. Use concrete materials. Draw a diagram or make a model. Make up a table or chart. Look for a pattern in a number or shape. Simplify by rounding or replacing larger numbers with smaller, or breaking it into parts. Identify a sub goal.

Carry out the plan

Implement the best strategy in step 2. Show all working including diagrams and tables in a final neat, clear format. Summarize and explain what you’ve found.

Work backwards.

Once an answer or a solution is found, it is important to check that solution. Check all steps and calculations. Is the answer reasonable? Does the answer fit the problem data? Does the answer fulfill all condition or requirement of the problem?

Answer the question with a final sentence. Put your answer into a sentence that makes sense.

Note

When your problem is simple the solution is usually obvious and you don’t need to follow the entire steps.

Example 1

Find two numbers whose sum is 15 and their product is 56.

Solution

Step 1. Define the problem

Two numbers whose sum is 15 and product is 56

The unknown are two numbers; the two numbers must add up to 15 and the product of the two numbers must be 56.

Step 2. Generate alternatives strategies

The two numbers could be 5 and 10, 6 and 9, 7and 8 etc.

The two numbers must sum up to 15

 5+10=15;       9+7=15        and   7+8=15

The product of the two numbers must be 56.

5×10=50;                9×7=63           and   7×8=56

Since the first two set of numbers does not satisfy all the rules, therefore

7 and 8 are the two numbers.

Step 3. Carry out the plan

The two numbers must be 7 and 8.

The two numbers must sum up to 15.

  7 + 8 = 15

The product of the two numbers must be 56.

7 × 8 = 56

Step 5. Answer the question with a final sentence

Two numbers whose sum is 15 and product is 56 are 7 and 8.