__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.

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