Guide :Middle School

Compatible numbers for 2.4 and –0.18 are 2.5 and –0.2. What is the estimation of the product of (2.4)(–0.18) using these compatible numbers?

Compatible numbers for 2.4 and –0.18 are 2.5 and –0.2. What is the estimation of the product of (2.4)(–0.18) using these compatible numbers?
1 P´olya’s Problem-Solving Process Problem-solving is the cornerstone of school mathematics. The main reason of learning mathematics is to be able to solve problems. Mathematics is a powerful tool that can be used to solve a vast variety of problems in technology, science, business and finance, medecine, and daily life. It is strongly believed that the most efficient way for learning mathematical concepts is through problem solving. This is why the National Council of Teachers of Mathematics NCTM advocates in Principles and Standards for School Mathematics, published in 2000, that mathematics instruction in American schools should emphasize on problem solving and quantitative reasoning. So, the conviction is that children need to learn to think about quantitative situations in insightful and imaginative ways, and that mere memorization of rules for computation is largely unproductive. Of course, if children are to learn problem solving, their teachers must themselves be competent problem solvers and teachers of problem solving. The techniques discussed in this and the coming sections should help you to become a better problem solver and should show you how to help others develop their problem-solving skills. P´olya’s Four-Step Process In his book How to Solve It, George P´olya identifies a four-step process that forms the basis of any serious attempt at problem solving. These steps are: Step 1. Understand the Problem Obviously if you don’t understand a problem, you won’t be able to solve it. So it is important to understand what the problem is asking. This requires that you read slowly the problem and carefully understand the information given in the problem. In some cases, drawing a picture or a diagram can help you understand the problem. Step 2. Devise a Plan There are many different types of plans for solving problems. In devising a plan, think about what information you know, what information you are looking for, and how to relate these pieces of information. The following are few common types of plans: • Guess and test: make a guess and try it out. Use the results of your guess to guide you. 4 • Use a variable, such as x. • Draw a diagram or a picture. • Look for a pattern. • Solve a simpler problem or problems first- this may help you see a pattern you can use. • make a list or a table. Step 3. Carry Out the Plan This step is considered to be the hardest step. If you get stuck, modify your plan or try a new plan. Monitor your own progress: if you are stuck, is it because you haven’t tried hard enough to make your plan work, or is it time to try a new plan? Don’t give up too soon. Students sometimes think that they can only solve a problem if they’ve seen one just like it before, but this is not true. Your common sense and natural thinking abilities are powerful tools that will serve you well if you use them. So don’t underestimate them! Step 4. Look Back This step helps in identifying mistakes, if any. Check see if your answer is plausible. For example, if the problem was to find the height of a telephone pole, then answers such as 2.3 feet or 513 yards are unlikely-it would be wise to look for a mistake somewhere.  ...

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