1.1 Integers and Rational Numbers

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$Lesson 2a – Assessment - Scottsdale Community College - Math Blog$

www.ck12.org Chapter 13. Problem Solving13.1 A Problem-Solving PlanMuch of mathematics apply to real-world situations. To think critically and to problem solve are mathematicalabilities. Although these capabilities may be the most challenging, they are also the most rewarding.To be successful in applying mathematics in real-life situations, you must have a “toolbox” of strategies to assistyou. The last few lessons of many chapters in this FlexBook are devoted to filling this toolbox so you to become abetter problem solver and tackle mathematics in the real world.Step #1: Read and Understand the Given ProblemEvery problem you encounter gives you clues needed to solve it successfully. Here is a checklist you can use to helpyou understand the problem.√ Read the problem carefully. Make sure you read all the sentences. Many mistakes have been made by failing tofully read the situation.√ Underline or highlight key words. These include mathematical operations such as sum, difference, product, andmathematical verbs such as equal, more than, less than, is. Key words also include the nouns the situation isdescribing such as time, distance, people, etc.√ Ask yourself if you have seen a problem like this before. Even though the nouns and verbs may be different, thegeneral situation may be similar to something else you’ve seen.√ What are you being asked to do? What is the question you are supposed to answer?√ What facts are you given? These typically include numbers or other pieces of information.Once you have discovered what the problem is about, the next step is to declare what variables will represent thenouns in the problem. Remember to use letters that make sense!Step #2: Make a Plan to Solve the ProblemThe next step in the problem-solving plan is to make a plan or develop a strategy. How can the information youknow assist you in figuring out the unknown quantities?Here are some common strategies that you will learn.• Drawing a diagram• Making a table• Looking for a pattern• Using guess and check• Working backwards271
13.1. A Problem-Solving Plan www.ck12.org• Using a formula• Reading and making graphs• Writing equations• Using linear models• Using dimensional analysis• Using the right type of function for the situationIn most problems, you will use a combination of strategies. For example, drawing a diagram and looking forpatterns are good strategies for most problems. Also, making a table and drawing a graph are often used together.The “writing an equation” strategy is the one you will work with the most frequently in your study of algebra.Step #3: Solve the Problem and Check the ResultsOnce you develop a plan, you can use it to solve the problem.The last step in solving any problem should always be to check and interpret the answer. Here are some questionsto help you to do that.• Does the answer make sense?• If you substitute the solution into the original problem, does it make the sentence true?• Can you use another method to arrive at the same answer?Step #4: Compare Alternative ApproachesSometimes a certain problem is best solved by using a specific method. Most of the time, however, it can be solvedby using several different strategies. When you are familiar with all of the problem-solving strategies, it is up toyou to choose the methods that you are most comfortable with and that make sense to you. In this book, we willoften use more than one method to solve a problem. This way we can demonstrate the strengths and weaknesses ofdifferent strategies when applied to different types of problems.Regardless of the strategy you are using, you should always implement the problem-solving plan when you aresolving word problems. Here is a summary of the problem-solving plan.Step 1: Understand the problem.Step 2: Devise a plan – Translate. Come up with a way to solve the problem. Set up an equation, draw a diagram,make a chart, or construct a table as a start to begin your problem-solving plan.Step 3: Carry out the plan – Solve.Step 4: Check and Interpret: Check to see if you have used all your information. Then look to see if the answermakes sense.Solve Real-World Problems Using a PlanExample 1: Jeff is 10 years old. His younger brother, Ben, is 4 years old. How old will Jeff be when he is twice asold as Ben?Solution: Begin by understanding the problem. Highlight the key words.Jeff is 10 years old. His younger brother, Ben, is 4 years old. How old will Jeff be when he is twice as old as Ben?The question we need to answer is. “What is Jeff’s age when he is twice as old as Ben?”You could guess and check, use a formula, make a table, or look for a pattern.272
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1.1 Integers and Rational Numbers

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