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7. A gardener is asked to plant ten trees in five rows, with each row containing four trees. How did he do this?

7. A gardener is asked to plant ten trees in five rows, with each row containing four trees. How did he do this?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve each of the following problems using the problem-solving strategies discussed in this section. Include what type of strategy was used in solving the problem. Note: Lesson in the Photo attached
7. A gardener is asked to plant ten trees in five rows, with each row containing four trees. How did he do this?
Transcribed Image Text:7. A gardener is asked to plant ten trees in five rows, with each row containing four trees. How did he do this?
8:00 cdn.fbsbx.com Mathematics in the Modern World Hand Outs Done Problem Solving and Reasoning Problem-solving has been an integral part of the mathematics curriculum that must be taught alongside the various mathematical concepts and skills necessary for success in school and in real life. Most occupations require good problem-solving skills. This section aims to help you become a better problem solver and to show that problem-solving can be an enjoyable experience. In cognitive psychology, problem-solving refers to the mental process people go through to discover, analyze, and solve problems. George Polya (1877-1985) defines it as an act to find a way out of difficulty, find a way around an obstacle, find a way where none is known, and attain a desired end that is not immediately attainable by direct means. Problem-solving involves all of the steps in the problem process, including the discovery of the problem, the decision to tackle the issue, understanding the problem, researching the available options and taking actions to achieve your goals. Common Problem-Solving Strategies/Heuristics Heuristics are procedures or strategies that do not guarantee a solution to a problem but provide a more highly probable method for discovering the solution to a problem. There are many reasonable ways to solve problems. You will find choosing a strategy increasingly easy. Here is a partial list of problem-solving strategies: 1. Working backwards - This strategy is used to solve problems is used to solve problems that include a number of linked factors or events, where some of the information has not been provided, usually at the beginning of the problem. This entails starting with the end results and reversing the steps you need to get those results to figure out the answer to the problem. 2. Guess and Check-Often referred to as "Trial and Error", it is important to recognize that an error really isn't a mistake at all, it helps to guide the problem solver to the next attempt at the answer. The following are the essential features of the guess and check strategy: a. Make an "educated" guess at the solution. b. Check the guess against the conditions of the problem. c. Use the information obtained in checking to make a better guess. d. Continue this procedure until the correct answer is obtained 3. Make a Diagram - Drawing a diagram is the most common problem-solving strategy. Very often, a problem solver needs to draw a diagram just to understand the meaning of the problem. The diagram represents the problem in a way we can see it, understand it, and think about it while looking for the next step. When you draw a diagram, you organized information spatially, which then allows the visual part of your brain to become more involved in the problem-solving process. 4. Make a List - Making a list is a systematic method of organizing information in rows and/or columns. By putting the given information in an organized list, you can clearly analyze this information and then solve the problem by completing the list. By making a systematic list, one will see every possible combination. 5. Look for a Pattern - This strategy entails looking for patterns in the data in order to solve the problem, that is, the solver looks for items or numbers that are repeated or at
Transcribed Image Text:8:00 cdn.fbsbx.com Mathematics in the Modern World Hand Outs Done Problem Solving and Reasoning Problem-solving has been an integral part of the mathematics curriculum that must be taught alongside the various mathematical concepts and skills necessary for success in school and in real life. Most occupations require good problem-solving skills. This section aims to help you become a better problem solver and to show that problem-solving can be an enjoyable experience. In cognitive psychology, problem-solving refers to the mental process people go through to discover, analyze, and solve problems. George Polya (1877-1985) defines it as an act to find a way out of difficulty, find a way around an obstacle, find a way where none is known, and attain a desired end that is not immediately attainable by direct means. Problem-solving involves all of the steps in the problem process, including the discovery of the problem, the decision to tackle the issue, understanding the problem, researching the available options and taking actions to achieve your goals. Common Problem-Solving Strategies/Heuristics Heuristics are procedures or strategies that do not guarantee a solution to a problem but provide a more highly probable method for discovering the solution to a problem. There are many reasonable ways to solve problems. You will find choosing a strategy increasingly easy. Here is a partial list of problem-solving strategies: 1. Working backwards - This strategy is used to solve problems is used to solve problems that include a number of linked factors or events, where some of the information has not been provided, usually at the beginning of the problem. This entails starting with the end results and reversing the steps you need to get those results to figure out the answer to the problem. 2. Guess and Check-Often referred to as "Trial and Error", it is important to recognize that an error really isn't a mistake at all, it helps to guide the problem solver to the next attempt at the answer. The following are the essential features of the guess and check strategy: a. Make an "educated" guess at the solution. b. Check the guess against the conditions of the problem. c. Use the information obtained in checking to make a better guess. d. Continue this procedure until the correct answer is obtained 3. Make a Diagram - Drawing a diagram is the most common problem-solving strategy. Very often, a problem solver needs to draw a diagram just to understand the meaning of the problem. The diagram represents the problem in a way we can see it, understand it, and think about it while looking for the next step. When you draw a diagram, you organized information spatially, which then allows the visual part of your brain to become more involved in the problem-solving process. 4. Make a List - Making a list is a systematic method of organizing information in rows and/or columns. By putting the given information in an organized list, you can clearly analyze this information and then solve the problem by completing the list. By making a systematic list, one will see every possible combination. 5. Look for a Pattern - This strategy entails looking for patterns in the data in order to solve the problem, that is, the solver looks for items or numbers that are repeated or at
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