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  • 问题解决模型

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    Mario has a new baby sister. Mario's mom told him that his sister will gain weight pretty quickly at the beginning. When Mario's sister was one week old she weighed 8 pounds. A week later she weighed 8.5 pounds. A week later she weighed 9 pounds. Mario is impressed by how fast his sister is gaining weight and wonders when she will be 11 pounds if she keeps gaining weight in the same  pattern . After how many more weeks will Mario's sister weigh 11 pounds?
    ::Mario的妈妈告诉他说,他妹妹的体重会很快增加。当Mario的妹妹一周大时,她体重8磅。一周后,她体重8.5磅。一周后,她体重9磅。Mario对她的体重增速有多快印象深刻,并想知道如果她继续以同样方式增重,她什么时候会长11磅。之后,Mario的妹妹还要再多几个星期才能长11磅?

    In this concept, you will learn how to solve real world problems by making and implementing a plan.
    ::在这个概念中,你们将学会如何通过制定和执行一个计划来解决现实世界的问题。

    Problem-Solving Models
    ::解决问题模型

    Solving real world problems can be challenging when you don't know how to start to solve them. A great strategy for starting the solving process is to ask yourself three key questions.
    ::当您不知道如何开始解决现实世界问题时,解决现实世界问题可能具有挑战性。 启动解决进程的伟大策略是问自己三个关键问题。

    Key Questions:
    ::关键问题:

    1. What am I trying to find out?
      ::我到底想查出什么来?
    2. What do I know?
      ::我知道什么? 我怎么会知道? What do I know?
    3. How can I solve the problem?
      ::我怎样才能解决问题?

    Answering these questions helps you to slow down, understand the problem, and make a plan. You might have to read the problem a few times in  order  to answer the three questions and fully understand the problem.
    ::回答这些问题有助于你放慢步伐,理解问题,制定计划。你可能需要读过几次这个问题,以便回答这三个问题,并充分理解问题。

    Once you have a plan, your last two steps will be to implement your plan and then check to make sure your answer makes sense and is realistic.
    ::一旦你有一个计划,你的最后两步将是执行你的计划,然后检查以确保你的答复合理和现实。

    Here is an example.
    ::举一个例子。

    On Monday, Jake spent a total of 180 minutes on his math, history, and science homework. He spent 45 minutes on his math homework and 1 hour on his science homework. How many minutes did he spend on his history homework?
    ::星期一,Jake花在数学、历史和科学功课上的时间总共180分钟。 他用45分钟做数学功课,用1小时做科学功课。 他用多少分钟做历史功课?

    First, ask yourself "what am I trying to find out?"
    ::首先,问自己 "我到底想了解什么?"

    The last sentence of the problem tells you that you are trying to find out how many minutes Jake spent on his history homework.
    ::问题的最后一句话 告诉你,你试图找出 杰克花了多少分钟 在他的历史作业。

    Next, ask yourself "what do I know?"
    ::接下来,问自己 "我知道什么?"

    You know the following pieces of information:
    ::您知道以下信息:

    • Jake spent 180 minutes total on his math/history/science homework.
      ::Jake在数学/历史/科学功课上总共花了180分钟。
    • Jake spent 45 minutes on math homework.
      ::Jake花45分钟做数学功课
    • Jake spent 60 minutes (1 hour) on science homework.
      ::Jake花了60分钟(1小时)做科学作业。

    Then, ask yourself "how can I solve the problem?"
    ::然后问自己 "我怎样才能解决问题?"

    You know that the amount of time Jake spends on each of his three subjects combined should equal the total amount of time he spent on his homework. You can write this relationship as an  equation  and  substitute  what you know.
    ::你知道Jake花在三个科目上的时间总和 应该等于他花在家庭作业上的时间总数。你可以写这个关系作为一个方程式, 并取代你所知道的东西。

    Now, implement your plan. Your unknown value is the amount of time Jake spent on history homework so you can let  x = History Time .
    ::现在,执行你的计划。你未知的价值是 Jake花在历史作业上的时间, 这样你就可以让x=历史时间。

    Now, simplify the right side of the equation.
    ::现在,简化方程的右侧。

    180 = 105 + x
    ::180=105+x

    Next, solve the equation using mental math. "180 equals 105 plus what number?" 105 plus 75 equals 180, so  x  must be equal to 75.
    ::接下来,用心理数学解析方程式。 “ 180等于105加什么数字? ” 105加75等于180, 所以x必须等于75。

    x = 75
    ::x = 75

    The answer is that Jake spent 75 minutes on his history homework.
    ::答案是Jake花75分钟做历史作业

    Once you have an answer, make sure that you have actually answered the original question that was asked and that your answer seems realistic. You were trying to find out how much time Jake spent on his history homework and that's exactly what you did. 75 minutes is a realistic amount of time to spend on a homework assignment so your answer makes sense.
    ::一旦你得到答案,请确定你实际上已经回答了最初提出的问题,而且你的答复似乎很现实。你试图弄清楚Jake花了多少时间做他的历史作业,而这正是你所做的。75分钟是用于做家庭作业的实际时间,所以你的答复是有道理的。

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Mario and his new baby sister.
    ::之前,你得到一个问题 关于马里奥和他的新妹妹。

    She is gaining weight each week. When she was one week old she weighed 8 pounds. Then one week later she weighed 8.5 pounds. Then one week later she weighed 9 pounds. Mario wonders when she will weigh 11 pounds if she keeps gaining the same amount of weight each week.
    ::她每星期都在增加体重。当她一周大时,她体重8磅。 一周后,她体重8.5磅。 一周后,她体重9磅。 Mario想知道,如果她每星期的体重仍然相同,她什么时候会重11磅。

    First, ask yourself "what am I trying to find out?"
    ::首先,问自己 "我到底想了解什么?"

    You are trying to figure out in how many weeks Mario's sister will weigh 11 pounds.
    ::你想弄清楚马里奥的妹妹 几星期内会重11磅

    Next, ask yourself "what do I know?"
    ::接下来,问自己 "我知道什么?"

    You know the following pieces of information:
    ::您知道以下信息:

    • At one week Mario's sister weighed 8 pounds, then one week later 8.5 pounds, then one week later 9 pounds.
      ::一个星期,Mario的妹妹体重8磅, 一周后8.5磅, 一周后9磅。
    • There is a pattern to how much Mario's sister weighs each week.
      ::马里奥妹妹每周体重是多少 是有规律的

    Then, ask yourself "how can I solve the problem?"
    ::然后问自己 "我怎样才能解决问题?"

    You should first figure out what the pattern is and see if you can extend it. Then, you can figure out when Mario's sister will hit 11 pounds.
    ::你应该先弄清楚图案的图案,然后看能不能延长。然后,你可以弄清楚马里奥的妹妹什么时候会重11磅。

    Mario's sister's weights each week so far are
    ::马里奥妹妹每周体重

    8, 8.5, 9, ...

    The pattern is that she is gaining 0.5 pound each week. If she continues gaining at that  rate  her weights will look like
    ::模式是,她每星期增加0.5磅,如果她继续以这个速度增长,她的体重就会像

    8, 8.5, 9, 9.5, 10, 10.5, 11, ...

    If Mario's sister currently weighs 9 pounds, that means in 4 more weeks she will weigh 11 pounds.
    ::如果马里奥的妹妹现在体重9磅 也就是说再过4周她就会重11磅

    The answer is that Mario's sister will weigh 11 pounds in 4 weeks.
    ::答案是马里奥的妹妹 4周内会重11磅

    Remember that once you have an answer, you want to check that you have actually answered the original question that was asked and that your answer seems realistic. You were trying to find out in how many weeks Mario's sister will weigh 11 pounds and that's what you did. 4 weeks is a realistic amount of time for Mario's sister to gain 2 pounds so your answer makes sense.
    ::记住,一旦你得到答案,你想要确认你实际上回答了最初提出的问题,而且你的答复似乎很现实。你试图弄清楚马里奥的妹妹在几星期内会重11磅,这就是你所做的。4周是马里奥的妹妹得到2磅的实际时间,所以你的回答是有道理的。

    Example 2
    ::例2

    Solve the following real world problem.
    ::解决以下现实世界问题。

    A sandwich shop sold 36 tuna fish sandwiches and 45 roast beef sandwiches. The shop sold three times as many turkey sandwiches as tuna sandwiches. How many turkey sandwiches did the shop sell?
    ::一家三明治店卖了36个金枪鱼三明治和45个烤牛肉三明治,卖的火鸡三明治是金枪鱼三明治的三倍。

    First, ask yourself "what am I trying to find out?"
    ::首先,问自己 "我到底想了解什么?"

    The last sentence of the problem tells you that you are trying to find out how many turkey sandwiches the shop sold.
    ::问题的最后一句话 告诉你,你试图找出 有多少火鸡三明治 商店出售。

    Next, ask yourself "what do I know?"
    ::接下来,问自己 "我知道什么?"

    You know the following pieces of information:
    ::您知道以下信息:

    • The shop sold 36 tuna fish sandwiches.
      ::该店出售了36个金枪鱼三明治。
    • The shop sold 45 roast beef sandwiches.
      ::商店卖了45个烤牛肉三明治
    • The shop sold 3 times as many turkey sandwiches as tuna sandwiches.
      ::商店卖的火鸡三明治是金枪鱼三明治的三倍。

    Then, ask yourself "how can I solve the problem?"
    ::然后问自己 "我怎样才能解决问题?"

    You can use the fact that the shop sold 3 times as many turkey sandwiches as tuna sandwiches to determine the number of turkey sandwiches. Take the number of tuna sandwiches and multiply it by 3.
    ::你可以利用店里卖的火鸡三明治是金枪鱼三明治的三倍 来决定火鸡三明治的数量。用金枪鱼三明治的数量乘以3。

    Now, implement your plan.
    ::现在,执行你的计划

    The answer is that the shop sold 108 turkey sandwiches.
    ::答案是商店卖了108个火鸡三明治

    Notice that this problem contained extra information. You didn't need to know the number of roast beef sandwiches. Sometimes extra information is added to distract you.
    ::请注意这个问题包含额外信息。 您不需要知道烤牛肉三明治的数量。 有时会添加额外信息来分散您的注意力 。

    Now that you have your answer, you want to make sure that you have actually answered the original question that was asked and that your answer seems realistic. You were trying to find out how many turkey sandwiches the shop sold and that's what you did. 108 turkey sandwiches seems like a realistic number of sandwiches for a sandwich shop to sell, so your answer makes sense.
    ::现在你有了答案,你想要确保你实际上已经回答了最初提出的问题,而且你的答案似乎很现实。你试图弄清楚商店卖了多少火鸡三明治,这就是你做的。108个火鸡三明治似乎是一个三明治店卖的三明治,所以你的答案是有道理的。

    Example 3
    ::例3

    When approaching a problem, what is the first thing you should do?
    ::当面对一个问题时,你首先应该做什么?

    The answer is that the first thing you always have to do is read the problem carefully. Then, you should ask yourself "what am I trying to figure out?" as you start to understand the problem.
    ::答案是,你必须做的第一件事就是仔细阅读问题。然后,你应该问自己:“我到底想了解什么?” 当你开始理解问题的时候。

    Example 4
    ::例4

    Solve the following real world problem.
    ::解决以下现实世界问题。

    William began a fitness schedule. He ran 2 miles the first week, 2.5 miles the second week, and 3 miles the third week. If the pattern continues, how many miles will William have  run  after 5 weeks?
    ::威廉开始健身计划。他第一周跑2英里,第二周跑2.5英里,第三周跑3英里。如果模式继续下去,威廉在5周后会跑多少英里?

    First, ask yourself "what am I trying to find out?"
    ::首先,问自己 "我到底想了解什么?"

    The last sentence of the problem tells you that you are trying to find out how many miles William will have run total after 5 weeks.
    ::问题的最后一句话告诉你 你试图找出 威廉在5周后 总共会跑多少英里

    Next, ask yourself "what do I know?"
    ::接下来,问自己 "我知道什么?"

    You know the following pieces of information:
    ::您知道以下信息:

    • William ran 2 miles the first week.
      ::威廉第一周跑2英里
    • William ran 2.5 miles the second week.
      ::威廉在第二周跑了2.5英里
    • William ran 3 miles the third week.
      ::威廉在第三周跑3英里
    • There is a pattern to how many miles he runs each week.
      ::他每周跑多少英里是有规律的

    Then, ask yourself "how can I solve the problem?"
    ::然后问自己 "我怎样才能解决问题?"

    You should first figure out what the pattern is and see if you can extend it. Then, you can determine how many miles William ran in weeks 4 and 5. Finally, you can add up how many miles he ran in each of the five weeks to find the total.
    ::首先你应该先弄清楚图案的图案,然后看能不能延长图案。然后,你可以确定威廉在4周和5周中跑了多少英里。最后,你可以算出他在这5周中每一周跑了多少英里来寻找总数。

    Now, implement your plan.
    ::现在,执行你的计划

    The number of miles he ran in the first three weeks is
    ::他前三个星期跑的里程数是

    2, 2.5, 3,...

    The pattern is that he is running 0.5 mile more each week. If he continued the pattern it would look like
    ::模式是,他每星期多跑0.5英里,如果他继续这种模式,就会看起来像

    2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, ...

    This means in the fourth week William ran 3.5 miles and in the fifth week William ran 4 miles.
    ::这意味着在第四周威廉跑3.5英里 第五周威廉跑4英里

    Now, you can figure out how many miles William ran total in 5 weeks by adding up the number of miles from each of the 5 weeks.
    ::现在,你可以计算出威廉在5周内 总共跑了几英里, 加上5周里每一英里的英里数。

    2 + 2.5 + 3 + 3.5 + 4 = 15   m i l e s
    ::2 + 2.5 + 3 + 3.5 + 4 = 15米i l e s

    The answer is that William ran 15 miles in 5 weeks.
    ::答案是威廉在5周内跑15英里

    Remember that once you have an answer, you want to make sure that you have actually answered the original question that was asked and that your answer seems realistic. You were trying to find out how many miles William ran in 5 weeks and that's what you did. 15 miles is a realistic number of miles to run in 5 weeks so your answer makes sense.
    ::记住,一旦你得到答案,你想要确保你实际上已经回答了最初提出的问题,而且你的答复似乎很现实。你试图弄清楚威廉在5周内跑了多少英里,这就是你所做的。15英里是一个现实的5周内跑多少英里,所以你的答复是有道理的。

    Example 5
    ::例5

    True or false: Once you have an answer your work is finished.
    ::真实的或虚假的:一旦你得到答案,你的工作就完成了。

    The answer is this statement is false. It's always important to check your answer before moving on. You want to make sure you have answered the question that was asked and that your answer is realistic and makes sense.
    ::答案是这个声明是虚假的。 在继续之前检查您的回答总是很重要。 您想要确认您已经回答了询问的问题, 您的回答是现实的, 并且合理 。

    Review
    ::回顾

    Solve each real world problem by first asking yourself the key questions and making a plan. Be sure to check your answers.
    ::解决现实世界的每一个问题,先向自己提出关键问题,然后制定计划。一定要检查一下答案。

    1. Giovanni is working to improve his scores on his weekly science quizzes. The following were his scores for the first four weeks of school: 64, 70, 76, 82. If the pattern continues, in which week will Giovanni’s score be 100?
      ::乔瓦尼正在努力提高他每周科学测验的得分。 以下是他上学头四个星期的得分:64、70、76、82。 如果这种模式继续下去,那么乔瓦尼的得分将在哪个星期是100?
    2. Lola’s Bakery uses 62 pounds of flour and 19 pounds of sugar each week. The bakery uses half as much butter as flour each week. How much butter will the bakery use in a month’s time?
      ::罗拉斯面包店每周使用62磅面粉和19磅糖。 面包店每周使用一半的黄油和面粉。 一个月后面包店将使用多少黄油?
    3. A children’s pool holds 6 cubic meters of water. The length of the pool is three times the height and the width of the pool is twice the height. What is the height of the pool?
      ::儿童游泳池有6立方米的水,水池长度是水池高度的三倍,水池宽度是水池高度的两倍。游泳池的高度是多少?
    4. Martin went to the state fair with $30. He rode on 17 rides and came home with $4.50. How much did each ride cost?
      ::马丁带着30美元去州集市 他骑了17次车 带着4.50美元回家
    5. Lionel arranged 24 photos in an album. The number of photos in each row is two more than the number of rows. How many rows of photos are there?
      ::Lionel在相册中安排了 24 张照片。 每行的相片数比行数多两行。 有多少行相片?
    6. An aquarium has four fish tanks it wants to arrange on a shelf. The shelf has an area of 196 square feet. The area of second tank is twice the area of the first tank, and the area of the third tank is four times the area of the second tank. The area of the third tank is 56 square feet. If the aquarium puts all three tanks on the shelf, how much shelf area will be left over?
      ::水族馆有4个鱼箱,它想在架子上安排。大陆架面积为196平方英尺。第二坦克面积是第一坦克面积的两倍,第三坦克面积是第二坦克面积的四倍。第三坦克面积是56平方英尺。如果水族馆将所有3个水箱都放在架子上,那么将留下多少架子面积?
    7. The Durands are driving 456 miles to the family reunion. If they split the drive equally over three days, how many miles will they drive each day?
      ::Durands夫妇开着456英里的车去家庭团聚。 如果他们在三天内将驱动器平分,他们每天开多少英里?
    8. At the end of a video game tournament, Raul and Martha had both scored twice as many points as Justice. If their total combined points is 285, how many points did each Justice score?
      ::游戏比赛结束时,劳尔和玛莎的得分都是正义的两倍。 如果他们的总得分是285,那么每个正义得分有多少?
    9. At the lunch counter, Ariana bought a sandwich and lemonade. The sandwich cost five times as much as the lemonade. She paid with $10 and got $2.50 in change. How much did the sandwich cost? How much did the lemonade cost?
      ::在午餐柜台,阿丽亚娜买了三明治和柠檬汁,三明治的价格是柠檬汁的五倍,她付了10美元,换了2.50美元。三明治花了多少钱?柠檬水花了多少钱?
    10. The area of a playground is  40.5   m 2 . The width of the playground is 4.5 meters. What is the length of the playground?
      ::运动场的宽度是4.5米。操场的长度是多少?

    Write five of your own problems. Be sure that one uses addition, one uses subtraction, one uses multiplication, one uses division and one uses a pattern that requires a table.
    ::写入您自己的问题 。 请确定一个使用添加, 一个使用减法, 一个使用乘法, 一个使用分数, 一个使用需要表格的模式 。

    Review (Answers)
    ::回顾(答复)