1.17猜测和检查，向后工作

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  猜测和检查，向后工作

  

  [Figure 1]

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  Jenn is washing cars with her volleyball team to raise money for the state competition. At first, she kept careful track of the number of cars the team washed per hour, but then things got really busy, and she lost count. She knows that the team earned $2.00 per car, and that they earned $144 total by the end of the day on Sat. If Jenn knows from her notes that they washed 5 cars the first hour, 5 the second hour, and 10 the third hour, how many did they average per hour for the last 4 hours?
  ::Jenn正和她的排球队一起洗车,为州比赛筹集资金。 首先,她仔细追踪了团队每小时洗车的车数,但随后事情变得非常繁忙,她失去了计数。 她知道团队每辆车挣2美元,在周日当天结束时他们总共赚了144美元。 如果Jenn从她的笔记中知道他们头一小时洗5辆汽车,第二小时5辆,第三小时10辆,过去4小时每小时平均洗多少车?

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  In this concept, you will learn how to solve problems using the strategy 'Guess, Check and Revise.'
  ::在这个概念中,你将学会如何用“建议、检查和审校”的战略解决问题。

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  Guess and Check
  ::猜测和检查

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  Sometimes, the most efficient way to solve a problem is to simply make an 'educated guess' and see how close it comes to being correct. Then you can apply what you learned from the first guess to improve future guesses until you have the right answer.
  ::有时候,解决问题的最有效方法就是简单地做个“教育猜想 ” , 并看看它离正确程度有多近。 然后,你可以应用从第一个猜想中学到的东西来改进未来的猜想,直到你找到正确的答案。

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  The trick to making the  Guess and Check  method work well is to pay attention to how each new guess affects the answer. This way, even if it requires multiple guesses, they each get closer to being correct instead of you just hoping that a wild guess will happen to work (which may  never  happen)!
  ::让猜和检查方法成功的关键在于关注每个新猜想如何影响答案。 这样,即使需要多个猜想,它们都更接近于正确,而不是你只希望一个疯狂猜想会成功(可能永远不会发生 ) !

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  Examples
  
  ::实例

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  Example 1
  
  ::例1

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  Earlier, you were given a problem about Jenn and her car wash cash conundrum.
  ::早些时候,你得到一个问题 关于珍和她的洗车 现金难题。

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  She knows that the team earned $2.00 per car, that they earned $144 total, that they washed 5 cars the first hour, 5 the second hour, and 10 the third hour. She wants to know how many cars they washed (on average) per hour for the last 4 hours.
  ::她知道小组每辆车挣2美元,总共赚144美元,头一小时洗5辆,第二小时5辆,第三小时10辆。 她想知道过去4小时每小时(平均)洗多少辆。

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  First, write an  expression  to represent the number of cars the team washed, based on the money they earned. $2 times the number of cars Jenn wrote down plus 4 times the average for each of the four hours she didn't, equals $144.
  ::首先,写一个表达式来代表团队洗过的汽车数量, 以他们赚到的钱为基础。 珍写下来的汽车数量是珍写下来的2倍, 加上她没有洗过的四个小时中每个小时的平均数的4倍, 等于144美元。

  $$\begin{array}{r}\$2(5+5+10+4x)=\$144\end{array}$$

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  Then, make an educated guess at the number of cars the team washed per hour during the last 4 hours. Since the team washed 10 cars during the last hour Jenn recorded, start by guessing 10:
  ::然后,对过去4小时内每小时洗的车数进行有教育性的猜测。 由于小组在最后1小时里洗了10辆汽车,首先猜测10辆:

  $$\begin{array}{rl}\$2(5+5+10+4\times 10)=& \$144\text{Is this true?}\\ \$2(5+5+10+40)=& \$144\\ \$2(60)=& \$144\\ \$120=& \$144\text{No, this is not true. It is too low}\end{array}$$

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  If the team had washed 10 cars per hour for the last 4 hours, they would have only earned $120. Since they earned more than that (although not a  lot  more), try a slightly larger number, 13 cars per hour.
  ::如果小组在过去4小时里每小时洗10辆汽车,他们只挣120美元。 由于他们挣的钱(虽然不多)超过120美元,所以尝试多一点,每小时13辆。

  $$\begin{array}{rl}\$2(5+5+10+4\times 13)=& \$144\text{Is this true?}\\ \$2(5+5+10+52)=& \$144\\ \$2(72)=& \$144\\ \$144=& \$144\text{Yes, this is true.}\end{array}$$

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  Jenn's team washed an average of 13 cars per hour for the last four hours.
  ::Jenn的小队过去四个小时平均每小时洗13辆车。

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  Example 2
  
  ::例2

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  Betsy picked a bunch of apples. She wanted to give some to her neighbor. She kept a bowl of apples for herself and gave her neighbor five more apples than she kept for herself.
  ::贝茜摘了一堆苹果,她想给邻居一些。她为自己留了一碗苹果,给邻居的苹果比自己多5个。

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  If the total number of apples picked was 25, how many did Betsy keep for herself?
  ::如果摘的苹果总数是25个 贝茜自己留了多少?

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  To solve this problem, you can write the following expression.
  ::要解决这个问题,您可以写入下面的表达式。

  $$\begin{array}{r}x+(x+5)=25\end{array}$$

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  In this case, the  $\begin{array}{r}x\end{array}$  represents the number of apples Betsy kept for herself. 
  ::在本案中,x代表自己保存的苹果Betsy的数量。

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  Next, simply guess and check until you get the correct answer.
  ::接下来,只是猜测和检查,直到你得到正确的答案。

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  Guess that Betsy kept 7 apples for herself:
  ::我猜贝茜为自己留了7个苹果

  $$\begin{array}{rl}7+\left(7+5\right)=& 25\text{Is this true?}\\ 7+12=& 25\\ 19=& 25\text{No, this is not true.}\end{array}$$

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  The answer you want is 25, not 19. So Betsy kept more than 7 apples for herself.
  ::你想要的答案是25,而不是19 所以Betsy为自己保留了超过7个苹果

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  Guess that she kept 12 apples:
  ::我猜她留了12个苹果

  $$\begin{array}{rl}12+(12+5)=& 25\text{Is this true?}\\ 12+17=& 25\\ 29=& 25\text{No, this is not true.}\end{array}$$

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  29 is too many, but it is closer, since 29 is only 4 more than 25.
  ::29是太多,但更接近,因为29比25多4。

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  Try a number between 7 and 12, that is a little closer to 12 than 7.
  ::尝试在 7 到 12 之间的数字, 离 12 到 7 略近一点 。

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  Try guessing that Betsy kept 10 apples for herself.
  ::试猜猜贝茜为自己留了10个苹果

  $$\begin{array}{rl}10+(10+5)=& 25\text{Is this true?}\\ 10+15=& 25\\ 25=& 25\text{Yes, this is true!}\end{array}$$

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  This works!
  ::这行得通!

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  The answer is Betsy kept 10 apples and gave her neighbor 15 apples.
  ::答案是贝茜保留了10个苹果 给了她的邻居15个苹果

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  Example 3
  ::例3

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  Kyle caught 15 fish in one day. In his first bucket he put 1 more fish than his second. How many fish were in his first bucket?
  ::Kyle在一天内捕获了15条鱼,在第一个桶里,他放的鱼比第二个多1条。他的第一个桶里有几条鱼?

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  First, consider the information given in the problem. There are 15 fish in two buckets, and the second bucket has one less fish than the first bucket.
  ::首先,考虑问题中提供的信息。两桶中有15条鱼,第二桶的鱼比第一桶少1条。

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  Next, write an  equation  to represent the information. If  $\begin{array}{r}f\end{array}$  represents the number of fish in the first bucket, then  $\begin{array}{r}f-1\end{array}$  would be the number in the second bucket.
  ::接下来,写一个方程式来表示信息。如果 f 表示第一个桶中的鱼数量,那么f - 1 将是第二个桶中的数量。

  $$\begin{array}{r}f+(f-1)=15\end{array}$$

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  Then, make an educated guess about the number of fish in the first bucket. You know the number of fish in each bucket is nearly the same, so try a number close to half of 15. Try 8:
  ::然后,对第一个桶里鱼的数量做一个有教育性的猜测。你知道每个桶里鱼的数量几乎相同, 所以尝试一个接近15的一半的数, 尝试8:

  $$\begin{array}{rl}8+(8-1)=& 15\text{Is this true?}\\ 8+7=& 15\\ 15=& 15\text{Yes, this is true.}\end{array}$$

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  The answer is 8 fish.
  ::答案是8条鱼

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  Example 4
  ::例4

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  How many fish were in Kyle's second bucket?
  ::凯尔第二桶里有几条鱼?

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  The answer is 7 fish.
  ::答案是7条鱼

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  Example 5
  ::例5

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  Kyle's friend Jane went fishing also. If the number of fish they caught were all put together, there would be 33. How many fish did Jane catch?
  ::凯尔的朋友简也去钓鱼了 如果他们捕获的鱼数量被加在一起

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  First, write an expression to show the information given in the problem. Use  $\begin{array}{r}j\end{array}$  to represent Jane's fish.
  ::首先,写一个表达式来显示问题中所提供的信息。 使用 j 来代表 Jane 的鱼 。

  $$\begin{array}{r}15+j=33\end{array}$$

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  Next, make an educated guess about the number of fish Jane caught. Since 15 times 2 would only be 30, Jane must have caught at least a few more fish than Kyle. Try 19:
  ::接下来,你对珍捕获的鱼数做一个教育性的猜测。因为15乘以2只有30,简一定比凯尔多捕了几条鱼。尝试19:

   

  $$\begin{array}{rl}15+19=& 33\text{Is this true?}\\ 34=& 33\text{No, this is not true. The number is a little too high.}\end{array}$$

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  Jane could not have caught 19 fish, since that would have made the total just a bit too high. Try 18:
  ::Jane不可能捕到19条鱼,因为这会使鱼总数太高。

  $$\begin{array}{rl}15+18=& 33\text{Is this true?}\\ 33=& 33\text{Yes, this is true.}\end{array}$$

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  Jane caught 18 fish.
  ::Jane钓到18条鱼

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  Review
  ::回顾

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  Solve each of the following problems using the four part problem solving plan.
  ::使用四个部分的解决问题计划解决以下每一个问题。

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  A small lion weighs in at 330 pounds. A large lion weighs in at 500 pounds.
  ::一只小狮子体重330磅 一只大狮子体重500磅

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  1. If there are four large lions in the habitat, how much do the lions weigh in all?
     ::如果在栖息地里有四头大狮子, 狮子的重量有多大呢?
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  2. If there are five small lions in the habitat, what is the total weight of the small lions?
     ::如果栖息地里有五只小狮子 那么小狮子的总重量是多少?
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  3. If a lion can sleep 20 hours in one day, how many hours is a lion asleep over a period of five days?
     ::如果狮子一天能睡20小时, 狮子在五天内睡了多少小时?
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  4. If a lion sleeps this much, how many hours is the lion awake over a period of three days?
     ::如果狮子睡了这么多, 狮子在三天的时间里醒了多少小时?
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  5. A Burchell’s zebra is smaller than a Grevy’s zebra, the Burchell’s zebra weighs about 550 pounds. What is the difference between the small zebra and the large Grevy's zebra weighing 990 pounds?
     ::布尔切尔的斑马比格雷维的斑马小得多,布尔切尔的斑马体重约为550磅。 小斑马和大的格雷维的斑马之间有什么区别呢?
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  6. What is the weight difference between a small Burchell's zebra and a zebra weighing 880 pounds?
     ::小伯切尔斑马和体重880磅的斑马之间的重量差是多少?
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  7. What is the weight difference between a small Burchell's zebra and a large zebra weighing 900 pounds?
     ::一个小伯切尔斑马和一个重900磅的大斑马之间的重量差是多少?
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  8. An adult African male elephant weighs 15,400 pounds. What is the difference between its weight and the weight of a large Grevy’s zebra?
     ::非洲成年雄象重15,400磅。 它的重量和大块格雷维斑马的重量有什么区别?
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  9. What is the difference between the African elephant’s weight and the weight of the small Burchell's zebra?
     ::非洲大象的重量与小伯切尔斑马的重量有什么区别?
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  10. Dana caught twenty-eight fish. She wants to divide the fish into four baskets. If she does this, how many fish will be in each basket? Can she put the same number of fish in each basket?
      ::Dana捕获了28条鱼,她想把鱼分成4个篮子。如果她这样做,每个篮子里会有多少鱼?她能在每篮子里放同样的鱼吗?
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  11. Carl also went fishing. He caught five fish on the first day and four fish on the next day. If he continues this pattern on what day will he not catch any fish?
      ::卡尔也去钓鱼,第一天钓了五条鱼,第二天钓了四条鱼。如果继续这种模式,他哪一天不钓鱼?
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  12. Jessie loves to cook fish after she catches them. She is having ten people over for dinner. If each person eats a half of a fish, how many fish will she need to cook to feed all ten people?
      ::杰西在钓到鱼后喜欢煮鱼,她有十个人来吃晚饭,如果每人吃一半鱼,她需要多少鱼来喂养所有十个人?
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  13. Cass takes people out on a fishing boat to go deep sea fishing. With his strategies, people often catch double the amount of fish that they do regularly. If someone normally catches three fish in a day, how many fish will they catch using Cass’ strategy?
      ::卡塞带人上渔船去深海钓鱼。 以他的策略,人们往往能捕到比他们经常捕到的鱼量高出一倍的鱼量。 如果通常有人在一天内捕到三条鱼,他们用卡塞的策略能捕到多少鱼?
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  14. If you were someone who usually caught thirty-five fish in one week, how many fish would you catch per day if you started using Cass' strategy?
      ::如果你是通常在一周内捕到35条鱼的人 如果你开始用卡斯的策略 每天能捕到多少条鱼呢?
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  15. If you normally caught thirty-five fish in one week, how many fish would you catch using Cass' strategy if the month that was 30 days long?
      ::如果你通常在一周内捕到35条鱼, 你会用Cass的策略捕到多少条鱼, 如果这个月是30天那么长?

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  Review (Answers) 
  ::回顾(答复)

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  Click   to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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  Resources
  ::资源