章节大纲

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  • 问题解决计划，小数估计

    Petr has $95 to shop for clothes. He goes to his favorite store and sees that most of the clothing items are on sale. He places two shirts, one pair of pants and a light jacket in his shopping cart. The prices of the items are: $12.99, $15.79, $24.75 and $33.15. Petr decides to estimate the total cost to make sure that he has enough money to pay for all of the items in the cart. Can you estimate how much the items in his cart will cost?
    ::Petr有95美元购买衣服。他去了他最喜欢的商店,看到大部分衣服都在出售。他把两件衬衫、一条裤子和一件轻外套放在他的购物车里。这些物品的价格是:12.99美元、15.79美元、24.75美元和33.15美元。Petr决定估算总成本,以确保他有足够的钱支付车上所有物品的费用。你能估计一下他车上的物品要花多少钱吗?

    In this concept, you will learn when  estimation  is a reasonable option to solve problems.
    ::在这个概念中,当估算是解决问题的合理选择时,你就会知道。

    Using Estimation to Solve Problems
    ::使用估计来解决问题

    You can use estimation in several different situations. To use estimation, you need to read and understand the problem. There will be clues in the problem to let you know if estimation is a good option for solving that specific problem.
    ::您可以在几种不同情况下使用估算。 要使用估算, 您需要阅读和理解问题。 问题中会有线索可以让你知道估算是否是解决这一具体问题的好选择 。

    Estimating  means finding an answer that is an approximate answer. When estimating, your answer must make sense, but it does not need to be exact. You need to find an answer that is reasonable.
    ::估计意味着找到一个大致答案的答案。 当估计时, 您的答案必须合理, 但不需要精确。 您需要找到一个合理的答案 。

    When looking at a problem, read the problem to see if estimation is a good option. You can look for key words to help us with this. Here are some of the key words that suggest estimation:
    ::当看到一个问题时, 读读问题, 看看估算是否是一个好选项。 您可以寻找关键字来帮助我们解决这个问题。 以下是一些关键字, 表明估算 :

    • Close to
      ::关闭至
    • Approximate
      ::近近
    • Estimate
      ::估计估计数
    • An answer that makes sense
      ::一个有道理的答案
    • About
      ::关于

    If you see these words in a word problem, you can estimate to find the answer.
    ::如果你在单词问题中看到这些词,你可以估计找到答案。

    Let's look at an example.
    ::让我们举个例子。

    Marcus wants to get an idea how much he is spending at the grocery store. On the way to the checkout, he looks at the items in his cart. Here are the prices of the food in his cart: $0.50, $2.50, $3.45 and $6.79. About how much will Marcus spend when he checks out?
    ::Marcus想知道他在杂货店花了多少钱。在去取票的路上,他看了车内的东西。这是他的车里的食物价格:0.50美元、2.50美元、3.45美元和6.79美元。关于Marcus在检查时会花多少钱?

    Are there any key words in this problem?
    ::这一问题中是否有任何关键词?

    Yes, the word "about" lets you know that you can estimate to find the answer.
    ::是的,"约"这个词让你知道 你可以估计找到答案。

    Next, use  rounding  and  round  to the nearest whole number.
    ::接下来,使用四舍五入和四舍五入到最近的整数。

    0.50 becomes 1
    ::0.50 变成 1

    2.50 becomes 3.00
    ::2.50改为3.00

    3.45 becomes 3.00
    ::3.45变成3.00

    6.79 becomes 7
    ::6.79变成7

    Then, add up the rounded answers: 1 + 3 + 3 + 7 = 14.
    ::然后,加上四舍五入的答复:1+3+3+3+7=14。

    The answer is $14.00. Marcus will spend approximately $14.00 at the store.
    ::答案是14美元 马库斯会在商店花14美元

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Petr and his shopping cart.
    ::早些时候,你被问及彼得和他的购物车的问题

    Petr has $95 to pay for the items. He has items in his cart that cost $12.99, $15.79, $24.75 and $33.15. What is the estimated cost of the items in Petr's cart?
    ::Petr有95美元来支付这些物品,他的车内有价值12.99、15.79、24.75和33.15美元的物品。 Petr的车内物品的估计费用是多少?

    First, round each value to the nearest dollar.
    ::首先,将每个值的四舍五入至最接近的美元。

    12.99 becomes 13
    ::12.99变成13

    15.79 becomes 16
    ::15.79变成16

    24.75 becomes 25
    ::24.75变成25

    33.15 becomes 33
    ::33.15变成33

    Next, add the rounded values.
    ::下加四舍五入值。

    13 + 16 + 25 + 33 = 87

    Then, write the estimated cost.
    ::然后,写下估计费用。

    87

    The answer is $87. Petr's items will cost approximately $87, so he has enough money to buy the items.
    ::答案是87美元 彼得的物品将花费约87美元 所以他有足够的钱买这些物品

    Example 2
    ::例2

    Tyrone is working to buy presents for his family for the holidays. He has picked out a CD for his sister for $14.69, a vase for his mother at $32.25 and a picture frame for his father at $23.12. What is the estimated total cost of Tyrone's purchases?
    ::Tyrone在为家人购买假期礼物,他为妹妹挑选了一张CD,价14.69美元,为母亲选了花瓶,价32.25美元,为父亲选了相框,价23.12美元。 估计Tyrone购买的总成本是多少?

    First, round each price to the nearest dollar.
    ::首先,按每一价到最接近的美元来四舍五入。

    32.25 rounds to 32
    ::32.25发至32发

    23.12 rounds to 23
    ::23.12发至23发

    Next, add the rounded values.
    ::下加四舍五入值。

    32 + 23 = 55 

    Then, write the estimated cost.
    ::然后,写下估计费用。

    55

    The answer is $55. Tyrone will spend approximately $55.
    ::答案是55美元 泰隆会花大约55美元

    Example 3
    ::例3

    Kelly bought a shirt for $26.78 and a pair of pants for $25.10. What is the estimated total cost of her purchases?
    ::Kelly买了一件26.78美元的衬衫和一件25.10美元的裤子。

    First, round each value to the nearest dollar.
    ::首先,将每个值的四舍五入至最接近的美元。

    26.78 becomes 27
    ::2678变成27

    25.10 becomes 25
    ::25.10变成25

    Next, add the rounded values.
    ::下加四舍五入值。

    27 + 25 = 52

    Then, write the estimated cost.
    ::然后,写下估计费用。

    52

    The answer is $52. Kelly will spend approximately $52.
    ::答案是52美元 Kelly会花大约52美元

    Example 4
    ::例4

    Julia ran 16.5 miles one day and 22.8 miles the next. What is her estimated total mileage?
    ::Julia一天跑16.5英里 第二天跑22.8英里 她估计的总里程数是多少?

    First, round each distance to the nearest mile.
    ::首先,每一公里到最近的里程。

    16.5 becomes 17
    ::16.5变成17

    22.8 becomes 23
    ::22.8变成23

    Next, add the rounded values.
    ::下加四舍五入值。

    17 + 23 = 40

    Then, write the estimated mileage.
    ::然后写下估计的里程数

    40

    The answer is 40 miles. Julia ran approximately 40 miles.
    ::答案是40英里 茱莉亚跑约40英里

    Example 5
    ::例5

    Keisha biked 25.75 miles one day and 16.2 miles the next. What is her estimated total mileage?
    ::Keisha骑自行车一天25.75英里,次日16.2英里。她估计的总里程数是多少?

    First, round each distance to the nearest mile.
    ::首先,每一公里到最近的里程。

    25.75 becomes 26
    ::25.75变成26

    16.2 becomes 16
    ::16.2变成16

    Next, add the rounded values.
    ::下加四舍五入值。

    26 + 16 = 42

    Then, write the estimated mileage.
    ::然后写下估计的里程数

    42

    The answer is 42 miles. Keisha biked approximately 42 miles.
    ::答案是42英里,凯莎骑自行车大约42英里

    Review
    ::回顾

    Look at each problem and use what you have learned about estimation to solve each problem.
    ::看看每个问题,用你所学到的关于估算的知识来解决每个问题。

    1. Susan is shopping. She has purchased two hats at $5.95 each and two sets of gloves at $2.25 each. If she rounds each purchase price, how much can she estimate spending?
      ::Susan在购物,她购买了两顶帽子,每人5.95美元,两套手套,每人2.25美元,每套2.25美元,如果她每套买价打一回合,她能估计支出多少?
    2. If she uses front–end estimation, how does this change her answer?
      ::如果她使用前端估计,这如何改变她的答案?
    3. Which method of estimation gives us a more precise estimate of Susan’s spending?
      ::究竟用哪种估算方法更精确地估算苏珊的支出?
    4. If she brings $20.00 with her to the store, about how much change can she expect to receive?
      ::如果她带20000美元到商店, 有关她预期能得到多少改变?
    5. If she decided to purchase one more pair of gloves, would she have enough money to make this purchase?
      ::如果她决定再买一双手套,她是否有足够的钱来购买?
    6. Would she receive any change back? If yes, about how much?
      ::她会收到任何零钱吗?如果是,多少钱?
    7. Mario is working at a fruit stand for the summer. If a customer buys 3 oranges at $.99 a piece and two apples for $.75 a piece, about how much money will the customer spend at the fruit stand? Use rounding to find your answer.
      ::Mario在夏天的水果摊上工作。如果一个顾客用99美元买3个橙子和2个苹果,每块75美元,客户在水果摊上要花多少钱?用四舍五入来寻找答案。
    8. What is the estimate if you use front–end estimation?
      ::如果您使用前端 - 端估计, 估计值是多少?
    9. Why do you think you get the same answer with both methods?
      ::为什么你认为两种方法都有同样的答案?
    10. If the customer gives Mario a $10.00 bill, about how much change should the customer receive back?
      ::如果客户给马里奥100美元的帐单, 客户应该收到多少改变?
    11. Christina is keeping track of the number of students that have graduated from her middle school over the past five years. Here are her results.
      ::Christina正在追踪五年来中学毕业的学生人数,结果如下:

    2004 – 334

    2005 – 367

    2006 – 429

    2007 – 430

    2008 – 450

    Estimate the number of students who graduated in the past five years.
    ::估计过去五年毕业的学生人数。

    1. Did you use rounding or front–end estimation?
      ::您是否使用四舍五入或前端估计 ?
    2. Why couldn’t you use front–end estimation for this problem?
      ::为何不能使用前端估算来解决这个问题?
    3. Carlos has been collecting change for the past few weeks. He has 5 nickels, 10 dimes, 6 quarters and four dollar bills. How much money does he have exactly?
      ::卡洛斯过去几周来一直在收集零钱,他有五分钱,十分,六分四十五和四张钞票。他到底有多少钱?
    4. Use rounding to estimate the sum of Carlos’ money.
      ::使用四舍五入估计卡洛斯的钱总额。
    5. Use front–end estimation to estimate the sum of Carlos’ money.
      ::使用前端估计来估计卡洛斯的钱总额。
    6. Which method gives you a more accurate estimate? Why?
      ::哪种方法能给你更准确的估计?