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  • 理解百分比

    Battle of the Big Men
    ::大人之战

    Two friends, Joe and Lauren, are basketball fans and are having a debate about which player is a better 3-point shooter: The Boston Celtics Center Al Horford or the Minnesota Timberwolves center Karl Anthony Towns. In the 2017-2018 NBA season, Towns made 120 of 285 3-point shots attempted, and Horford made 97 of 226 3-point shots attempted. Joe believes that Karl Anthony Towns is the better 3-point shooter because he made more 3-point shots whereas Lauren believes that Al Horford is a better 3-point shooter because he is more efficient. Given their numbers, who do you think is the better 3-point shooter? Describe why you think your choice is correct.
    ::两个朋友,乔和劳伦,都是篮球球迷,并且正在辩论哪个球员是更好的三点射手:波士顿凯尔特克思中心阿尔霍福德(Boston Celltics Center Al Horford)或明尼苏达木材狼中心卡尔安东尼汤斯(Karl Anthony Towns)。在2017-2018年NBA赛季,Towns在285 3点射击中做了120次尝试,而霍尔福德在226 3点射击中做了97次尝试。乔认为卡尔安东尼汤斯(Karl Anthony Towns)是更好的三点射击手,因为他做了更多三点射击,而劳伦认为艾尔霍福德(Al Horford)是一个更好的三点射击手,因为他效率更高。考虑到他们的人数,你认为谁是更好的三点射击手?你为什么认为你的选择是正确的?

    One way to think about the question posed above is as two . We could use what we know about proportions to determine who would make more 3-pointers if they took the same number of shots. Use the interactive below to explore how many 3-pointers each player would make for any number of shot attempt at their respective rates.
    ::思考上述问题的一种方式是两个。我们可以使用我们所知道的关于比例的方法来决定如果用相同数目的镜头,谁能做更多的三分。 使用下面的交互方式来探索每个玩家将做多少个三分的射击尝试,按他们各自的射击速度。

    INTERACTIVE
    Battle of the Big Men
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    • Drag the sliders to see how many 3 point shots Town and Horford make.
      ::拖动滑动滑动器以查看 Town 和 Horford 制作了多少场 3 点射击 。
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    Use the slider to change the total number of shots for both players to 130. After 130 shots, Towns should make three pointers and Horford should make three pointers.
    ::使用滑块将两个玩家的射击总数修改为 130 。 130 射击后, Towns 应该让 Enter 回答 3 指针, Horford 应该让 Enter 回答 3 指针。

    Discussion Questions
    ::讨论问题 讨论问题

    Which number of shot attempts did you choose for each player? Is this important? Why or why not?
    ::您为每个玩家选择了多少次射击尝试 ? 这重要吗 ? 为什么或为什么不重要 ?

    Does this conclusively prove Lauren’s argument that Al Horford is a superior 3-point shooter to Karl Anthony Towns? If yes state why, if not then state what more information would be needed to for either Joe or Lauren to prove that one player is a better 3-point shooter than another?
    ::这是否确凿地证明了劳伦关于艾尔·霍尔福德是卡尔·安东尼·汤斯的三点射击高手的论点? 如果不是的话,请说明为什么,如果不是,那么乔或劳伦需要哪些信息来证明一个玩家比另一个玩家更优秀三点射击?

      

    One way to answer the question posed above is by writing them as a percent. A percent is a number or ratio expressed as a fraction of 100. In this scenario, the rates of each player would represent a percent if the rate was out of 100 3-point shot attempts.
    ::回答上述问题的一种方法是以百分比表示。 1%是以百分数或百分数表示的百分数或百分数。 在这种假设中,如果每一玩家的射击率超过一百三点的射击率,则每个玩家的射击率将达到百分之一。

    Discussion Question
    ::讨论问题

    What is the benefit of converting every rate to being out of 100? Why not just compare them using common denominators?
    ::将每一税率转换为100以上有什么好处? 为什么不用共同的分母来比较它们呢?

    Converting Between Fractions, Decimals, and Percents
    ::分数、 十进制和百分数之间的转换

    To understand the relationship between fractions, decimals, and percents, it will be helpful to review how to convert between them.
    ::为了了解分数、小数和百分数之间的关系,审查它们之间如何转换将是有益的。

    Use the interactive below to practice converting decimals, fractions, and percents.
    ::使用下面的交互数据来转换小数、分数和百分数。

    INTERACTIVE
    Converting Between Fractions, Decimals, and Percents
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    • Enter the corresponding fraction, decimal, or percent into the boxes.
      ::在框中输入相应的分数、小数或百分比。
    • Enter decimals to the nearest thousandth.
      ::输入最接近千位的十进位数。
    • Enter percents to the nearest tenth.
      ::输入百分率到最近的十分之一 。
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    A Slice of Pie
    ::馅饼的切片

    In addition to being used to display rates so that they can be easily compared, percents are also used to express a number as a . This use of percentages is often seen in pie graphs. A pie graph breaks up a whole into parts and uses percents to represent how much of the whole each part makes up.
    ::除了用于显示率以便很容易比较之外,百分比还用来表示数字。这种百分比的使用通常见于派图中。一个派图将一个整块分成,并使用百分比来表示每个部分的构成数量。

    The pie chart below represents the responses of 2,500 teenagers when asked what their favorite genre of music was. Use the interactive below to look at the results.
    ::下面的馅饼图表代表了2500名青少年在被问及他们最喜爱的音乐类型时的反应。 使用下面的交互式图表来查看结果。

    INTERACTIVE
    Pie Chart
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    Convert the votes in the table to percent values, then create a pie chart that represents those values.
    ::将表格中的票数转换为百分比值,然后创建一个代表这些值的派图。

    • Use each red point to adjust the size of each sector of the graph, starting with rap and then moving on to the next genre.
      ::使用每个红点来调整图中每个区段的大小, 从 rap 开始, 然后继续到下一个流派 。
    • New points will appear when you correctly place the previous one.
      ::正确放置上一个点时会出现新点 。
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    Discussion Questions
    ::讨论问题 讨论问题

    1. Which music genre received the most votes?
      ::哪个音乐流派得票最多?
    2. How many more votes did the highest voted genre receive than the lowest votes genre?
      ::得票最高阶层获得的选票比得票最低阶层多多少票?
    3. How many people did not vote for Rock?
      ::有多少人没有投票支持摇滚?
    4. What fraction of the votes did each genre receive? Reduce the fractions.
      ::每一族获得多少分数的选票?减少分数。
    5. How many times greater is the number of votes for Rap compared to the number of votes for Other?
      ::与其他人的票数相比, " 饶舌 " 的票数是其他票数的多少倍?
    6. What percentage of people did not vote for Rock?
      ::有多少人没有投票支持摇滚?
    7. How do the percentages on a pie graph help us understand the data displayed?
      ::馅饼图上的百分率如何帮助我们理解显示的数据?

      

    Percents Greater Than 100%
    ::百分率大于100%

    Since percents are a number or ratio expressed as a fraction of 100,  you can express any number as a percent.  You can also use a percent to express a number greater than 1. Since 100% represents 1 whole, we can 200% can be used to represent 2 wholes because 100% + 100% = 200%. Since 50% represents half of a whole, 250% can be used to represent two and a half wholes because 100% + 100% + 50% = 250%.
    ::由于百分数为百分数或百分数,您可以用百分数表示任何数字。您也可以用百分数表示一个大于1的数。由于100%代表一个整数,我们可以用200%代表两个整数,因为100%+100%=200%。由于50%代表一个整数的一半,250%可以用来表示两个半整数,因为100%+100%+50%=250%。

    Use the interactive to estimate the location of percents greater than 100% on a number line .
    ::使用互动来估计数字线上百分率大于100%的百分率位置。

    INTERACTIVE
    Parachuting Percents to Fractions
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    • Drag the red point to pick where to drop the parachute person so they land at the equivalent number on the number line to the given percent.
      ::拖曳红色点以选择降落伞人员下落, 让他们降落在数行的等量数字上, 到给定百分比 。
    • Click the buttons to see where the parachute lands, retry, and practice different percents.
      ::单击按钮以查看降落伞的着陆、重试和练习不同百分比的位置。
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        Summary
    ::摘要

    • A percent is a number or ratio expressed as a fraction of 100.
      ::A%是一个数字或比率,表示为100的一小部分。
    • This means that a percentage can be represented as a fraction or a decimal value. For example:  25 % , 1 4 , and  0.25 are all equivalent.
      ::这意味着一个百分比可以作为分数或小数点值表示。例如:25%、14和0.25等值。