Section outline

  • What's the time?
    ::几点了?

    In this section, you will explore more number lines and how they relate to ratios and tape diagrams.
    ::在本节中,您将探索更多的数字行,以及它们与比率和磁带图表的关系。

    With the following interactive, practice labeling points by where they belong on the number line . Later you will learn to use number lines to find .
    ::使用以下互动点, 练习在数字线上标记属于哪个点。 稍后您将学会使用数字线查找 。

    INTERACTIVE
    Values on Multiple Number Lines
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    • Order the red points onto the red line, the blue points onto the blue line and green points onto the green line.

      ::将红点排在红线上, 蓝色点排在蓝线上, 绿点排在绿线上。
    • Compare the values on different lines with each other.
      ::比较不同行的数值。
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    1.

    Use the number lines in the interactive to help you choose the TRUE statements.
    ::使用互动中的数字行来帮助您选择 TRUE 语句。

    Select all that apply
    a

    6600 seconds is equivalent to 110 minutes
    ::6600秒等于110分钟

    b

    600 seconds is greater than 110 minutes
    ::600秒大于110分钟

    c

    1 hour is equivalent to 3600 seconds
    ::1小时等于3600秒

    d

    1.5 hours is equivalent to 90 minutes
    ::1.5小时等于90分钟

    What does a double number line look like?
    ::双倍数线长什么样?

    Use the interactive to switch from the tape diagrams to a double number line. The double number line is incomplete so you can use the text boxes to fill in the missing values.  As you work with the interactive , think about  how double number lines  are similar to tape diagrams and how both can represent equivalent ratios between centimeters and millimeters.
    ::使用交互式线将磁带图从磁带图转换为双数行。 双数行不完整, 以便您可以使用文本框填入缺失的值。 在您与互动线一起工作时, 想想双数行与磁带图如何相似, 以及两者如何代表厘米和毫米之间的等值比例 。

    INTERACTIVE
    Double Number Lines and Tape Diagrams
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    • Enter the correct values for each of the input boxes according to the ratio and tape diagram.
      ::根据比例和磁带图表输入每个输入框的正确值。
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    Do you see any numbers that appear on both number lines? Why do you think these numbers appear twice?
    ::你看到两个数字行都有数字吗?

    The numbers 1, 2, and 3 appear in both number lines. The numbers have different meanings depending on which number line they appear. Because each number line has a different meaning (centimeters and millimeters) the same numbers on  different lines  represent different lengths .
    ::数字1、2 和 3 出现在两个数字行中。 数字有不同的含义, 取决于它们出现的数字行。 因为每个数字行有不同的含义( 人口普查和毫米) , 不同行的相同数字代表不同的长度 。

    Discussion Question: What are the differences between a tape diagram and a number lines? Discuss your answer with your classmates.
    ::讨论问题:磁带图表和数字行之间有什么区别?与同学讨论你的答复。

    How much sugar in a can of energy drink?
    ::能量饮料罐里有多少糖?

    In the following interactive, you  can practice finding the missing values in a double number line . The double number line  represents the ratio between the amount of sugar in some amount of energy drink.
    ::在接下来的互动中,您可以在双倍数字行中练习查找缺失值。双倍数字线代表某种能量饮料中糖量的比率。

    INTERACTIVE
    Double Number Lines and Equivalent Ratios
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    A typical energy drink holds 16 fluid ounces but these energy drinks are way too sugary! 
    ::典型的能量饮料 拥有16盎司的液体 但是这些能量饮料太糖了!

    • Type in the values on the double number line that maintain the ratio of fluid ounces to grams of sugar.
      ::在保持液盎司与糖克之比的双数线上的值中键入。
    • Then click to see the visual relationship of this ratio.
      ::然后单击以查看此比例的视觉关系 。
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    Discussion Question
    ::讨论问题

    The label also says "Servings per Container: 2." What do you think this means?
    ::标签上还写着"每个集装箱服务: 2" 你觉得这是什么意思?

    How many students per teacher?
    ::每名教师有多少学生?

    In fall 2016, the ratio of the average number of students to teachers in the United States was about 160 to 10.
    ::2016年秋季,美国平均学生人数与教师人数之比约为160比10。

    Use the interactive below to relate the equivalent ratios in a tape diagram to the equivalent ratios represented in a double number line.
    ::使用下文互动方式将平面图中的等值比率与数字双行中的等值比率联系起来。

    INTERACTIVE
    Tape Diagrams & Double Number Lines
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    • Use the slider to change the amount students and teachers.
      ::使用滑板来改变学生和教师的金额。
    • Click the button to switch between a tape diagram and a double number line.
      ::单击按钮可在磁带图表和双数字行之间切换。
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    How do you mix brown paint? 
    ::你怎么混合褐色涂料的?

    In this interactive, you can make multiple batches of brown paint by mixing colored paint in this ratio: 3 parts of yellow paint to 4 parts of red paint to 5 parts of blue paint. Observe how the number line represents the ratios between the amounts of paint.
    ::在此互动中, 您可以混合染色涂料, 制成多批棕色涂料, 比例是: 黄涂料3到红涂料4到蓝涂料5。 注意数字线如何代表涂料量之间的比例 。

    INTERACTIVE
    Mix the Paint
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    • Click Increase to add 4 red, 3 yellow, and 5 blue to the bucket.
      ::点击加注以在桶中添加 4 红色、 3 黄色 和 5 蓝色 。
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    Discussion Question: When would you prefer to use a tape diagram and when would you prefer to use a number line?
    ::讨论问题:你希望何时使用磁带图? 你希望何时使用数字线?

     

    CK-12 PLIX Interactive: Pie Baking Contest
    ::CK-12 PLIX 互动:派烘烤比赛

       Summary
    ::摘要

    •  Double number lines can be used to find equivalent ratios and convert units.
      ::双倍数线可用来找出等效比率和转换单位。

    Review Questions
    ::回顾问题

    True or False: On a double number line, matching quantities line up vertically.
    ::True 或 False: 在双数行上, 垂直匹配数量行 。

    You are given a double number line with the ratio of dollars to quarters. How would you determine how many quarters are equivalent to $5?
    ::给您一个与美元对季度之比的双倍数字行。 您如何确定多少季度等于5美元?

    Can you explain how to use a double number line to find the amount of sugar in a given amount of energy drink?
    ::请解释您如何使用双倍数线来寻找特定能量饮料中的糖量 ?

    When would you prefer to use a tape diagram and when would you prefer to use a number line?
    ::你想什么时候用磁带图,什么时候用数字线?

    Some students argue that tape diagrams are more useful than double number lines for understanding ratios, while others disagree. Which side do you agree with and why?
    ::有些学生认为磁带图表比双倍数字线对理解比率有用,而另一些学生则不同意。 你同意哪一边,为什么?