章节大纲

  • The Smoot
    ::斯穆特人,

    lesson content
    Measuring with Smoots

    When measuring the length of an object, we can use inches, feet, centimeters, meters, miles, or smoots. If the smoot seems unfamiliar to you, it should. The smoot is only used as a unit of measure on one bridge in Massachusetts connecting Boston to the MIT campus in Cambridge. In 1958, Fred Smoot, an MIT student, repeatedly laid down across the entire Harvard Bridge to measure the length of the bridge in terms of his height as a joke. The length of the bridge measured 364.4 smoots + 1 ear (approximately 2,165 feet).
    ::当测量物体的长度时,我们可以使用英寸、英尺、厘米、米、英里或短距。 如果您不熟悉弹道,应该使用。弹道只在连接波士顿和剑桥麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省校园的一座桥上使用。1958年,麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省麻省大学学生Fred Smoot多次跨过整个哈佛大桥铺设,以他的身高为笑柄测量桥的长度。桥长度为3644.4米+1耳(约2 165英尺)。

    For millennia, humans have used measurement systems to explain the world around them. We measure distance, weight, time, and even value or cost. However, the units we choose can present challenges: we may need to measure an object that is abnormally large or small. 
    ::几千年来,人类一直使用测量系统来解释周围的世界。我们测量距离、重量、时间甚至价值或成本。然而,我们选择的单位可以带来挑战:我们可能需要测量一个异常大或小的物体。

    For this interactive, you will create your own unit of length and use this to measure different sized objects. What are some benefits and challenges to using your unit?
    ::对于此互动, 您将创建您自己的长度单位, 并使用此单位测量不同的大小对象。 使用您的单位有哪些好处和挑战 ?

     

    INTERACTIVE
    Making Your Own Unit
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    First, create your own unit by
    ::首先,首先, 创建您自己的单位, 由

    • dragging the red point to choose the length
      ::拖拖红色点以选择长度
    • entering the name of your unit in the box
      ::在框中输入单位的名称
    • clicking the button to set it
      ::点击按钮设定它

    Then, use your unit to measure different objects by
    ::然后,使用您的单位来测量不同的对象

    • dragging the red points to lengthen and rotate the ruler
      ::拖拖红色点以拉长和旋转标尺
    • clicking the button to switch objects
      ::单击按钮切换对象

    Once you have seen all five objects, order them from smallest to largest.
    ::一旦你看到所有五个物体 将它们从最小变成最大

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    Discussion Questions
    ::讨论问题 讨论问题

    1. Can you make a unit to measure something other than length? Create your own unit for measuring length, weight, and time.
      ::您能否用一个单位来测量长度以外的东西? 创建您自己的单位来测量长度、 重量和时间 。
    2. How would you use your unit of length to measure the length of a pencil? The length of a truck? The length of a city? What tools would help you take these measurements?
      ::你如何用你的单位长度来测量铅笔的长度?卡车的长度?城市的长度?什么工具可以帮助你测量这些尺寸?
    3. How would you use your unit of weight to measure the weight of a tennis ball? The weight of a paper clip? The weight of a car? What tools would help you take these measurements?
      ::如何用重量单位来衡量网球的重量?纸片的重量?汽车的重量?什么工具可以帮助你测量这些重量?
    4. How would you use your unit of time to measure the time it takes for a ball you drop to hit the ground? The time it takes for one class period? The time it takes for the Earth to complete one orbit around the Sun? What tools would help you take these measurements?
      ::您如何使用单位时间来测量您投下球撞击地面所需的时间? 它需要一个班级的时间? 地球完成一个围绕太阳的轨道所需的时间? 什么工具能帮助您测量这些测量?

     

    Rational Numbers
    ::理性数字

    To address the challenges posed when taking measurements, we use . A rational number is any number that can be expressed as a ratio between two integers.
    ::为了应对在进行测量时所带来的挑战,我们使用 。一个合理的数字是任何可以表示为两个整数之比的数字。

    Rational Numbers → { … -5⅓, -4.631, -2, -¼, 0, 1, 2.01, 3⅕…}
    ::合理数字 { { { 51.5 3 - 4. 631, - 2 - 1⁄4 0, 1 2. 01, 31⁄5}

    Discussion Questions
    ::讨论问题 讨论问题

    1. Is every integer a whole number?
      ::每个整数都是整数吗?
    2. Is every whole number an integer?
      ::每个数字都是整数吗?
    3. Is every integer a rational number?
      ::每个整数都是合理数字吗?
    4. Is every rational number an integer?
      ::每个理性数字都是整数吗?

    Using the next interactive, you will split a unit into fractions and describe the space between them with rational numbers.
    ::使用下一次互动,您会将一个单位拆分为分数,用合理数字描述它们之间的空间。

     

    INTERACTIVE
    Rational Numbers
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    • Drag the red point to adjust the number of notches on the ruler which measures inches.
      ::拖曳红色点以调整测量英寸的标尺上的记点数。
    • Split the ruler into 6 even parts.
      ::将标尺分成6个偶数部分
    • Once you complete the above step, fill in the ruler with correct values (type the value as an improper fraction).
      ::一旦完成上述步骤,请填写正确值的标尺(将数值输入不适当的分数)。
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    Measuring Force
    ::度量力

    In the previous activity, we used fractions to represent the units between whole numbers . However, we can also use decimals to represent space between whole numbers in increments of tenths, hundredths, etc.
    ::在先前的活动中,我们使用分数来表示整数之间的单位。然而,我们也可以使用小数点来表示整数之间的间距,以十、一百等的递增。

    The interactive below displays a spring scale which is used to measure the weight of an object. Fill out the missing values of the spring scale to practice representing rational numbers as decimals between whole numbers.
    ::以下互动显示用于测量对象重量的弹簧比例尺。填写弹簧比例尺缺失的数值,以练习将合理数字作为整数之间的小数表示。

     

    INTERACTIVE
    Measuring Force
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    • Fill in the rest of the values of this spring scale.
      ::填充此春季比额表的其余值 。
    • Once your answer is correct, it will turn green.
      ::一旦回答正确,它就会变成绿色。
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    Out in the Cold Part 2
    ::在冷冷的第二部分

    T hus far we have seen examples of fractional and decimal numbers. However, rational numbers also include negative numbers . For the interactive below, fill in the missing values on the thermometer for the Fahrenheit and Celsius scales. You will be using both decimals and fractions as rational numbers to describe these temperatures. 
    ::到目前为止,我们看到了分数和小数数字的例子。 但是, 理性数字也包括负数。 对于下面的交互数字, 请填入Fahrenheit 和 Colombo 比例尺温度计中缺失的值。 您将使用小数和小数作为合理数字来描述这些温度 。

     

    INTERACTIVE
    Out in the Cold Part 2
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    • Click on either the  °F or   °C buttons to switch between Fahrenheit or Celcius.
      ::单击 °F 或 °C 按钮可在 Fahrenheit 或 Celcius 之间切换 。
    • Select a blue segment to fill in a value.
      ::选择要填充值的蓝色段 。
    • On the left segments, type in a decimal value
      ::左侧段,按小数点值键入
    • On the right segments, type in a fraction.
      ::在右侧的区段, 分几部分键入 。
    • When filling in a fraction, type the whole number in the left input box and the fraction in the right input box using "/".
      ::在填入分数时,使用“ /” 键入左输入框中的整数和右输入框中的分数。
    • Check your answers using the "Check" button.
      ::使用“ 检查” 按钮检查您的答案 。
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      Summary
    • A rational number is any number that can be expressed as a ratio between two integers.
      ::合理数字是指以两个整数之比表示的任何数字。
    • The same value can be represented by different rational numbers. For example,  1 2 = 2 4  or  3 = 9 3  
      ::同样值可以用不同的理性数字表示。 例如, 12=24 或 3=93