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  • 对数行的对称

    On the Gridiron
    ::在格里迪隆河边

    lesson content
    Football

    In football, a player is given positive yards for moving forward and negative yards for moving backward. In this interactive, you will measure how far a football team moves the ball between plays using positive and negative numbers to describe position and distance.
    ::在足球赛中,球员的前进场为正码,向后移动场为负码。在这个互动游戏中,你将用正码和负码来描述位置和距离,测量足球队在球赛中移动球的距离。

     

    INTERACTIVE
    Net Yardage
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    The line of scrimmage is where the football starts. The net yardage is how many yards the ball ends up past the line of scrimmage. There is only enough time on the clock to run two more plays.
    ::球场线是足球的起点。 网场线是球场的几码处, 球场最后越过了球场线。 时间上只有足够的时间再打两场球。

    • Drag the red points to adjust the line of scrimmage and the position of the football.
      ::拖曳红色点以调整纵横线和足球位置。
    • Press the button to run the play.
      ::按下按钮播放播放 。
    • Then move the ball to another position and press the button to run the second play.
      ::然后将球移动到另一个位置, 按下按钮来运行第二部播放 。
    • The last button will let you run two new plays.
      ::最后一个按钮将允许您运行两个新剧本 。
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    Symmetry on the Number Line
    ::对数行的对称

    In this next interactive, you will identify negative numbers on the number line . Notice that negative numbers are similar to positive numbers that are the same distance from zero but on the opposite side of zero on the number line.
    ::在接下来的交互式互动中,您将在数字行中识别负数。请注意,负数与正数相似,正数与零的距离相同,但数字行的对面是零。

     

    INTERACTIVE
    Symmetry on the Number Line
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    • Enter the negative number of the blue point in the input box.
      ::在输入框中输入蓝色点的负数。
    • Click the "Check" button to check your answer. 
      ::单击“ 检查” 按钮来检查您的回答 。
    • Click the "Try Again" button if you get the answer wrong.
      ::如果您答错, 请单击“ 重试” 按钮 。
    • Click the "New Number" button once you get the answer right.
      ::一旦答案正确, 单击“ 新数字” 按钮 。
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    Discussion Questions
    ::讨论问题 讨论问题

    1. How were you able to determine the value of the point?
      ::你如何确定点的价值?
    2. What does this interactive tell you about the relationship of the values on either side of the number line?
      ::这个互动性如何告诉您数字行两边的值之间的关系 ?

     

    Opposites
    ::反对者

    In the previous activity, we saw that numbers on both sides of the number line are related. The overlapping numbers in the interactive above are opposite numbers. The opposite of a number, also known as the additive inverse , comes from the additive inverse property . The additive inverse property states that for any real number n , there exists an additive inverse which is the same distance from zero in the opposite direction. Additionally, the sum of a number and its additive inverse will always be zero: n + (-  n) = 0. A trick is to change the sign of the number, for example, the opposite of 7 is -7 and the opposite of -15 is 15.
    ::在先前的活动中,我们看到数字线两侧的数字是相关的。以上互动中的重叠数字是相反的数字。一个数字的反面,又称添加反转,来自添加反函数。添加反函数表示,对于任何实际数字 n ,存在一个同零的反差。此外,一个数字及其添加反差的总和总是零: n+ (- n) = 0。一个诀窍是改变数字的符号,例如,对7的反面是-7,对15的反面是15。

    For this interactive, you will change the original value of a number and look at how additive inverses represent the opposite of that number.
    ::对于此互动, 您将更改数字的原始值, 并查看添加反向值与该数字的反向值 。

     

    INTERACTIVE
    Additive Inverse
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    • Drag the red point to change the value in red and its additive inverse.
      ::拖曳红色点以改变红色值及其添加剂反转值。
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    The additive inverse property applies to all .
    ::添加反向属性适用于所有 。

    Example
    ::示例示例示例示例

    Find the opposite of the real numbers below:
    ::发现与以下真实数字相反:

    1.   11.7

    The opposite of 11.7 is -11.7 because both 11.7 and (-11.7) are 11.7 units from 0.
    ::与11.7相反的是-11.7,因为11.7和(11.7)在0之间为11.7个单位。

    2.   -3¼

    The opposite of -3¼ is 3¼. Recall that an easy way to find the opposite is to change the sign.
    ::3⁄4 的反面是 31⁄4 。 回顾找到相反的简单方法就是改变标志 。

     

    Discussion Questions
    ::讨论问题 讨论问题

    1. What is the opposite of 0?
      ::与0相反的是什么呢?
    2. What is the opposite of the opposite of 7?
      ::7的反面有什么相反的呢?

      

    Making a Robot Part 3
    ::使机器人第3部分成为机器人第3部分

    In ,  you continued programming  a robot. At this point, the robot accepts  the following commands:
    ::在其中,您继续编程机器人。此时,机器人接受以下命令:

    • stepsNo - This command will move the robot n steps forward, or n steps backward. The command steps(4) will move the robot 4 steps forward, and the command steps(-2) will move the robot 2 steps backward.
      ::步骤No - 此命令会向前移动机器人 n 步或向后移动 n 步。 命令步骤(4) 会向前移动机器人 4 步, 命令步骤( 2) 会向后移动机器人 2 步 。
    • location() - This command will tell you the current location of the robot
      ::位置 () - 此命令会告诉您机器人当前的位置

    How can you use your knowledge of opposites to return the robot to its original position ?
    ::你如何利用对立面知识 将机器人恢复到原来的位置?

    In the interactive below, you will continue moving the robot forward and backward a certain number of steps. You will also use positive and negative numbers to describe where the robot is relative to where the robot’s starting location is.
    ::在下面的互动中,您将继续向前移动机器人,向后移动一定数量的步数。您还将使用正数和负数来描述机器人相对于机器人起始位置的位置。

     

    INTERACTIVE
    Making a Robot pt 3
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    • Drag the slider to set a number of steps.
      ::拖动滑块以设置若干步骤。
    • Click the button to execute the command.
      ::单击按钮执行命令。
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    Discussion Question
    ::讨论问题

    The next step is to build a reset function that will return the robot from any location to its starting position of 0. What would this function look like? How would the function return the robot from any location to its starting position?
    ::下一步是建立一个重置函数, 将机器人从任何位置返回到零的起始位置。 这个函数会是什么样子 ? 该函数如何将机器人从任何位置返回到起始位置 ?

      Summary
    • The opposite of a number, also known as the additive inverse .
      ::数字正好相反, 也称为添加反转。
    • If a positive number and a negative number are opposites they are the same distance away from 0.
      ::如果正数和负数正好相反,则与0的距离相同。
    • The sum of a number and its additive inverse will always be zero.
      ::数字之和及其添加剂反向总和总是为零。
    • Zero is its own opposite.
      ::零是它自己的对立面。