章节大纲

  • 常规

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  • 四长方

    The Fly on the Ceiling
    ::最高天顶上的飞翔

    The famous French mathematician Rene Descartes spent much of his childhood sick and in bed. He would spend many of his days staring at his ceiling daydreaming about math, science, and philosophy. One day a fly flew in his room and began crawling on his tiled ceiling. Descartes thought about how to describe the location of the fly using only numbers.
    ::著名的法国数学家雷内·德夏尔特(Rene Descartes)在童年生病和卧床上度过了大部分时间。 他将花很多天盯着天花板的白日梦看数学、科学和哲学。 一天,一只苍蝇飞进他的房间,开始爬上他的瓷砖天花板。 笛卡尔思考了如何用数字描述苍蝇的位置。

    In this interactive, you will start to use a coordinate plane to try to describe the position of a fly on a ceiling.
    ::在此互动中,您将开始使用协调飞机,试图描述天花板上苍蝇的位置。

     

    INTERACTIVE
    The Fly on the Ceiling pt 1
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    • Click the button to change the position of the fly and figure out a system to describe its location.
      ::单击按钮以改变苍蝇的位置,并找出一个系统来描述它的位置。
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    Two Dimensions
    ::两维

    Over the course of the chapter, we have been measuring the positions of objects using number lines. However, a number line can only be used to measure an object in one dimension. To measure the location of an object in two dimensions , we will need to use two number lines: a vertical number line and a horizontal number line.
    ::在本章中,我们一直在用数字线测量对象的位置。然而,数字线只能用来在一个维度中测量物体的位置。为了测量物体在两个维度中的位置,我们需要使用两个数字线:一个垂直数字线和一个水平数字线。

    For the next interactive, you will use positive numbers to identify the position of a frog on the coordinate plane.
    ::下次互动时,您将使用正数来识别坐标平面上的青蛙位置。

     

    INTERACTIVE
    Two Dimensions
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    Figure out a way to describe where the frog is.
    ::想办法描述青蛙的位置

    • Press the white buttons to move through the interactive.
      ::按下白色按钮以通过交互方式移动。
    • Drag the red point to match the frog's location.
      ::拖曳红色点以匹配青蛙的位置 。
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    Discussion Questions
    ::讨论问题 讨论问题

    1. How can we use the horizontal and vertical number lines to identify the location of the frog?
      ::我们如何使用水平和垂直数字线来识别青蛙的位置?
    2. What if the frog jumped to the left of the grid or below the grid?
      ::如果青蛙跳到网格的左边 或者低于网格呢?

      

    The Four Quadrants
    ::四长方

    This system above works great for identifying the frog, but what if the frog jumped to the left or below the grid?
    ::上面的这个系统对识别青蛙很有效 但如果青蛙跳到左边或下面呢?

    In this interactive, you will look at how to describe the position of a frog on all four quadrants of a coordinate plane using positive and negative numbers.
    ::在此互动中,你将研究如何用正数和负数来描述青蛙在坐标平面所有四个四方位的位置。

     

    INTERACTIVE
    Four Quadrants
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    • Move the points and click the Jump button to control the frog.
      ::移动点并单击跳动按钮控制青蛙。
    • Try to catch the fly through the 4 quadrants.
      ::试着从四象限中捕到苍蝇
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    The use of a horizontal and vertical number lines to identify the location of an object is vital to the wireless networks on which our phones run . This system may be better known to you as latitude and longitude .
    ::使用水平和垂直数字线来识别对象的位置,对于我们电话运行的无线网络至关重要。这个系统也许更能称为纬度和经度。

    Using the interactive, you will apply your understanding of a coordinate grid system to a real world example of finding locations on a map based on longitude and latitude. Notice that similar to vertical number lines, negative latitude values appear below the equator.
    ::使用互动关系,您将会将您对坐标网格系统的理解应用到一个基于经度和纬度的地图上定位位置的真实世界范例。请注意,与垂直数字线相似,负纬度值出现在赤道下方。

     

    INTERACTIVE
    Longitude and Latitude
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    • Using the given latitude and longitude press the corresponding country.
      ::使用给定的纬度和经度按相应的国家。
    • Each degree is 111 km.
      ::每度111公里。
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    Making a Robot Part 5
    ::使机器人第5部分成为机器人第5部分

    A robot that moves back and forth is moving in 1-dimension. A robot would be more effective if it could move in 2-dimensions. Let’s  consider the robot that  has been improving its programming over a number of lessons .
    ::转而转动的机器人正在以一分为二的方式移动。 机器人如果能移动到二分为二的机器人将会更加有效。 让我们来想想一个一直在不断改进其编程的机器人,该机器人将吸取许多教训。

    How could the commands meant for one dimension  be improved to move in two dimensions?  You will need to change each of the commands that  the robot has developed thus far. They are listed below.
    ::如何改进用于一个维度的命令, 才能在两个维度上移动 ? 您需要更改机器人迄今所开发的每个命令 。 它们是下面列出的 。

    • steps否 - 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.
      ::步骤否 - 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
    • reset() - This command will return the robot to the starting position and will set the total number of steps taken to 0.
      ::重置 () - 此命令将把机器人返回起始位置, 并将将所采取步骤的总数设置为 0 。
    • total() - This command will return the total number of steps the robot has taken.
      ::总计 () - 此命令将返回机器人所采取步骤的总数 。

    In the interactive below, you will move a robot one step a time forward, backward, left, right, or one of those directions randomly. This will help you use positive and negative numbers in two dimensions to describe location.
    ::在下面的互动中,您会随机向后、向左、向右或向中任意移动机器人一步。这将帮助您使用两个维的正负数字来描述位置。

     

    INTERACTIVE
    Making a Robot pt 5
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    • Click the buttons to move the robot forward, backward, left, right, or randomly.
      ::单击按钮将机器人向前、向后、向左、向右或随机移动。
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    Discussion Questions:
    ::讨论问题:

    1. Press the “Random Movement” button. How can we use numbers to identify the position of the robot?
      ::按下“ 兰多运动” 按钮。 我们如何使用数字来识别机器人的位置 ?
    2. Press the “Random Movement” button three times. What position is the robot in?
      ::按下“ 兰多运动” 按钮三次。 机器人处于什么位置 ?
    3. How did identifying the position of the robot change from 1-dimension?
      ::辨别机器人的位置 是如何改变的?
    4. Does the backward and forward command still work in 2-dimensions?
      ::后方和前方的指挥 是否还在二层运作?
    5. Will we need 4 different commands: 1 for each direction?
      ::我们需要4个不同的命令吗? 每个方向1个?
      Summary
    • Two dimensions can be used to describe the position of an object using two numbers: one for a horizontal position and the other number for the vertical position.
      ::两个维可用于用两个数字描述对象的位置:一个用于水平位置,另一个用于垂直位置。