章节大纲

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  • 坐标平面的形状

    Ladybugs on a Plane
    ::平板上的女虫

    Nina is playing a game where a ladybug will randomly appear on the  screen below . She must predict what color the ladybug will land on.  Which color will give her the best chance to win?
    ::尼娜正在玩一个游戏, 女虫会随机出现在下面的屏幕上。 她必须预测女虫会降落在什么颜色上。 哪一种颜色能给她最佳的获胜机会?

    In the following interactive, you will play the same game as Nina and see if you can use what you know about areas of polygons to figure out the best strategy.
    ::在接下来的互动中,你将和尼娜玩同样的游戏,看看能不能利用你所了解的多边形区域,找出最佳策略。

     

    INTERACTIVE
    Ladybugs on a Plane
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    • Choose a color from the dropdown for what color you think the ladybug will land on.
      ::选择从下调点选择一种颜色, 来选择您认为 Ladybug 会降落的颜色 。
    • Click the "Play" button to see if you were right.

      ::单击“ 玩耍” 按钮来查看您是否正确 。
    • Play again with the "Try again" button.
      ::重玩“ 再试一次”按钮 。
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    Area on the Coordinate Plane
    ::协调计划领域

    Coordinate planes allow us to easily find the dimensions of a shape necessary to find the area .  Questions like the one in the previous interactive can be answered using a coordinate plane . 
    ::坐标平面让我们可以轻松地找到找到区域所需的形状的尺寸。 像上次互动中的问题一样,可以使用坐标平面回答。

    Coordinate planes are especially useful  for finding area involving distances too great to be measured by hand. Computers use satellite data and coordinate planes to make accurate measurements in seconds.
    ::坐标飞机对于寻找距离太远、无法用手测量的区域特别有用,计算机使用卫星数据和协调飞机,以在秒内进行准确测量。

    For this interactive, you will graph a polygon on the coordinate plane given the coordinates of the vertices and practice finding areas of shapes on the coordinate plane.
    ::对于此互动, 您将在坐标平面上绘制一个多边形图, 以坐标平面上的顶点坐标 并练习在坐标平面上找到形状区域 。

     

    INTERACTIVE
    Areas on the Coordinate Plane
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    • Drag the red points to the given coordinates to graph a shape.
      ::将红色点拖到给定坐标处,以图示形状。
    • Enter the area of the shape into the white box when it appears.
      ::当形状出现时,输入形状区域进入白色框中。
    • Click the "Next" button to go to the next set of coordinates.
      ::单击“ 下一步” 按钮可以转到下一个坐标组 。
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    Population Density
    ::人口密度

    An important application of area is population density. Population density  tells you the ratio of people to square miles and is determined by dividing the population of a geographic location by the area of that location. Population density is important in determining where businesses, schools, and hospitals  should be  located.
    ::人口密度向你们说明人口与平方英里的比率,人口密度是通过按某一地理位置的区域划分该地理位置的人口来确定的,人口密度对于确定企业、学校和医院的地点十分重要。

    Using the next interactive independently, you will estimate the population density of states by creating polygons on a grid to approximate their area.
    ::您将独立使用下个互动点,通过在网格上创建多边形以接近其区域来估计各州的人口密度。

     

    INTERACTIVE
    Population Density
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    • Click Show shapes to show the approximation of the state area in terms of simple geometric shapes.
      ::单击显示形状以显示以简单几何形状表示的状态区域的近似值。
    • Use the scale to convert units in the interactive to real life units (miles).
      ::使用比例尺将互动中的单位转换为实际生命单位(英里)。
    • Divide the population by the area of the state to find the population density.
      ::人口按州划分,以找到人口密度。
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    Ladybugs on a Plane Continued
    ::飞机上的Ladybugs 继续

    Now that you know how to find the areas of shapes on the coordinate plane, you can answer the question from the opening activity.
    ::既然你知道如何在坐标平面上找到形状区域, 你可以在开始活动时回答问题。

    Use this interactive to play Nina’s ladybug game again, but this time you will be able to see a grid so you can find the areas of the colored polygons and find which color gives you the best chance of winning.
    ::使用此互动来再次玩 Nina 的 ladybug 游戏, 但这次您将能看到网格, 以便找到彩色多边形的区域, 并找到哪一种颜色能给你最佳的胜出机会 。

     

    INTERACTIVE
    Ladybugs on a Plane Continued
    minimize icon
    • Choose a color from the dropdown for what color you think the ladybug will land on.
      ::选择从下调点选择一种颜色, 来选择您认为 Ladybug 会降落的颜色 。
    • Click the "Play" button to see if you were right.

      ::单击“ 玩耍” 按钮来查看您是否正确 。
    • Play again with the "Try again" button.
      ::重玩“ 再试一次”按钮 。
    • Click "Show grid" to help you find the area of the shapes to answer the question "Which color will give Nina the best chance of winning the game?".
      ::点击“ 显示网格” 来帮助您找到形状区域来回答一个问题, “ 哪个颜色能给尼娜赢得比赛的最佳机会? ” 。
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     Summary
    ::摘要

    • Coordinate  planes are useful for seeing the dimensions of shapes.
      ::坐标平面有助于观察形状的维度。
    • To find the distance between two coordinate points with the same first coordinate, subtract the second coordinates. Similarly, if the second coordinates are the same, subtract the first coordinates.
      ::要找到同一第一个坐标的两个坐标点之间的距离,请减去第二个坐标。同样,如果第二个坐标相同,请减去第一个坐标。