Section outline

  • General

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  • 等等价比

    Variable Conundrum
    ::不稳定的难题

    In the  lesson , the following example about was introduced.
    ::在教训中,介绍了以下例子。

    Example
    ::示例示例示例示例

    Zoe is printing a picture. The picture can be any size, but the width should be half the length to keep the  ratio the same.
    ::Zoe 正在打印图片。 图片可以是任意大小, 但宽度应该为一半, 才能保持比例不变 。

    Use the interactive below to see how the dependent and independent variables can be switched in this scenario as long as the relationship between them is maintained.
    ::使用下面的交互效果来查看在这种假设情景中,只要保持依附变量和独立变量之间的关系,这些变量是如何被转换的。

     

    INTERACTIVE
    Variable Conundrum
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    • Drag the red point to change the length or width of the image. 
      ::拖曳红色点以更改图像的长度或宽度。
    • Press the button to switch between making length change based on width or making width change based on length.
      ::按下按钮在根据宽度作出长度变化或根据长度作出宽度变化之间切换。
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    This interactive  is an example of an equivalent ratio. In an equivalent ratio, there are no dependent and independent variables defined by the relationship. Rather, you can choose which variable will take the role of the independent variable and which variable will take the role of the dependent variable.
    ::此互动性是等值比率的一个例子。 在等值比率中, 不存在由关系定义的依附和独立的变量。 相反, 您可以选择哪个变量将扮演独立变量的角色, 而哪个变量将扮演依附变量的角色 。

     

    Progress
    0 / 3
    1.

    What can be said about the relationship between the two sides?
    ::双方之间的关系如何?

    Select all that apply
    a

    The height of the picture is half of its length.
    ::图片的高度是其长度的一半。

    b

    The height of the picture is twice its length.
    ::图片的高度是其长度的两倍。

    c

    The length of the picture is twice the height.
    ::图片的长度是高度的两倍。

    d

    The length of the picture is half the height.
    ::图片的长度是高度的一半。

     

     

    Equivalent Ratios Revisited
    ::重审的等等同比率

    Recall that e quivalent ratios are two or more ratios that represent the same relationship. Ratios that are equivalent can be simplified to the same ratio in simplest form.
    ::回顾等同比率是代表同一关系的两个或两个以上比率,等同比率可以简化为最简单的相同比率。

    In this interactive, create a table by finding pairs of values that share an equivalent ratio.
    ::在此互动中,通过找到相同比例的对等数值来创建表格。

     

    INTERACTIVE
    Action Figures Ratios
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    • Try to make equivalent ratios with the different action figures.
      ::尝试用不同的动作数字做出等值比率 。
    • The boxes turn green when you get the ratios right.
      ::当你得到正确的比率时,盒子会变成绿色。
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    In addition to using a table to represent equivalent specific ratios,  you can also use a graph to represent equivalent ratios .
    ::您除了使用一个表格来表示相应的具体比率外,还可以使用一个图表来表示相应的比率。

    Use the following interactive to graph points representing values for with equivalent ratios.
    ::将以下交互式点用于表示具有等值比率的数值的图形点。

     

    INTERACTIVE
    Graphing Action Figure Ratios
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    • Select the labels for the axes from the dropdown menus.
      ::从下拉菜单中选择轴的标签。
    • Drag the red points to plot the action figure and character heights.
      ::拖曳红色点以绘制动作图和字符高度。
    • Click the "Next" button to move to the next step.
      ::单击“ 下一步” 按钮移动到下一步 。
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    Writing Equivalent Ratio Equations
    ::同等等价物价比率

    Graphs and tables are helpful in determining equivalent ratios. However, there is another strategy that  you can use now that  you know how to solve a one-step equation . A statement that two ratios are equal is also known as a proportion .
    ::图表和表格有助于确定等值比率。然而,如果您知道如何解决一个单步方程,您现在可以使用另一种策略。两个比例相等的语句也被称为比例。

    In the next interactive, cross multiply to solve this proportion.
    ::在下一次互动中,要解决这个比例,要交叉倍数。

     

    INTERACTIVE
    Writing Equivalent Ratio Equations
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    Follow the directions in the interactive to understand a new method of solving ratio expressions.
    ::遵循互动中的方向,了解解决比率表达方式的新方法。

    • Press the "Next" button to move onto the next step.
      ::按下“ 下一步” 按钮移动到下一步 。
    • Enter the missing value into the box as a decimal.
      ::将缺值作为小数输入框中。
    • Drag the slider when it appears to look through the steps.
      ::当滑动滑动滑动滑动滑动器似乎通过各个步骤查看时拖动滑动滑动器。
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    Equivalent Ratio Review Continued
    ::同等比率审查继续

    Earlier in this lesson, you found the action figure heights and  'real'  heights of varying superhero characters. This task would have been more difficult if the heights of the characters varied more.
    ::在此课的前面, 您发现动作数字的高度和“ 真实” 高度 , 包括不同的超级英雄人物。 如果字符的高度变化更大, 这项任务本会更加困难 。

    Use the interactive below to create a table of toy figure heights by finding pairs of values that share the equivalent ratio. Remember that the ratio of the height of toys to the height of the characters is 1:5.  
    ::使用下面的交互效果来创建玩具形高的表格, 找到相同比例的对数值。 记住玩具高度与字符高度的比例是1: 5 。

     

    INTERACTIVE
    Find the Missing Heights
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    • You have been given the toy height and real height for The Cricket. 
      ::你被授予了"板球"的玩具身高和实身身高
    • Use the ratio between the different heights of the Cricket to find the missing heights of the other characters.
      ::使用板球不同高度之间的比例来查找其他字符缺失的高度。
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    Extension: Hero Design
    ::扩展号:英雄设计

     

    INTERACTIVE
    Hero Design
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    First student:
    ::第一学生:

    1. Put the height of your superhero in the input. Any number will be put in as feet
      ::在输入中输入您的超级英雄的高度。 任何数字都将以脚表示
    2. Make a name and superpower for your hero
      ::为你英雄出名 创造超能力
    3. Choose how much you want to scale down the figure, so the toy model will have an appropriate height (in inches) (less than 1)
      ::选择您想要缩放图像多少, 所以玩具模型会有一个合适的高度( 英寸) (小于 1)
    4. Hand it off to the second student
      ::把它交给第二个学生

    Second Student:
    ::第二学生:

    1. Use the different tools on the top bar to make an illustration of the hero*
      ::使用顶端栏上的不同工具来显示英雄*
    2. Choose different colors listed on the bottom panel
      ::选择底面板上列出的不同颜色
    3. Input the toy's height
      ::输入玩具的高度

    *The tool will show a preview, and if you notice a mistake, press the mouse icon to remove the preview before you click again. New parts will be layered over the old ones, so plan before hand!
    ::* 此工具将显示预览, 如果您发现错误, 请按鼠标图标在再次单击前删除预览。 新部件将分层在旧部件之上, 请先计划 !

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      Summary
    • Equivalent ratios are two or more ratios that represent the same relationship
      ::等等值比率是代表相同关系的两个或两个以上比率
    • A proportion is an equation with two ratios set equal to each other.
      ::比例是一个等式,两个比率对等。
    • To solve a proportion, find the least common denominator and cancel them to get rid of the denominators.
      ::解决一个比例,找到最小的公分母 并取消它们 以摆脱分母。