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  • 以不同形式比较比例关系

    Proportional Relationships in CPR
    ::国家方案建议中的比例关系

    In this lesson , you will look at how the form in which a proportional relationship is displayed can affect how you understand it. The forms you will be looking at are ones which you  may have used to display proportional relationships before;  verbal descriptions, equations, tables, and graphs.  You will begin by looking at how CPR is a process that involves performing actions in a proportional relationship to save lives. CPR (cardiopulmonary resuscitation) is a sequence of chest compressions and rescue breaths that help a patient who is unresponsive and not breathing. CPR is something that all doctors, nurses and first responders must know. Additionally, teachers and many other professionals are required to know the steps for performing CPR. Emergency situations can arise anywhere, and CPR may be the key to saving a life.
    ::在此课程中, 您将查看显示比例关系的形式会如何影响您如何理解它。 您将要看到的是那些您可能曾经用来显示比例关系的形式; 口头描述、 方程式、 表格和图表。 您将首先查看CPR是如何在比例关系中采取行动以拯救生命的过程。 心肺复苏( 心肺复苏) 是一个胸部压缩和呼吸的序列, 帮助一个不反应和不呼吸的病人。 CPR是所有医生、 护士和第一反应者都必须知道的。 此外, 教师和其他许多专业人士都必须知道实施CPR的步骤。 紧急情况在任何地方都会发生, CPR可能是拯救生命的关键。

     

    Proportional Relationships in CPR Continued
    ::国家方案建议中的比例关系

    Outside of a hospital, it is always important to check for responsiveness and call 911 before beginning CPR. When a trained professional is performing CPR on an adult, the first step is to clear the patient's airway by tilting the patient's head back. After this comes a proportional sequence of chest compressions and rescue breaths in a one minute cycle. Look at the interactive below to compare the rate of chest compressions per minute and rescue breaths per minute.  
    ::在医院之外,在开始CPR之前检查反应和拨打911总是重要的。当受过训练的专业人员对成年人进行心肺复苏时,第一步是通过将病人头部向后倾斜来清除病人的呼吸道。在这之后,将胸部压缩和呼吸在一分钟的循环中成比例的顺序。看看下面的交互反应,比较每分钟的胸部压缩速度和每分钟的呼吸速度。

     

    INTERACTIVE
    Proportional Relationships in CPR
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    Drag the red points to observe the rate of occurrences between rescue breaths and chest compressions.
    ::拖曳红色点以观察救援呼吸和胸部压缩之间的发生率。

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    Discussion Question
    ::讨论问题

    Think about the lines mathematically. What can you say about the steepness or of each line? Use this to make a comparison within a context.
    ::从数学角度思考线条。 您可以对陡度或每条线表示什么 ? 用它来比较上下文 。

     

    Need for Speed
    ::需要速度

    Another common proportional relationship is that of distance and time when traveling at a constant speed . The average speeds of two swimmers, Gabriel and Sam, during a 100m freestyle race are shown below as a proportional relationship between time (in seconds) and distance (in meters). Gabriel’s average  speed during the race is expressed in the graph below, with the x - axis representing time and the y - axis representing distance . Sam’s average  speed during the race is expressed in an equation with the variable  x  representing time, and the variable  y  representing distance. Use the  graph and equation below to determine who won the race.
    ::另一个常见的成比例关系是以恒定速度行驶时的距离和时间关系。 加布里埃尔和萨姆两个游泳运动员在100米自由式赛跑中的平均速度显示在下面的时间(秒)和距离(米)之间的比例关系中。加布里埃尔在比赛中的平均速度在下面的图表中表示,X轴代表时间,y轴代表距离。萨姆在赛跑中的平均速度用一个方程式表示,变量x代表时间,变量y代表距离。使用下面的图表和方程式确定谁赢得比赛。

    Sam:   y = 5 8 x
    ::萨姆:y=58x

    Gabriel:
    ::加布里埃尔:

     

    INTERACTIVE
    Gabriel's Average Speed
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    • Drag the points to observe how far Gabriel swims in meters over a certain number of seconds.
      ::拖动点以观察加布里埃尔在几秒内 游泳的米数有多远
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    Better Buy
    ::更好买

    Proportional relationships are also used by stores to help sell items in large quantities. However, it can be hard to compare prices when they are displayed in different quantities or forms. To see this , consider the cost of paper towels. Below is the pricing information for two brands of paper towels: Spongy brand paper towels and Absorbia brand paper towels. The prices for different quantities of Spongy paper towels  are expressed in  the table below. The unit price for Absorbia paper towels is stated in a verbal description. Use the table and  description below to determine which brand costs less money.
    ::商店也利用比例关系帮助大量销售物品,但是,如果以不同数量或形式展示,价格可能很难比较。为了解这一点,可考虑纸巾的成本。下面是两品牌纸巾的定价信息:海绵品牌纸巾和阿博尔比亚品牌纸巾。不同数量的海绵纸巾的价格见下表。Absorbia纸巾的单价以口头说明形式说明。使用下面的表格和说明来确定哪些品牌成本低于钱。

    Spongy:
    ::海绵:

    Quantity Price ($)
    6 5.46
    8 7.28
    12 10.82

    Absorbia:
    ::阿博尔比亚:

    Absorbia paper towels are on sale at the unit price of $0.86 per roll.
    ::Absorbia纸巾以每卷0.86美元的单价出售。

     

     

    Discussion Question
    ::讨论问题

    What is the constant of proportionality for Spongy and Absorbia? What does it mean for each of them?
    ::海绵和阿伯索比亚的相称性是多少?这对每个海绵和阿伯索比亚都意味着什么?

     

     Summary
    ::摘要

    • Finding the equation for proportional relationships will make it easier to compare two proportional relationships represented in different ways.
      ::寻找比例关系方程式将使比较以不同方式体现的两种比例关系更加容易。
    • The equation for a proportional relationship is  y = k x .
      ::比例关系方程式是y=kx。