章节大纲

  • 常规

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  • 不同代表制的经常比例

    Emergency Medical Services
    ::紧急医疗服务

    One of the most important uses of proportions in the medical field is when administering medicine. Many dosages are dependent on a patient’s weight. The more a patient weighs, the more medicine  is  needed to  create the desired effect. This concept is something that doctors, nurses, and EMTs consider on a daily basis. In this lesson , you are going to explore the math that takes place when an EMS professional needs to save a patient's life.
    ::医疗领域最重要的比例用途之一是使用医学。 许多剂量都取决于病人的体重。 病人体重越重,就越需要药物来创造预期的效果。 这一概念是医生、护士和急救人员每天考虑的。 在这个教训中,你会探索当急救系统专业人员需要拯救病人生命时发生的数学。

    EMS stands for emergency medical services, which are made up of EMTs ( E mergency M edical T echnicians who provide lifesaving medical care onsite), 'Flight for Life' helicopters and other transportation, and firefighters . These are the people who arrive at the scene of an emergency to help if someone is hurt.
    ::紧急医疗服务是指紧急医疗服务,由紧急医疗队(现场提供救生医疗服务的紧急医疗技术员 ) 、 “ 生命之光”直升机和其他交通工具以及消防员组成。 这些人是到达紧急情况现场帮助受伤的人。

    Conversions
    ::改划

    Before you can see how EMS professionals determine how much medicine to give someone, you need to learn the units they use. All medicine dosages are in metric units. The  volume  of medicine is generally measured in milliliters (mL), which often does not need to be converted. However, the weight of the patient is usually  described in kilograms (kg) for determining how much medicine to use.  This can be  a challenge in the United States, since the standard unit of weight is the pound (lb). If a patient states their weight in pounds, there is a proportional relationship to determine their weight in kilograms. The relationship states that 1 pound is equal to 0.45 kilograms. The number 0.45 represents the constant of proportionality . U se this information to write an equation , make a table, and graph the relationship.
    ::在您看到 EMS 专业人员如何确定给人提供多少药品之前, 您需要了解他们使用的单位。 所有药品剂量都是用量单位表示的。 药品的量一般用毫升( mL)衡量, 通常不需要转换。 但是, 病人的重量通常用公斤( kg) 来描述, 以确定需要使用多少药品。 在美国, 这可能是个挑战, 因为标准重量单位是磅( lb ) 。 如果病人用磅表示体重, 则有比例关系来决定他们的重量。 关系显示 1磅等于 0. 45 公斤。 数字 0. 45 表示比例的常数。 使用此信息来写一个方程式, 绘制一个表格, 并绘制关系图 。

    Use the interactive below to create a table and make a graph which expresses the proportional relationship between pounds and kilograms.
    ::使用下方的交互作用来创建表格和图表,以显示磅与公斤之间的比例关系。

    INTERACTIVE
    Comparing Kilograms to Pounds
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    • Input different whole numbers into the kilogram column and the corresponding number of pounds in the next column.
      ::将不同的整数输入公斤列,并将相应的磅数输入下一列。
    • Drag the points to place them into the coordinates based on the table you filled.
      ::根据填充的表格,拖曳这些点,将其放入坐标中。
    • Press the white button to check your point placement.
      ::按白按钮检查点位置位置 。
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    Discussion Questions
    ::讨论问题 讨论问题

    1. How did you decide which values to put into the table?
      ::您是如何决定将哪些值放入表格的?
    2. How did you decide which scale to use?
      ::你是如何决定使用哪种比例尺的?
    3. What were your axis labels?
      ::你的轴轴标签是什么?
    4. What would the equation for the relationship be?
      ::这种关系的方程式是什么?
    5. Did you use any math tricks for any of the conversions?
      ::你有没有用任何数学把戏 来转换?
    6. If you were trying to convert pounds to kilograms would you find a table, graph or equation more helpful? Why?
      ::如果你试图将磅转换成公斤 你会发现一个表格、图表或方程式更有用吗?
    7. Could this graph be useful when converting pounds to grams? How?
      ::这个图在将磅转换成克时有用吗? 如何转换 ?

       

    Proportional Relationships in Medicine Continued
    ::医学中的比例关系持续

    When paramedics and EMT’s arrive upon the scene at an emergency, they need to be able to make smart decisions quickly. If they arrive on the scene and a patient has chest pain they  might give the patient  Diltiazem to relax the muscles and increase blood flow in the patient’s chest. The amount of the medicine they give  would depend on the patient’s weight. A graph of this relationship is shown in the interactive below.
    ::当急救人员和急救队在紧急情况下到达现场时,他们必须能够迅速做出明智的决定。 如果他们到达现场,病人胸口疼痛,他们可能会给病人Diltiazem放松肌肉,增加病人胸腔的血液流动。 他们提供的药品数量将取决于病人的体重。 下个互动的图表显示了这种关系的图示。

    Use the interactive to populate the table, determine the relationship between weight and medicine dosage, and express that relationship as an equation.
    ::使用互动来填充表格,确定重量和药用剂量之间的关系,并将这种关系表述为一个方程式。

    INTERACTIVE
    What Does Your Dose Do?
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    • Move the red point to see the dosage for different weights.
      ::移动红点以查看不同重量的剂量。
    • Fill in the table by typing in five different kg to mL ratios.
      ::以五种不同的千克对毫升比打字填充表格。
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    Discussion Questions
    ::讨论问题 讨论问题

    1. What should represent x and y variables in the equation? How do you know?
      ::方程中的 x 和 Y 变量应该代表什么? 你怎么知道 ?
    2. Based on the table and graph, what is the relationship between weight and dosage?
      ::根据表格和图表,重量和剂量之间的关系是什么?
    3. What is the constant of proportionality and equation for this relationship?
      ::这种关系的相称性和等式的一贯性是什么?
    4. Do you think that it would be most helpful for an EMT or paramedic to carry a graph for each medicine, carry a table with specific weights and dosages for each medicine or to carry a paper with the equation for each medicine?
      ::你认为由急救队或医护人员携带每个药品的图表,携带每药品有具体重量和剂量的表格,或携带每药品有方程的纸张,最有帮助吗?

    Gravity
    ::重力

    W hen considering  the constant of proportionality, it just makes sense  to  explore what is arguably the most important constant known to man: Earth’s gravitational constant of acceleration. As an object falls, it falls faster and faster by a proportional amount in the absence of air resistance and friction. This number can be measured and is represented by the letter  g .  Galileo Galilei, an Italian scientist, became the first person to calculate this number around 1600 CE. To determine  the value, Galileo set up a ramp and rolled a ball down it from different heights. He timed how long it took the ball to roll down the ramp and noticed that the ball got faster the longer it rolled. Next, he set out to measure the amount by which it was getting faster. He made a table of speeds and times from various heights. From this table, Galileo was able to determine the constant of proportionality at which the velocity of a falling object increases over time. In the interactive below, you will recreate Galileo’s experiment by dropping a the ball from varying heights and comparing the relationship between time and the velocity of the ball when it hits the ground.  You will be dropping the ball straight down rather than at an angle to avoid having to use the trigonometry principles that Galileo used.
    ::当考虑相称性的常数时,探索人类已知的最重要常数,即地球的引力加速常数,是有道理的。当一个物体坠落时,在没有空气阻力和摩擦的情况下,它会以一个成比例的幅度加速下降。这个数目可以用字母来测量和代表。意大利科学家伽利略·加利莱成为第一个在1600摄氏度左右计算这个数字的人。为了确定数值,伽利略设置了一个斜坡,从不同高度向下滚一个球。他计时了球推下斜坡的速度有多长,并且注意到球滚得越长,球速度越快。接着,他开始测量速度越快,速度越快。他从不同高度制作了一个速度和时间表。从这个表上看,伽利略能够确定一个坠落对象速度在一段时间内增加的相称性常数。在下面的互动中,你将重新建立伽利略的实验,将球从不同高度扔下来,并将时间与球速度之间的关系比起来越快。你将球飞到地面时,会直接使用一个轨道来避免。

    INTERACTIVE
    Gravity
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    • Drag the ball to the desired height and drop the ball by clicking on the "Drop" button.
      ::将球拖到理想的高度, 按下“ 拖放” 按钮, 将球拖到所需的高度, 并放下球 。
    • Drop the ball from multiple heights.
      ::把球从多重高度扔下来
    • Click the "Table" button to see the data from the last 5 drops.
      ::单击“表”按钮查看最后5滴的数据。
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    Discussion Questions
    ::讨论问题 讨论问题

    1. What should represent x and y in the equation? How do you know?
      ::方程中 X 和 y 代表什么? 你怎么知道 ?
    2. Based on the table and graph, what is the relationship between time and final velocity? How did you get it and what does it mean?
      ::根据表格和图表,时间和最终速度之间的关系是什么?你怎么得到的?它意味着什么?
    3. What is the constant of proportionality and how did you determine it?
      ::相称性的常数是什么? 你是如何决定的?
    4. What is the equation for this relationship? 
      ::这种关系的方程式是什么?

      Summary
    ::摘要

    • The constant of proportionality  is used to describe the relationship between two quantities, x  and  y .
      ::相称性的常数用来描述两个数量(x和y)之间的关系。
    • Use coordinates from a table to find the constant of proportionality:   k = y x .
      ::使用表格中的坐标查找相称性常数: k=yx。