章节大纲

  • 常规

    全部折叠 展开全部

  • 使用双级方程式解决问题

    In T his L esson
    ::在本课程中

    You will apply methods for interpreting word problems and checking solutions ( and ). You will be given a few different scenarios and will need to determine the equations and solve the problem, Once you have found a solution, rework the problem to double check your answer for viability.
    ::您将应用语言问题解析和校验解决方案( 和 ) 的方法。 您将得到一些不同的方案, 并且需要确定方程并解决问题。 一旦找到解决方案, 您将重新研究问题, 以双重检查您对可行性的答案 。

     

    Time to Skydive
    ::滑行时间到天行时间

    Alex is skydiving for the first time. In order to jump, the plane he is in needs to get to an altitude of 15,000 feet. The airport the plane takes off from has an elevation of 1500 feet and the plane climbs at a rate of 20 feet per second.
    ::亚历克斯第一次跳伞。为了跳跃,他需要的飞机高度达到15,000英尺。飞机起飞的机场高度为1500英尺,飞机以每秒20英尺的速度攀升。

    Use the interactive to figure out h ow long it takes for the plane to get to 15,000 feet. Then  w rite an equation for the plane's travel time.  Let   t   be time.
    ::使用互动来计算飞机到达15,000英尺需要多长时间。 然后为飞机的旅行时间写一个方程。 让我们不要浪费时间 。

     

    INTERACTIVE
    Time to Skydive
    minimize icon
    • Drag the red point to see how the airplane moves.
      ::拖曳红色点以查看飞机如何移动 。
    Your device seems to be offline.
    Please check your internet connection and try again.
    +
    Do you want to reset the PLIX?
    Yes
    No

     

     

    Progress
    0 / 5
    1.

    What are you trying to find and what are the units it will be in once solved?
    ::你想找到什么 和它一旦解决后会进入的单位是什么?

    a

    The time, in hours, until the plane reaches the jumping altitude.
    ::时间,小时,直到飞机到达跳跃高度。

    b

    The time, in minutes, until the plane reaches the jumping altitude.
    ::时间,几分钟,直到飞机到达跳跃高度。

    c

    The altitude of the plane, in feet.
    ::飞机的高度,足。

    d

    The distance, in feet, that the plane is away from the airport.
    ::飞机距离机场很远

    e

    The time, in seconds, until the plane reaches the jumping altitude.
    ::时间,秒,直到飞机到达跳跃高度

     

    C o nsider the following  arithmetic solution:
    ::考虑以下算术解决方案:

    Step 1 : Subtract 1,500 from 15,000 to find the height he needs to travel from the airport to the desired altitude.
    ::第1步:从15 000人中减去1 500人,以找到从机场到理想高度所需的高度。

    15,000 - 1,500 = 13,500 feet
    ::15 000 - 1 500 = 13 500英尺

    Step  2:   D ivide 13,500 by the distance per second, 20, to get the time it takes to travel 13,500 feet.
    ::第2步:将13 500除以每秒20的距离,以获得13 500英尺旅行所需的时间。

    13,500 ÷ 20 = 675 seconds
    ::13 500 20 = 675 秒

    Discussion Question
    ::讨论问题

    How does this method of solving compare to how you solved for the time?
    ::这个解答方法 与你当时解答的方法相比如何?

    It is important that you know how to interpret the problem so that you can determine what you are solving for. Notice that all the units in the problem are either feet or seconds. Because the problem is asking for time, the variable will be time, and the units will be in seconds. It is important to understand what a question is asking so you can adjust units when needed. If a question asks for the time in minutes, make sure you convert the answer correctly. Remember, there are 60 seconds in a minute, and 60 minutes in an hour.
    ::您必须知道如何解释问题, 以便您能够确定您正在解决的问题。 请注意, 问题所在的所有单位都是脚或秒。 问题在于时间, 变量是时间, 单位是秒。 重要的是要理解一个问题是什么, 以便您在需要时可以调整单位。 如果问题需要时间, 请确保您正确转换答案 。 记住, 每分钟有60秒, 每小时有60分钟 。

     

    Free Fall 
    ::自由瀑布

    The plane is now at jumping altitude and Alex is ready to go! He  jumps from the plane at an altitude of 15,000 feet and hits a speed of 160 feet per second. The parachute must be deployed when he hits 5,000 feet. How long is he in free fall?
    ::飞机现在处于跳跃高度,亚历克斯准备出发了!他从飞机上跳下,高度为15,000英尺,速度为每秒160英尺。降落伞必须部署,当他达到5000英尺时。他自由坠落的时间有多长?

    Use the interactive to figure out how long he is in free fall. Then write an equation for his travel time.  Let t  represent the time.  
    ::使用互动来计算他在自由坠落中的时间。 然后为他的旅行时间写一个方程。 让我们来代表时间 。

     

    INTERACTIVE
    Free Fall
    minimize icon
    • Move the point to see how the sky diver's position changes based upon the time.
      ::移动点以查看潜水员的位置如何根据时间变化 。
    Your device seems to be offline.
    Please check your internet connection and try again.
    +
    Do you want to reset the PLIX?
    Yes
    No

     

     

     

    Discussion Question
    ::讨论问题

    Looking back at the answers for some of the inline questions, are any of the answers not possible? Could you automatically eliminate any?
    ::回顾一些内含问题的答案,难道任何答案都不可能吗?你能自动消除任何答案吗?

     

    Extreme  Temperatures
    ::极端温度

    Alex was warned that the temperature in the air, before jumping, is quite windy and cold, so he needed to dress accordingly. At the airport it was 65°F, which is equal to five times the difference between the temperature at 15,000 ft and 2 .
    ::亚历克斯被警告说,在跳跃前,空气中的温度是风和冷的,所以他需要穿相应的衣服。 在机场,温度是65°F,等于15 000英尺和2英尺温度的五倍之差。

    Use the interactive to figure out w hat the temperature is at 15,000 feet. Then d etermine and solve the equation for the temperature at 15,000 feet.
    ::使用交互程序来确定 15,000 英尺的温度。 然后确定并解析 15,000 英尺温度的方程式 。

     

    INTERACTIVE
    Extreme Temperatures
    minimize icon
    • Drag the red point to see how cold it gets the higher you fly.
      ::拖红色点,看它有多冷 你飞得越高。
    Your device seems to be offline.
    Please check your internet connection and try again.
    +
    Do you want to reset the PLIX?
    Yes
    No

     

     

     

       Summary
    ::摘要

    • To solve two-step equations, use inverse operations (re verse PEMDAS)
      ::要解析两步方程,请使用反向操作(逆 PEMDAS)
    • It is important to use the correct units when solving problems within a context. 
      ::在解决某种背景下的问题时,必须使用正确的单位。