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  • 表达式

    Are you a math detective?
    ::你是数学侦探吗?

    lesson content

    Use the interactive below to move the " data-term="Parentheses" role="term" tabindex="0"> parentheses around in the expression . How many different ways can you evaluate this expression?  (Hint: there are more than 4 ways)
    ::使用下面的交互效果来移动表达式中的圆括号。您可以用多少种不同的方式来评价这个表达式? (提示:有4种以上的方式)

     

    INTERACTIVE
    Math Detective
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    Look at the equation with blue parentheses. The expression from the left side of the equation is copied below. Depending on which operation is performed first, the value of the expression changes. For example, If you add  @$3+4@$  before performing any other operations in the first equation, then the expression equals  @$37@$ .  

    ::以蓝色括号查看方程式。 方程式左侧的表达式复制如下。 取决于先执行哪个操作, 表达式的值会发生变化 。 例如, 如果您在第一个方程式中执行任何其他操作前加上@ $3+4@ $, 那么表达式等于@ $37@ $ 。

    • Move the red points to change which operation is performed first.
      ::将红点移动到更改先执行哪个操作。
    • Move the red point so the second expression equals  @$18@$ .
      ::移动红点, 第二个表达式等于 @ $18@ $。
    • Move the red point so the third expression equals  @$1@$ .
      ::移动红点,使第三个表达式等于@ 1@ $。
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    C onsider grouping more than 2 numbers into a set of parentheses or having more than one set of parentheses.  How could this change the resulting value of the equations used above?
    ::考虑将超过2个数字分组为一组括号或多为一组括号。 这如何改变上述方程式的生成值 ?

     

    Can you make the math?
    ::你能算数吗?

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    Addition, Subtraction, Multiplication and Division

     

     

    There are lots of ways  that people can say  add, subtract, multiply and divide. You can  also represent these operations with  well-known symbols .
    ::人们可以用多种方式说添加、减、乘、分。您也可以用众所周知的符号来代表这些操作。

    Try finding the right symbols  to complete the math in the interactive below.
    ::尝试找到正确的符号来完成以下互动中的数学。

     

    INTERACTIVE
    Can you make the math?
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    • Select the operations needed to complete the expression.
      ::选择完成表达式所需的操作 。
    • Check your answer by clicking the button.
      ::按下按钮来检查您的回答 。
    • Click Next when you are ready to move on.
      ::准备向前移动时, 下单击 。
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    What are the race times for Olympic bobsledders?
    ::奥林匹克骑手的赛跑时间是多少?

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    Consider this table of times from an olympic competition:
    ::从奥林匹克竞赛中考虑此表格的时间 :

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    Standings for women's bobsled race by country

    Each of the race times in the chart above are from the 2014 Olympic Women's Bobsleigh race.
    ::以上图表中的每个赛事时间都来自2014年奥运女性Bobsleigh比赛。

    A t the end of racing events in the actual Olympics, a table shows up listing the rankings, countries, and the times for the competitors. However, unlike the table above, only one full time actually shows up. All of the times for the other countries are listed by how much longer it took them to finish the race than the first place winner.
    ::在实际奥林匹克运动会赛事结束时,一张表格列出了竞争对手的排名、国家和时间。 然而,与上表不同,只有一次全时出现。 其他国家的所有时间都以他们完成赛事所需的时间比第一胜者多长而列出。

    Use the times given in the reference table above to complete the interactive table below to show how you would find the race times for all of the  competitors. 
    ::使用上文参考表格中给出的时间填写以下交互式表格,以显示如何找到所有竞争对手的赛跑时间。

     

    INTERACTIVE
    Bobsled Times
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    • Complete the expressions for the competitors' times by typing in the white boxes. Second place is already done for you as an example.
      ::通过在白盒中打字来完成竞争对手时间的表达式。 第二位已经作为示例为您完成 。
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    Extension Activity : Use race times from your local track team, cross country team, or mile times from PE class. Write expressions to show comparative times similar to the ones you wrote in the interactive.
    ::扩展活动: 使用本地轨道团队的种族时间, 跨国别团队, 或PE类的英里数。 写入表达式以显示与您在互动中写入的比较时间相似的比较时间 。

    Use the interactive below to write an expression for how you can give change from $20.
    ::使用下面的交互效果来写一个表达式,表示您如何对 20 美元进行更改 。

     

    INTERACTIVE
    Hat Price Table
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    • Fill the input boxes with the appropriate expression for finding the change from $20. Make sure there is a minus sign in your answer.
      ::在输入框中填入查找从 20 美元变化的适当表达式。 请确认在您的答复中有一个减号 。
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    Wordy Mathematical Operators
    ::Wordy 数学运算符

    In this interactive, you will match  different parts of an expression and operations with words.
    ::在此互动中, 您将把表达式和操作的不同部分与单词匹配 。

     

    INTERACTIVE
    Mathematical Operators
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    • Click the mathematical operators at the top and match them to their associated vocabulary words below.
      ::单击顶部的数学运算符,使其与下面相关的词汇单词匹配。
    • Press "Check" when you think you're done.
      ::当你认为你做完了就按"检查"键
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    How much water is there at the wettest place in the USA?
    ::美国最湿的地方有多少水?

    lesson content
    Mt. Waialeale, The Wettest Place in the USA

    The wettest place in the USA is a  volcano  in Hawaii called Mt. Waialeale (pronounced "why uh lay uh lay"). It rains 373 inches of rain a year on the mountain. However, the rain varies from day to day.
    ::美国最湿的地方是夏威夷的一座名为Waialealele山的火山(宣布为“为什么下山 ” ) 。 山上每年降雨373英寸雨。 然而,降雨量每天都在变化。

    Use the interactive to find the average (mean) inches of rain over 3 days.
    ::使用交互方式查找三天的平均(平均)雨英寸。

     

    INTERACTIVE
    How Much Water at the Wettest Place in the USA?
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    • Click three days on the calendar for which you want to find the average rainfall.
      ::单击日历上的3天,以查找平均降雨量。
    • Use the buttons to calculate the average or select new days.
      ::使用按钮计算平均值或选择新天数。
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    Discussion Questions
    ::讨论问题 讨论问题

    1. How can you describe the expression in the interactive using words like "sum," " difference ," "product," and/or "quotient?"
      ::如何用“和”、“差异”、“产品”和(或)“引用”等词描述互动中的表达方式?
    2. Division can be explained as multiplying by the reciprocal . Try turning the multiplication in the expression into division. Now, how would you describe the expression?
      ::“除法”可以被解释为乘以对等。尝试将表达式中的乘法转换为除法。现在,您如何描述表达式?
    3. How many sums, quotients, products, and differences are there in the expression?
      ::表达方式中有多少金额、商数、产品和差异?

    Extension Activity : Find the 3 wettest days of the year in your hometown and find the average of those days. Rewrite the expression you used in more than one way. Use multiple ways to describe the operations in the expression.
    ::扩展活动: 在家乡查找一年中3个湿度天, 并找到这些天的平均时间。 重写您使用的表达式, 以多种方式重写。 使用多种方式描述表达式中的操作 。

      Summary
    • When writing an expression remember the different ways to say add, subtract, multiply, and divide. Here are some terms that relate to these operations:
      • Add: “sum”, “and”, “more”
        ::加:“和”,“和”,“更多”
      • Subtract: “less than”, “difference”, “reduced by”
        ::减: " 小于 " , " 差异 " , " 减少 "
      • Multiply: “times”, “of”, “product”
        ::乘以: " 时间 " 、 " 时间 " 、 " 产品 "
      • Divide: “split between”, “quotient”, “over”
        ::除号: “在”、“引号”、“超过”

      ::写一个表达式时,要记住用不同方式表示添加、减、乘、除、增、除。这里有一些与这些操作有关的术语:加上:“总”、“和”、“更多”减:“小于”、““差异”、“减少”乘以:“时间”、“时间”、“数量”、“产品”除以:“在时间”、“数量”、“替代”