章节大纲

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  • 评价表达式

    Can you build an expression?
    ::你能造一个表情吗?

    In the interactive below, you will identify and sort different parts of an expression . Throughout this lesson, you will evaluate expressions by substituting different values into the variables.
    ::在下面的互动中,您将识别和排序表达式的不同部分。在整个课程中,您将用不同的数值替换为变量来评估表达式。

     

    INTERACTIVE
    Building an Expression
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    • Move the different parts of the expression into their corresponding boxes.
      ::将表达式的不同部分移动到相应的框中。
    • Press the button to check your work.
      ::按下按钮检查您的工作 。
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    How many squares and unit cubes are there in  an  'exploded' cube?
    ::“爆炸”方块中有多少方块和单位立方体?

    lesson content

    In the interactive below, you can find the volume of a cube by breaking one big cube into smaller unit cubes and counting them out. You can find the surface area of a cube in the interactive by counting the number of little painted squares on the outside of the cube.
    ::在下面的互动中,您可以通过将一个大立方体破碎成一个小的立方体来找到一个立方体的体积,并将其数出来。您可以通过计算立方体外的画面小方块数来找到互动中立方体的表面面积。

     

    INTERACTIVE
    Cube Exploration
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    • Explore how the side length affects the number of little squares in the cube by adding and subtracting side length.
      ::通过增减副长度,探索侧长度如何影响立方体中小方形的数量。
    • Click "Expand" to separate the big cube into little cubes and "Shrink" to put them back together.
      ::点击“ 扩展” 将大立方体分解成小立方体, 并单击“ 尖刻” 把它们重新组合起来。
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    CK-12 PLIX Interactive: Fish Tank Cube
    ::CK-12 PLIX 互动:鱼缸立方体

    In the PLIX Interactive below, you will substitute in different side lengths to find the volume of a cube-shaped fish tank.
    ::在下面的PLIX互动中,您将用不同的侧边长度来替代一个立方体形鱼缸的体积。

     

     

     

    S wirly Spiral Art
    ::流动螺旋艺术

    Change the numbers of teeth on the gears in the interactive below and them spin them to see spiral art. Find the GCF between each of the smaller gears with the big gear.  Look for   relationships between  the GCFs and the patterns in the spiral art.
    ::查找每个小的齿轮与大齿轮之间的绿色气候基金。 查找绿色气候基金与螺旋艺术模式之间的关系。

     

    INTERACTIVE
    Harmonograph
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    • Pick the size of the gears using the dropdown menus.
      ::使用下拉菜单选择齿轮大小 。
    • Press the buttons to spin the gears and set down the pen.
      ::按下按钮来旋转齿轮 放下笔
    • Drag the red points to adjust the curves.
      ::拖曳红色点以调整曲线。
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    Discussion Question
    ::讨论问题

    You can only sometimes count the numbers of bumps on the spiral. When is it useful to substitute numbers into the expression to find the number of bumps?
    ::您只能有时计算螺旋顶点数。 在表达式中替换数字以找到顶点数什么时候有用 ?

     

    How high up is the skydiver?
    ::天空潜水员有多高?

    lesson content

    A skydiver jumps from a plane at the height of 12,000 feet. The  rate  at which the skydiver falls increases every second until she pulls her parachute. The height of the parachuter can be found by substituting the number of seconds she has been in the air into  a mathematical expression.  Let  t  represent the number of seconds in  − 16 t 2 + 12 , 000.
    ::12,000英尺高度的飞机上跳下天空潜水器。 天空潜水器坠落的速度每秒增加一次, 直到她拉起降落伞。 降落伞的高度可以通过将她在空中的秒数替换为数学表达式来找到。 以 16t2+12000 秒数表示。

    Use the interactive below to find how high up the skydiver is when she opens the parachute.
    ::当她打开降落伞时, 使用下面的交互功能来查找天空投影器的高度 。

     

    INTERACTIVE
    How high up is the skydiver?
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    • Enter a value for  t   in the box.
      ::在框中输入 t 的值。
    • Click the button of the operation that should be done at each step.
      ::单击每个步骤应该执行的操作的按钮。
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    Food for Thought
    ::" 思想食品 " 组织

    In the interactive, we ignored air resistance. In real life, a skydiver accelerates only until he or she reaches about 120 mph (about 200 kph). At that speed , the air pushes against the skydiver's body with so much force that gravity no longer causes acceleration (although the diver does keep falling at 120 miles per hour)!
    ::在互动中,我们忽略了空气抵抗。在现实生活中,一个天空潜水员只会加速速度,直到达到大约120英里(约200公里 ) 。 以这种速度,空气会以如此巨大的力量向天空潜水员的身体推进,以至于重力不再导致加速(尽管潜水员每小时的潜水员确实会持续下降120英里 ) !

    Learn more about terminal velocity and skydiving here: !
    ::更多了解终端速度和跳伞情况:

      Summary
    • There are different parts to expressions and equations:
      • Variables are letters used to represent unknown values.
        ::变量是用于表示未知值的字母。
      • Coefficients are numbers that come before a variable.
        ::系数是变量之前的数字。
      • Constants are fixed numbers that are on their own (not being multiplied/divided by a variable).
        ::常数是自成一体的固定数字(不按变量乘/分)。
      • Terms are separated by addition or subtraction.
        ::用语以增减分开。

      ::表达式和方程式有不同的部分:变量是用于代表未知值的字母。系数是变量之前的数字。常数是自成一体的固定数字(不由变量乘/分)。用增或减来分隔术语。
    • Use a number to represent the unknown value. Substitute values into the letter to find different values for the expression.
      ::使用数字来表示未知值。在字母中替换值以查找表达式的不同值。