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  • 使用指数

    How many bubbles can you make?
    ::你能制造多少泡泡?

    lesson content
    Bubbles

    Use the interactive below to make patterns with  bubbles.  How can you figure out the numbers of bubbles without counting them all individually?
    ::使用下面的交互效果来用气泡制作模式。 您如何在不单独计算气泡数量的情况下找到气泡数量 ?

    In this lesson, you will learn  how to use and make exponential patterns.
    ::在这个教训中,你将学会如何使用和制作指数模式。

     Discussion Question
    ::讨论问题

    How can you figure out the numbers of bubbles without counting them all individually?
    ::你怎么能不单独计算气泡的数量 就能找出这些气泡的数量呢?

      

    How many branches are there on the fractal tree?
    ::分形树上有多少树枝?

    Fractals are mathematical patterns that  can make beautiful artwork. Try building your own fractal tree in the interactive below.
    ::分形是数学模式,可以制作美丽的艺术作品。尝试在下面互动的分形树中构建自己的分形树。

    You can learn more about Fractals from this CK-12 lesson : .
    ::您可以从这个 CK-12 课中学习更多分形: 。

    How  can you shorten repeated multiplication?
    ::您如何缩短重复乘法 ?

    lesson content
    Exponents represent repeated multiplication

    As the number of  steps  gets bigger, the number of times you have to multiply a number gets to be too much. You can show repeated multiplication in a shorter way with exponents.
    ::随着步骤的数量增加,您要乘一个数字的次数会太多。您可以用缩略语用较短的方式显示重复的乘法。

    Try making expressions with exponents in the interactive below.
    ::尝试在下面互动的语句中用引言制作表达式 。

    Can you fit the teddy bear in the gift box?
    ::你能把泰迪熊装进礼物盒里吗?

    lesson content

    You can find the volume of a box by multiplying the length times the width times the height of the box. When a box is a cube, each of the dimensions of the box (length, width, and height) are the same. 
    ::您可以通过乘以框的宽度乘以其高度的倍数找到框的体积。当框为立方体时,框的每个维度(长度、宽度和高度)是相同的。

    In the interactive below, try to find a box size that would snuggly fit a teddy bear. Check out all of the ways that volume of the box can be expressed.
    ::在下面的交互式框中, 尝试找到一个可以折叠成泰迪熊的盒子大小 。 请检查该盒子的体积可以表达的所有方式 。

    Remember that an inch  is a measure of length and in 2 is a measure of area.  There are other units to measure volume including cm 3  and ft 3 .
    ::记住, 英寸是长度的量度, 英寸是面积的量度。 还有其它单位可以测量体积, 包括 cm3 和 ft3 。

    CK-12 PLIX Interactive: Teddy Bear Box
    ::CK-12 PLIX 互动:泰迪熊盒

    In this PLIX, you again resize a box for a teddy bear and you will answer 5 questions about exponential questions. The different forms of the exponential expression do not show up in the interactive. The last question asks you to think up an example of a real life application for exponential expressions.
    ::在此 PLIX 中, 您再次调整泰迪熊的框大小, 您将回答5个有关指数问题的问题。 交互式的指数表达式的不同形式不会出现。 最后的问题要求您为指数表达式设想一个真实生活应用实例 。

      Summary
    • Exponents represent repeated multiplication. For example, in  7 3 = 7 ⋅ 7 ⋅ 7  
      • 7 is the base and 3 is the exponent.
        ::7是基数,3是指数。
      • This can be read as “seven to the third”
        ::这可以读作“七至三”

      ::指数表示重复乘法。 例如,在 73= 7+7-7 7 7 中, 基数为 73= 7+7-7 7 中, 3 是 指数 。 这可以被解读为 “ 7 到 3 ” 。