章节大纲

  • What is the ratio of the heights of the lollipops?
    ::棒棒糖高度的比例是多少?

    Use the interactive below to see how fast the lollipop trees grow in Lollipop Land. Throughout the lesson you will be using tables, how might you make a table for the heights of the lollipops and what would you expect their ratios to be?
    ::使用下面的互动来查看棒棒糖树在 Lollipop land 的生长速度。 在整个课程中, 您将使用表格, 您将如何为棒棒糖的高度做一张桌子, 以及您期望它们的比例是什么 ?

    INTERACTIVE
    Properties of Rational Numbers: Lollipop Trees
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    In Lollipop Land, the purple lollipops and red lollipop trees grow in pairs. The ratio between these paired trees is a constant ratio.
    ::在洛利波普地,紫棒棒糖和红棒棒糖树成对生长,这些配对树之间的比例是不变的。

    • Drag the red lollipop to change its height.
      ::拖动红色棒棒糖以改变其高度。
    • The ratio of the height of the trees is shown near the ground next to the trees.
      ::树木高度之比显示在树木旁边的地面附近。
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    1.

    Choose the appropriate statements that describe the relationship between the two heights as they increase. (Select all possible)
    ::选择合适的语句,以描述两高度之间随着升高而增加的关系。 (尽可能选择)

    Select all that apply
    a

    If the red lollipop increases by 4 ft., the purple lollipop increases by 5 ft.
    ::如果红棒棒糖增加4英尺,紫棒棒糖增加5英尺。

    b

    If the red lollipop increases, the purple lollipop stays the same.
    ::如果红棒棒糖增加,紫棒棒糖就保持不变。

    c

    If the red lollipop increases by 12 ft., the purple lollipop increases by 15 ft.
    ::如果红棒棒糖增加12英尺,紫棒棒糖增加15英尺。

    d

    If the red lollipop increases by 15 ft., the purple lollipop increases by 10 ft.
    ::如果红棒棒糖增加15英尺,紫棒棒糖增加10英尺。

    How tall are the  space  heroes ? 
    ::太空英雄有多高?

    lesson content
    Space Hero action figure

    Action figures from a series of popular space movies are built using a 1:6 scale. In the following interactive, fill in the table’s missing values using .
    ::从一系列流行空间电影中得出的动作数字是用1:6的比例构建的。 在接下来的互动中,请填写表格中缺少的数值。

    INTERACTIVE
    Equivalent Ratios Table
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    • Use the information given in the table to determine the unknown values.
      ::使用表中提供的信息来确定未知值。
    • All of the characters have equivalent ratios between their Toy Height and Real Height.
      ::所有字符的玩具身高与实际身高的比例相当。
    • The boxes turn green when the ratios are equal!
      ::当比例相等时, 盒子会变成绿色!
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    How many beats in a song sample?
    ::歌曲样本中有多少拍子?

    How many beats are there in this 12 second song sample? The total number of beats for 60 seconds of a song is the B eats P er M inute or BPM. In the interactive below , you will listen to part of a song and find a table’s missing values using equivalent ratios to determine how many beats are in the entire 60 second song.
    ::12 首歌曲样本中有多少节拍? 60 秒歌曲的节拍总数是 Beats Per minute 或 BPM 。 在下面的互动中,您将聆听歌曲的一部分,并用相当的比例找到一张表格的缺失值,以确定整个60 秒歌曲中有多少节拍。

    INTERACTIVE
    Beats per Minute
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    • Press the play button at the top of the table to hear a 12 second song clip.
      ::按下桌面顶端的播放按钮, 听12秒的音乐剪辑 。
    • Count the number of beats and input that number into the table.
      ::计算表格中的节拍和输入数。
    • Use this to find out the number of beats if the song played longer.
      ::使用此选项来查找如果歌曲播放时间更长, 节拍次数 。
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    Which gears are best for bike riding?
    ::哪种装备最适合骑自行车?

    lesson content
    Racing Bicycle Gears

    Bicyclists change gears on their bikes to change the speed. Many bicycle enthusiasts say that 44:16 is the perfect gear ratio for normal bike riding. Others prefer 46:16 for faster bike riding.
    ::许多自行车爱好者说,44:16是正常自行车骑车的完美齿轮比率。 其他人则更喜欢46:16,以加快自行车骑车速度。

    Using the next interactive, observe how different gears will move by adjusting the ratio of teeth between them.
    INTERACTIVE
    Gearing Up
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    • Move the red point to change the size of the big gear.
      ::移动红点以改变大齿轮的大小 。
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    Discussion Question
    ::讨论问题

    When we talk about gears on bikes, we say it is a 'low gear' when there is a much smaller number of teeth on the front gear than on the back gear. Which gears do you think are usually better for biking up steep hills, low or high? Why? Discuss in class or with your friends. Do others agree? Critique their answers and defend your position!
    ::当我们谈论自行车上的齿轮时,我们说它是“低齿轮”,因为前齿轮上的牙齿数量比后齿轮少得多。你认为哪种齿轮通常更适合在陡峭的山坡上骑车,低或高?为什么?在课堂上讨论,还是与你的朋友讨论。其他人同意吗?回答并捍卫你的立场!

    (Hint: The bigger the difference between the number of teeth on the front gear and the number on the back gear, the more times the front gear goes around for each time the back gear and wheel goes around! If you pedal more times to move the bike a certain distance - like one turn of the back wheel - you expend more energy. Where would that energy go?)
    :伤心提示: 前齿齿齿数和后齿数的差别越大, 每次后齿轮和轮轮转时,前齿齿数的间隔越大! 如果您在移动自行车的偏移时间越长, 就像一个后轮的转弯, 你花费的能量就越大。 能量会流向哪里? )

    You can find the gear ratio by counting the number of teeth in the front gear and the number of teeth in the back gear and setting the numbers into a ratio like this:
    ::您可以通过计算前齿牙数和后齿牙数,并将数字设置成这样的比例,找到齿轮比率:

    Number of teeth in front gear : Number of teeth in rear gear
    ::前齿牙数:后齿牙数

    For this interactive, practice finding equivalent ratios for bike gears by using the table to help you.
    ::对于这一互动性做法,通过使用表格帮助你找到自行车齿轮的等同比率。

    INTERACTIVE
    Bike Gear Fill in Blank
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    • Using the given number of front and back teeth, find the ratio and then make equivalent ratios with the rest of the boxes. 
      ::使用前牙和后牙的给定数目,找到比率,然后与箱中的其余部分作出等值比率。
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      Summary
    ::摘要

    • Equivalent ratios are two ratios that express the same relationship between values.
      ::等值比率是表示价值之间相同关系的两个比率。
    • To find an equivalent ratio, multiply or divide both values in the ratio by the same number.
      ::为了找到相等比率,将两个数值乘以或除以相同数字。

    Review Questions
    ::回顾问题

    True or False: If the ratio of the heights of two lollipops is 2:3, the taller lollipop is always 3 units tall. Explain your answer.
    ::真理或假的: 如果两个棒棒糖的高度比是2: 3, 高一点的棒棒糖总是高3个单位。 请解释您的答复 。

    True or False: If the scale of the action figures changes to 1:8, the action figures will be taller. Explain your answer.
    ::真理或假的: 如果动作的大小改变为1: 8, 动作的数字会更高。 请解释您的答复 。

    If a song has 20 beats in a 12 second sample, how many beats would it have in a full minute? Show your work.
    ::如果一首歌在12秒的样本里有20拍子, 整整一分钟里有多少拍子? 展示你的工作。

    How can you find a missing value in a ratio table?
    ::您如何在比例表中找到缺失值 ?