Section outline

  • Which gears are perfect for bike riding?
    ::哪种装备最适合骑自行车?

    lesson content

    Bicyclists change gears on their bikes to change the speed and make it easier to ride on different slopes.
    ::骑自行车者改变自行车的齿轮,以改变速度,使骑车更容易在不同斜坡上行驶。

    Use this interactive to practice  completing a table of by finding different ratios between the number of teeth on the front gear versus the back gear on a bike.
    ::使用这种互动方式来完成一张表格,找到前齿轮上的牙齿数量与自行车上的后齿轮数量之间的不同比例。

    INTERACTIVE
    Bike Gear Table
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    • Type in different values for the number of front and back teeth to get new ratios that are equivalent to 26:8.
      ::输入前牙和后牙数的不同值,以获得相当于26:8的新比率。
    • When the ratio is correct, the row will turn green!
      ::当比例正确时,行就会变绿!
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    How  do you  draw an  optical illusion?
    ::你如何画一个光学幻觉?

    Look at all the black dots in the picture!
    ::看看照片上所有的黑点!

    lesson content
    The Hermann grid optical illusion

    For  this interactive, you will  make your own optical illusion by changing the ratio between the size of the squares to the size of the bars.
    ::对于这种互动,你将改变方形大小与条形大小的比率,从而产生你自己的光学幻觉。

    INTERACTIVE
    Optical Illusion
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    • Using ratios of 1:2 and 5:2, change the square and bar size to see if you can make the optical illusion appear.
      ::使用1:2和5:2的比率,改变正方形和条形大小,看能否出现光学幻觉。
    • The white dots should look gray or black when seen from the corner of your eye and move around when you look at different spots of the grid!
      ::从你眼角看到白点应该灰色或黑色, 当你看到网格的不同位置时, 白色点应该看起来灰色或黑色。
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    The dots seem to appear depending on the square size to bar width ratio (the bar is the space in between the black squares). For this interactive, you will practice creating equivalent ratios by filling in the table’s missing values with square and bar sizes that create the optical illusion.
    ::圆点的出现似乎取决于正方形大小和条形宽度比( 条形宽度比( 条形是黑方之间的空间 ) ) 。 对于此互动关系, 您将练习通过将表格缺失的数值填入平方形和条形大小来创建等值比率, 从而产生光学幻觉 。

    INTERACTIVE
    Optical Illusions Table
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    • Once you have played with the black and white grid, try inputting different square and bar sizes.
      ::一旦您玩过黑白格, 尝试输入不同的正方形和条形大小 。
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    Which gears are best for biking fast?
    ::哪种装备最适合快速骑车?

    Bicyclists change gears on their bikes to  choose the best ratio for different purposes.
    ::骑自行车者改变自行车的轮椅,为不同目的选择最佳比率。

    • A low  gear  ratio, like 22:30 , is best for climbing hills and when you first start pedaling.
      ::像22: 30一样低的齿轮比率 最适合攀登山峰 当你第一次踏上踏板时
    • A high gear ratio, like 44:11, is best for riding fast and traveling long distances.
      ::高渔具比率,如44:11,最适合快速和长途旅行。

    Use this interactive to visualize how different gear ratios affect gear movement.
    ::使用此互动来直观显示不同的渔具比率如何影响渔具的移动。

    INTERACTIVE
    Bike Gear Interactive
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    • Use the dropdown menus to change the number of teeth on Gear 1 and Gear 2.
      ::使用下拉菜单来改变 Gear 1 和 Gear 2 上的牙齿数量。
    • Press Pause/Play to stop and start the animation.
      ::按 Pause/ Play 键停止并启动动画 。
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    For the next few interactives, you will look at how some gear shifts result in equivalent ratios . Find these ratios  by filling in the table’s missing values. Then, you will compare the gear ratios to find which set of gear shifts is highest or lowest.
    ::对于接下来的几场互动,您将查看一些齿轮变换是如何导致等效比率的。 通过填充表格缺失的数值来查找这些比率。 然后,您将比较齿轮变换比率,以找到哪种最大或最低的齿轮变换。

    INTERACTIVE
    Gear Shifts #1
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    • Continue the pattern and input the numbers of front and back teeth to create an equivalent ratio to the ones already on the table.

      ::继续此图案, 输入前牙和后牙的编号, 以建立与表上已经列出的对应比例 。
    • The text will turn green if your ratio values are correct!
      ::如果您的比值正确的话, 文本会变成绿色 !
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    INTERACTIVE
    Gear Shifts #2
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    • Continue the pattern and input the numbers of front and back teeth to create an equivalent ratio to the ones already on the table.
      ::继续此图案, 输入前牙和后牙的编号, 以建立与表上已经列出的对应比例 。
    • The text will turn green if your ratio values are correct!
      ::如果您的比值正确的话, 文本会变成绿色 !
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    INTERACTIVE
    Gear Shifts #3
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    • Continue the pattern and input the numbers of front and back teeth to create an equivalent ratio to the ones already on the table .
      ::继续此图案, 输入前牙和后牙的编号, 以建立与表上已经列出的对应比例 。
    • The text will turn green if your ratio values are correct !
      ::如果您的比值正确的话, 文本会变成绿色 !
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    Discussion Question
    ::讨论问题

    Order the table from the highest gear ratio to the lowest gear ratio. Notice that the first table and the second table do not share any of the same numbers. How can you compare the ratios in those tables? How  would you  know if your answer is correct?
    ::将表格从最高的齿轮比率排序到最低的齿轮比率。 注意第一个表格和第二个表格不分享相同数字中的任何数字。 您如何比较这些表格中的比率? 您如何知道答案是否正确 ?

    What do full screen and widescreen ratios mean for TVs?

    ::电视的全屏和宽屏比例意味着什么?

    Most TV's and computer screens you have seen are probably in what is called 'widescreen format'. It was not always that way though. Prior to the early 2000's, it was very common to see 'full screen format' TV's and computer monitors.
    ::您所看到的多数电视和计算机屏幕可能都在所谓的“全屏格式 ” 中。 虽然并不总是这样。 在2000年代初期之前,看到“全屏格式”的电视和计算机显示器是非常常见的。

    In the interactive below, you will look at how ratios  can be used to represent the resolution of digital pictures on TVs or computer screens.
    ::在下文互动部分,你将研究如何利用比率来代表电视或计算机屏幕上数字图片的分辨率。

    INTERACTIVE
    Resolution Comparison
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    • Use the buttons to change between aspect resolutions, and see how wide-screen and full-screen differ from each other.
      ::使用按钮来更改各部分的分辨率, 并查看宽屏和全屏之间的差别 。
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    In  the next interactive, you see how the resolution of a picture changes as the ratio between the number of pixels in an image changes.  Notice that al though the number of pixels change based on the picture resolution, the ratio is equivalent across all images.
    ::在下一次互动中,您会看到图片的分辨率是如何变化的,作为图像变化中的像素数量之间的比。请注意,虽然根据图像分辨率变化的像素数量,但所有图像中的比例都相等。

    INTERACTIVE
    Pixel Progression
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    • Resolution, or the density of pixels, determines how clear an image is.
      ::分辨率或像素密度决定图像的清晰度。
    • Use the button on the screen to get clearer images. 
      ::使用屏幕上的按钮获取更清晰的图像 。
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    The width to height ratio of a TV is called the aspect ratio. Pixels are each of the tiny, little dots that make the image on a screen. The resolution of a TV screen is the ratio of pixels across the width to pixels  up and down the height of the screen.
    ::电视的宽度与高度之比被称为宽度比。 像素是屏幕上制作图像的每一个小点。 电视屏幕的分辨率是宽度与屏幕上下像素之比。

    For the next few interactives, you will practice filling in the missing values of tables  of equivalent ratios. Then, you will compare the aspect ratios and resolutions of TVs.
    ::在接下来的几场互动中,您将练习填充相等比率表格的缺失值。 然后,您将比较电视的侧比和分辨率。

    INTERACTIVE
    Aspect Ratio vs Resolution Table #1
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    The Aspect Ratio is simply the dimensions of whatever screen it is describing. The Resolution is the density of pixels, and is an equivalent ratio to the Aspect Ratio.
    ::外观比只是它所描述的屏幕的维度。 分辨率是像素的密度, 与外观比相当 。

    • Try making some other equivalent ratios. The text will turn green when you get it right.
      ::尝试做一些其他等值比例。 文本在正确时会变成绿色 。
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    INTERACTIVE
    Aspect Ratio vs Resolution Table #2
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    The Aspect Ratio is simply the dimensions of whatever screen it is describing. The Resolution is the density of pixels, and is an equivalent ratio to the Aspect Ratio.
    ::外观比只是它所描述的屏幕的维度。 分辨率是像素的密度, 与外观比相当 。

    • Try making some other equivalent ratios. The text will turn green when you get it right.
      ::尝试做一些其他等值比例。 文本在正确时会变成绿色 。
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       Summary
    ::摘要

    • 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。
    • When comparing ratios, find an  equivalent ratio such that one of the values in each of the ratios is the same, making them easier to compare.
      ::在比较比率时,找到一个等值比率,使每一比率中的一个数值相同,使其更容易比较。

    Review Questions
    ::回顾问题

    Look at this student's work: They said that the ratios 3:4 and 6:8 are not equivalent because 3+4 does not equal 6+8. Where did the student make a mistake in their reasoning?
    ::看看这名学生的工作:他们说3:4和6:8的比率不相等,因为3+4不等于6+8。 学生在推理中哪里犯了错误?

    Would you prefer to create an optical illusion with a high square size to bar width ratio or a low one? Explain your reasoning.
    ::您是否希望制造一种光学幻觉, 光学幻觉的平方大小比条宽度比高或低? 请解释您的推理 。

    How can you determine if one gear ratio is higher or lower than another?
    ::如何确定一个渔具比率是否高于或低于另一个渔具比率?

    Predict what would happen to the aspect ratio if the number of pixels across the width of a TV screen was doubled, but the number of pixels up and down the height remained the same.
    ::如果电视屏幕宽度的像素数量翻了一番,但向上和向下高度的像素数量保持不变,那么对宽度比率会发生什么预测。