Section outline

  • Make Ratios with Blocks
    ::带块的比率

    Make your own groups by sorting the blocks in the interactive below. Think about how you can make ratios with the groups of blocks. 
    ::通过在下面交互的区块中进行排序, 建立自己的区块组。 想想如何与区块组比 。

    INTERACTIVE
    Pictures of Ratios
    minimize icon
    • Sort the shapes by dragging them into the boxes that match their color.
      ::将形状拖放到符合颜色的框中, 以此排序形状 。
    • After you sort the shapes, fill in the blanks to complete the ratio sentences.
      ::在排序形状后,填写空白以完成比例句。
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    If there are 6 red blocks and 4 blue blocks. What are the possible ways to express the ratio between the number of red blocks to blue blocks? (Select all possible)
    ::如果有6个红区块和4个蓝区块。 表示红区块数与蓝区块数之比的可能方法是什么? (尽可能选择)

    Select all that apply
    a

    For every 4 blue blocks, there are 6 red blocks.
    ::每4个蓝色区块就有6个红色区块

    b

    For every 4 red blocks, there are 6 red blocks.
    ::每4个红区,就有6个红区

    c

    4:6

    d

    10:4

    e

    For every 6 red blocks, there are 4 blue blocks.
    ::每6个红区就有4个蓝区

    f

    6:4

    How Cool w as President Coolidge? 
    ::库立奇总统有多酷?

    lesson content
    The "I Voted" sticker people get after they vote!

    If  you are curious, here are the actual results from the 1924 presidential election:
    ::如果你好奇, 以下是1924年总统选举的实际结果:

    Candidate Popular Votes
    Calvin Coolidge 15,725,016
    John W. Davis 8,386,503
    Robert M. LaFollette 4,822,856

    T ape D iagrams
    ::磁带图图

    For the next interactive, you will practice reading tape diagrams that represent ratios .
    ::在接下来的互动中,你将练习阅读代表比率的磁带图表。

    INTERACTIVE
    Ratios and Tape Diagrams
    minimize icon
    • Type in the whole numbers that correctly represent the visual ratio you see here.
      ::键入正确代表您在这里看到的视觉比例的全部数字。
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    How many miles can a car go on a tank full of gasoline ? 
    ::车能坐满汽油的油箱走多少英里?

    It is good to know how many miles your car can travel on a full tank of gasoline. Use the interactive to explore how you could write ratios between miles and gallons and how this ratio could change depending on the number of miles traveled and gallons of gas consumed.
    ::很高兴知道你的车能用满箱汽油行驶多少英里。 利用互动来探索如何在英里和加仑之间写出比例,以及根据行驶的英里数和消耗的天然气加仑数,这个比例会如何改变。

    INTERACTIVE
    Miles per Gallon
    minimize icon
    • Enter the number of miles and gallons for each truck.
      ::输入每辆卡车的里程数和加仑数。
    • Click the buttons for different trucks.
      ::单击不同卡车的按钮。
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    M ixing Paint Colors
    ::混合油漆颜色

    Red, blue, and yellow are called primary colors. Orange, purple, and green are called secondary colors, and are each created by combining two primary colors:
    ::红色、蓝色和黄色被称为主要颜色。橙色、紫色和绿色被称为次要颜色,每个颜色由两种主要颜色组合而成:

    • Red and yellow together create orange
      ::红色和黄色一起创造橙色
    • Red and blue together create purple
      ::红色和蓝色一起创造紫色
    • Blue and Yellow together create green
      ::蓝色和黄色一起创造绿色

    Through the interactive below, experiment with creating different colors by mixing different ratios of red, yellow and blue paint. Try to make brown paint by using a ratio of 3 cups of yellow paint to 4 cups of red paint to 5 cups of blue paint.
    ::通过下文的互动, 通过混合红色、黄色和蓝色涂料的不同比例, 尝试创造不同的颜色。 尝试通过使用3杯黄色涂料和4杯红色涂料与5杯蓝色涂料的比例来做棕色涂料 。

    INTERACTIVE
    Mix the Paint
    minimize icon
    • Click on the colors to pour the paint into the cup.
      ::点击颜色将油漆倒入杯中。
    • You can mix 12 colors.
      ::你可以混合12种颜色
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    Discussion Questions
    ::讨论问题 讨论问题

    1. How can you use a ratio to describe the numbers of cups of paint it takes to make this shade of brown paint?
      ::如何用比例来描述 制造棕色涂料的颜色 所需的涂料杯数?
    2. You can make different shades of brown by mixing different ratios of red, blue, and yellow. Use the interactive to draw a picture to show the ratio for a different shade of brown.
      ::您可以混合不同的红、 蓝色和黄色比例来制作不同的棕色阴影。 使用互动来绘制图片来显示不同棕色阴影的比例 。
    3. How can you describe the shade of brown you created as a ratio between a primary color (red, blue, or yellow) and a complementary color (green, purple, or orange)?
      ::您如何描述您创建的棕色阴影是初级颜色( 红色、 蓝色或黄色) 与补充颜色( 绿色、 紫色或橙色) 之间的比例 ?

       Summary
    ::摘要

    • A ratio is the relationship between two or more quantities.
      ::A比率是两个或两个以上数量之间的关系。
    • Words such as, "for every", "for each", and "per" are used to describe ratios.
      ::诸如“每个”、“每个”和“每个”等词用来描述比率。
    • Some examples of ratios written numerically: 3:4, 2:1, 1:3:1
      ::数字编制比率的一些例子:3:4、2:1、1:3:1:1:1:3:1

    Review Questions
    ::回顾问题

    Look at this student's work: they have 8 green blocks and 4 yellow blocks and they say the ratio of yellow blocks to green blocks is 8:4. Where did they make a mistake?
    ::看看这个学生的工作:他们有8个绿区和4个黄区, 他们说黄区和绿区的比例是8: 4。他们哪里搞错了?

    Would you rather have a 2:1 ratio of votes in your favor or a 3:2 ratio of votes in your favor? Explain your reasoning.
    ::您是否更希望获得2:1的赞成票比例或3:2的赞成票比例?解释一下您的推理。

    True or False: If a tape diagram is divided into 8 sections with 5 sections shaded and 3 not shaded, the ratio it represents is 5:3. Explain your answer.
    ::真理或假的:如果磁带图表分为8节,有5节为阴影,3节为阴影,5:3. 请解释答案。

    Predict what would happen to the ratio of miles to gallons if a car could travel further on the same amount of gasoline.
    ::如果一辆汽车能用同样数量的汽油继续行驶,那么预测里程与加仑的比率会如何。

    Predict what would happen to the shade of brown if you changed the ratio of yellow paint to 2 cups, but kept the amounts of red and blue paint the same.
    ::如果你把黄漆与两个杯子的比例 改变成两个杯子 红色和蓝色涂料的数量保持不变 棕色的阴影会怎样