Section outline

  • How many gel pens do we need to buy? 
    ::我们要买几根凝胶笔?

    A 6th grade teacher buys boxes of gel pens for her classes. Use the interactive to increase and decrease the numbers of pens in each box and the numbers of boxes. Try showing and hiding the tape diagram to show  how  to use tape diagrams to visually represent the ratio between gel pens and boxes, or the parts and whole.
    ::A6级教师为其班级购买一箱凝胶笔。 使用交互操作来增加和减少每个框中的笔数和盒数。 尝试显示并隐藏磁带图, 以显示如何使用磁带图来显示凝胶笔和盒之间或部分和整体之间的比例 。

     

    INTERACTIVE
    Gel Pen Tape Diagram
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    • Use the sliders to change the number of gel pens and boxes.
      ::使用滑动符更改凝胶笔和盒的数目。
    • Click the button to show or hide the tape diagram.
      ::单击该按钮以显示或隐藏磁带图。
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    The teacher wants to buy 20 pens total. Select the different ways she can buy pens.
    ::老师想总共买20支笔 选她买笔的不同方式

    Select all that apply
    a

    5 boxes with 4 pens per box
    ::5箱5箱,每箱4支,每箱4支

    b

    7 boxes with 3 pens per box
    ::7箱,每箱3支笔,每箱3支

    c

    2 boxes with 10 pens per box
    ::2箱,每箱10支,每箱10支

    d

    10 boxes with 2 pens per box
    ::10箱,每箱2支笔,每箱2支

     

     

    What does "miles per gallon" mean?
    ::"每加仑英里"是什么意思?

    Use the truck in the interactive to visualize how the ratio of miles per gallons changes and use it to solve part and whole ratio problems.
    ::用交互式卡车来想象每加仑里程比率的变化, 用它来解决部分和整个比例问题。

     

    INTERACTIVE
    Miles per Gallon
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    Cars are often rated based on how many miles they can travel on a full tank of gasoline. Use the truck here to explore how the simplified ratio of miles per gallon changes depending on the number of miles traveled and gallons of gas consumed.
    ::汽车通常根据他们乘坐满箱汽油能行驶多少英里来评定等级。 使用卡车来探索如何根据行驶的英里数和消耗的天然气加仑数来简化每加仑里数的变化比例。

    • Move the red point along the road to change how many miles the car can drive.
      ::沿路移动红点 改变车能开多少英里
    • Move the blue point in the truck to change the amount of gas the truck can hold.
      ::移动卡车的蓝色点 以改变卡车能持有的煤气数量
    • Observe how both the amount of gasoline and number of miles traveled affect the overall miles per gallon rating of the truck.
      ::观察汽油的数量和行驶的里程数如何影响卡车每加仑总里程数。

    The miles per gallon value is rounded to the nearest hundredths place.
    ::每加仑的英里值四舍五入到最接近的百分百位数。

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    Cars are often rated based on how many miles they can travel on a full tank of gasoline. For this interactive, you will visualize the part and whole ratio relationship between miles and gallons using tape diagrams.
    ::汽车通常根据他们能乘坐满箱汽油行驶多少英里来评分。 对于这一互动,您将使用磁带图来直观英里和加仑之间的部分和整个比例关系。

     

    INTERACTIVE
    Gas Mileage
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    • Move the red and blue points to change the miles per gallon value and the number of gallons.
      ::移动红点和蓝色点以改变每加仑的英里数和加仑数。
    • The white boxes represent the size of a 'full tank'.
      ::白箱代表一个“满箱”的大小。
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    Discussion Questions
    ::讨论问题 讨论问题

    1. What do the numbers of boxes represent? What do the numbers in each box represent?
      ::框数代表什么? 每个框数代表什么 ?
    2. Before going on a big trip, you may want to know how many miles your car can drive on a tank of gas. How can you use the information in the tape diagram to find the total number of miles?
      ::在进行一次大型旅行之前,你可能想知道你的车能开多少英里的油箱。你怎么用磁带图中的信息来找到总英里数?
    3. Find the number of miles could you drive a vehicle with a given number of gallons of gas and an engine that runs at a given number of miles per gallon.
      ::找到能开多少英里的车 能开多少加仑的汽油和引擎 以每加仑多少英里的速度运行

     

    How much paint do you need?
    ::你需要多少油漆?

    Use the interactive to create the color brown using the ratio of 3 parts yellow paint to 4 parts red paint to 5 parts blue paint.  You will be using these paint amounts and their tape diagram to write ratios between the red, yellow, and blue parts to the whole combined color .
    ::使用互动来创建彩色褐色, 使用3个部分的黄色涂料与4个部分的红色涂料与5个部分的蓝色涂料之比。 您将使用这些涂料数量及其磁带图来写出红色、 黄色和蓝色部分与整个组合颜色之间的比例 。

     

    INTERACTIVE
    Mix the Paint
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    • 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. What are some possible amounts that you could use to make a "part" of each color of paint?
      ::你可以用什么数量 来做每一色油漆的“部分”?
    2. If a "part" is the same amount across each color of paint, why is it that the colors are in different amounts?
      ::如果一个“ part” 与每个颜色的油漆量相同, 为什么颜色是不同的呢?
    3. Increase the total amount of this shade of brown paint. What is the effect on the "parts" and the "whole?"
      ::增加棕色涂料的阴影总量。 对“ 片段” 和“ 整片” 有何影响 ?
    4. The mixing instructions say that a certain color requires 3 parts yellow paint, 4 parts red paint, and 5 parts blue paint. Sophia believes that whether she uses 3 cups of yellow paint, 4 cups of red paint, and 5 cups of blue paint or 3 gallons of yellow paint, 4 gallons of red paint, and 5 gallons of blue paint she will get the same color. Is she correct? Why would the instructions use the word "parts"?
      ::混合指示说,某种颜色需要3个部分黄色涂料,4个部分红色涂料,5个部分蓝色涂料。 索菲亚认为,无论她使用3个黄色涂料,4个红色涂料,5个蓝色涂料,或3加仑黄色涂料,4加仑红色涂料,5加仑蓝色涂料,她都会得到相同的颜色。她正确吗?为什么该说明使用“部分”一词?

     

    How many marshmallow pieces?
    ::有多少棉花糖碎片?

    A mini-box of Yummy Charms cereal has oat pieces and five kinds of marshmallow pieces: balloons, suns, flowers, comets and hearts.  In the following interactive, use the number of marshmallow pieces and oat pieces to solve ratio problems involving parts and a whole.
    ::Yummy Charms谷类小盒有燕麦片和五种棉花糖片:气球、太阳、鲜花、彗星和心脏。在以下互动中,使用棉花糖片和燕麦片的数量来解决与部件和整体有关的比例问题。

     

    INTERACTIVE
    Cereal Sort
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    • Press the button to count the amount of oats and marshmallows.
      ::按下按钮来计算燕麦和棉花糖的数量。
    • Move the sliders to change how many oats and marshmallows are represented in the "part".
      ::移动滑块以更改“ 部分” 中代表的燕麦和棉花糖数量 。
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       Summary
    ::摘要

    • Use ratios to show the relationship between a part and the whole, P art :   W hole.
      ::显示一个部分与整个部分之间关系的使用比率, 部分: 整体。
    • The amounts of each item are called the parts.
      ::每个物品的金额都称为部件。
    • The total amount of all the parts is called the whole.
      ::所有部件的总数都称为整体。