Section outline

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

    In this lesson, you will explore how different ratios can represent the same relationship. Using the following interactive, you will make observations about by adjusting how many gallons a truck has and how far it can drive. 
    ::在此教训中, 您将探索不同比例如何代表相同关系。 使用以下互动方式, 您将调整卡车有多少加仑, 以及卡车能开多远, 来观察 。

    INTERACTIVE
    Miles per Gallon
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    • Move the red point along the road to change how many miles the truck can drive.
      ::沿路移动红点 改变卡车能开多少英里
    • 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 affect the overall miles per gallon rating of the truck.
      ::观察汽油的数量和里程数如何影响卡车每加仑总里程数。
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    Which ratio of miles to gallons below would a person driving the truck like most to have?
    ::驾驶卡车的人会像大多数人一样 拥有多少英里到加仑的比?

    In other words, choose the option below that represents the most miles travelled with the fewest gallons of gas used.
    ::换句话说,在下面选择一个选项,即使用最少的加仑气体行驶的里程最多。

    a

    5:25

    b

    100:5

    c

    140:5

    d

    5:5

    How many boxes of gel pens do we need to buy? 
    ::我们要买多少盒凝胶笔?

    A 6th grade teacher buys boxes of gel pens for her classes.  Use the interactive to make ratios between the number of gel pens and boxes through images and tape diagrams.
    ::A6级教师为其班级购买一箱凝胶笔。使用互动工具,通过图像和磁带图表,在凝胶笔数和盒数之间做出比率。

    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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    You order 6 boxes of pens. Each box contains 4 pens. How many pens did you order?
    ::你订了6箱笔,每盒有4支笔,你订了多少笔?

    Discussion Questions
    ::讨论问题 讨论问题

    1. The teacher needs at least one pen for each student for a full class of 3 0 students. How many different ways can you get 3 0 pens using the interactive? Think of all the factors of 3 0, why might some of these not be ideal in a real-world context?
      ::教师需要为每个学生提供至少一支笔,才能让30名学生全班学习。使用互动能用多少种不同的方式获得30支笔?想想所有30种因素,为什么在现实世界中,有些因素并不理想?
    2. The students may want two pens each. How many ways can 4 0 pens be represented?
      ::学生们可能各要两支笔,40支笔可以代表多少种方式?
    3. In the interactive, what parts of the tape diagram change ?  What parts of a tape diagram stay the same?
      ::在互动中,磁带图的哪些部分变化?磁带图的哪些部分保持不变?

    How is a ruler sort of like a tape diagram?
    ::统治者像磁带图一样如何?

    Since rulers are rectangular and divided into parts, they have some similarities to tape diagrams.  
    ::由于标尺是长方形的,分为若干部分,因此与磁带图表有一些相似之处。

    In the interactive below, you will work with tape diagrams and see how they can be used to relate millimeters and centimeters on a ruler .
    ::在下文互动中,您将使用磁带图,看看如何用磁带图来连接尺尺上的毫米和厘米。

    INTERACTIVE
    Rulers and Tape Diagrams
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    • Use the drop-down menu to choose between Rulers and Tape Diagrams.

      ::使用下拉菜单来选择标尺和磁带图表。
    • Drag the slider at the bottom of the interactive to change the tape diagram or rulers.
      ::拖动互动的底部的滑动器以更改磁带图或标尺。
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    Discussion Question
    ::讨论问题

    A textbook mentions that 1 centimeter is equivalent to 10 millimeters. Jerusha says that this means 1 centimeter is equal to 10 millimeters. Do you agree or disagree?
    ::一本教科书提到,1厘米等于10毫米。 Jerrusha说,这意味着1厘米等于10毫米。 你同意还是不同意?

    Are there enough teachers for all of the students out there?
    ::外面所有学生都有足够的老师吗?

    In fall 2016, the ratio of the average numbers of students to teachers in the United States was about 160 to 10.
    ::2016年秋季,美国平均学生人数与教师人数之比约为160比10。

    Just so you know - the count of  teachers includes educators and school staff beyond traditional classroom teachers.
    ::教师人数包括传统课堂教师以外的教育工作者和学校工作人员。

    lesson content

    Discussion Questions
    ::讨论问题 讨论问题

    1.  Use the image above to help you answer the questions about the average student to teacher ratio.
    ::1. 使用以上图像帮助回答关于学生与教师平均比例的问题。

    • H ow many students are there for every 20 teachers?
      ::每20名教师有多少学生?
    • How many students are there for every 30 teachers?
      ::每30名教师有多少学生?
    • How many teachers are there for every 480 students?
      ::每480名学生有多少教师?
    • How many teachers are there for every 320 students?
      ::每320名学生有多少教师?

    2.  On a tape diagram, boxes can be split into even sections and extra boxes can be added to the diagram.  What would you change about the tape diagram to find the following amounts?
    ::2. 在磁带图中,框可以分成偶数部分,在图表中可以添加额外的框。您对磁带图有什么修改,以找到以下数额?

    • The number of  teachers for every 1600 students.
      ::每1 600名学生的教师人数。
    • The number of students for every 5 teachers.
      ::每5名教师的学生人数。

    3.   Consider the changes you would make to the tape diagram to  help you answer the following questions:
    ::3. 考虑对磁带图作何种修改,以帮助回答下列问题:

    • How many teachers are there for every 1600 students?
      ::每1600名学生有多少教师?
    • How many teachers are there for every 80 students?
      ::每80名学生有多少教师?
    • How many students are there for every 5 teachers?
      ::每5名教师有多少学生?
    • How many students are there for every 40 teachers?
      ::每40名教师有多少学生?
    • How many students are there for every 15 teachers?
      ::每15名教师有多少学生?

    How can you mix the color brown with paints?
    ::你怎么能把棕色和油漆混在一起?

    Through this interactive, you can mix multiple batches of brown paint using the ratio 3 parts of yellow paint to 4 parts of red paint to 5 parts of blue paint . Observe the changes in the tape diagram representing this ratio as you increase the amount of brown paint. 
    ::通过此互动, 您可以使用黄漆三部分对红油漆四部分对蓝油漆五部分的比例混合多批棕色涂料。 当您增加棕色涂料数量时, 观察磁带图中显示此比例的变化 。

    INTERACTIVE
    Mix the Paint
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    • Click "Increase" to add brown paint to the bucket with a ratio of 4 red to 3 yellow to 5 blue.
      ::点击“ 增加” 将棕色涂料添加到桶中, 比例为 4 红色对 3 黄色对 5 蓝色 。
    • After there are 36 cups in the bucket, click "Reset" to start over.
      ::在桶里有36个杯子之后,请单击“重置”重新开始。
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    Discussion Question: When the total amount of paint increases or  decreases but the ratio of paint colors remains equivalent, does the shade of brown change? Use the idea of equivalence to help explain why or why not.  
    ::讨论问题:当涂料总量增加或减少,但涂料颜色比例仍然相等时,棕色变化的阴影是否暗淡?使用等值概念来解释为什么或为什么没有。

       Summary
    ::摘要

    • Equivalent ratios are two ratios that express the same relationship between numbers.
      ::等值比率是表示数字之间相同关系的两个比率。
    • To find an equivalent ratio, multiply or divide the numerator and denominator by the same number.
      ::要找到等值比例,要将分子和分母乘以或除以相同数字。
    • F o r example, 1:2 and 5:10 are equivalent ratios.
      ::例如,1:2和5:10是等值比率。

    Review Questions
    ::回顾问题

    True or False: If a car can travel 60 miles on 2 gallons of gas, it can travel 120 miles on 4 gallons of gas. Explain your answer.
    ::真实或假的:如果一辆汽车能用2加仑的气体行驶60英里,它就能用4加仑的气体行驶120英里。请解释您的答复。

    A teacher needs to buy gel pens for 50 students. Each box contains 10 pens. However, the teacher only has enough money to buy 4 boxes. How can the teacher solve this problem?
    ::教师需要为50名学生购买凝胶笔。 每盒都有10支笔。然而,教师只有足够钱购买4箱。教师如何解决这个问题?

    A textbook mentions that 1 centimeter is equivalent to 10 millimeters. Jerusha says that this means 1 centimeter is equal to 10 millimeters. Do you agree or disagree?
    ::一本教科书提到,1厘米等于10毫米。 Jerrusha说,这意味着1厘米等于10毫米。 你同意还是不同意?

    If the ratio of students to teachers is 160 to 10, how many students would there be for every 50 teachers?
    ::如果学生与教师的比例是160比10,那么每50名教师有多少学生?

    What is an equivalent ratio and how can you find one?
    ::什么是等值比率,你如何找到一个等值比率?