章节大纲

  • Properties of Addition
    ::添加属性

    In this lesson, you will combine multiple addition and subtraction expressions and solve. To help solve these types of problems, there are two properties that can be used. The first is the Commutative Property of Addition , which states that the order in which you add two rational numbers does not matter . So, for any two rational numbers a and b , 
    ::在此课中, 您将结合多个加法和减法表达式并解决。 为了帮助解决这些类型的问题, 有两个属性可以使用。 第一个是加法的通融属性, 其中指出添加两个合理数字的顺序无关紧要 。 因此, 对于任何两个合理数字 a 和 b,

    a + b = b + a

    ::a+b=b+a +b=b+a +

    The second property is the Associative Property of Addition .  This property states that for any three rational numbers, you may pick the two that you want to add together first. You do not have to add them in the order in which they appear in the problem. So, in this case, for any three rational numbers; a , b and c , 
    ::第二个财产是 " 连带附加财产 " 。该财产规定,对于任何三个合理数字,您可以先选择要加在一起的两个数字。您不必在问题出现的顺序中加上这两个数字。因此,在这种情况下,对于任何三个合理数字,a、b和c,

    a + b + c = ( a + b ) + c = a + ( b + c )

    ::a+b+c=(a+b)+c=a+(b+c)

    Notice the grouping symbols (parentheses) here. They indicate that it does not matter which two numbers you add together first. Pick the two that are easiest for you, then add the third.  Other grouping symbols are braces, { }, brackets , [ ], and even absolute value , | |. 
    ::注意在此分组符号( 括号) 。 它们表示, 您先将两个数字组合到一起并不重要。 选择对您最简单的两个数字, 然后添加第三个。 其他分组符号是括号 {} 、 括号 、 [ ] , 甚至绝对值 ,\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \ \ \ \ \ \\\ \ \\\\\\\\\\\ \ \ \ \\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

    This property also works for more than three rational numbers. 
    ::该财产的用途也超过三个合理数字。

     

    Switch the Order
    ::切换顺序

    How many different ways can you add  7 + 4 + ( − 6 ) + ( − 3 ) ?
    ::您可以增加 7+4+( - 6)+( - 3) 多少种不同的方式?

     

    INTERACTIVE
    Switch the Order
    minimize icon
    • Move the red dots to change the order of the integers.
      ::移动红色点以更改整数的顺序。
    • Move the blue and green dots to change the placement of the parentheses.
      ::移动蓝点和绿点以更改括号的位置。
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    Discussion Question
    ::讨论问题

    Which grouping was easier for you to add across? Discuss with your classmates why grouping different numbers together for an addition problem would be helpful or even easier in certain cases.
    ::与同学讨论为什么将不同的数字组合在一起来增加问题会有所帮助, 在某些情况下甚至更容易。

     

    Exploring  Washington DC
    ::探索华盛顿特区

    Cheryl's friend Annika is visiting her in Washington DC. Cheryl wants to minimize the walking, but hit all the red points on the map and the Capitol Building. Other criteria:
    ::Cheryl的朋友Annika正在华盛顿拜访她。

    • They must start at a Metro stop (the pink M's).
      ::他们必须从Metro站(粉红色M's)开始。
    • They must end at the Wizard's game.
      ::他们必须在巫师的游戏中结束
    • Lunch must be the second or third stop.
      ::午餐必须是第二或第三站。

    Find the shortest route for the girls using city block distances between each location.
    ::利用每个地点之间的城市街区距离为女孩寻找最短路线。

     

    INTERACTIVE
    Washington DC Map
    minimize icon
    • Move the red dot to find the shortest distance to reach all the purple dots.
      ::移动红点以找到最短距离 到达所有紫点
    • Click "Next Path" to trace the current path and to start a new path.
      ::单击“ 下一路径” 以追踪当前路径并启动新路径 。
    • Click "Set Start" to clear all the paths and to set the starting point at the current location of the red dot.
      ::单击“ 启动 ” 以清除所有路径, 并在当前红点的位置设定起点 。
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       Summary
    ::摘要

    • The Commutative Property of Addition for two rational numbers  a  and  b  states  a + b = b + a .   Order does not matter with addition.
      ::增加两个合理数字a和b的通融属性说明a+b=b+a。 命令与添加无关。
    • The Associative Property of Addition for three rational numbers,  a ,   b  and  c  states  a + b + c = ( a + b ) + c = a + ( b + c ) .  It does not matter which two numbers you group together to add first. 
      ::a、b和c为三个合理数字的 " 添加的连带属性 " 表示a+b+c=(a+b)+c=a+(b+c)。您将哪些数字组合为第一个,这无关紧要。
    • The two properties can be used together and with more than three numbers.
      ::这两种属性可以同时使用,并有三个以上的数字。