7.6 书写等量-interactive

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  书写等量

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  Website Development
  ::网站开发

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  Camryn is a website developer who is developing a website for a retail store. She needs to write a program that will allow the user to buy more than one item at once. When this program is finished, it will work similarly to the program below. What mathematical rules would allow this program to function ?
  ::Camryn 是一个网站开发者, 他正在为零售商店开发一个网站。 她需要写入一个程序, 使用户能够同时购买多个项目。 当这个程序完成后, 它会与下面的程序相似。 什么样的数学规则允许这个程序运行 ?

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  The interactive below shows the relationship between the cost and quantity of the retail store’s black pants. Can you determine what is the independent and dependent variable ?
  ::下面的互动显示了零售商店黑裤子的成本和数量之间的关系。 你能确定独立和依赖的变量是什么吗?

   

  

  INTERACTIVE

  Website Development

  

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  • Change the quantity and watch the total price change.
    ::改变数量 并观看总价格变化。
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  • Click Buy when you are satisfied with your amount.
    ::如果您对金额满意, 请单击“ 购买 ” 。

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  Discussion Question
  ::讨论问题

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  What would the independent variable be in this scenario? What would the dependent variable be?
  ::独立变量在这种假设中是什么?依赖变量是什么?

   

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  Writing Addition Equations and Subtraction Equations
  ::增加量和减法等量和减法等量

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  For many students, their initial tendency when writing equations is to try and solve them, but equations are for more than just solving. Equations are used  to express  the relationship between quantities . When writing equations , c arefully consider how the parts of  the equation relate to each other.
  ::对于许多学生来说,他们最初在写方程式时的倾向是尝试解答这些方程式,但方程式不仅仅是解决问题。 方程式用来表达数量之间的关系。 在写方程式时,要仔细考虑方程式的各个部分彼此之间的关系。

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  Addition Equations
  ::增量等量

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  An addition equation is used to represent a scenario where separate parts are combined to equal a whole. This type of equation can also be used to represent a scenario where an amount is being added to an initial value to produce a total.
  ::添加方程式用于代表一种假设情况,即将各部分合并成等于整部分。这种类型的方程式也可以用于代表一种假设情况,即将某一数额添加到初始值中以产生总计。

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  Example
  ::示例示例示例示例

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  Kaitlin is two years older than Brandon. Write an equation to find Kaitlin’s age using $\begin{array}{r}K\end{array}$  to represent Kaitlin’s age and $\begin{array}{r}B\end{array}$  to represent Brandon’s age.
  ::Kaitlin比Brandon大两岁。 写一个方程式来找到Kitlin的年龄,用K来代表Kaitlin的年龄,B来代表Brandon的年龄。

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  Since  Kaitlin is older than Brandon , you   could express this with an inequality :
  ::既然凯特林比布兰登大 你可以用不平等来表达

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  $$\begin{array}{r}K>B\end{array}$$

  
  ::K>B K>B

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  To write an equation,  you need to balance the inequality. Since the problem asks for Kaitlin’s age, treat this as the dependent variable. Kaitlin's age can be represented as two more than Brandon's age. In other words,  a dd 2 to Brandon’s age to equal Kaitlin’s age:
  ::写一个方程式时,您需要平衡不平等。 既然问题涉及Kaitlin的年龄,请将此作为依赖变量对待。 Kaitlin的年龄可以比Brandon的年龄多两岁。 换句话说,在Brandon的年龄中加上两个,等于Kaitlin的年龄:

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  $$\begin{array}{r}K=B+2\end{array}$$

  
  ::K=B+2 K=B+2

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  Subtraction Equations
  ::减减法等量

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  S ubtraction equations are used to represent situations where a part of something is being taken away or an amount is being decreased.  They can also be used to find the difference between or distance to  specific values.
  ::减法方程式用来代表部分东西被拿走或某一数额正在减少的情况。它们也可以用来查找具体数值之间的差别或距离。

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  Subtraction equations can be written  from addition equations. In the previous example,  you could have stated that Brandon’s age was 2 less than Kaitlin’s  and written the equation $\begin{array}{r}B=K-2.\end{array}$   You could also have  described this relationship by using the equation $\begin{array}{r}K-B=2\end{array}$  to show that the difference between their ages is 2.
  ::减法方程可以从加方程中写出。 在前一个例子中,你本可以说明布兰登的年龄比凯特林小两岁,并写出方程B=K-2。你也可以用方程K-B=2来描述这种关系,以表明他们年龄的差异是2岁。

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  Discussion Question
  ::讨论问题

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  Is Kaitlin’s age or Brandon’s age the dependent variable?
  ::Kaitlin 的年龄或 Brandon 的年龄是依附变量吗?

   

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  The chart below shows keywords that will help identify addition and subtraction relationships:
  ::下表显示有助于识别增减关系的关键词:

  Addition	Subtraction
  播放段落   •   Added to ::• 加入 播放段落   •   More than ::• 超过 播放段落   •   Sum ::• 总和 播放段落   •   Increased ::• 增加 播放段落   •   Total ::• 共计	播放段落   •   Subtracted from ::• 减去 播放段落   •   Less than ::• 小于 播放段落   •   Difference ::• 差异 播放段落   •   Decreased ::• 减少

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  Can you write the addition or subtraction equation that represents the scenario in the following interactive? What is the relationship between the height of the mountain and where the climbers are on it?
  ::您能写出以下交互式中代表情景的增法或减法方程式吗? 山高与登山者在山上的位置之间有什么关系?

   

  

  INTERACTIVE

  Hiking Equation

  

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  A mountain climber is climbing Purple Peak. The elevation of the summit or top of the mountain is  $h$  meters. He is currently at the Base Camp, at an elevation of 1527.4 meters.
  ::登山者正在攀登紫峰,峰顶或山顶的高度是h米。他目前在基地营地,高度为1527.4米。

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  • Drag the red point (the climber) up the mountain and see how high he climbs.
    ::将红点拖上山,看他爬多高。

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  Writing Multiplication and Division Equations
  ::乘数和除法等量

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  Multiplication Equations
  ::乘数

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  A multiplication equation is used to represent a  situation  where something is being added repeatedly. This type of equation can also be used to represent a scenario where you are taking a fraction of an amount.
  ::乘法方程式用于代表正在重复添加某种东西的情况。这种方程式也可以用来代表您正在取取一个数额的一小部分的假想。

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  Example
  ::示例示例示例示例

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  Kayla went to the store bought a bunch of pineapples. One pineapple costs $4.50. If she bought $\begin{array}{r}P\end{array}$  pineapples and spent a total of $\begin{array}{r}D\end{array}$  dollars, write an equation to represent this relationship.
  ::Kayla去店里买了一堆菠萝,一个菠萝要花4.50美元,如果她买了菠萝,花了总计D美元,写一个方程式来代表这种关系。

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  The amount of money spent by Kayla  depends how many pineapples she bought, so the total amount of money spent will be the dependent variable.  Think of this situation as Kayla buying one pineapple after another, so  you are repeatedly adding the price of one pineapple to  the total $\begin{array}{r}P\end{array}$  times. Repeated addition can be expressed using multiplication. The total will be determined by the price of an item multiplied by the number of items purchased:
  

  $$\begin{array}{r}D=4.5\cdot P\end{array}$$

  
  ::Kayla花的钱金额取决于她买了多少菠萝,所以所花的钱总额将是一个依附变量。把这种情况想象成Kayla在购买一个菠萝之后又购买一个菠萝,这样你就会反复将一个菠萝的价格加到总共P倍数中。重复增加的金额可以用乘法表示。总额将取决于一个物品的价格乘以购买的物品数量:D=4.5P。

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  Division Equations
  ::平方

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  A division equation is used to represent  a situation where an amount is being broken up into equal groups.  They can also be used to express a ratio or the average of a collection of values.  Division equations can be written  from multiplication equations.
  ::分裂方程式用于表示一个数额被分成等分组的情况,也可以用来表示一个比率或一个数值集合的平均值。分割方程式可以从乘法方程式中写出。

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  Example
  ::示例示例示例示例

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  Darius and three friends go out to dinner. They decide to split the bill between them equally. Write an equation to represent this relationship. Use  $\begin{array}{r}x\end{array}$  to represent the independent variable and  $\begin{array}{r}y\end{array}$  to represent the dependent variable.
  ::达利乌斯和三个朋友出去吃晚饭。 他们决定平分帐单。 写一个方程式来代表这种关系。 使用 x 代表独立的变量, y 代表依赖变量 。

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  The amount each friend pays depends on the value of the bill, so the value of the bill will be represented by  $\begin{array}{r}x\end{array}$  and the amount each friend pays will be represented by  $\begin{array}{r}y.\end{array}$  The bill is divided equally 4 ways.  You can use the following equation to represent this:
  

  $$\begin{array}{r}y=\frac{x}{4}\end{array}$$

  
  ::每个朋友支付的数额取决于帐单的价值,所以帐单的价值将以x表示,每个朋友支付的数额将以y表示。帐单以四种方式平均分配。您可以用以下方程式来表示:y=x4。

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  Discussion Questions
  ::讨论问题 讨论问题

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  1. How could this have been written as a multiplication equation to find the total bill?
  ::1. 如何将此写成一个乘法方程式,以找到总帐单?

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  2. Why is a division equation more appropriate for the situation?
  ::2. 为什么分裂等式更适合这种情况?

   

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  The chart below shows keywords that will help identify  multiplication and  division relationships:
  ::下表显示有助于识别乘法和分法关系的关键词:

  Multiplication	Division
  播放段落   •  Product ::• 产品 播放段落   •   Double, Triple, etc. ::• 双倍、三倍等 播放段落   •   Of ::• 在 播放段落   •   Half of, one-third of, ... ::• 半数、三分之一、...	播放段落   •   Quotient ::• 引文 播放段落   •   Per ::• 人均 播放段落   •   Average ::• 平均数 播放段落   •   Split ::• 拆分

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  Can you write the multiplication or division equation that represents the scenario in the following interactive? What is the relationship between the number of baskets and the number of plums in each?
  ::您能写出以下交互式中代表情景的乘法或除法方程式吗? 篮子数和每颗李子数之间的关系是什么?

   

  

  INTERACTIVE

  Picking Plums

  

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  A group of 6 friends decides to go plum picking and split the plums evenly among them.
  ::一群六位朋友决定去采梅子 平分梅子

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  • Drag the slider to change the number of plums picked altogether.
    ::拖动滑块以全部改变所选李子的数量 。

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  Computer Programming Continued
  ::计算机编程继续

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  When writing an equation, it is important to consider which variable is the independent variable and which variable is the dependent variable. Typically the letter x is used to represent the independent variable and the letter y is used to represent the dependent variable.
  ::写入公式时, 必须考虑哪个变量是独立的变量, 哪个变量是独立的变量。 通常, 字母 x 用来代表独立的变量, 字母 y 用来代表独立的变量 。

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  At the beginning of this lesson ,  you   were introduced to  Camryn, a website developer who is developing a website for a retail store. She needs to write a program that will allow the user to buy more than one item at once. When this program is finished, it will work similarly to the program below.
  ::课程开始时,你被介绍给Camryn, Camryn是一个网站开发商,他正在为零售商店开发一个网站。她需要写一个程序,让用户能够同时购买不止一个项目。当这个程序完成时,它将与下面的程序类似。

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  What mathematical rule would allow this program to function?
  ::什么样的数学规则能让这个程序发挥作用?

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  Find your independent and dependent variable then use this interactive to write the equation that models the cost of buying multiple items at once.
  ::查找独立且依赖的变量,然后使用此互动来写入公式,该方程式同时计算购买多个项目的成本。

   

  

  INTERACTIVE

  Computer Programming Continued

  

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  • Choose variables from the dropdown menus in the code to tell the system how to calculate the total price.
    ::从代码中的下调菜单中选择变量,以告诉系统如何计算总价格。
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  • Enter the quantity you would like.
    ::输入您想要的数量 。
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  • Click Buy to complete your transaction! You will only be able to proceed if the system calculates total price the correct way.
    ::点击购买以完成您的交易 ! 只有系统以正确的方式计算总价时, 您才能继续 。

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   Summary
  ::摘要

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  • Equations are used to express relationships between quantities.
    ::方程式用于表示数量之间的关系。
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  • Quantities could be related through addition, subtraction, multiplication, and division.
    ::数量可以通过增加、减法、乘法和分割等方法联系起来。
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  • Pay attention to keywords to determine which operation to use.
    ::注意关键词,以决定使用哪种操作。