课程： 6.18问题解决计划、图表

章节大纲

选择节常规

折叠展开
常规

全部折叠展开全部
- 选择活动新闻通告
  
  新闻通告讨论区
选择节问题解决计划、图表

折叠展开
问题解决计划、图表
Katie is trying out a new cake recipe. The cake recipe said to add $\begin{aligned} 2 \frac{1}{4} \end{aligned}$ cups of flour. The cake turned out to be too moist. She tried the recipe again, but added $\begin{aligned} \frac{1}{3} \end{aligned}$ cup of flour to the recipe. The cake was much better this time. How many cups of flour did Katie add in all?
::凯蒂正在尝试一个新的蛋糕食谱。蛋糕食谱说要加214杯面粉。蛋糕结果太潮湿了。她又试了食谱, 但给食谱加了13杯面粉。这次蛋糕好多了。凯蒂总共加了多少杯面粉?

In this concept, you will learn how to use the problem solving strategy: draw a diagram.
::在这个概念中,你将学会如何使用解决问题的战略:绘制图表。

Problem-Solving with Diagrams
::用图解解决问题

Drawing a diagram or a picture is a strategy to help you solve many different problems involving fractions. The first thing that you should do when approaching a problem is to identify the given information and what the problem is asking for. Here is an example.
::绘制图表或图片是帮助您解决涉及分数的许多不同问题的策略。在处理一个问题时,首先要做的是确定给定的信息和问题要求什么。这里举一个例子。

John ate $\begin{aligned} \frac{1}{5} \end{aligned}$ of the cake. What fraction is left?
::约翰吃了15块蛋糕剩下多少分数?

First, the problem gives you the amount of cake that John ate. The solution is how much cake he has left. This problem requires subtraction. Draw a diagram to show what is known about John and his cake.
::首先,问题给了你约翰吃了多少蛋糕。答案是他剩下多少蛋糕。这个问题需要减去。绘制一张图表, 显示约翰和他的蛋糕的已知情况。

This is a diagram of fraction bars to represent John’s cake. The blue section shows how much of the cake John has eaten. The white bars represent the amount of cake that is left. You can see that there are four-fifths left.
::这是代表约翰蛋糕的分数条图。蓝色部分显示约翰吃过多少蛋糕。白条代表剩下的蛋糕数量。您可以看到剩下五分之四。

The answer to the problem is John has $\begin{aligned} \frac{4}{5} \end{aligned}$ of the cake left.
::问题的答案是约翰剩下4 5个蛋糕

You can use a diagram to solve a problem or create a numeric expression. Often times both ways will work, but one will make more sense than the other. Let's look at another problem.
::您可以使用图表来解决问题或创建数字表达式。通常两种方式都会起作用, 但一种方式比另一种方式更有意义。让我们来看看另一个问题。

Shannon jogged $\begin{aligned} 1 \frac{3}{20} \end{aligned}$ miles yesterday. Today, she jogged $\begin{aligned} \frac{1}{2} \end{aligned}$ mile. How many total miles did Shannon jog?
::香农昨天跑了1320英里,今天她跑了12英里香农跑了多少英里?

Method 1 –– Draw a diagram:
::方法 1 绘制图表 :

One way to solve this problem is to draw a diagram. Look at the first distance that Shannon jogged. Draw two same-sized rectangles. Divide the rectangles into 20 equal-sized sections. Then shade $\begin{aligned} 1 \frac{3}{20} \end{aligned}$ of the diagram.
::解决这个问题的一个办法是绘制图表。看看香农慢跑的第一个距离。绘制两个大小相同的矩形。将矩形分为20个等大小的区块。然后是图表的阴影 13 20。

This represents the $\begin{aligned} 1 \frac{3}{20} \end{aligned}$ miles that Shannon jogged yesterday.
::这是香农昨天慢跑的1320英里

Shannon also jogged $\begin{aligned} \frac{1}{2} \end{aligned}$ mile today.
::香农今天还跑了12英里

So, shade $\begin{aligned} \frac{1}{2} \end{aligned}$ of the partially filled rectangle to represent the distance she jogged today.
::所以,部分填充的矩形的阴影12 代表她今天慢跑的距离。

The diagram is $\begin{aligned} 1 \frac{13}{20} \end{aligned}$ shaded. Therefore, Shannon jogged a total of $\begin{aligned} 1 \frac{13}{20} \end{aligned}$ miles on those two days.
::这张图是1320个阴影。因此,香农在这两天共跑了1320英里。

Method 2–– Set up an addition problem:
::设置添加问题 :

To find out how many miles she jogged all together, add $\begin{aligned} 1 \frac{3}{20} + \frac{1}{2} \end{aligned}$ . The fractional part of the mixed number has a different denominator than $\begin{aligned} \frac{1}{2} \end{aligned}$ . Find the least common multiple (LCM) of both denominators. The least common multiple of 20 and 2 is 20. Next, rename the fractions with a common denominator .
::要知道她一起跑多少英里, 加1 3 20 + 1 2。混合数的分数部分有与 12 不同的分母。找到两个分母中最不常见的多个( LCM ) 。最不常见的20 和 2 的多个是 20 。下一步, 用一个共同分母重命名分数。

$\begin{aligned} \frac{1}{2} = \frac{10}{20} \end{aligned}$

Now you can add the fractions together.
::现在您可以将分数加在一起。

$\begin{aligned} 1 \frac{3}{20} + \frac{10}{20} = 1 \frac{13}{20} \end{aligned}$

Notice that the answer is the same. Both methods will produce the same result. Choose the method that you find easiest when working on problems like this.
::注意答案是相同的。两种方法都会产生相同的结果。选择您在处理类似问题时最容易找到的方法。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Katie's cake recipe.
::早些时候,你得到一个问题关于凯蒂的蛋糕食谱。

Katie started with $\begin{aligned} 2 \frac{1}{4} \end{aligned}$ cups of flour, but added $\begin{aligned} \frac{1}{3} \end{aligned}$ cup of flour to the recipe. Add the flour quantities to find the total amount of flour used for the cake.
::凯蒂开始用两杯14杯面粉,但在食谱上加了13杯面粉。加上面粉数量,以找到蛋糕使用的面粉总量。

$\begin{aligned} 2 \frac{1}{4} + \frac{1}{3} \end{aligned}$

Look at the fractions. They do not have a common denominator.
::看看这些分数,它们没有共同的分母

First, rewrite the fractions with a common denominator. The LCM of 3 and 4 is 12.
::首先,以共同分母重写分数。 LCM 3 和 4 是 12 。

$\begin{aligned} 2 \frac{1}{4} = 2 \frac{3}{12} \frac{1}{3} = \frac{4}{12} \end{aligned}$

$\begin{aligned} 2 \frac{1}{4} + \frac{1}{3} = 2 \frac{3}{12} + \frac{4}{12} \end{aligned}$

Then, draw a diagram to find the sum
::然后绘制一个图表以找到和

$\begin{aligned} 2 \frac{3}{12} + \frac{4}{12} = 2 \frac{7}{12} \end{aligned}$

Katie used a total of $\begin{aligned} 2 \frac{7}{12} \end{aligned}$ cups of flour.
::凯蒂总共用了2 7 12杯面粉

Example 2
::例2

Use problem solving strategies-- make a diagram and set up an addition problem-- to solve.
::使用解决战略问题的方法绘制一个图表设置一个额外的问题来解决

Teri ran $\begin{aligned} 1 \frac{1}{2} \end{aligned}$ miles yesterday, and she ran $\begin{aligned} 2 \frac{1}{2} \end{aligned}$ miles today. How many miles did she run in all?
::Teri昨天跑了12英里她今天跑了12英里她跑了多少英里?

If John ran 7 miles, what is the difference between his total miles and Teri’s total miles? How many miles have they run altogether?
::如果约翰跑7英里,他的总里程和泰里的总里程之间有什么区别?他们总共跑了多少里?

First, draw a diagram to find the total miles for Teri.
::首先,绘制一个图图找到Teri的总里程数

Let's start with Terri.
::先从泰莉开始吧

$\begin{aligned} 1 \frac{1}{2} + 2 \frac{1}{2} = 4 \end{aligned}$

Terri ran 4 miles.
::Terri跑了四英里

Next, find the difference between Teri and John's total miles.
::接下来找出Teri和John总里程的区别

7 - 4 = 3

There is a difference of 3 miles.
::相差三英里

Finally, find the sum of their total miles.
::最后找到他们总里程的总和

7 + 4 = 11

Together, they ran 11 miles.
::他们一起跑了11英里

Example 3
::例3

Draw a diagram to solve the problem: $\begin{aligned} 2 \frac{1}{3} + 4 \end{aligned}$ .
::绘制一个解决问题的图表: 2 1 3+ 4 。

The sum is $\begin{aligned} 6 \frac{1}{3} \end{aligned}$ .
::总共是613

Example 4
::例4

Draw a diagram to solve the problem: $\begin{aligned} \frac{4}{5} - \frac{1}{5} \end{aligned}$ .
::绘制解决问题的图表: 4 5 - 1 5 。

The difference is $\begin{aligned} \frac{3}{5} \end{aligned}$ .
::差异是3 5。

Example 5
::例5

Draw a diagram to solve the problem: $\begin{aligned} \frac{3}{4} + \frac{2}{4} \end{aligned}$ .
::绘制一个解决问题的图表: 3 4+ 2 4 。

The sum is $\begin{aligned} 1 \frac{1}{4} \end{aligned}$ .

::总额是14美元。

Review
::回顾

Solve each of the following problems by using a problem solving strategy.
::通过采取解决问题的战略来解决以下每一个问题。

Tyler has eaten one-fifth of the pizza. If he eats another two-fifths of the pizza, what part of the pizza does he have left?
::泰勒吃了五分之一的比萨饼如果他吃了另外五分之二的比萨饼

What part has he eaten in all?
::他吃了什么东西?

How many parts of this pizza make a whole?
::这批披萨有多少部分能完整?

Maria decides to join Tyler in eating pizza. She orders a vegetarian pizza with six slices. If she eats two slices of pizza, what fraction has she eaten?
::Maria决定和Tyler一起吃披萨。她点了6片的素食披萨。如果她吃了两片披萨,她吃了多少?

What fraction does she have left?
::她还剩下什么分数?

If Tyler was to eat half of Maria’s pizza, how many pieces would that be?
::如果泰勒要吃一半的玛丽亚披萨那会有多少块呢?

If Maria eats one-third, and Tyler eats half, what fraction of the pizza is left?
::如果玛利亚吃三分之一泰勒吃一半披萨还剩多少?

How much of the pizza have they eaten altogether?
::他们吃了多少披萨?

John and Terri each ran 18 miles. If Kyle ran half the distance that both John and Teri ran, how many miles did he run?
::约翰和泰瑞每人跑18英里如果凯尔跑一半的距离约翰和泰瑞跑多少英里?

If Jeff ran $\begin{aligned} 3 \frac{1}{2} \end{aligned}$ miles, how much did he and Kyle run altogether?
::如果Jeff跑32英里他和Kyle一共跑多少?

What is the distance between Jeff and Kyle’s combined mileage and John and Teri’s combined mileage?
::Jeff和Kyle的里程数加在一起,John和Teri的里程数加在一起之间的距离是多少?

Sarah gave Joey one-third of the pie. Kara gave him one-fourth of another pie. How much pie did Joey receive altogether?
::莎拉给了乔伊三分之一的馅饼卡拉给了他四分之一的馅饼

Is this less than or more than one-half of a pie?
::这是小于半个馅饼还是超过半个馅饼?

Who gave Joey a larger part of the pie, Kara or Sarah?
::谁给了乔伊一大部分馅饼卡拉还是莎拉?

What is the difference between the two fractions of pie?
::馅饼的两部分有什么区别?

Review (Answers)
::回顾(答复)

Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键。

Resources
::资源

章节大纲

常规

问题解决计划、图表

Problem-Solving with Diagrams ::用图解解决问题

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源

Problem-Solving with Diagrams
::用图解解决问题

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Example 5
::例5

Review
::回顾

Review (Answers)
::回顾(答复)

Resources
::资源