### 数学代写|数学建模代写math modelling代考|Diagram equation

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|数学建模代写math modelling代考|Diagram equation

Let’s look at the lower panel, or the diagram equation:
The first box in the diagram equation represents the boxes of cookies sold, the second box represents the leftover unsold boxes of cookies, and the big box on the other side of the equation represents the total number of boxes of cookies for sale. Adding the two parts (boxes sold and the boxes unsold) together should make up, or equal, the whole.
In summary, the bar model and the diagram equation representations tell the same story in the problem.

To find out the answer to “How many boxes of cookies will the Girl Scouts have to take back home?” we can generate a math sentence based on the bar model. That is, in order to find the difference between the long bar and the short bar we subtract. The math sentence would read:
$$?=93-47$$
Therefore, ? $=46$.
Now we know that the 2 nd short, clear bar is 46 , meaning there are 46 boxes of cookies that were not sold, or 46 boxes that the girl scouts have to take back home.
However, if we use the PPW diagram equation, the math sentence for solving the problem is given by the diagram equation. That is, if we “peel off” the boxes from the diagram equation, we get
$$47+?=93$$
Because the number we are adding is unknown, we have to “undo” the addition to find out the unknown addend. That is, we subtract the given part from the whole (or total) for solving for the unknown part. The math sentence would read:
$$\begin{gathered} ?=93-47 \ ?=46 \end{gathered}$$
[Note: For higher level students, the teacher can simply use basic algebra properties for the instruction on how to find out the unknown in the equation. That is-
Given: $47+?=93$,
To solve for the unknown (i.e., the question mark, ?), we need to isolate the unknown ? by subtracting 47 from both sides of the equation:
$$\text { 47-47 + ? =93-47 }$$
We get: ? $=93-47$, or ? $=46$
In fact, we can verify the algebraic way of solving for the unknown from the bar model presented in the upper panel of slide $2-3-2-\mathrm{d}$. That is, to find out the difference between the whole and one part, we subtract. In other words, ? $=93-47=46$.]

## 数学代写|数学建模代写math modelling代考|What is a complete answer to this problem

What is a complete answer to this problem?
Students: The answer is: The Girl Scouts will have to take 46 boxes of cookies back home.
Teacher: Very good!
We have gone through several problems using both the bar model and the PPW diagram equation, and learned that the PPW diagram equation tells the same story (that is, “Part and Part make up the Whole”) as the bar model. Because the PPW diagram equation directly provides us with the math sentence, or equation for solving the problem, we may not need to draw the bar model for future PPW problems. Instead we can directly use the PPW diagram equation to set up the math equation for accurate problem solving. Let’s try it out with the next problem. That is, we will only use the PPW diagram equation to solve the PPW problems.
Problem #2-3-3
Travis ordered 68 baseball cards from a magazine. Then he ordered some more for his brother. In all, he ordered 129 baseball cards. How many did he order for his brother?
Teacher: What is this problem all about?
Teacher: How many baseball cards did he order the first time?
Students: 68 baseball cards.
Teacher: How many more did he order for his brother?
Students: He ordered some more… we do not know how many he ordered for his brother.
Teacher: Correct. That is, in fact, the question we are asked to solve for. Let’s underline the question in the problem. (Teacher does so on the board; students do so in their worksheet).
Teacher: What else do we know?
Students: He ordered a total of 129 baseball cards.
Teacher: Great! So Travis ordered 68 baseball cards. Then he ordered some more, but we do not know that number. We do know that, at the end, he ordered a total of 129 baseball cards in all. Is this still the part-part-whole (PPW) type of problem?
Students: Yes.

## 数学代写|数学建模代写math modelling代考|the PPW problem structure

Teacher: You are right. It is still the PPW problem structure. So let’s use the PPW diagram to represent the information from the problem.

Teacher: I will make the PPW diagram on the board. I will ask for your help to fill the numbers into the PPW model equation.
(Teacher presents the PPW diagram equation without filling any numbers in the boxes)
Teacher: What is the total number of baseball cards Travis ended up with after ordering some for himself and for his brother?
Students: 129 baseball cards.
Teachers: So 129 is the total, or the whole amount.
Where do I write ” 129 “, the total number of baseball cards in the diagram equation?
Students: In the big box.
Teacher: That is right. We always input the total, or the whole, into the big box on one side of the equation by itself. (Teacher enters ” 129 ” in the big box. Students do the same in their worksheets.)

Teacher: do we know any information about the two parts, or the two orders Travis made that makes up the total?
Students: We know he ordered 68 baseball cards for himself the first time.
Teacher: OK. That is one part. Let’s write ” 68 in the first box in the diagram. Do we know the other part?
Students: We do not know.
Teacher: You are right. We do not know how many he ordered for his brother. We are asked to solve for this part.
I will write a ” ?” in the second small box in the PPW diagram. Instead of using a question mark, we can also use a letter to represent the unknown quantity. (Teacher writes a letter “a” in the 2nd box that is labeled “Part”). In your worksheet, please write the letter ” $a$ ” in the 2 nd box for the part that is not known.
Now let’s look at the completed diagram (Slide 2-3-3)

## 数学代写|数学建模代写math modelling代考|Diagram equation

?=93−47

47+?=93

?=93−47 ?=46
[注：对于较高水平的学生，教师可以简单地使用基本代数性质来指导如何找出方程中的未知数。那是-

47-47 + ? =93-47

（学生一起读故事）

## 数学代写|数学建模代写math modelling代考|the PPW problem structure

（老师展示了PPW图方程，没有在方框中填写任何数字）

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## MATLAB代写

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