### 数学代写|数学建模代写math modelling代考|REPRESENTING AC-LESS PROBLEMS

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|REPRESENTING AC-LESS PROBLEMS

Learning Outcome: $\quad$ Be able to represent $\mathrm{AC}$ word problem stories with the bar model and the PPW diagram equation

Teacher: During the last lesson, we learned how to use the Bar model and Diagram Equation to represent a type of comparison problem. Today we will learn how to represent more comparison problem situations.
Problem #3-5-10
Cristal has 29 pens, and she has 71 fewer pens than a boy named Warren. Warren has 100 pens.
(Students read the story together.)
Teacher: What is this story all about?
Students: This story compares the number of pens Cristal has to the number of pens that Warren has.

Teacher: Correct! It is a comparison story that involves a statement of “more” or “less.” Mathematically, we name this type of story Additive Compare (AC).
Teachers: Do you know who has more pens?
Students: “Cristal has 71 fewer pens than Warren,” and so Warren has more.
Teacher: That is right! Warren has more. I will underline the comparison sentence on board, and you will do the same on your worksheet.
Let’s first represent the story using the bar model. (Teacher calls on student volunteers and student(s) come to board and make the segment of bars that represent the number of pens Cristal has, and the number of pens Warren has. In addition, student volunteers indicate on the bar graph the difference between the bar for Cristal and the bar for Warren). See Slide 3-5-10-a.

## 数学代写|数学建模代写math modelling代考|represents the number of pens

In Slide 3-5-10-a, the 2 nd bar represents the number of pens Warren has, a total of 100 . As indicated in the bar model, it is 71 longer than Cristal’s bar, or in other words, as stated in the story, Cristal has 71 fewer pens than Warren. In short, the difference between the number of pens Cristal has and the number of pens Warren has is 71 , which is indicated by the clear part of the longer bar (Teacher points to the segment of the bar that is not shaded in the longer bar)

Teacher: If we look at the longer bar (Warren’s bar), it is actually made up of two parts: (a) the first part (shaded bar), which is the same as Cristal (29); and (b) the second part (clear bar), which is the additional pens that Warren has. These two parts (a and b) make up the total number of pens that Warren has.
So now we are ready to represent the same story in the PPW diagram equation.
(Teacher presents the PPW diagram equation)
Who can tell us the two parts (that make up the bigger quantity) that we should enter into the two small boxes on the left side of the PPW diagram equation?
Students: 29 and $71 .$
Teacher: That is correct. I will write 29 in the first small box that is labeled “smaller.” I will write 71 in the 2nd small box that is labeled “difference.”

What should I write in the big box for the “larger” quantity on the other side of the equation?
Students: 100 .
Teacher: That is correct. The big box is for the total number of pens Warren has. I will write 100 in the big box that is labeled “bigger” or “whole.” You will do the same in your worksheet. See Slide 3-5-10-b for a completed bar model and PPW diagram equation.

## 数学代写|数学建模代写math modelling代考|the difference amount

Teacher: As shown in the above PPW diagram equation (the lower panel of Slide 3-5-10-b), when representing the comparison story onto the PPW diagram equation, the smaller quantity (Cristal in this case) of the two being compared (Cristal and Warren) AND the difference amount between the bigger and the smaller quantities, or between Cristal and Warren’s pens (as indicated by “71 fewer … than” in this story) will make up the “whole” or the Bigger quantity (Warren in this case), as shown exactly in the bar model.

Lets’ check to see whether the sum of the two quantities on the left side (LS) of the equal sign is the same as (or equal to) the quantity on the right side (RS) of the equal sign.
LS: $29+71=100$
RS: 100
Does the LS equal the RS of the equation and why?
Students: Yes, they are the same, because “100” from the LS is the same as or equals ” 100 ” from the RS of the equation.

Teacher: That means, “part” and “part” from the left side (LS) of the diagram equation did make up the “whole” in the right side (RS) of the equation. Both the bar model and the PPW diagram equation model tell exactly the same story (teacher points to the Bar model and the PPW diagram equation in Slide 3-5-10-b during the explanation).
Let’s try to do two more similar comparison problems. Instead of using both the bar model and the PPW diagram equation, we will simply use the PPW diagram equation (but if you feel you need the bar model to help you, please feel free to use both).

## 数学代写|数学建模代写math modelling代考|REPRESENTING AC-LESS PROBLEMS

Cristal 有 29 支钢笔，她的钢笔比一个名叫 Warren 的男孩少 71 支。沃伦有 100 支笔。
（学生一起读故事。）

（教师展示 PPW 图方程）

## 数学代写|数学建模代写math modelling代考|the difference amount

LS：29+71=100
RS：100
LS 是否等于方程的 RS，为什么？

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