### 数学代写|数学建模代写math modelling代考|DIRECTIONS FOR THE INDEPENDENT WORKSHEET

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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|SUMMARY

In this unit, we have used PPW diagram equation to represent the AC problems. Figure 3-5 present a story grammar prompt card (Xin et al., 2008) that students can use to facilitate meaningful representation of AC problems. As presented in Figure 3-5, word problem (WP) story grammar questions and prompts were generated in accordance with the key elements in the AC stories (or problems) to help students understand the problem structure and correctly map information from the problem to the PPW diagram equation. As shown in Figure 2-3, the diagram equation emphasizes algebraic expression of mathematical relations among key elements of the problem structure. Specifically, an additive compare $(\mathrm{AC})$ problem describes one quantity as “more than” the other quantity (i.e., the $A C$-more type) or “less than” the other quantity (i.e., the AC-less type). Please refer to Table C2-1 in Chapter 2 (page 15 ) for three variations of $\mathrm{AC}$-more problem structure and three variations of $\mathrm{AC}$-less problem structure.

## 数学代写|数学建模代写math modelling代考|Independent Work–AC Problem Representation

In the worksheets below, you will use the PPW diagram equation (see Figure 3-5) to represent the story. After you read and understand the story, if it is an additive comparison (AC) problem (see definition of AC problem in Figure 3-5: AC problem story grammar prompt card), you will find the comparison sentence that tells who has “more” “or “less” (or which quantity is the bigger one and which quantity is the smaller one) and how many more (or less). Underline that sentence as the comparison sentence is where you will decide who has the bigger quantity and who has the smaller quantity.

It will be helpful if you name the bigger box and smaller box in the diagram so that you make sure the bigger quantity goes into the “bigger” box on one side of the equation, and the smaller quantity goes to the “smaller” box on the other side of the equation. But please note that: When there is an unknown in the problem, the unknown quantity may be the bigger or smaller quantity. Therefore, you do not judge the “big” or “small” by looking at the size of the numbers given in the problem; you need to read the comparison sentience, which tells you who has more, or which quality is the bigger one. Remember, the unknown quantity you are asked to solve for, might be the bigger quantity! In the next Unit, you will learn how to use the diagram equation to solve real AC problems when there is an unknown.

The comparison sentence also tells how many more or how many less, which is the difference quantity that goes into the 2 nd small box in the PPW diagram labelled “difference”. The smaller quantity and the difference amount should make up, or equal, the bigger quantity on the other side of the equation.

If you are ever confused about the story situation, draw the bar model to help you understand the story, or specifically, the two parts that make up the whole, or total (which is the bigger quantity in comparison stories).

## 数学代写|数学建模代写math modelling代考|SOLVING MIXED AC PROBLEMS

$\begin{array}{ll}\text { Learning Outcome: } & \begin{array}{l}\text { Be able to solve mixed AC word problems with the PPW } \ \text { diagram equation }\end{array} \ \begin{array}{ll}\text { Materials Needed: }\end{array} & \text { Part-Part-Whole (PPW) Diagram Equation Model } \ \text { Posters } & \text { AC Word Problem }(\text { WP) Story Grammar Poster } \ \text { Overhead Modeling } & \text { Modeling AC Problem Solving 1, 2, 3, and } 4 \ \text { Student Worksheets } & \text { Modeling AC Problem Solving 1, 2, 3, and } 4 \ & \text { Try-It-Out Worksheet-AC problem solving } 5 \text { and } 6 \ \text { Independent worksheet-AC problem solving } 7,8, \text { and } 9 \ \text { Reference Guide } & \text { Reference Guide-AC problem solving } 1-9\end{array}$
Teacher: In the last Unit, we learned how to represent $A C$ stories (including $\mathrm{AC}-\mathrm{more}$ and $\mathrm{AC}$-less) using the bar model and the PPW diagram equation. As all three quantities are given (the bigger quantity, the smaller quality, and the difference quantity) in the story, we are able to see whether the PPW diagram equation can still be used to represent the mathematical relations in the AC stories. We discovered that in the case of $\mathrm{AC}$ stories the bigger quantity is made up of the smaller quantity AND the difference between the bigger and smaller quantities. As presented in the PPW diagram equation, the bigger quantity represents the whole, and the smaller quantity and the difference between the two quantities are the two parts. Further, the bigger quantity is the sum of the smaller quantity and the difference between the two quantities.

During this lesson, we will discover that the Part-Part-Whole diagram equation will help us solve the $A C$ problems when one quantity (the smaller quantity, the bigger quantity, or the difference amount) is the unknown.

We will use the Word Problem Story Grammar Prompt Cards (see Figure 2-3 in page 47 and Figure $3-5$ in page 67 ) to help us represent the problem in the diagram equation, and then we will solve for the unknown quantity in the equation.

## 数学代写|数学建模代写math modelling代考|SOLVING MIXED AC PROBLEMS

学习成果：  能够使用 PPW 解决混合 AC 单词问题   图方程   所需材料：  部分-部分-整体 (PPW) 图方程模型   海报  交流单词问题 ( WP) 故事语法海报   架空建模  建模交流问题解决 1、2、3 和 4  学生工作表  建模交流问题解决 1、2、3 和 4  Try-It-Out Worksheet-AC 问题解决 5 和 6  独立工作表-AC问题解决 7,8, 和 9  参考指南  参考指南-AC问题解决 1−9

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