Bridging British Education Virtual Academy

1. Course Basic Information 1. 课程基本信息

Course Name: Miraiku Maths C2 G1 课程名称： Miraiku 数学 C2 G1

Topic: Mixed Number Arithmetic (Addition, Subtraction, Multiplication, Division) and Cross Simplification in Multiplication/Division 主题： 带分数运算（加、减、乘、除）及乘除法中的交叉化简

Date: January 26 日期： 1月26日

Student: Stella and Jack 学生： Stella and Jack

Teaching Focus 教学重点

Reviewing mixed number operations and introducing/practicing the cross-simplification method for multiplication and division of fractions.

复习带分数运算，并引入和练习分数乘除法中的交叉化简方法。

Teaching Objectives 教学目标

Successfully perform addition, subtraction, multiplication, and division with mixed numbers. 成功完成带分数的加、减、乘、除运算。
Understand and apply the cross-simplification method to efficiently solve complex fraction multiplication/division problems. 理解并应用交叉化简方法，高效解复杂分数乘除问题。

2. Course Content Overview 2. 课程内容概览

Main Teaching Activities and Time Allocation 主要教学活动和时间分配

Recap of Mixed Number Arithmetic: Reviewing and practicing addition, subtraction, multiplication, and division of mixed numbers (e.g., 2 1/4 + 3 4/5, 3 1/4 - 2 5/7, etc.).

带分数运算复习： 复习并练习带分数的加、减、乘、除（例如：2又1/4 + 3又4/5, 3又1/4 - 2又5/7等）。

Introduction and Practice of Cross-Simplification: Detailed explanation and practice of using cross-simplification for multiplication (including division converted to multiplication) to handle large numbers efficiently, demonstrated with several complex examples.

交叉化简的介绍与练习： 详细解释并练习使用交叉化简方法处理分数乘法（包括转换后的除法），以高效处理大数字，并通过多个复杂示例进行演示。

Consolidation and Wrap-up: Final practice problems focusing on cross-simplification to solidify the method's application and identify when it is most useful.

巩固与总结： 进行最后的练习题，重点关注交叉化简的应用，以巩固该方法的掌握程度并识别其最适用的情境。

Language Knowledge and Skills 语言知识与技能

Vocabulary:
Mixed number, improper fraction, cross-simplification, common factors, simplify, numerator, denominator.

词汇：
带分数, 假分数, 交叉化简, 公因数, 化简, 分子, 分母

Concepts:
Converting mixed numbers to improper fractions, 'Keep Change Flip' for division, criteria for using cross-simplification (large numbers & common diagonal factors).

概念：
带分数转假分数, 除法中的“保持-改变-翻转”法, 交叉化简的使用标准（数字大且对角线有公因数）。

Skills Practiced:
Mental arithmetic for small fraction manipulations, structured step-by-step calculation for mixed number operations, strategic application of simplification techniques.

练习技能：
针对小分数操作的心算能力, 带分数运算的结构化分步计算, 简化技巧的策略性应用。

Teaching Resources and Materials 教学资源与材料

Whiteboard/Digital Screen for problem demonstration and writing out steps. 白板/电子屏幕用于问题演示和步骤书写。

3. Student Performance Assessment (Stella and Jack) 3. 学生表现评估 (Stella and Jack)

Participation and Activeness 参与度和积极性

Both students were actively engaged, often providing immediate answers to initial review questions. 两位学生都积极参与，通常对初步复习问题立即给出答案。
Stella showed initial hesitation/forgetfulness on division steps but recovered well; Jack demonstrated stronger initial retention of the cross-simplification steps. Stella在除法步骤上表现出初始的犹豫/遗忘，但恢复得很好；Jack在交叉化简步骤上表现出更强的初步记忆力。

Language Comprehension and Mastery 语言理解和掌握

Comprehension of basic mixed number arithmetic was solid, though minor errors occurred (e.g., mixing up signs in subtraction). 对基本带分数运算的理解很扎实，尽管出现了一些小错误（例如，减法中混淆了符号）。
Understanding of the cross-simplification mechanism required teacher guidance (especially identifying common factors on diagonals), but the concept was grasped by the end. 对交叉化简机制的理解需要老师指导（尤其是识别对角线的公因数），但在课程结束时学生掌握了这一概念。

Language Output Ability 语言输出能力

Oral: 口语：

Both students spoke clearly and confidently when answering simple calculations. 两位学生在回答简单计算题时口齿清晰、自信。
Clarity decreased slightly when articulating complex simplification steps, indicating a need for more procedural verbalization practice. 在阐述复杂化简步骤时，清晰度略有下降，表明需要更多的程序口头练习。

Written: 书面：

N/A (Focus was on oral/demonstrated calculation, minor transcription errors noted during initial review problems).

不适用（重点在于口头/演示计算，初步复习问题中记录到轻微的转录错误）。

Student's Strengths 学生的优势

Jack grasped the cross-simplification trick quickly and applied it effectively in the latter half of the lesson. Jack快速掌握了交叉化简技巧，并在课程后半段有效地应用了它。
Stella demonstrated resilience in correcting errors and worked through the complex, non-simplified multiplication example successfully, even if slowly. Stella展现了修正错误的韧性，并成功地完成了复杂、未化简的乘法示例，尽管速度较慢。
Strong recall of basic multiplication/addition facts required for initial checks. 对基础乘法/加法事实的回忆能力很强，有助于初步检查。

Areas for Improvement 需要改进的方面

Stella needs reinforcement on retaining the correct operation sign (e.g., subtraction vs. addition) in mixed number problems. Stella需要加强在带分数问题中保持正确运算符号（如减法与加法）的记忆。
Both students need more practice identifying larger common factors quickly to maximize the benefit of cross-simplification. 两位学生需要更多练习，以便快速识别更大的公因数，从而最大限度地发挥交叉化简的优势。
Avoid skipping steps in the division process until the 'Keep Change Flip' method is second nature. 在“保持改变翻转”方法成为本能之前，避免在除法过程中跳过步骤。

4. Teaching Reflection 4. 教学反思

Effectiveness of Teaching Methods 教学方法的有效性

The teacher effectively demonstrated the high contrast in difficulty between the standard simplification method and the cross-simplification method using large problems. 教师通过使用大数字问题，有效地展示了标准简化方法与交叉化简方法在难度上的巨大差异。
The teaching style was highly encouraging, praising effort even when errors were made. 教学风格非常鼓励人，即使出现错误也对努力给予赞扬。

Teaching Pace and Time Management 教学节奏和时间管理

The pace was fast during the initial review phase, which benefited Jack but challenged Stella momentarily. 初始复习阶段的节奏很快，这对Jack有利，但让Stella暂时感到吃力。
The pace slowed down appropriately when introducing the complex cross-simplification concept, allowing for detailed explanation and multiple examples. 在引入复杂的交叉化简概念时，节奏放慢得当，允许进行详细解释和多个示例。

Classroom Interaction and Atmosphere 课堂互动和氛围

Positive, inquisitive, and focused, with a strong emphasis on strategy over rote calculation.

积极、探究性强且专注，重点强调策略而非死记硬背的计算。

Achievement of Teaching Objectives 教学目标的达成

Objective 1 (Mixed number operations) was largely met, with minor procedural errors noted. 目标1（带分数运算）基本达成，记录到少量程序性错误。
Objective 2 (Cross-simplification) was successfully introduced, and both students demonstrated the ability to apply it by the end of the session. 目标2（交叉化简）成功引入，两位学生在课程结束时都展示了应用该方法的能力。

5. Subsequent Teaching Suggestions 5. 后续教学建议

Teaching Strengths 教学优势

Identified Strengths: 识别的优势：

Use of high-stakes, large-number examples to dramatically illustrate the necessity and efficiency of cross-simplification. 使用高风险、大数字的例子，极大地突显了交叉化简的必要性和效率。
Clear articulation of the criteria for when to use the advanced method (when numbers are awkward/big and diagonals share factors). 清晰阐述了何时使用高级方法的标准（当数字笨拙/大，且对角线有公因数时）。

Effective Methods: 有效方法：

Juxtaposing the long, error-prone simplification method with the shortcut method in real-time. 实时对比冗长易错的简化方法和快捷方法。
Encouraging students to 'feel' when a problem might require the shortcut ('No, please don't make me do this'). 鼓励学生“感受”何时问题可能需要快捷方式（‘不，请不要让我做这个’）。

Positive Feedback: 正面反馈：

Compliments on achieving perfect answers (e.g., 121/20, 15/28) during the initial warm-up. 对初始热身中取得完美答案（如121/20, 15/28）的赞扬。
Positive reinforcement when students correctly identified common factors during cross-simplification. 当学生在交叉化简中正确识别公因数时给予积极的肯定。

Next Teaching Focus 下一步教学重点

Intensive practice on the two criteria for cross-simplification: recognizing 'awkwardly big' numbers and spotting common diagonal factors. 集中练习交叉化简的两个标准：识别“笨拙的大数”和发现共同的对角线因数。
Application of cross-simplification in multi-step word problems involving multiplication/division. 在涉及乘除法的多步骤文字题中应用交叉化简。

Specific Suggestions for Student's Needs 针对学生需求的具体建议

Calculation Strategy: 计算策略：

When tackling mixed number division, always explicitly write out the 'Keep Change Flip' step before multiplying to avoid losing track of the inverted fraction. 处理带分数除法时，务必明确写出“保持-改变-翻转”的步骤，避免遗漏被倒置的分数。

Simplification Fluency: 化简流畅度：

Practice identifying the greatest common factor (GCF) for pairs of numbers quickly, especially for the 11s, 12s, and 7s, to speed up cross-simplification. 练习快速识别数字对的最大公因数（GCF），尤其针对11、12和7的倍数，以加快交叉化简的速度。

Accuracy in Operations: 运算准确性：

Stella should focus on double-checking the operation sign when performing subtraction with mixed numbers to prevent sign errors. Stella应重点检查带分数减法中的运算符号，以防止符号错误。

Recommended Supplementary Learning Resources or Homework 推荐的补充学习资源或家庭作业

Assign 5-7 multiplication/division problems involving complex mixed numbers designed to benefit heavily from cross-simplification. 布置5-7个涉及复杂带分数，并且通过交叉化简能极大简化的乘除法问题。
Review worksheet focusing specifically on converting mixed numbers and identifying common factors between numbers up to 100. 复习练习题，专门针对带分数转换和识别100以内数字的公因数。