Bridging British Education Virtual Academy 伦桥国际教育
Miraiku Maths C2 G1 Session Miraiku 数学 C2 G1 课程
1. Course Basic Information 1. 课程基本信息
Teaching Focus 教学重点
Review and practice of mixed number arithmetic operations (addition, subtraction, multiplication, division) and solving multi-step fraction word problems.
复习和练习带分数的算术运算（加、减、乘、除）以及解决多步骤的分数应用题。
Teaching Objectives 教学目标
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Accurately convert between mixed numbers and improper fractions. 准确地在带分数和假分数之间进行转换。
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Perform addition and subtraction of mixed numbers by finding a common denominator. 通过找到公分母进行带分数的加减运算。
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Perform multiplication and division of mixed numbers. 进行带分数的乘除运算。
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Solve complex word problems involving fractions (including finding a fraction of an amount and finding the remaining fraction/amount). 解决涉及分数的复杂应用题（包括求一个量的分数以及求剩余分数/数量）。
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
Greetings and Context Setting: Teacher greeted students, noted the early morning time in the UK (8 am) and established the time difference with students in Tokyo (5 pm). Noted Jack needed to leave early.
问候与情境设置： 教师问候学生，注意到英国的清晨时间（上午8点）并确认了与东京学生的时间差（下午5点）。注意到Jack需要提前离开。
Recap: Fraction Conversion (Mixed to Improper and vice versa): Quick recap with Jack and Stella on converting 3 1/4 to 13/4 and 2 1/5 to 11/5. Also reviewed improper to mixed conversion (e.g., 25/4 to 6 1/4).
复习：分数转换（带分数到假分数及反之）： 与Jack和Stella快速复习了1/4转换为13/4和2 1/5转换为11/5。还复习了假分数到带分数的转换（例如，25/4到6 1/4）。
Mixed Number Arithmetic: Addition and Subtraction: Practiced addition (2 4/5 + 1 1/4) focusing on finding the LCM (20) and Stella's preferred method of converting everything to improper fractions first. Reviewed subtraction (3 3/5 - 1 5/8).
带分数运算：加法和减法： 练习加法（2 4/5 + 1 1/4），重点是找到最小公倍数（20）以及Stella首选的先将所有数转换为假分数的方法。复习了减法（3 3/5 - 1 5/8）。
Mixed Number Arithmetic: Multiplication and Division: Covered multiplication (2 1/4 x 3 2/3) emphasizing the lack of need for common denominators and introducing cross-simplification as a handy trick. Applied the 'Keep, Change, Flip' rule for division (3 1/5 ÷ 1 1/3), also showing cross-simplification.
带分数运算：乘法和除法： 讲解了乘法（2 1/4 x 3 2/3），强调不需要公分母，并引入交叉约分作为快捷技巧。对除法（3 1/5 ÷ 1 1/3）应用了'保持、改变、翻转'规则，并展示了交叉约分。
Fraction Word Problems (Finding a Fraction of an Amount): Worked on problems like '3/4 of 36' and '2/5 of 35 days'. Stella initially struggled with the structure but quickly grasped the underlying concept (fraction * amount).
分数应用题（求一个量的分数）： 处理了'36的3/4'和'35天的2/5'等问题。Stella最初对结构有些困惑，但很快掌握了基本概念（分数 * 数量）。
Complex Multi-Step Fraction Word Problems: Tackled high-mark questions involving spending fractions of a total amount (James's salary) and comparing quantities (a half of 280 vs three eighths of 400). Stella excelled at these harder problems.
复杂多步骤分数应用题： 处理了涉及花费总金额分数（James的工资）和比较数量（280的一半 vs 400的3/8）的高分问题。Stella在这些难题上表现出色。
Language Knowledge and Skills 语言知识与技能
Mixed number, Improper fraction, Denominator, Numerator, Common denominator, LCM (Least Common Multiple), Cross simplify, Top heavy fraction, Pounds (£)
带分数, 假分数, 分母, 分子, 公分母, 最小公倍数, 交叉约分, 分子大于分母的分数, 英镑 (£)
Conversion methods, Adding/Subtracting fractions, Multiplying fractions (no common denominator needed), Dividing fractions (Keep Change Flip), Fraction of an amount (Fraction x Whole Number), Multi-step word problem analysis.
转换方法, 分数的加减, 分数的乘法（无需公分母）, 分数的除法（KCF）, 求一个量的分数（分数 x 整数）, 多步骤应用题分析。
Arithmetic fluency with mixed numbers, Logical problem decomposition, Calculation accuracy, Interpreting word problem constraints (e.g., asking for fraction vs. actual amount).
带分数的算术流畅性, 逻辑问题分解, 计算准确性, 理解应用题的限制（例如，要求分数还是实际数量）。
Teaching Resources and Materials 教学资源与材料
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Corbettmaths worksheet questions for word problems. Corbettmaths 工作表中的应用题。
3. Student Performance Assessment (Stella (Jack was also present but left early)) 3. 学生表现评估 (Stella (Jack was also present but left early))
Participation and Activeness 参与度和积极性
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Stella was highly engaged throughout, actively participating in calculations and discussions, even after Jack left. Stella全程高度参与，积极参与计算和讨论，即使在Jack离开后也是如此。
Language Comprehension and Mastery 语言理解和掌握
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Strong comprehension of conversion rules and basic operations. Needed gentle prompting for simplification/final answer format in complex problems. 对转换规则和基本运算的理解很强。在复杂问题中需要温和的提示来确定约分/最终答案格式。
Language Output Ability 语言输出能力
Oral: 口语：
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Clear in stating intermediate steps (e.g., common denominator calculation), though occasional hesitation when shifting between methods (improper vs. mixed). 在陈述中间步骤（例如，公分母计算）时很清晰，但在方法转换（假分数与带分数）时偶尔会有犹豫。
Written: 书面：
N/A (In-class verbal calculation assessment)
不适用（课堂口头计算评估）
Student's Strengths 学生的优势
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Preference and mastery of converting everything to improper fractions first, which simplifies all four operations. 偏爱并将所有数先转换为假分数的方法，这简化了所有四种运算。
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Excellent grasp of multi-step word problem logic, particularly in understanding fractions of an amount and remaining amounts. 对多步骤应用题的逻辑理解出色，尤其是在理解一个量的分数和剩余数量方面。
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Ability to follow and apply new concepts quickly, such as cross-simplification. 能够快速跟进和应用新概念，例如交叉约分。
Areas for Improvement 需要改进的方面
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Consistency in fully simplifying the final answer when required (e.g., 99/12 simplification). 在需要时确保最终答案完全约分（例如，99/12的约分）。
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Distinguishing between questions asking for a 'fraction left' versus an 'amount left' in word problems. 在应用题中区分要求“剩余分数”还是“剩余金额”的提问。
4. Teaching Reflection 4. 教学反思
Effectiveness of Teaching Methods 教学方法的有效性
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The pace was appropriate, covering substantial ground by utilizing Stella's existing method while smoothly integrating alternative approaches like cross-simplification. 节奏恰当，通过利用Stella现有方法并流畅地融入交叉约分等替代方法，覆盖了大量内容。
Teaching Pace and Time Management 教学节奏和时间管理
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Well-managed. The initial recap was quick, allowing for deeper focus on complex word problems towards the end. 管理良好。初步复习很快，使得课程末尾能更深入地关注复杂应用题。
Classroom Interaction and Atmosphere 课堂互动和氛围
Positive, encouraging, and focused. The teacher managed the dual audience (Stella present for the full session, Jack leaving early) effectively.
积极、鼓励和专注。教师有效地管理了双重听众（Stella全程在场，Jack提前离开）。
Achievement of Teaching Objectives 教学目标的达成
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All objectives were met, with a particularly strong demonstration of solving complex application problems. 所有目标均已达成，特别是复杂应用题的解决能力得到了很好的展示。
5. Subsequent Teaching Suggestions 5. 后续教学建议
Teaching Strengths 教学优势
Identified Strengths: 识别的优势：
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Effective use of scaffolding by revisiting previous concepts (conversion) before diving into new operations. 通过在深入新运算之前回顾旧概念（转换）来有效地进行脚手架搭建。
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Validating and building upon the student's preferred method (converting all to improper fractions) rather than forcing a single pathway. 肯定并建立在学生偏好的方法（将所有数转换为假分数）之上，而不是强迫单一途径。
Effective Methods: 有效方法：
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Explicit demonstration of cross-simplification as an optional but efficient method for multiplication/division. 明确展示了交叉约分作为乘法/除法的可选但高效的方法。
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Breaking down multi-step word problems by first calculating the fractional part remaining before finding the final monetary value. 通过先计算剩余的等分分数，然后再求最终金额来分解多步骤应用题。
Positive Feedback: 正面反馈：
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High praise given for Stella's clear logic when tackling the 800-pound spending problem. 对Stella解决800英镑支出问题时清晰的逻辑给予了高度赞扬。
Next Teaching Focus 下一步教学重点
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Continue reinforcing the understanding of when and how to use cross-simplification, as it speeds up calculation significantly. 继续巩固何时以及如何使用交叉约分的理解，因为它能显著加快计算速度。
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Introduce simple percentage conversions within the context of these fraction problems. 在这些分数问题的背景下引入简单的百分比转换。
Specific Suggestions for Student's Needs 针对学生需求的具体建议
Calculation Accuracy & Simplification: 计算准确性与约分：
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Practice fully simplifying improper fractions after converting them back to mixed numbers (e.g., simplifying 99/12 to 33/4 then 8 1/4). 练习将假分数转换回带分数后，确保完全约分（例如，将99/12约分为33/4，再到8 1/4）。
Word Problem Interpretation: 应用题解读：
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When answering word problems, always re-read the final question to confirm if it asks for the 'fraction amount' or the 'actual monetary/unit amount'. 回答应用题时，务必重新阅读最终问题，以确认它要求的是“分数数量”还是“实际货币/单位数量”。
Recommended Supplementary Learning Resources or Homework 推荐的补充学习资源或家庭作业
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Complete the remaining mixed number operations practice from the Corbettmaths sheet focusing on full simplification. 完成Corbettmaths工作表中剩余的带分数运算练习，重点放在完全约分上。