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: Percentage Calculations (Direct and Reverse) 主题： 百分比计算（直接和反向）

Date: December 15 日期： 12月15日

Student: Jack 学生： Jack

Teaching Focus 教学重点

Consolidating direct percentage calculations and introducing reverse percentage problems.

巩固直接百分比计算并介绍反向百分比问题。

Teaching Objectives 教学目标

Successfully calculate direct percentage increase and decrease. 成功计算直接的百分比增加和减少。
Understand and apply the concept of reverse percentages using algebraic representation. 理解并应用反向百分比的概念，使用代数表示法。

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

Classroom Administration/Check-in: Teacher checked on a potential second student joining the class.

课堂管理/签到： 老师确认是否有第二位学生加入。

Direct Percentage Arithmetic Practice: Practicing calculating percentages of a number (e.g., 20% of 500, 15% of 40, 2% of 600, 92% of 1000).

直接百分比运算练习： 练习计算数字的百分比（例如，500的20%，40的15%，600的2%，1000的92%）。

Percentage Increase/Decrease (Worded Problems): Working through worded problems involving a 20% decrease and an 80% increase, comparing two methods for calculating percentage change.

百分比增减（应用题）： 解决涉及20%减少和80%增加的应用题，比较计算百分比变化的两种方法。

Introduction to Reverse Percentages: Introduction to reverse percentage questions (finding the original value given the final value after a percentage change), using algebra (e.g., 20% growth resulting in 480 cm, 20% usage resulting in 24 left).

反向百分比介绍： 介绍反向百分比问题（已知百分比变化后的最终值，求原始值），使用代数（例如，20%增长后为480厘米，使用了20%后剩下24个）。

Language Knowledge and Skills 语言知识与技能

Vocabulary:
Decrease, Increase, Percentage, Decimal, Intuitive, Algebra, Original value, Reverse percentage, Salary, Antique

词汇：
减少/降低, 增加, 百分比, 小数, 直观的, 代数, 原始值, 反向百分比, 薪水, 古董

Concepts:
Converting percentages to decimals (e.g., 15% = 0.15), Two methods for percentage change (calculating change amount vs. calculating remaining/total percentage), Introduction to setting up algebraic equations for reverse percentages (e.g., 1.2p = 480).

概念：
百分比转小数（例如，15% = 0.15），百分比变化的两种方法（计算变化量 vs. 计算剩余/总百分比），反向百分比的代数方程建立介绍（例如，1.2p = 480）。

Skills Practiced:
Mental arithmetic for simple percentages, Decimal multiplication, Subtraction/Addition for percentage change factors, Solving one-step linear equations using division.

练习技能：
简单百分比的心算，小数乘法，百分比变化的加减法，使用除法解一元一次方程。

Teaching Resources and Materials 教学资源与材料

Whiteboard/Screen for calculation examples. 白板/屏幕用于计算示例。
Real-life scenarios (iPhone drop, jeans value, salary, potato usage, lemon tree growth). 现实生活场景（iPhone掉落、牛仔裤价值、薪水、土豆使用、柠檬树生长）。

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

Participation and Activeness 参与度和积极性

Jack was highly engaged and responsive throughout the session. Jack在整个课程中参与度很高，反应积极。
Student provided correct answers quickly during the direct percentage practice. 在直接百分比练习中，学生快速给出了正确答案。

Language Comprehension and Mastery 语言理解和掌握

Strong understanding of direct percentage calculations (both increase and decrease). 对直接百分比计算（增加和减少）有很强的理解。
Demonstrated ability to choose the correct method for calculating percentage decrease (Method 2: 100% - X%). 展示了选择正确方法计算百分比减少的能力（方法2：100% - X%）。
Initial grasping of the logic behind reverse percentages, although some algebraic manipulation required guidance. 初步掌握了反向百分比背后的逻辑，尽管一些代数运算需要指导。

Language Output Ability 语言输出能力

Oral: 口语：

Clear and articulate responses, using appropriate mathematical language (e.g., stating the percentage equivalence for increase/decrease). 回答清晰明确，使用了适当的数学语言（例如，陈述增加/减少的百分比等价物）。
Showed good self-correction when prompted (e.g., adjusting decimal places for money or applying division correctly in reverse percentages). 在得到提示时表现出良好的自我纠正（例如，为货币调整小数位或在反向百分比中正确应用除法）。

Written: 书面：

N/A (No formal written work provided in transcript, calculations performed mentally or verbally confirmed.)

不适用（转录中未提供正式书面作业，计算为心算或口头确认。）

Student's Strengths 学生的优势

Speed and accuracy in basic percentage calculations. 在基础百分比计算中的速度和准确性。
Quickly understood the conversion of percentage decrease/increase into a single factor (e.g., 80% remaining or 180% total). 快速理解了将百分比减少/增加转换为单一因子的过程（例如，剩余80%或总计180%）。
Good numerical intuition regarding expected answers (e.g., knowing 15% of 40 must be small). 对预期答案具有良好的数字直觉（例如，知道40的15%必须很小）。

Areas for Improvement 需要改进的方面

Ensuring correct decimal alignment when multiplying decimals during the introduction to reverse percentages. 在引入反向百分比时，确保小数乘法中小数点位置的正确性。
Fluency in the final step of reverse percentages (division by a decimal, e.g., 24 / 0.8). 在反向百分比的最后一步（除以小数，例如 24 / 0.8）的流畅性。

4. Teaching Reflection 4. 教学反思

Effectiveness of Teaching Methods 教学方法的有效性

Teacher effectively transitioned from direct calculation to the more complex increase/decrease scenarios. 老师有效地从直接计算过渡到了更复杂的增减情景。
The use of two methods for percentage change was beneficial for conceptual understanding, leading to the preferred second method. 使用两种方法计算百分比变化对概念理解有益，并引导至更优选的第二种方法。
The introduction to reverse percentages was well-paced, using clear analogies (growth) and linking back to algebra fundamentals. 反向百分比的引入节奏得当，使用了清晰的比喻（生长）并与代数基础知识相关联。

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

The pace was fast but managed well during the direct practice section, allowing Jack to shine. 节奏很快，但在直接练习部分得到了很好的控制，让Jack得以发挥。
The introduction of reverse percentages was appropriately slowed down to ensure foundational steps (100% + 20% = 120% and setting up 1.2p) were clear. 反向百分比的引入节奏被适当放慢，以确保基础步骤（100% + 20% = 120% 和设置 1.2p）清晰明确。

Classroom Interaction and Atmosphere 课堂互动和氛围

Engaging, supportive, and focused, with the teacher using personalized anecdotes (dropping the phone) to maintain interest.

引人入胜、支持性强且专注，老师使用了个性化的轶事（掉手机）来保持兴趣。

Achievement of Teaching Objectives 教学目标的达成

Objective 1 achieved through solid performance in the first half of the lesson. 通过课程前半部分的扎实表现，目标1达成。
Objective 2 partially achieved; the concept was introduced, and Jack participated in solving the first two reverse problems, showing promise but requiring further consolidation. 目标2部分达成；概念已引入，Jack参与解决了前两个反向问题，显示出潜力但需要进一步巩固。

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

Teaching Strengths 教学优势

Identified Strengths: 识别的优势：

Effective scaffolding from known concepts (direct percentages) to new concepts (reverse percentages). 从已知概念（直接百分比）到新概念（反向百分比）的有效脚手架搭建。
Excellent use of contextual, relatable word problems. 出色地使用了贴合实际、有联系的文字题。

Effective Methods: 有效方法：

Presenting two distinct methods for percentage increase/decrease to build deeper understanding. 展示计算百分比增减的两种不同方法，以建立更深层次的理解。
Explicitly linking algebra (using 'p') to unknown values in reverse percentage problems. 明确地将代数（使用'p'）与反向百分比问题中的未知值联系起来。

Positive Feedback: 正面反馈：

Positive reinforcement after every correct answer, maintaining high energy. 每次正确回答后都有积极的强化，保持了高昂的能量。

Next Teaching Focus 下一步教学重点

Further practice and solidifying reverse percentage problems, ensuring comfort with the algebraic step. 对反向百分比问题进行进一步练习和巩固，确保对代数步骤感到得心应手。
Introducing percentage change as a percentage (e.g., If a price goes from 400 to 480, what is the percentage increase?). 引入百分比形式的百分比变化（例如，如果价格从400上涨到480，百分比增幅是多少？）。

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

Calculation Technique: 计算技巧：

Practice dividing by decimals (e.g., 24 / 0.8 = 240 / 8) repeatedly to increase speed and automaticity for reverse percentage calculations. 反复练习除以小数（例如，24 / 0.8 = 240 / 8），以提高反向百分比计算的速度和熟练度。

Speaking & Communication: 口语与交流：

Encourage Jack to verbalize the structure of the reverse percentage equation before solving it (e.g., 'Original amount times 1.2 equals 480'). 鼓励Jack在求解反向百分比方程之前，口述其结构（例如，‘原始数量乘以1.2等于480’）。

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

Provide a worksheet with 5-7 reverse percentage word problems, focusing on both increases and decreases. 提供一份包含5-7个反向百分比应用题的工作表，重点关注增加和减少。