Bridging British Education Virtual Academy 伦桥国际教育

1v1 Maths Lesson - Charlie 1对1数学课程 - Charlie

1. Course Basic Information 1. 课程基本信息

Course Name: 1106 Maths Charlie 课程名称： 1106 数学 Charlie

Topic: Number Theory, Algebra, and Probability (Exam Questions) 主题： 数论、代数和概率（考试题）

Date: Date not specified in transcript 日期： 日期未在文本中明确说明

Student: Charlie 学生： Charlie

Teaching Focus 教学重点

Reviewing and solving complex multiple-choice math problems, focusing on parity (even/odd), algebraic word problems, rounding to the nearest hundred, and basic probability concepts, concluding with linear graphing.

复习和解决复杂的数学选择题，重点关注奇偶性、代数应用题、四舍五入到百位、基础概率概念，最后进行线性图表绘制。

Teaching Objectives 教学目标

Review and correctly solve problems related to even/odd number properties. 复习并正确解答与奇偶数性质相关的题目。
Apply algebraic skills to solve cost comparison problems. 运用代数技能解决成本比较问题。
Master rounding rules to the nearest hundred. 掌握四舍五入到最近百位的规则。
Analyze basic probability scenarios (even chance, greater than, less than). 分析基础概率场景（机会均等、大于、小于）。
Solve inverse proportion problems involving work rate. 解决涉及工作效率的负相关问题。
Introduce linear functions and plot points on a coordinate plane. 介绍线性函数并在坐标平面上描点。

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

Parity Problem Review (Even/Odd): Discussing a problem involving multiplying by 7 and adding/subtracting numbers to determine the final parity (even/odd). Student initially struggled but arrived at the correct conclusion.

奇偶性问题复习： 讨论一个涉及乘以7并加减数字以确定最终奇偶性的问题。学生最初遇到困难，但最终得出了正确的结论。

Algebraic Word Problem (Cost): Solving problem Q16 about orange and apple costs using a variable 'x'. Student successfully set up the expressions and identified the 'odd one out'.

代数应用题（成本）： 使用变量'x'解决关于橙子和苹果成本的第16题。学生成功建立了表达式并识别出了“异类”。

Rounding to the Nearest Hundred: Detailed explanation of rounding 700 to the nearest 100, identifying the critical boundary (650).

四舍五入到最近的百位： 详细解释四舍五入到最近的100，确定了关键边界（650）。

Probability Concepts: Reviewing concepts like 'even chance', 'greater than', and analyzing probability scenarios (dice roll, coin toss, picking balls).

概率概念： 复习了“机会均等”、“大于”等概念，并分析了概率场景（掷骰子、抛硬币、摸球）。

Work Rate/Inverse Proportion Problem: Solving Q21 about 4 people taking 6 hours. Student struggled initially with the inverse relationship calculation but correctly established the work constant (48 person-hours) and found the answer for 10 people.

工作效率/反比例问题： 解决关于4人工作6小时的第21题。学生最初在反比关系计算上遇到困难，但正确建立了工作常量（48人时）并找到了10人所需的时间。

Sequences and Introduction to Graphing: Analyzing a sequence converging to 1. Transitioned to graphing the linear function y = 2x + 3, successfully generating values and plotting points.

数列与图表介绍： 分析一个收敛于1的数列。过渡到绘制线性函数y = 2x + 3，成功生成数值并描点了点。

Language Knowledge and Skills 语言知识与技能

Vocabulary:
Even, Odd, Multiply, Subtract, Cost, Orange, Apple, Nearest to 100, Rounding, Probability, Even chance, Gradient, Axes, Plot, Coefficient

词汇：
偶数，奇数，乘，减，成本/费用，橙子，苹果，四舍五入到100，舍入，概率，机会均等，梯度/斜率，轴，描点，系数

Concepts:
Parity properties, Inverse proportion (work rate), Boundaries for rounding, Interpretation of probability terms (even chance), Linear equations (y=mx+c) and graphing.

概念：
奇偶性性质，反比例（工作效率），四舍五入的边界，概率术语的解释（机会均等），线性方程（y=mx+c）和图表绘制。

Skills Practiced:
Logical deduction, Algebraic manipulation, Estimation and precision in numerical work, Interpretation of quantitative data, Coordinate plotting.

练习技能：
逻辑推理，代数运算，数值计算中的估算和精确性，定量数据解释，坐标点描绘。

Teaching Resources and Materials 教学资源与材料

Maths exam practice questions (various topics) 数学考试练习题（多个主题）
Whiteboard/digital tool for plotting coordinates 用于绘制坐标的白板/数字工具

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

Participation and Activeness 参与度和积极性

High engagement, actively involved in problem-solving steps, especially during the complex work-rate problem. 参与度高，积极投入到解题步骤中，尤其是在复杂的工作效率问题上。

Language Comprehension and Mastery 语言理解和掌握

Strong understanding of algebraic substitution (Q16). Showed slight initial hesitation on rounding boundaries but quickly grasped the concept. 对代数代入（Q16）理解很强。对四舍五入的边界最初有些犹豫，但很快掌握了概念。

Language Output Ability 语言输出能力

Oral: 口语：

Student communicates thoughts clearly when explaining reasoning, although sometimes needs prompting to articulate the mathematical term for the concept. 学生在解释推理时能清晰表达想法，尽管有时需要提示才能说出概念的数学术语。

Written: 书面：

Not directly observed, but inferred strong procedural accuracy in algebraic setup and numerical calculations (e.g., work-rate constant).

未直接观察到，但推断出代数设置和数值计算（例如，工作常量）中具有很强的程序准确性。

Student's Strengths 学生的优势

Excellent grasp of algebraic problem setup and variable assignment (Q16). 对代数问题设置和变量分配有出色的掌握（Q16）。
Shows persistence in tackling difficult, multi-step inverse proportion problems (Q21). 在处理困难、多步骤的反比例问题（Q21）时表现出坚持不懈。
Quickly understood the concept of a sequence approaching a limit. 很快理解了数列趋近于极限的概念。

Areas for Improvement 需要改进的方面

Quick mental calculation for simple arithmetic operations within complex problems. 在复杂问题中进行简单算术运算时的快速心算能力。
Initial confusion regarding the boundary case in 'rounding to the nearest hundred'. 在“四舍五入到最近的百位”的边界情况上最初有些混淆。

4. Teaching Reflection 4. 教学反思

Effectiveness of Teaching Methods 教学方法的有效性

The teacher effectively used guided questioning to help the student self-correct parity rules and rounding concepts. 教师有效地使用了引导性提问来帮助学生自我修正奇偶性规则和四舍五入概念。
The transition from abstract math concepts (probability, sequences) to concrete graphing was managed well. 从抽象的数学概念（概率、数列）到具体的图表绘制的过渡管理得当。

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

Pace was appropriate, slowing down significantly for the complex work-rate problem and the final graphing section. 节奏适中，在复杂的工作效率问题和最后的图表绘制部分明显放慢了速度。

Classroom Interaction and Atmosphere 课堂互动和氛围

Positive, encouraging, and collaborative. The teacher provided ample positive reinforcement, especially towards the end when the student felt confident.

积极、鼓励和协作。老师提供了大量的正面强化，尤其是在学生感到自信时。

Achievement of Teaching Objectives 教学目标的达成

Most core mathematical concepts tested (parity, algebra, rounding, basic work-rate) were successfully reviewed and reinforced. 测试的大部分核心数学概念（奇偶性、代数、四舍五入、基础工作效率）都得到了成功复习和巩固。

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 techniques, especially by breaking down the work-rate problem into person-hours. 有效的脚手架技术，特别是通过将工作效率问题分解为人时数。
Clear explanations of abstract concepts like rounding boundaries and limits. 对四舍五入边界和极限等抽象概念的清晰解释。

Effective Methods: 有效方法：

Using the student's own incorrect answer as a starting point for correcting mathematical logic (e.g., in parity discussion). 使用学生自己的错误答案作为纠正数学逻辑的起点（例如，在奇偶性讨论中）。
Integrating graphing skills as a concluding practical application. 将图表绘制技能整合为结论性的实际应用。

Positive Feedback: 正面反馈：

Teacher acknowledged student's success in handling entrance-level exam questions. 老师认可了学生在处理入学考试题目方面的成功。

Next Teaching Focus 下一步教学重点

Reinforce the plotting of linear graphs and understanding the relationship between the equation and the line's position. 巩固线性图表的绘制，并理解方程与线条位置之间的关系。

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

Mental Math & Arithmetic Speed: 心算与运算速度：

Practice rapid recall of multiplication tables and basic divisions to speed up complex calculations. 练习快速回忆乘法表和基本除法，以加快复杂计算的速度。

Algebra & Equations: 代数与方程：

Focus on explicitly labeling variables (x, 2x) when setting up algebraic word problems to avoid confusion. 在建立代数应用题时，重点明确标记变量（x, 2x），以避免混淆。

Graphing & Coordinates: 图表与坐标：

Review the definition of gradient (m) and y-intercept (c) in the form y=mx+c before the next lesson. 在下一课之前，复习y=mx+c形式中梯度（m）和y轴截距（c）的定义。

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

Complete further practice sets on inverse proportion problems (work rate/time). 完成关于反比例问题（工作效率/时间）的额外练习集。
Review 10 examples of rounding to the nearest 100, ensuring boundary numbers are handled correctly. 复习10个四舍五入到最近的100的例子，确保边界数字处理正确。