Bridging British Education Virtual Academy

1. Course Basic Information 1. 课程基本信息

Course Name: Maths Charlie Shi 课程名称： 数学查理·施

Topic: Logic Puzzles (Number Placement) and Linear Equations/Graphs 主题： 逻辑谜题（数字定位）和线性方程/图表

Date: December 18th 日期： 12月18日

Student: Charlie 学生： Charlie

Teaching Focus 教学重点

Reviewing a difficult logic puzzle, revisiting and applying concepts of linear equations (gradient and y-intercept), and introducing a symmetry puzzle.

回顾一个有难度的逻辑谜题，重温并应用线性方程（斜率和y轴截距）的概念，并介绍一个对称性谜题。

Teaching Objectives 教学目标

Successfully apply deduction to solve the initial number connection puzzle. 成功应用演绎法解决初始的数字连接谜题。
Recall and apply the concepts of gradient and y-intercept in linear equations. 回忆并应用线性方程中斜率和y轴截距的概念。
Understand the concept of symmetry required for the final coloring puzzle. 理解最终涂色谜题所需的对称性概念。

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

Logic Puzzle Review (Number Connection): Revisiting the puzzle where numbers must be placed so that consecutive numbers are not adjacent. Teacher guides student to realize the strategy of placing numbers with the most connections first (1 and 6).

逻辑谜题回顾（数字连接）： 回顾数字不能相邻的谜题。老师引导学生认识到先放置连接数最多的数字（1和6）的策略。

Algebraic Equations Review (Color Variables): Student struggles to set up equations to solve the color-variable system (e.g., Red + Purple = 38). Teacher guides towards variable substitution/elimination, comparing it to the 'chickens and rabbits' problem.

代数方程回顾（颜色变量）： 学生在建立方程来解颜色变量系统时遇到困难。老师引导学生进行变量代换/消元，并与“鸡兔同笼”问题进行类比。

Graphing Linear Equations: Gradient and Y-Intercept: Reviewing how to determine the gradient (rise/run) and y-intercept from plotted points and standard forms (y=mx+c). Student successfully identifies these in given equations.

线性方程图表：斜率和Y轴截距： 回顾如何从描点和标准形式（y=mx+c）中确定斜率（纵/横）和y轴截距。学生成功识别了给定方程中的这些元素。

Symmetry Puzzle Introduction: Introducing a final puzzle involving coloring based on vertical and horizontal symmetry and ratios. Teacher emphasizes the critical position of the single blue square.

对称性谜题介绍： 介绍一个涉及基于垂直和水平对称性及比例的涂色谜题。老师强调单个蓝色方块的关键位置。

Language Knowledge and Skills 语言知识与技能

Vocabulary:
Consecutive, Connection, Strategy, Gradient, Y-intercept, Symmetry, Ratio, Vertical, Horizontal, Eliminate, Variable.

词汇：
连续的, 连接, 策略, 斜率, Y轴截距, 对称性, 比例, 垂直的, 水平的, 消去, 变量。

Concepts:
Deductive Reasoning (in logic puzzles), System of Linear Equations, Interpretation of y=mx+c, Gradient as 'rise over run', Symmetry properties.

概念：
演绎推理（在逻辑谜题中）, 线性方程组, y=mx+c的解释, 斜率作为“纵向变化量/横向变化量”, 对称性性质。

Skills Practiced:
Logical deduction, Algebraic manipulation (substitution/elimination), Reading and interpreting graph data, Problem-solving transfer (from concrete to abstract).

练习技能：
逻辑推理, 代数运算（代入/消元）, 读取和解释图表数据, 问题解决的迁移（从具体到抽象）。

Teaching Resources and Materials 教学资源与材料

Number Placement Logic Puzzle 数字放置逻辑谜题
Color Variable System of Equations Worksheet 颜色变量方程组练习题
Linear Graph Plotting Examples 线性图表绘制示例
Symmetry Coloring Puzzle 对称性涂色谜题

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

Participation and Activeness 参与度和积极性

Charlie demonstrated sustained focus during the algebraic review and graph plotting sections. 查理在代数回顾和图表绘制部分表现出持续的专注力。
Active engagement when comparing the current algebraic struggle to previous, easier problems. 在比较当前代数难题与之前较简单问题时表现出积极参与。

Language Comprehension and Mastery 语言理解和掌握

Initial difficulty in algebraic setup, but quick grasp of the concepts of gradient and y-intercept upon review. 初始在代数设置上存在困难，但在回顾后迅速掌握了斜率和y轴截距的概念。
Understood the necessity of symmetry for the final puzzle, particularly locating the central blue square. 理解了最终谜题中对称性的必要性，特别是确定了中央蓝色方块的位置。

Language Output Ability 语言输出能力

Oral: 口语：

Spoke clearly when discussing algebraic relationships ('Red is twelve more than Blue'). 在讨论代数关系（'红色比蓝色多十二'）时表达清晰。
Showed clear thought processes when verbally walking through the graph plotting steps (e.g., 'if x is one, y is minus two'). 在口头梳理图表绘制步骤时（例如，“如果x是1，y是负2”）展现出清晰的思维过程。

Written: 书面：

N/A (Focus was on verbal manipulation and whiteboard work)

不适用（重点在于口头操作和白板工作）

Student's Strengths 学生的优势

Strong logical breakthrough on the first puzzle (identifying high-connection numbers first). 在第一个谜题上取得了很强的逻辑突破（首先识别出高连接数的数字）。
Excellent recall of definitions and application of gradient and y-intercept after initial prompts. 在初步提示后，对斜率和y轴截距的定义和应用记忆得非常好。
Ability to recognize when a strategy (like in the color equations) is not working and seek a different path. 能够识别何时一种策略（如颜色方程）不起作用，并寻求不同的路径。

Areas for Improvement 需要改进的方面

Initial setup of complex multi-variable equations (Color puzzle) needs more systematic practice. 复杂多变量方程（颜色谜题）的初始设置需要更系统化的练习。
Maintaining confidence when algebraic steps become confusing or recursive. 在代数步骤变得令人困惑或循环时，需要保持信心。

4. Teaching Reflection 4. 教学反思

Effectiveness of Teaching Methods 教学方法的有效性

Highly effective in scaffolding the graph concepts by moving from plotted points to the algebraic form. 通过从描点到代数形式的转换，非常有效地搭建了图表概念的脚手架。
The teacher's patience and refusal to 'give the answer' for the color puzzle allowed the student to re-engage with necessary abstract thinking skills. 老师在颜色谜题上保持的耐心和不直接给出答案的做法，使得学生能够重新参与必要的抽象思维技能。

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

The pace was appropriate, slowing down significantly for the difficult algebraic review, but still managing to introduce the final concept. 节奏是合适的，在困难的代数回顾部分显著放慢了速度，但仍成功介绍了最后的概念。
The teacher managed time well by deciding to save the full algebraic solving and the maze for another time. 老师通过决定将完整的代数求解和迷宫留到下次来管理时间，做得很好。

Classroom Interaction and Atmosphere 课堂互动和氛围

Collaborative and encouraging. The teacher maintained a positive tone even when the student expressed frustration with the algebraic problem.

协作且鼓励性强。即使学生对代数问题感到沮丧，老师也保持了积极的语调。

Achievement of Teaching Objectives 教学目标的达成

Objective 1 (Logic Puzzle) achieved through guided strategy change. 通过指导策略改变，实现了目标1（逻辑谜题）。
Objective 2 (Algebra/Graph Review) strongly achieved through targeted practice. 通过有针对性的练习，有力地实现了目标2（代数/图表回顾）。

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

Teaching Strengths 教学优势

Identified Strengths: 识别的优势：

Skilled at linking new concepts (like graph interpretation) back to familiar analogies (like the 'chickens and rabbits' problem). 擅长将新概念（如图表解释）与熟悉的类比（如“鸡兔同笼”问题）联系起来。
Excellent scaffolding when reviewing graph components (gradient, intercept). 在回顾图表组成部分（斜率、截距）时，脚手架搭建得非常出色。

Effective Methods: 有效方法：

Using color variables (Red, Blue, Purple) to make abstract algebraic problems more tangible. 使用颜色变量（红、蓝、紫）使抽象的代数问题更具体化。
Breaking down the process of finding the gradient into 'size of the steps' taken. 将寻找斜率的过程分解为所采取的“步长”大小。

Positive Feedback: 正面反馈：

Praising the student's strategic thinking in the first puzzle: 'Good, good job.' 表扬了学生在第一个谜题中的策略思维：‘好，干得好。’
Acknowledging the difficulty of the algebra, 'Sometimes our brain is tired, but let's come back to this one.' 承认了代数的难度，‘有时候我们的大脑很累，但我们回到这个问题上来。’

Next Teaching Focus 下一步教学重点

Systematic solution of multi-variable word problems using substitution/elimination. 使用代入/消元法系统地解决多变量应用题。
Completing the symmetry coloring puzzle, focusing on spatial reasoning. 完成对称性涂色谜题，重点关注空间推理。

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

Algebraic Manipulation: 代数运算：

Practice setting up two-variable equations using only symbols (A, B, C) before introducing numbers, to isolate the setup skill. 练习在引入数字之前，仅使用符号（A, B, C）设置二元方程，以隔离设置技能。
When solving systems, systematically list the known equations before attempting substitution, similar to the 'chickens and rabbits' template. 在求解方程组时，在尝试代入之前，系统地列出已知方程，类似于“鸡兔同笼”的模板。

Logic & Problem Solving: 逻辑与解题：

For symmetry puzzles, always prioritize finding the location of any element that appears only once (like the blue square). 对于对称性谜题，总是优先找出只出现一次的元素（如蓝色方块）的位置。

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

Complete the symmetry coloring puzzle introduced at the end of the lesson. 完成课程最后介绍的对称性涂色谜题。
Review sheet on rearranging linear equations into the standard slope-intercept form (y=mx+c). 关于将线性方程重新排列成标准斜截式（y=mx+c）的复习材料。