《小学一年级数学知识思维导图竖版》

一、数与运算 (Number and Operations)

• 1. 认识数字 (Number Recognition)

  • 1. 1 数字 0-10 的认识
       • 1. 1. 1 数数 (Counting)
       • 1. 1. 2 认读 (Reading)
       • 1. 1. 3 书写 (Writing)
       • 1. 1. 4 顺序 (Order)
       • 1. 1. 5 大小比较 (Comparison) - 多、少、一样多
  • 1. 2 11-20 的认识
       • 1. 2. 1 数位 (Place Value): 个位，十位
       • 1. 2. 2 十和几 (Tens and Ones): 理解 1 个十和几个一组成一个数
       • 1. 2. 3 读写 (Reading and Writing)
       • 1. 2. 4 大小比较 (Comparison)

• 2. 数的组成 (Number Composition)

  • 2. 1 10 以内的数的组成
       • 2. 1. 1 分与合 (Decomposition and Composition)
       • 2. 1. 2 应用于加减法 (Application in Addition and Subtraction)
  • 2. 2 20 以内数的组成
       • 2. 2. 1 理解十位和个位的含义 (Understanding Tens and Ones)
       • 2. 2. 2 组合练习 (Composition Practice)

• 3. 加法 (Addition)

  • 3. 1 5 以内的加法
       • 3. 1. 1 理解加法的意义 (Understanding the Meaning of Addition): 合并
       • 3. 1. 2 用图示辅助计算 (Using Diagrams to Aid Calculation)
       • 3. 1. 3 应用题 (Word Problems)
  • 3. 2 10 以内的加法
       • 3. 2. 1 凑十法 (Making Ten)
       • 3. 2. 2 加法口诀 (Addition Facts)
       • 3. 2. 3 应用题 (Word Problems)
  • 3. 3 20 以内的进位加法
       • 3. 3. 1 凑十法 (Making Ten) - 重点
       • 3. 3. 2 看大数，分小数 (Start with the Larger Number)
       • 3. 3. 3 应用题 (Word Problems)

• 4. 减法 (Subtraction)

  • 4. 1 5 以内的减法
       • 4. 1. 1 理解减法的意义 (Understanding the Meaning of Subtraction): 拿走，剩余
       • 4. 1. 2 用图示辅助计算 (Using Diagrams to Aid Calculation)
       • 4. 1. 3 应用题 (Word Problems)
  • 4. 2 10 以内的减法
       • 4. 2. 1 倒数法 (Counting Backwards)
       • 4. 2. 2 减法口诀 (Subtraction Facts)
       • 4. 2. 3 应用题 (Word Problems)
  • 4. 3 20 以内的退位减法
       • 4. 3. 1 破十法 (Breaking Ten)
       • 4. 3. 2 想加算减 (Thinking of Addition to Solve Subtraction)
       • 4. 3. 3 应用题 (Word Problems)

• 5. 混合运算 (Mixed Operations)

  • 5. 1 连加 (Consecutive Addition)
  • 5. 2 连减 (Consecutive Subtraction)
  • 5. 3 加减混合 (Addition and Subtraction Mixture)
  • 5. 4 从左往右计算 (Calculate from Left to Right)

• 6. 简单应用 (Simple Application)

  • 6. 1 加法应用题 (Addition Word Problems)
  • 6. 2 减法应用题 (Subtraction Word Problems)
  • 6. 3 理解“一共”、“还剩”、“比…多”、“比…少”等关键词 (Understanding Keywords)

二、图形与几何 (Geometry)

• 1. 认识图形 (Shape Recognition)

  • 1. 1 平面图形 (2D Shapes)
       • 1. 1. 1 长方形 (Rectangle)
       • 1. 1. 2 正方形 (Square)
       • 1. 1. 3 三角形 (Triangle)
       • 1. 1. 4 圆形 (Circle)
  • 1. 2 立体图形 (3D Shapes)
       • 1. 2. 1 长方体 (Cuboid)
       • 1. 2. 2 正方体 (Cube)
       • 1. 2. 3 球 (Sphere)
       • 1. 2. 4 圆柱 (Cylinder)

• 2. 图形的位置 (Position of Shapes)

  • 2. 1 上、下、前、后、左、右 (Up, Down, Front, Back, Left, Right)
  • 2. 2 里、外、中间 (Inside, Outside, Middle)
  • 2. 3 用语言描述物体的位置关系 (Describing the Positional Relationship of Objects)

• 3. 简单分类 (Simple Classification)

  • 3. 1 按照形状分类 (Classification by Shape)
  • 3. 2 按照颜色分类 (Classification by Color)
  • 3. 3 按照大小分类 (Classification by Size)

三、测量 (Measurement)

• 1. 认识长度 (Length Recognition)

  • 1. 1 长短、高矮 (Long, Short, Tall, Short)
  • 1. 2 直接比较 (Direct Comparison)
  • 1. 3 间接比较 (Indirect Comparison)

• 2. 认识时间 (Time Recognition)

  • 2. 1 今天、昨天、明天 (Today, Yesterday, Tomorrow)
  • 2. 2 上午、下午、晚上 (Morning, Afternoon, Evening)
  • 2. 3 认识整时 (Recognizing Whole Hours)
       • 2. 3. 1 看时针 (Looking at the Hour Hand)

四、统计 (Statistics)

• 1. 简单统计 (Simple Statistics)
  • 1. 1 数一数 (Counting)
  • 1. 2 填一填 (Filling in)
  • 1. 3 简单象形统计图 (Simple Pictorial Statistics)
  • 1. 4 能根据统计图回答简单问题 (Answering Simple Questions Based on the Statistics Chart)

五、规律 (Patterns)

• 1. 简单的排列规律 (Simple Arrangement Patterns)
  • 1. 1 ABAB 形式 (ABAB Pattern)
  • 1. 2 AABAAB 形式 (AABAAB Pattern)
  • 1. 3 颜色规律 (Color Patterns)
  • 1. 4 形状规律 (Shape Patterns)
  • 1. 5 数字规律（简单的递增、递减）(Number Patterns - Simple Increments and Decrements)

六、核心能力培养 (Core Competency Development)

• 1. 数感 (Number Sense)

  • 1. 1 理解数的实际意义 (Understanding the Practical Meaning of Numbers)
  • 1. 2 数的大小比较 (Number Size Comparison)
  • 1. 3 对数量的估计 (Estimation of Quantity)

• 2. 符号意识 (Symbol Sense)

  • 2. 1 理解 +、-、= 的含义 (Understanding the Meaning of +, -, =)
  • 2. 2 用符号表示数量关系 (Using Symbols to Represent Quantitative Relationships)

• 3. 空间观念 (Spatial Sense)

  • 3. 1 识别物体形状 (Identifying Object Shapes)
  • 3. 2 理解物体之间的位置关系 (Understanding the Positional Relationship Between Objects)

• 4. 应用意识 (Application Awareness)

  • 4. 1 运用所学知识解决实际问题 (Using Learned Knowledge to Solve Practical Problems)
  • 4. 2 培养数学的应用意识 (Cultivating Awareness of the Application of Mathematics)

• 5. 推理能力 (Reasoning Ability)

  • 5. 1 简单的逻辑推理 (Simple Logical Reasoning)
  • 5. 2 发现规律 (Discovering Patterns)

• 6. 数据分析观念 (Data Analysis Concept)

  • 6. 1 对简单数据的收集、整理、描述 (Collecting, Organizing, and Describing Simple Data)
  • 6. 2 从数据中提取信息 (Extracting Information from Data)

七、学习方法指导 (Learning Method Guidance)

• 1. 动手操作 (Hands-on Operation)

  • 1. 1 用学具进行操作 (Operating with Learning Tools)
  • 1. 2 用实物进行演示 (Demonstration with Real Objects)

• 2. 合作学习 (Cooperative Learning)

  • 2. 1 小组讨论 (Group Discussion)
  • 2. 2 互相帮助 (Mutual Assistance)

• 3. 独立思考 (Independent Thinking)

  • 3. 1 鼓励提问 (Encouraging Questions)
  • 3. 2 培养独立解决问题的能力 (Cultivating the Ability to Solve Problems Independently)

• 4. 及时复习 (Timely Review)

  • 4. 1 复习课堂笔记 (Reviewing Class Notes)
  • 4. 2 完成作业 (Completing Homework)

• 5. 错题分析 (Error Analysis)

  • 5. 1 找出错误原因 (Finding the Cause of the Error)
  • 5. 2 纠正错误 (Correcting Mistakes)

八、数学素养 (Mathematical Literacy)

• 1. 良好的学习习惯 (Good Learning Habits)

  • 1. 1 认真听讲 (Listening Attentively)
  • 1. 2 积极思考 (Thinking Actively)
  • 1. 3 规范书写 (Standardized Writing)

• 2. 对数学的兴趣 (Interest in Mathematics)

  • 2. 1 在游戏中学习数学 (Learning Mathematics Through Games)
  • 2. 2 在生活中发现数学 (Discovering Mathematics in Life)

• 3. 勇于探索的精神 (Spirit of Exploration)

  • 3. 1 鼓励尝试 (Encouraging Attempts)
  • 3. 2 不怕失败 (Not Afraid of Failure)

九、易错点总结 (Common Mistakes Summary)

• 1. 计算错误 (Calculation Errors)
• 2. 审题不清 (Unclear Understanding of the Question)
• 3. 单位遗漏 (Omission of Units)
• 4. 概念混淆 (Confusion of Concepts)
• 5. 漏写答案 (Missing Answers)