{
  "metadata": {
    "subject": "小学数学",
    "standard": "《义务教育数学课程标准（2022年版）》· 人教版",
    "exam_alignment": "小学（小升初/毕业考）",
    "depth_level": "B：知识点 + 典型题型/解题方法（典型例题单独置于顶层 examples 数组）",
    "structure_note": "层级：module(模块/章节) → knowledge_point(知识点) → question_type(题型，仅含题型名称 type)。涉及公式处一律使用 LaTeX（$...$ 行内公式）。典型例题统一在顶层 examples 中，每条例题按 module_id / knowledge_point_id / question_type 索引到对应知识点与题型，并承载 solution_method（解题方法）与 difficulty（难度）字段。",
    "generated": "2026-08-01"
  },
  "modules": [
    {
      "id": "M01",
      "name": "数与代数·数的认识",
      "book": "一年级下册~四年级上册",
      "knowledge_points": [
        {
          "id": "M01-K01",
          "name": "100以内数的认识",
          "key_content": "数位（个位/十位）、数的组成（几个十和几个一）、读写100以内的数、比较大小。",
          "question_types": [
            {
              "type": "数位与组成（几个十几个一）"
            },
            {
              "type": "100以内数的读写与比较大小"
            }
          ]
        },
        {
          "id": "M01-K02",
          "name": "万以内及亿以内大数的认识",
          "key_content": "计数单位（个、十、百、千、万、亿）、数位顺序表、亿以内数的读写、改写与近似数。",
          "question_types": [
            {
              "type": "大数的读写（万以内及亿以内）"
            },
            {
              "type": "大数的改写与近似数"
            }
          ]
        },
        {
          "id": "M01-K03",
          "name": "小数的意义与性质",
          "key_content": "小数的意义（十分位、百分位、千分位）、小数的读写、小数的性质与大小比较、小数点位置移动引起小数大小的变化。",
          "question_types": [
            {
              "type": "小数的意义与读写"
            },
            {
              "type": "小数大小比较与小数点移动"
            }
          ]
        },
        {
          "id": "M01-K04",
          "name": "分数的意义与性质",
          "key_content": "分数的意义、分数单位、真分数与假分数、约分与通分、分数与小数互化。",
          "question_types": [
            {
              "type": "分数的意义与分数单位"
            },
            {
              "type": "约分与通分"
            }
          ]
        },
        {
          "id": "M01-K05",
          "name": "负数与百分数",
          "key_content": "负数的意义（相反意义的量、零下温度）、百分数的意义与读写。",
          "question_types": [
            {
              "type": "负数的认识与读写"
            },
            {
              "type": "百分数的意义与读写"
            }
          ]
        }
      ]
    },
    {
      "id": "M02",
      "name": "数与代数·数的运算",
      "book": "一年级下册~六年级上册",
      "knowledge_points": [
        {
          "id": "M02-K01",
          "name": "万以内加减法",
          "key_content": "多位数加减法笔算（相同数位对齐、从个位算起、满十进一/退一当十）、加减法估算与验算。",
          "question_types": [
            {
              "type": "多位数加减法竖式计算"
            },
            {
              "type": "加减法估算与验算"
            }
          ]
        },
        {
          "id": "M02-K02",
          "name": "多位数乘除法",
          "key_content": "多位数乘一位数/两位数的笔算乘法、除数是一位数/两位数的笔算除法、商中间或末尾有0的情况。",
          "question_types": [
            {
              "type": "多位数乘除法竖式计算"
            }
          ]
        },
        {
          "id": "M02-K03",
          "name": "分数加减法",
          "key_content": "同分母分数加减法（分母不变、分子相加减）、异分母分数加减法（先通分再计算）。",
          "question_types": [
            {
              "type": "同分母分数加减法"
            },
            {
              "type": "异分母分数加减法"
            }
          ]
        },
        {
          "id": "M02-K04",
          "name": "小数加减法",
          "key_content": "小数加减法笔算（小数点对齐）、小数的性质在计算中的应用。",
          "question_types": [
            {
              "type": "小数加减法竖式计算"
            }
          ]
        },
        {
          "id": "M02-K05",
          "name": "小数乘除法",
          "key_content": "小数乘法（先按整数乘法计算再点小数点）、小数除法（除数化成整数、商的小数点与被除数对齐）。",
          "question_types": [
            {
              "type": "小数乘法竖式计算"
            },
            {
              "type": "小数除法竖式计算"
            }
          ]
        },
        {
          "id": "M02-K06",
          "name": "四则混合运算与简便运算",
          "key_content": "四则混合运算顺序（先乘除后加减、有括号先算括号内）、加法乘法运算定律与减法除法运算性质。",
          "question_types": [
            {
              "type": "四则混合运算与简便运算"
            }
          ]
        }
      ]
    },
    {
      "id": "M03",
      "name": "数与代数·常见的量",
      "book": "一年级上册~五年级下册",
      "knowledge_points": [
        {
          "id": "M03-K01",
          "name": "人民币的认识",
          "key_content": "元、角、分及进率（$1$ 元 $= 10$ 角，$1$ 角 $= 10$ 分）、人民币的简单计算。",
          "question_types": [
            {
              "type": "人民币单位换算"
            }
          ]
        },
        {
          "id": "M03-K02",
          "name": "时间与年月日",
          "key_content": "时、分、秒及进率（$1$ 时 $= 60$ 分，$1$ 分 $= 60$ 秒）、大月小月与平年闰年、24 时计时法。",
          "question_types": [
            {
              "type": "时分秒的换算"
            },
            {
              "type": "年月日与24时计时法"
            }
          ]
        },
        {
          "id": "M03-K03",
          "name": "长度、面积、体积单位",
          "key_content": "长度单位（千米、米、分米、厘米、毫米）、面积单位（平方千米、公顷、平方米、平方分米、平方厘米）、体积与容积单位（立方米、立方分米、升、毫升）及进率。",
          "question_types": [
            {
              "type": "长度单位换算"
            },
            {
              "type": "面积单位换算"
            },
            {
              "type": "体积与容积单位换算"
            }
          ]
        },
        {
          "id": "M03-K04",
          "name": "质量单位",
          "key_content": "克、千克、吨及进率（$1$ 吨 $= 1000$ 千克，$1$ 千克 $= 1000$ 克）。",
          "question_types": [
            {
              "type": "质量单位换算"
            }
          ]
        }
      ]
    },
    {
      "id": "M04",
      "name": "数与代数·式与方程及正反比例",
      "book": "五年级上册~六年级下册",
      "knowledge_points": [
        {
          "id": "M04-K01",
          "name": "用字母表示数与简易方程",
          "key_content": "用字母表示数及数量关系、方程的意义、等式的性质、解方程与检验。",
          "question_types": [
            {
              "type": "用字母表示数"
            },
            {
              "type": "解方程"
            }
          ]
        },
        {
          "id": "M04-K02",
          "name": "比的意义与性质",
          "key_content": "比的意义（两个数相除又叫两个数的比）、比的基本性质、化简比与求比值、按比例分配。",
          "question_types": [
            {
              "type": "比的意义与化简比"
            },
            {
              "type": "按比例分配"
            }
          ]
        },
        {
          "id": "M04-K03",
          "name": "比例与正反比例",
          "key_content": "比例的意义与基本性质（内项之积等于外项之积）、解比例、正比例（商一定）与反比例（积一定）的判断。",
          "question_types": [
            {
              "type": "解比例"
            },
            {
              "type": "正比例与反比例的判断"
            }
          ]
        },
        {
          "id": "M04-K04",
          "name": "分数百分数应用题与折扣利率",
          "key_content": "分数、百分数应用题（求一个数是另一个数的百分之几、求一个数的百分之几是多少）、折扣、成数、税率与利率。",
          "question_types": [
            {
              "type": "分数与百分数应用题"
            },
            {
              "type": "折扣、税率与利率"
            }
          ]
        }
      ]
    },
    {
      "id": "M05",
      "name": "图形与几何·平面图形与周长面积",
      "book": "二年级上册~六年级上册",
      "knowledge_points": [
        {
          "id": "M05-K01",
          "name": "线与角及平面图形的认识",
          "key_content": "线段、射线、直线的区别、角的度量与分类、三角形与四边形的特征及内角和（$180°$、$360°$）。",
          "question_types": [
            {
              "type": "线与角的度量"
            }
          ]
        },
        {
          "id": "M05-K02",
          "name": "长方形与正方形",
          "key_content": "长方形、正方形的周长公式 $C = (a+b) \\times 2$（正方形 $C = 4a$）与面积公式 $S = ab$（正方形 $S = a^2$）。",
          "question_types": [
            {
              "type": "长方形正方形周长"
            },
            {
              "type": "长方形正方形面积"
            }
          ]
        },
        {
          "id": "M05-K03",
          "name": "平行四边形、三角形、梯形的面积",
          "key_content": "平行四边形面积 $S = ah$、三角形面积 $S = \\dfrac{1}{2}ah$、梯形面积 $S = \\dfrac{(a+b)h}{2}$。",
          "question_types": [
            {
              "type": "平行四边形面积"
            },
            {
              "type": "三角形面积"
            },
            {
              "type": "梯形面积"
            }
          ]
        },
        {
          "id": "M05-K04",
          "name": "圆",
          "key_content": "圆的周长 $C = \\pi d = 2\\pi r$、圆的面积 $S = \\pi r^2$、环形面积 $S = \\pi (R^2 - r^2)$。",
          "question_types": [
            {
              "type": "圆的周长"
            },
            {
              "type": "圆的面积"
            }
          ]
        }
      ]
    },
    {
      "id": "M06",
      "name": "图形与几何·立体图形与体积",
      "book": "五年级下册~六年级下册",
      "knowledge_points": [
        {
          "id": "M06-K01",
          "name": "长方体与正方体",
          "key_content": "长方体、正方体的特征与棱长总和、表面积 $S = 2(ab + ah + bh)$、体积 $V = abc = sh$（正方体 $V = a^3$）。",
          "question_types": [
            {
              "type": "长方体正方体的棱长总和与表面积"
            },
            {
              "type": "长方体正方体体积"
            }
          ]
        },
        {
          "id": "M06-K02",
          "name": "圆柱与圆锥",
          "key_content": "圆柱表面积 $S = 2\\pi rh + 2\\pi r^2$、圆柱体积 $V = \\pi r^2 h$、圆锥体积 $V = \\dfrac{1}{3}\\pi r^2 h$。",
          "question_types": [
            {
              "type": "圆柱的表面积与体积"
            },
            {
              "type": "圆锥的体积"
            }
          ]
        }
      ]
    },
    {
      "id": "M07",
      "name": "图形与几何·图形的运动与位置",
      "book": "二年级下册~六年级上册",
      "knowledge_points": [
        {
          "id": "M07-K01",
          "name": "平移、旋转与轴对称",
          "key_content": "平移（方向和距离）、旋转（中心、方向、角度）、轴对称图形与对称轴。",
          "question_types": [
            {
              "type": "平移与旋转"
            },
            {
              "type": "轴对称图形"
            }
          ]
        },
        {
          "id": "M07-K02",
          "name": "数对与方向确定位置",
          "key_content": "用数对（列、行）表示位置、用方向和距离确定位置。",
          "question_types": [
            {
              "type": "数对与方向确定位置"
            }
          ]
        }
      ]
    },
    {
      "id": "M08",
      "name": "统计与概率",
      "book": "三年级下册~六年级上册",
      "knowledge_points": [
        {
          "id": "M08-K01",
          "name": "统计图表",
          "key_content": "条形统计图、折线统计图、扇形统计图的特点与数据分析。",
          "question_types": [
            {
              "type": "统计图表分析"
            }
          ]
        },
        {
          "id": "M08-K02",
          "name": "平均数与可能性",
          "key_content": "平均数的意义与求法、简单事件发生的可能性大小。",
          "question_types": [
            {
              "type": "平均数"
            },
            {
              "type": "可能性"
            }
          ]
        }
      ]
    },
    {
      "id": "M09",
      "name": "综合与实践",
      "book": "四年级下册~六年级上册",
      "knowledge_points": [
        {
          "id": "M09-K01",
          "name": "植树问题与行程问题",
          "key_content": "植树问题（两端都栽、只栽一端、两端都不栽）与行程问题（相遇：路程 $=$ 速度和 $\\times$ 时间）。",
          "question_types": [
            {
              "type": "植树问题"
            },
            {
              "type": "行程问题"
            }
          ]
        },
        {
          "id": "M09-K02",
          "name": "鸡兔同笼",
          "key_content": "鸡兔同笼问题的假设法（先假设全是鸡或全是兔，再根据脚数差调整）。",
          "question_types": [
            {
              "type": "鸡兔同笼"
            }
          ]
        },
        {
          "id": "M09-K03",
          "name": "归一归总与工程问题",
          "key_content": "归一问题（先求单一量）、归总问题（先求总量）、工程问题（把工作总量看作单位 1）。",
          "question_types": [
            {
              "type": "归一归总问题"
            },
            {
              "type": "工程问题"
            }
          ]
        }
      ]
    }
  ],
  "examples": [
    {
      "id": "EX-M01-K01-1",
      "module_id": "M01",
      "knowledge_point_id": "M01-K01",
      "question_type": "数位与组成（几个十几个一）",
      "content": "35 里面有（ ）个十和（ ）个一。",
      "solution_method": "35 的十位是 3、个位是 5，所以 35 里面有 3 个十和 5 个一。",
      "difficulty": "易"
    },
    {
      "id": "EX-M01-K01-2",
      "module_id": "M01",
      "knowledge_point_id": "M01-K01",
      "question_type": "100以内数的读写与比较大小",
      "content": "在 ○ 里填上“＞”“＜”或“＝”：$78$ ○ $83$。",
      "solution_method": "78 的十位是 7，83 的十位是 8，十位大的数大，所以 $78 < 83$，填“＜”。",
      "difficulty": "易"
    },
    {
      "id": "EX-M01-K02-1",
      "module_id": "M01",
      "knowledge_point_id": "M01-K02",
      "question_type": "大数的读写（万以内及亿以内）",
      "content": "读出下面各数：$3070050$。",
      "solution_method": "从高位读起，先分级：307 0050，读作“三百零七万零五十”。",
      "difficulty": "中"
    },
    {
      "id": "EX-M01-K02-2",
      "module_id": "M01",
      "knowledge_point_id": "M01-K02",
      "question_type": "大数的改写与近似数",
      "content": "把 $365000$ 改写成用“万”作单位的数，并省略“万”后面的尾数求近似数。",
      "solution_method": "$365000 = 36.5$ 万；省略万位后面的尾数，看千位是 5，向万位进 1，约等于 $37$ 万。",
      "difficulty": "中"
    },
    {
      "id": "EX-M01-K03-1",
      "module_id": "M01",
      "knowledge_point_id": "M01-K03",
      "question_type": "小数的意义与读写",
      "content": "$0.3$ 表示（ ）个十分之一，$0.25$ 表示（ ）个百分之一。",
      "solution_method": "$0.3$ 的十分位是 3，表示 3 个十分之一；$0.25$ 的小数部分有两位，表示 25 个百分之一。",
      "difficulty": "易"
    },
    {
      "id": "EX-M01-K03-2",
      "module_id": "M01",
      "knowledge_point_id": "M01-K03",
      "question_type": "小数大小比较与小数点移动",
      "content": "把 $3.2$ 的小数点向右移动两位，得到的数是（ ）。",
      "solution_method": "小数点向右移动两位，原数扩大 100 倍，$3.2 \\times 100 = 320$。",
      "difficulty": "易"
    },
    {
      "id": "EX-M01-K04-1",
      "module_id": "M01",
      "knowledge_point_id": "M01-K04",
      "question_type": "分数的意义与分数单位",
      "content": "$\\dfrac{3}{4}$ 的分数单位是（ ），它有（ ）个这样的分数单位。",
      "solution_method": "分母是 4，分数单位是 $\\dfrac{1}{4}$；分子是 3，所以有 3 个这样的分数单位。",
      "difficulty": "易"
    },
    {
      "id": "EX-M01-K04-2",
      "module_id": "M01",
      "knowledge_point_id": "M01-K04",
      "question_type": "约分与通分",
      "content": "把 $\\dfrac{12}{18}$ 约分成最简分数，并把 $\\dfrac{2}{3}$ 与 $\\dfrac{5}{6}$ 通分。",
      "solution_method": "12 和 18 的最大公因数是 6，$\\dfrac{12}{18} = \\dfrac{12 \\div 6}{18 \\div 6} = \\dfrac{2}{3}$；通分：$2$ 和 $6$ 的最小公倍数是 6，$\\dfrac{2}{3} = \\dfrac{4}{6}$，$\\dfrac{5}{6}$ 不变。",
      "difficulty": "中"
    },
    {
      "id": "EX-M01-K05-1",
      "module_id": "M01",
      "knowledge_point_id": "M01-K05",
      "question_type": "负数的认识与读写",
      "content": "零下 5 ℃ 记作（ ），零上 5 ℃ 记作（ ）。",
      "solution_method": "零下 5 ℃ 记作 $-5$ ℃，零上 5 ℃ 记作 $+5$ ℃（也可记作 $5$ ℃）。",
      "difficulty": "易"
    },
    {
      "id": "EX-M01-K05-2",
      "module_id": "M01",
      "knowledge_point_id": "M01-K05",
      "question_type": "百分数的意义与读写",
      "content": "一件商品打八折出售，表示现价是原价的（ ）%。",
      "solution_method": "打八折就是按原价的 $80\\%$ 出售，所以现价是原价的 $80\\%$。",
      "difficulty": "易"
    },
    {
      "id": "EX-M02-K01-1",
      "module_id": "M02",
      "knowledge_point_id": "M02-K01",
      "question_type": "多位数加减法竖式计算",
      "content": "用竖式计算：$456 + 789$。",
      "solution_method": "相同数位对齐，从个位算起：$6+9 = 15$，写 5 进 1；$5+8+1 = 14$，写 4 进 1；$4+7+1 = 12$。所以 $456+789 = 1245$。",
      "difficulty": "易"
    },
    {
      "id": "EX-M02-K01-2",
      "module_id": "M02",
      "knowledge_point_id": "M02-K01",
      "question_type": "加减法估算与验算",
      "content": "估算：$203 + 497$ 的结果大约是（ ）。",
      "solution_method": "$203$ 接近 $200$，$497$ 接近 $500$，所以 $203+497 \\approx 200+500 = 700$。",
      "difficulty": "易"
    },
    {
      "id": "EX-M02-K02-1",
      "module_id": "M02",
      "knowledge_point_id": "M02-K02",
      "question_type": "多位数乘除法竖式计算",
      "content": "用竖式计算：$24 \\times 36$。",
      "solution_method": "先用 36 的个位 6 乘 24 得 144，再用十位 3 乘 24 得 720，把两次的积相加：$144+720 = 864$。",
      "difficulty": "中"
    },
    {
      "id": "EX-M02-K02-2",
      "module_id": "M02",
      "knowledge_point_id": "M02-K02",
      "question_type": "多位数乘除法竖式计算",
      "content": "用竖式计算：$864 \\div 24$。",
      "solution_method": "除数是两位数，先看被除数前两位 86 够除，商 3 余 14；落下个位 4 得 144，商 6 正好除尽，所以 $864 \\div 24 = 36$。",
      "difficulty": "中"
    },
    {
      "id": "EX-M02-K03-1",
      "module_id": "M02",
      "knowledge_point_id": "M02-K03",
      "question_type": "同分母分数加减法",
      "content": "计算：$\\dfrac{3}{8} + \\dfrac{2}{8}$。",
      "solution_method": "同分母分数相加，分母不变、分子相加：$\\dfrac{3+2}{8} = \\dfrac{5}{8}$。",
      "difficulty": "易"
    },
    {
      "id": "EX-M02-K03-2",
      "module_id": "M02",
      "knowledge_point_id": "M02-K03",
      "question_type": "异分母分数加减法",
      "content": "计算：$\\dfrac{1}{2} + \\dfrac{1}{3}$。",
      "solution_method": "先通分，$2$ 和 $3$ 的最小公倍数是 6：$\\dfrac{3}{6} + \\dfrac{2}{6} = \\dfrac{5}{6}$。",
      "difficulty": "中"
    },
    {
      "id": "EX-M02-K04-1",
      "module_id": "M02",
      "knowledge_point_id": "M02-K04",
      "question_type": "小数加减法竖式计算",
      "content": "用竖式计算：$3.75 + 2.6$。",
      "solution_method": "小数点对齐：把 $2.6$ 看作 $2.60$，$3.75 + 2.60 = 6.35$。",
      "difficulty": "易"
    },
    {
      "id": "EX-M02-K05-1",
      "module_id": "M02",
      "knowledge_point_id": "M02-K05",
      "question_type": "小数乘法竖式计算",
      "content": "计算：$0.8 \\times 1.5$。",
      "solution_method": "先按整数算 $8 \\times 15 = 120$，两个因数共有两位小数，点上小数点得 $1.20$，化简为 $1.2$。",
      "difficulty": "中"
    },
    {
      "id": "EX-M02-K05-2",
      "module_id": "M02",
      "knowledge_point_id": "M02-K05",
      "question_type": "小数除法竖式计算",
      "content": "计算：$3.6 \\div 1.2$。",
      "solution_method": "把除数 1.2 化成整数 12，被除数同时扩大 10 倍得 36：$36 \\div 12 = 3$。",
      "difficulty": "中"
    },
    {
      "id": "EX-M02-K06-1",
      "module_id": "M02",
      "knowledge_point_id": "M02-K06",
      "question_type": "四则混合运算与简便运算",
      "content": "用简便方法计算：$25 \\times 32 \\times 125$。",
      "solution_method": "把 32 拆成 $4 \\times 8$：$(25 \\times 4) \\times (8 \\times 125) = 100 \\times 1000 = 100000$。",
      "difficulty": "中"
    },
    {
      "id": "EX-M02-K06-2",
      "module_id": "M02",
      "knowledge_point_id": "M02-K06",
      "question_type": "四则混合运算与简便运算",
      "content": "用乘法分配律计算：$102 \\times 45$。",
      "solution_method": "$102 \\times 45 = (100+2) \\times 45 = 100 \\times 45 + 2 \\times 45 = 4500 + 90 = 4590$。",
      "difficulty": "中"
    },
    {
      "id": "EX-M03-K01-1",
      "module_id": "M03",
      "knowledge_point_id": "M03-K01",
      "question_type": "人民币单位换算",
      "content": "5 元 6 角 =（ ）角；80 分 =（ ）角。",
      "solution_method": "$5$ 元 $= 50$ 角，$50+6 = 56$ 角；$80$ 分 $= 8$ 角。",
      "difficulty": "易"
    },
    {
      "id": "EX-M03-K02-1",
      "module_id": "M03",
      "knowledge_point_id": "M03-K02",
      "question_type": "时分秒的换算",
      "content": "2 时 15 分 =（ ）分。",
      "solution_method": "$2$ 时 $= 2 \\times 60 = 120$ 分，$120+15 = 135$ 分。",
      "difficulty": "易"
    },
    {
      "id": "EX-M03-K02-2",
      "module_id": "M03",
      "knowledge_point_id": "M03-K02",
      "question_type": "年月日与24时计时法",
      "content": "2024 年是平年还是闰年？全年共有多少天？",
      "solution_method": "$2024 \\div 4 = 506$，能整除且不是整百年，所以是闰年，全年有 $366$ 天。",
      "difficulty": "中"
    },
    {
      "id": "EX-M03-K02-3",
      "module_id": "M03",
      "knowledge_point_id": "M03-K02",
      "question_type": "年月日与24时计时法",
      "content": "下午 3 时用 24 时计时法表示是（ ）时。",
      "solution_method": "下午 3 时是中午 12 时之后再过 3 小时，$12+3 = 15$ 时。",
      "difficulty": "易"
    },
    {
      "id": "EX-M03-K03-1",
      "module_id": "M03",
      "knowledge_point_id": "M03-K03",
      "question_type": "长度单位换算",
      "content": "$3.5$ 千米 =（ ）米。",
      "solution_method": "$1$ 千米 $= 1000$ 米，$3.5 \\times 1000 = 3500$ 米。",
      "difficulty": "易"
    },
    {
      "id": "EX-M03-K03-2",
      "module_id": "M03",
      "knowledge_point_id": "M03-K03",
      "question_type": "面积单位换算",
      "content": "$2$ 公顷 =（ ）平方米；$4$ 平方千米 =（ ）公顷。",
      "solution_method": "$1$ 公顷 $= 10000$ 平方米，所以 $2$ 公顷 $= 20000$ 平方米；$1$ 平方千米 $= 100$ 公顷，所以 $4$ 平方千米 $= 400$ 公顷。",
      "difficulty": "中"
    },
    {
      "id": "EX-M03-K03-3",
      "module_id": "M03",
      "knowledge_point_id": "M03-K03",
      "question_type": "体积与容积单位换算",
      "content": "$2.4$ 升 =（ ）毫升 =（ ）立方分米。",
      "solution_method": "$1$ 升 $= 1000$ 毫升 $= 1$ 立方分米，所以 $2.4$ 升 $= 2400$ 毫升 $= 2.4$ 立方分米。",
      "difficulty": "中"
    },
    {
      "id": "EX-M03-K04-1",
      "module_id": "M03",
      "knowledge_point_id": "M03-K04",
      "question_type": "质量单位换算",
      "content": "$3$ 吨 $50$ 千克 =（ ）千克。",
      "solution_method": "$3$ 吨 $= 3000$ 千克，$3000+50 = 3050$ 千克。",
      "difficulty": "易"
    },
    {
      "id": "EX-M04-K01-1",
      "module_id": "M04",
      "knowledge_point_id": "M04-K01",
      "question_type": "用字母表示数",
      "content": "一支钢笔 a 元，买 3 支共需（ ）元；当 $a = 8$ 时，应付（ ）元。",
      "solution_method": "买 3 支共需 $3a$ 元；当 $a = 8$ 时，$3 \\times 8 = 24$ 元。",
      "difficulty": "易"
    },
    {
      "id": "EX-M04-K01-2",
      "module_id": "M04",
      "knowledge_point_id": "M04-K01",
      "question_type": "解方程",
      "content": "解方程：$3x + 5 = 26$。",
      "solution_method": "根据等式的性质，两边同时减 5：$3x = 21$；两边同时除以 3：$x = 7$。检验：$3 \\times 7 + 5 = 26$，正确。",
      "difficulty": "中"
    },
    {
      "id": "EX-M04-K02-1",
      "module_id": "M04",
      "knowledge_point_id": "M04-K02",
      "question_type": "比的意义与化简比",
      "content": "化简比：$12 : 18$。",
      "solution_method": "比的前项和后项同时除以最大公因数 6：$12 : 18 = 2 : 3$。",
      "difficulty": "易"
    },
    {
      "id": "EX-M04-K02-2",
      "module_id": "M04",
      "knowledge_point_id": "M04-K02",
      "question_type": "按比例分配",
      "content": "学校把 180 本图书按 $2 : 3$ 分给五年级和六年级，六年级分得多少本？",
      "solution_method": "总份数 $2+3 = 5$，每份 $180 \\div 5 = 36$ 本，六年级占 3 份：$36 \\times 3 = 108$ 本。",
      "difficulty": "中"
    },
    {
      "id": "EX-M04-K03-1",
      "module_id": "M04",
      "knowledge_point_id": "M04-K03",
      "question_type": "解比例",
      "content": "解比例：$\\dfrac{x}{4} = \\dfrac{9}{12}$。",
      "solution_method": "根据比例的基本性质（内项之积等于外项之积）：$12x = 4 \\times 9 = 36$，解得 $x = 3$。",
      "difficulty": "中"
    },
    {
      "id": "EX-M04-K03-2",
      "module_id": "M04",
      "knowledge_point_id": "M04-K03",
      "question_type": "正比例与反比例的判断",
      "content": "判断：速度一定时，路程与时间成（ ）比例；路程一定时，速度与时间成（ ）比例。",
      "solution_method": "速度一定时，路程与时间的比值（速度）一定，成正比例；路程一定时，速度与时间的乘积（路程）一定，成反比例。",
      "difficulty": "中"
    },
    {
      "id": "EX-M04-K04-1",
      "module_id": "M04",
      "knowledge_point_id": "M04-K04",
      "question_type": "分数与百分数应用题",
      "content": "果园里有苹果树 60 棵、梨树 45 棵，梨树的棵数是苹果树的百分之几？",
      "solution_method": "$45 \\div 60 = 0.75 = 75\\%$，所以梨树的棵数是苹果树的 $75\\%$。",
      "difficulty": "中"
    },
    {
      "id": "EX-M04-K04-2",
      "module_id": "M04",
      "knowledge_point_id": "M04-K04",
      "question_type": "折扣、税率与利率",
      "content": "一件衣服原价 200 元，打八五折出售，现价是多少元？",
      "solution_method": "打八五折即现价是原价的 $85\\%$：$200 \\times 85\\% = 200 \\times 0.85 = 170$ 元。",
      "difficulty": "中"
    },
    {
      "id": "EX-M05-K01-1",
      "module_id": "M05",
      "knowledge_point_id": "M05-K01",
      "question_type": "线与角的度量",
      "content": "一个角是 $45°$，它是一个（ ）角；三角形三个内角的和是（ ）度。",
      "solution_method": "小于 $90°$ 的角是锐角，所以 $45°$ 的角是锐角；三角形的内角和是 $180°$。",
      "difficulty": "易"
    },
    {
      "id": "EX-M05-K02-1",
      "module_id": "M05",
      "knowledge_point_id": "M05-K02",
      "question_type": "长方形正方形周长",
      "content": "一块长方形菜地长 8 米、宽 5 米，它的周长是多少米？",
      "solution_method": "由周长公式 $C = (a+b) \\times 2$，得 $C = (8+5) \\times 2 = 26$ 米。",
      "difficulty": "易"
    },
    {
      "id": "EX-M05-K02-2",
      "module_id": "M05",
      "knowledge_point_id": "M05-K02",
      "question_type": "长方形正方形面积",
      "content": "一块正方形手帕边长 30 厘米，它的面积是多少平方厘米？",
      "solution_method": "由面积公式 $S = a^2$，得 $S = 30 \\times 30 = 900$ 平方厘米。",
      "difficulty": "易"
    },
    {
      "id": "EX-M05-K03-1",
      "module_id": "M05",
      "knowledge_point_id": "M05-K03",
      "question_type": "平行四边形面积",
      "content": "一个平行四边形的底是 12 厘米、高是 8 厘米，面积是多少平方厘米？",
      "solution_method": "由面积公式 $S = ah$，得 $S = 12 \\times 8 = 96$ 平方厘米。",
      "difficulty": "易"
    },
    {
      "id": "EX-M05-K03-2",
      "module_id": "M05",
      "knowledge_point_id": "M05-K03",
      "question_type": "三角形面积",
      "content": "一个三角形的底是 10 厘米、高是 6 厘米，面积是多少平方厘米？",
      "solution_method": "由面积公式 $S = \\dfrac{1}{2}ah$，得 $S = \\dfrac{1}{2} \\times 10 \\times 6 = 30$ 平方厘米。",
      "difficulty": "易"
    },
    {
      "id": "EX-M05-K03-3",
      "module_id": "M05",
      "knowledge_point_id": "M05-K03",
      "question_type": "梯形面积",
      "content": "一个梯形上底 6 厘米、下底 10 厘米、高 4 厘米，面积是多少平方厘米？",
      "solution_method": "由面积公式 $S = \\dfrac{(a+b)h}{2}$，得 $S = \\dfrac{(6+10) \\times 4}{2} = 32$ 平方厘米。",
      "difficulty": "中"
    },
    {
      "id": "EX-M05-K04-1",
      "module_id": "M05",
      "knowledge_point_id": "M05-K04",
      "question_type": "圆的周长",
      "content": "一个圆的半径是 5 厘米，它的周长是多少厘米？（$\\pi$ 取 3.14）",
      "solution_method": "由周长公式 $C = 2\\pi r$，得 $C = 2 \\times 3.14 \\times 5 = 31.4$ 厘米。",
      "difficulty": "中"
    },
    {
      "id": "EX-M05-K04-2",
      "module_id": "M05",
      "knowledge_point_id": "M05-K04",
      "question_type": "圆的面积",
      "content": "一个圆的半径是 3 厘米，它的面积是多少平方厘米？",
      "solution_method": "由面积公式 $S = \\pi r^2$，得 $S = 3.14 \\times 3^2 = 28.26$ 平方厘米。",
      "difficulty": "中"
    },
    {
      "id": "EX-M05-K04-3",
      "module_id": "M05",
      "knowledge_point_id": "M05-K04",
      "question_type": "圆的面积",
      "content": "一个环形，外圆半径 5 厘米、内圆半径 3 厘米，环形面积是多少平方厘米？",
      "solution_method": "由环形面积公式 $S = \\pi (R^2 - r^2)$，得 $S = 3.14 \\times (5^2 - 3^2) = 3.14 \\times 16 = 50.24$ 平方厘米。",
      "difficulty": "难"
    },
    {
      "id": "EX-M06-K01-1",
      "module_id": "M06",
      "knowledge_point_id": "M06-K01",
      "question_type": "长方体正方体的棱长总和与表面积",
      "content": "一个长方体长 8 厘米、宽 6 厘米、高 4 厘米，它的表面积是多少平方厘米？",
      "solution_method": "由表面积公式 $S = 2(ab + ah + bh)$，得 $S = 2 \\times (8 \\times 6 + 8 \\times 4 + 6 \\times 4) = 2 \\times (48+32+24) = 208$ 平方厘米。",
      "difficulty": "中"
    },
    {
      "id": "EX-M06-K01-2",
      "module_id": "M06",
      "knowledge_point_id": "M06-K01",
      "question_type": "长方体正方体体积",
      "content": "一个正方体的棱长是 5 分米，它的体积是多少立方分米？",
      "solution_method": "由体积公式 $V = a^3$，得 $V = 5^3 = 125$ 立方分米。",
      "difficulty": "易"
    },
    {
      "id": "EX-M06-K02-1",
      "module_id": "M06",
      "knowledge_point_id": "M06-K02",
      "question_type": "圆柱的表面积与体积",
      "content": "一个圆柱的底面半径是 3 厘米、高是 10 厘米，它的体积是多少立方厘米？",
      "solution_method": "由体积公式 $V = \\pi r^2 h$，得 $V = 3.14 \\times 3^2 \\times 10 = 282.6$ 立方厘米。",
      "difficulty": "中"
    },
    {
      "id": "EX-M06-K02-2",
      "module_id": "M06",
      "knowledge_point_id": "M06-K02",
      "question_type": "圆锥的体积",
      "content": "一个圆锥的底面半径是 2 厘米、高是 9 厘米，它的体积是多少立方厘米？",
      "solution_method": "由体积公式 $V = \\dfrac{1}{3}\\pi r^2 h$，得 $V = \\dfrac{1}{3} \\times 3.14 \\times 2^2 \\times 9 = 37.68$ 立方厘米。",
      "difficulty": "中"
    },
    {
      "id": "EX-M07-K01-1",
      "module_id": "M07",
      "knowledge_point_id": "M07-K01",
      "question_type": "平移与旋转",
      "content": "一个图形先向右平移 3 格，再向上平移 2 格，平移前后图形的（ ）和（ ）不变。",
      "solution_method": "平移只改变图形的位置，不改变图形的形状和大小。",
      "difficulty": "易"
    },
    {
      "id": "EX-M07-K01-2",
      "module_id": "M07",
      "knowledge_point_id": "M07-K01",
      "question_type": "轴对称图形",
      "content": "下列图形中，是轴对称图形的是：A.平行四边形 B.等腰三角形 C.任意三角形。",
      "solution_method": "等腰三角形沿底边上的高对折后两边完全重合，是轴对称图形；一般平行四边形和任意三角形不是轴对称图形，故选 B。",
      "difficulty": "易"
    },
    {
      "id": "EX-M07-K02-1",
      "module_id": "M07",
      "knowledge_point_id": "M07-K02",
      "question_type": "数对与方向确定位置",
      "content": "小明坐在教室的第 3 列第 4 行，用数对表示为（ ， ）。",
      "solution_method": "用数对表示位置时先列后行，所以小明的位置记作 $(3, 4)$。",
      "difficulty": "易"
    },
    {
      "id": "EX-M08-K01-1",
      "module_id": "M08",
      "knowledge_point_id": "M08-K01",
      "question_type": "统计图表分析",
      "content": "某班同学中，喜欢篮球的有 12 人、足球的有 8 人、跳绳的有 10 人，全班共有（ ）人，喜欢篮球的占全班的（ ）%。",
      "solution_method": "全班共有 $12+8+10 = 30$ 人；喜欢篮球的占 $12 \\div 30 = 0.4 = 40\\%$。",
      "difficulty": "中"
    },
    {
      "id": "EX-M08-K02-1",
      "module_id": "M08",
      "knowledge_point_id": "M08-K02",
      "question_type": "平均数",
      "content": "小明数学测验三次成绩分别是 92 分、96 分、94 分，他三次的平均分是多少？",
      "solution_method": "平均数 $= (92+96+94) \\div 3 = 282 \\div 3 = 94$ 分。",
      "difficulty": "易"
    },
    {
      "id": "EX-M08-K02-2",
      "module_id": "M08",
      "knowledge_point_id": "M08-K02",
      "question_type": "可能性",
      "content": "袋子里有 3 个红球和 1 个白球（除颜色外完全相同），任意摸出一个球，摸到（ ）球的可能性大。",
      "solution_method": "红球有 3 个、白球只有 1 个，红球数量多，所以摸到红球的可能性大。",
      "difficulty": "易"
    },
    {
      "id": "EX-M09-K01-1",
      "module_id": "M09",
      "knowledge_point_id": "M09-K01",
      "question_type": "植树问题",
      "content": "在一条长 100 米的小路一旁植树，每隔 5 米栽一棵（两端都栽），一共要栽多少棵？",
      "solution_method": "间隔数 $= 100 \\div 5 = 20$ 个，两端都栽时棵数 = 间隔数 + 1，所以栽 $20+1 = 21$ 棵。",
      "difficulty": "中"
    },
    {
      "id": "EX-M09-K01-2",
      "module_id": "M09",
      "knowledge_point_id": "M09-K01",
      "question_type": "行程问题",
      "content": "甲、乙两地相距 420 千米，客车每小时行 80 千米，货车每小时行 60 千米，两车同时从两地相向开出，几小时后相遇？",
      "solution_method": "相遇时间 = 路程 ÷ 速度和，$420 \\div (80+60) = 420 \\div 140 = 3$ 小时。",
      "difficulty": "中"
    },
    {
      "id": "EX-M09-K02-1",
      "module_id": "M09",
      "knowledge_point_id": "M09-K02",
      "question_type": "鸡兔同笼",
      "content": "笼子里有鸡和兔共 10 只，共有 28 只脚，鸡和兔各有多少只？",
      "solution_method": "假设全是鸡：$10 \\times 2 = 20$ 只脚，比 28 只少 $8$ 只；每把 1 只鸡换成 1 只兔可多 $2$ 只脚，兔有 $8 \\div 2 = 4$ 只，鸡有 $10-4 = 6$ 只。",
      "difficulty": "难"
    },
    {
      "id": "EX-M09-K03-1",
      "module_id": "M09",
      "knowledge_point_id": "M09-K03",
      "question_type": "归一归总问题",
      "content": "3 台拖拉机 5 小时耕地 90 公顷，照这样计算，1 台拖拉机 1 小时耕地多少公顷？",
      "solution_method": "先求单一量：$90 \\div 3 \\div 5 = 30 \\div 5 = 6$ 公顷，所以 1 台拖拉机 1 小时耕地 6 公顷。",
      "difficulty": "中"
    },
    {
      "id": "EX-M09-K03-2",
      "module_id": "M09",
      "knowledge_point_id": "M09-K03",
      "question_type": "工程问题",
      "content": "一项工程，甲队单独做 10 天完成，乙队单独做 15 天完成，两队合做几天可以完成？",
      "solution_method": "甲的工作效率是 $\\dfrac{1}{10}$，乙是 $\\dfrac{1}{15}$，合做效率 $\\dfrac{1}{10} + \\dfrac{1}{15} = \\dfrac{1}{6}$，完成时间 $= 1 \\div \\dfrac{1}{6} = 6$ 天。",
      "difficulty": "难"
    }
  ]
}