{"id": "ca_r4hvyjyX", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "数与代数", "dimension": "运算能力", "statement": "能用加法算式表示一个乘法算式所对应的连加运算", "verb": "用加法算式表示", "object": "乘法算式所对应的连加运算", "type": "PROCEDURAL", "literacy": ["运算能力"], "cognitive": "应用", "stageHint": {"min": "G1", "max": "G2"}, "courseType": null, "evidence": ["学生能写出 3×4=4+4+4", "学生能写出 5×2=2+2+2+2+2"], "assessment": "{{name}}能用加法算式写出像 3×4=4+4+4 这样的乘法算式吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["patterns", "scale-proportion"], "practice": ["math-computational"], "provenance": {"derivedFrom": "ca_6eLIhoVb", "method": "capability-rewrite", "why": "这条能力要求学生将乘法算式转化为具体的连加算式，这是一个可观察、可判定的操作过程。", "srcSubject": "数学", "srcPage": 26, "srcText": "乘法是加法的简便运算", "crosscuttingWhy": "识别重复模式并用数学表达", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "suspect", "overlap": 0.455, "verbatimCoverage": 0.353, "facts": ["乘法是加法的简便运算"]}, "fieldIssues": ["independent-check-suspect"]}
{"id": "ca_kwyViDAz", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "数与代数", "dimension": "运算能力", "statement": "能用一个乘法算式解释对应的除法算式", "verb": "解释", "object": "对应的除法算式", "type": "CONCEPTUAL", "literacy": ["运算能力"], "cognitive": "理解", "stageHint": {"min": "G1", "max": "G2"}, "courseType": null, "evidence": ["给出乘法算式3×4=12，能写出12÷3=4并说明两者关系", "给出除法算式15÷5=3，能写出5×3=15并说明两者关系"], "assessment": "{{name}}能根据一个乘法算式，写出对应的除法算式并说明它们的关系吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["patterns", "cause-effect"], "practice": ["explaining-designing"], "provenance": {"derivedFrom": "ca_l3Knq2wo", "method": "capability-rewrite", "why": "这条能力要求学生以「除法是乘法的逆运算」这条知识为对象，通过一个可观察的行为——用乘法算式解释除法算式——来展示其理解。旁观者可以通过学生写出的算式和说明文字来判定其会不会。", "srcSubject": "数学", "srcPage": 26, "srcText": "除法是乘法的逆运算", "crosscuttingWhy": "识别运算互逆关系并建构解释", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "suspect", "overlap": 0.444, "verbatimCoverage": 0.357, "facts": ["除法是乘法的逆运算"]}, "fieldIssues": ["independent-check-suspect"]}
{"id": "ca_JBPnXs7s", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "图形与几何", "dimension": "几何直观", "statement": "能准确指出两个已知点，并说出连接它们的线段长度就是这两点间的距离", "verb": "指出...并说出", "object": "两个已知点和连接它们的线段长度与两点间距离的关系", "type": "CONCEPTUAL", "literacy": ["几何直观"], "cognitive": "理解", "stageHint": {"min": "G3", "max": "G4"}, "courseType": null, "evidence": ["在标有A、B两点的地图或示意图上，学生能正确画出连接A、B的线段。", "学生能口头陈述：'图中线段AB的长度，就是点A到点B的距离'。"], "assessment": "{{name}}能在地图或示意图上画出连接A、B两点的线段吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["structure-function"], "practice": ["math-computational"], "provenance": {"derivedFrom": "ca_QVOW8KDI", "method": "capability-rewrite", "why": "这条能力要求学生将'两点间的距离'这个抽象概念，操作化为'连接两点的线段'这一具体图形，并陈述其长度关系，过程可观察、可判定。", "srcSubject": "数学", "srcPage": 38, "srcText": "感知线段长度与两点间距离的关系", "crosscuttingWhy": "理解线段定义并计算长度", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "aiIssues": [{"type": "resolved", "detail": "【裁决为不成立】原异议：“说出连接它们的线段长度就是这两点间的距离”是定义复述，无法判断一个孩子是否真正理解距离概念（例如能否在非标注图中识别最短路径），更像是对定义的机械背诵。"}], "adjudication": {"verdict": "overrule", "why": "课标原文明确要求学生‘感知线段长度与两点间距离的关系’，这包含了理解两者之间的对应关系。能力断言‘能准确指出两个已知点，并说出连接它们的线段长度就是这两点间的距离’是对这一要求的忠实转述，将‘感知关系’具体化为可观察的‘指出’和‘说出’行为。意见认为这是‘定义复述’，但课标本身的要求就是让学生感知并建立这种联系，说出定义正是感知和理解的外在表现之一，不应因此否定断言的忠实性。", "quote": "感知线段长度与两点间距离的关系", "method": "裁决者看课标原文，挑错者看不到；引文逐字核对过"}}
{"id": "ca_bQQ8xxF2", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "图形与几何", "dimension": "数学抽象", "statement": "能举例说明圆的周长与直径之比的恒定性", "verb": "说明", "object": "圆的周长与直径之比的恒定性", "type": "CONCEPTUAL", "literacy": ["数学抽象"], "cognitive": "理解", "stageHint": {"min": "G5", "max": "G6"}, "courseType": null, "evidence": ["学生能指出一个圆形物体并测量其周长和直径，然后计算比值", "学生能对不同大小的圆形重复上述过程并报告比值相同"], "assessment": "{{name}}能指出一个圆形物体并测量它的周长和直径，然后算出它们的比值吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["patterns", "scale-proportion"], "practice": ["explaining-designing"], "provenance": {"derivedFrom": "ca_pOb30KtA", "method": "capability-rewrite", "why": "这条能力要求学生通过实际操作和观察，来验证并解释圆周率的恒定性，这是一个可观察和判定的行为。", "srcSubject": "数学", "srcPage": 40, "srcText": "了解圆的周长与其直径之比是一个定值", "crosscuttingWhy": "发现规律并解释比例恒定", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "suspect", "overlap": 0.538, "verbatimCoverage": 0.588, "facts": ["圆的周长与其直径之比是一个定值"]}, "fieldIssues": ["independent-check-suspect"]}
{"id": "ca_ydqijQaz", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "统计与概率", "dimension": "数据意识", "statement": "能判断一组数据的平均数是否在最大数与最小数之间", "verb": "判断", "object": "一组数据的平均数是否在最大数与最小数之间", "type": "CONCEPTUAL", "literacy": ["数据意识"], "cognitive": "理解", "stageHint": {"min": "G3", "max": "G4"}, "courseType": null, "evidence": ["给出一组数据，学生能正确判断其平均数是否在最大数与最小数之间", "给出一个错误的判断（如平均数大于最大数），学生能指出错误并说明理由"], "assessment": "{{name}}能判断一组数据的平均数是否在最大数和最小数之间吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["scale-proportion", "patterns"], "practice": ["analyzing-data"], "provenance": {"derivedFrom": "ca_tcMgvYM9", "method": "capability-rewrite", "why": "这条能力要求学生运用‘平均数介于最大数与最小数之间’这一知识，对具体数据或判断进行检验和推理，是可观察、可判定的。", "srcSubject": "数学", "srcPage": 45, "srcText": "知道平均数是介于最大数与最小数之间的数", "crosscuttingWhy": "判断平均数范围涉及量级比较与数据规律", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "passed", "overlap": 0.583, "verbatimCoverage": 0.579, "facts": ["平均数是介于最大数与最小数之间的数"]}}
{"id": "ca_i85sHjxW", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": null, "dimension": "数据分析", "statement": "能从多个统计图中，指出使用条形统计图来表达数量多少的实例", "verb": "指出", "object": "使用条形统计图表达数量多少的实例", "type": "CONCEPTUAL", "literacy": ["数据分析"], "cognitive": "理解", "stageHint": {"min": "G3", "max": "G4"}, "courseType": null, "evidence": ["学生面对一组混合了折线图、扇形图和条形图的材料，正确圈出了所有用于表达数量多少的条形图", "学生口头解释了所选条形图是如何通过条形高度来体现数量多少的"], "assessment": "{{name}}能从折线图、扇形图和条形图里，把用来表示数量多少的条形图都圈出来吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["patterns", "scale-proportion"], "practice": ["analyzing-data"], "provenance": {"derivedFrom": "ca_OAlPzObf", "method": "capability-rewrite", "why": "这条能力要求学生运用对条形统计图功能的认知，去识别和判断其实际应用，属于概念性理解的应用与验证。", "srcSubject": "数学", "srcPage": 46, "srcText": "知道条形统计图的主要功能是表达数量的多少", "crosscuttingWhy": "识别图表模式与数量比例", "srcPageFrom": "extract-intermediate", "stageFixedFrom": "G5-G6", "srcStage": "第二学段"}, "schemaVersion": "0.1.0", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "passed", "overlap": 0.579, "verbatimCoverage": 0.565, "facts": ["条形统计图的主要功能是表达数量的多少"]}}
{"id": "ca_FTnQUjww", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "统计与概率", "dimension": "数据意识", "statement": "能举出两个生活中的随机现象，并说明它们可能发生也可能不发生", "verb": "举出并说明", "object": "生活中的随机现象及其特征", "type": "CONCEPTUAL", "literacy": ["数据意识"], "cognitive": "理解", "stageHint": {"min": "G5", "max": "G6"}, "courseType": null, "evidence": ["学生举出‘抛硬币’和‘明天是否下雨’两个例子，并解释‘抛硬币可能正面也可能反面’，‘明天可能下雨也可能不下雨’", "学生举出‘抽奖’和‘掷骰子’两个例子，并解释‘抽奖可能中奖也可能不中’，‘掷骰子可能出6也可能不出6’"], "assessment": "{{name}}能举出像抛硬币、掷骰子这样的生活例子，说明它们可能发生也可能不发生吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["patterns", "cause-effect"], "practice": ["explaining-designing"], "provenance": {"derivedFrom": "ca_dgnYxQYI", "method": "capability-rewrite", "why": "这条能力要求学生将‘随机现象可能发生也可能不发生’这一知识，应用于识别和解释具体实例，是知识的应用和外化，可被旁观者判定。", "srcSubject": "数学", "srcPage": 48, "srcText": "感知随机现象的基本特征，可能发生也可能不发生", "crosscuttingWhy": "识别随机现象并解释其不确定性", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "suspect", "overlap": 0.5, "verbatimCoverage": 0.5, "facts": ["随机现象可能发生也可能不发生"]}, "fieldIssues": ["independent-check-suspect"]}
{"id": "ca_jQVMHu9D", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "统计与概率", "dimension": "数据意识", "statement": "能举出两个随机现象的例子，并说明哪个发生的可能性更大", "verb": "举出并说明", "object": "随机现象及其可能性大小", "type": "CONCEPTUAL", "literacy": ["数据意识"], "cognitive": "理解", "stageHint": {"min": "G5", "max": "G6"}, "courseType": null, "evidence": ["学生举出‘抛硬币正面朝上’和‘掷骰子出现6点’，并说明前者可能性更大", "学生举出‘明天太阳从东边升起’和‘明天本地会下雪’，并说明前者可能性更大"], "assessment": "{{name}}能举出两个随机现象的例子，比如抛硬币和掷骰子，并说明哪个可能性更大吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["patterns", "scale-proportion"], "practice": ["explaining-designing"], "provenance": {"derivedFrom": "ca_Ii5gbk4U", "method": "capability-rewrite", "why": "这条能力要求学生将‘随机现象可能性可预测’的知识，应用于具体实例的判断和比较，其行为（举例并说明）是旁观者可观察和判定的。", "srcSubject": "数学", "srcPage": 48, "srcText": "让学生感知，许多随机现象发生可能性的大小是可以预测的", "crosscuttingWhy": "识别随机现象规律并比较可能性大小", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "suspect", "overlap": 0.471, "verbatimCoverage": 0.5, "facts": ["许多随机现象发生可能性的大小是可以预测的"]}, "fieldIssues": ["composite", "independent-check-suspect"], "composite": true}
{"id": "ca_WgCehUEC", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "综合与实践", "dimension": "应用意识", "statement": "能说出第一类主题活动的名称，并说明其核心特征是融入数学知识学习", "verb": "说出", "object": "第一类主题活动的名称与核心特征", "type": "CONCEPTUAL", "literacy": ["应用意识"], "cognitive": "理解", "stageHint": {"min": "G1", "max": "G6"}, "courseType": null, "evidence": ["学生能正确说出「第一类主题活动是融入数学知识学习的主题活动」", "在多个活动中，学生能区分哪些属于第一类主题活动并给出理由"], "assessment": "{{name}}能说出第一类主题活动的名称，并说明它核心是融入数学知识学习吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "disputed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": [], "practice": [], "provenance": {"derivedFrom": "ca_GhgVOL6i", "method": "capability-rewrite", "why": "这条能力要求学生能准确复述并确认第一类主题活动的定义，是知识「知道」的可观察行为化表达。", "srcSubject": "数学", "srcPage": 49, "srcText": "主题活动分为两类：第一类，融入数学知识学习的主题活动。", "crosscuttingWhy": "识记与复述，非跨学科思维或科学实践", "srcPageFrom": "extract-intermediate", "stageFixedFrom": "G1-G2"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "aiIssues": [{"type": "not-a-capability", "detail": "这是对课标中主题活动分类的识记，不是学生能展示的数学能力，而是对课程结构的了解"}], "composite": true, "fieldIssues": ["composite"]}
{"id": "ca_E5xPj8rt", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "综合与实践", "dimension": "量感", "statement": "能举出一个借助日常用品进行度量的例子，并说明度量的是什么", "verb": "举出、说明", "object": "借助日常用品进行度量的例子", "type": "CONCEPTUAL", "literacy": ["量感"], "cognitive": "理解", "stageHint": {"min": "G3", "max": "G4"}, "courseType": null, "evidence": ["学生说出「用脚步测量教室长度」", "学生说出「用绳子测量树干周长」"], "assessment": "{{name}}能举出一个用脚步测量教室长度，或者用绳子测量树干周长的例子吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["scale-proportion"], "practice": ["explaining-designing"], "provenance": {"derivedFrom": "ca_xGT7Yi0b", "method": "capability-rewrite", "why": "这条能力要求学生将「最初的度量方法借助日常用品」这一知识，转化为一个具体的、可观察的实例化行为。", "srcSubject": "数学", "srcPage": 54, "srcText": "知道最初的度量方法都是借助日常用品", "crosscuttingWhy": "度量与说明度量对象", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "suspect", "overlap": 0.444, "verbatimCoverage": 0.417, "facts": ["最初的度量方法都是借助日常用品"]}, "fieldIssues": ["independent-check-suspect"]}
{"id": "ca_e5SbNrA5", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": null, "dimension": "量感", "statement": "能举例说明度量的本质是表达量的多少", "verb": "举例说明", "object": "度量的本质是表达量的多少", "type": "CONCEPTUAL", "literacy": ["量感"], "cognitive": "理解", "stageHint": {"min": "G3", "max": "G4"}, "courseType": null, "evidence": ["学生能举出至少两个用不同工具测量同一物体长度的例子，并说明它们都是为了表达‘有多长’这个量", "学生能解释为什么用‘步’和用‘米尺’测量教室长度，虽然数值不同，但都是在表达‘教室的长度’这个量"], "assessment": "{{name}}能解释为什么用步和米尺测量教室长度数值不同，但都是在表达教室的长度吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["scale-proportion", "patterns"], "practice": ["explaining-designing"], "provenance": {"derivedFrom": "ca_FHyndzRV", "method": "capability-rewrite", "why": "这条能力要求学生将‘度量的本质是表达量的多少’这一抽象概念，通过具体的、可观察的举例和解释行为表现出来，从而判定其是否真正理解了这一核心概念。", "srcSubject": "数学", "srcPage": 55, "srcText": "了解最初的度量方法都是借助日常用品，理解度量的本质就是表达量的多少，知道计量单位是人为规定的；了解计量单位的发展历史，知道科学发展与度量精确的关系；在教师指导下，能对不同的量进行分类、整理、比较，丰富并发展量感。", "crosscuttingWhy": "理解度量本质，举例说明", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "passed", "overlap": 0.667, "verbatimCoverage": 0.733, "facts": ["最初的度量方法都是借助日常用品", "度量的本质就是表达量的多少", "计量单位是人为规定的", "科学发展与度量精确有关系"]}}
{"id": "ca_NE8NnHya", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": null, "dimension": "量感", "statement": "能举例说明至少两种计量单位（如长度、质量）是人为规定的，并解释其规定方式", "verb": "举例说明", "object": "计量单位是人为规定的", "type": "CONCEPTUAL", "literacy": ["量感"], "cognitive": "理解", "stageHint": {"min": "G3", "max": "G4"}, "courseType": null, "evidence": ["学生能说出‘米’最初被规定为地球子午线长度的四千万分之一，并解释这是一种人为约定。", "学生能举例说明‘千克’最初被规定为1立方分米水的质量，并指出这是为了方便度量而设定的标准。"], "assessment": "{{name}}能说出米和千克最初是怎么规定的吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["scale-proportion", "patterns"], "practice": ["explaining-designing"], "provenance": {"derivedFrom": "ca_qN8BFAbQ", "method": "capability-rewrite", "why": "这条能力要求学生基于‘计量单位是人为规定的’这一知识，通过举例和解释来展示其理解，这是可观察和判定的。", "srcSubject": "数学", "srcPage": 55, "srcText": "了解最初的度量方法都是借助日常用品，理解度量的本质就是表达量的多少，知道计量单位是人为规定的；了解计量单位的发展历史，知道科学发展与度量精确的关系；在教师指导下，能对不同的量进行分类、整理、比较，丰富并发展量感。", "crosscuttingWhy": "理解度量标准的人为约定与设计逻辑", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "aiIssues": [{"type": "resolved", "detail": "【裁决为不成立】原异议：断言要求‘能举例说明…并解释其规定方式’，这更接近于对数学史或计量常识的理解与复述，而非一个可以用‘会/不会’对具体学生进行判断的数学能力。它描述的是知识内容，而非能力表现。"}, {"type": "resolved", "detail": "【裁决为不成立】原异议：掌握证据描述的是‘能说出’历史事实（如米和千克的定义），这属于陈述性知识的回忆，不是运用数学概念解决问题的能力。"}, {"type": "resolved", "detail": "【裁决为不成立】原异议：证据（说出历史定义）与断言（说明单位是人为规定的并解释规定方式）之间存在逻辑跳跃。能复述历史定义，不等于能自主‘说明’和‘解释’这一抽象概念。"}], "composite": true, "fieldIssues": ["composite"], "adjudication": {"verdict": "overrule", "why": "课标原文明确要求学生‘知道计量单位是人为规定的’，断言‘能举例说明至少两种计量单位是人为规定的，并解释其规定方式’是对这一要求的忠实转述和具体化，属于可观察的能力表现。", "quote": "了解最初的度量方法都是借助日常用品，理解度量的本质就是表达量的多少，知道计量单位是人为规定的", "method": "裁决者看课标原文，挑错者看不到；引文逐字核对过"}}
{"id": "ca_uHD2N9is", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "数与代数", "dimension": "数学抽象", "statement": "能举例说明数与代数如何支撑其他数学知识的学习", "verb": "举例说明", "object": "数与代数如何支撑其他数学知识的学习", "type": "CONCEPTUAL", "literacy": ["数学抽象"], "cognitive": "理解", "stageHint": {"min": "G5", "max": "G6"}, "courseType": null, "evidence": ["学生能举出用代数式表示几何图形的周长或面积", "学生能解释用方程解决实际问题时，如何将问题转化为数与代数关系"], "assessment": "{{name}}能举例说明数与代数是怎么支撑其他数学知识学习的吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["systems", "structure-function"], "practice": ["explaining-designing"], "provenance": {"derivedFrom": "ca_K2SGBCiC", "method": "capability-rewrite", "why": "这条能力要求学生以具体例子，阐述数与代数作为基础的作用，其解释行为和所举实例是旁观者可观察判定的。", "srcSubject": "数学", "srcPage": 60, "srcText": "数与代数是数学知识体系的基础之一", "crosscuttingWhy": "理解数学分支间的支撑关系", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "suspect", "overlap": 0.333, "verbatimCoverage": 0.368, "facts": ["数与代数是数学知识体系的基础之一"]}, "fieldIssues": ["independent-check-suspect"]}
{"id": "ca_qikVHL75", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "数与代数", "dimension": "直观想象", "statement": "能正确描述一次函数 y = kx + b 在 k>0 与 k<0 时，图象在坐标系中的上升与下降趋势", "verb": "描述", "object": "一次函数图象的变化趋势", "type": "CONCEPTUAL", "literacy": ["直观想象"], "cognitive": "理解", "stageHint": {"min": "G7", "max": "G9"}, "courseType": null, "evidence": ["学生能画出 y = 2x + 1 与 y = -2x + 1 的草图，并指出前者从左到右上升，后者从左到右下降。", "学生能根据函数表达式中 k 的正负，预测图象的倾斜方向。"], "assessment": "{{name}}能画出 y = 2x + 1 和 y = -2x + 1 的草图，并说出哪个从左到右上升、哪个下降吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["patterns", "scale-proportion"], "practice": ["explaining-designing"], "provenance": {"derivedFrom": "ca_OHz7AOHA", "method": "capability-rewrite", "why": "这条能力要求学生将 k 的符号与图象的视觉特征（上升/下降）进行关联和描述，是可观察的输出。", "srcSubject": "数学", "srcPage": 64, "srcText": "探索并理解 k > 0 和 k < 0 时图象的变化情况", "crosscuttingWhy": "识别函数变化规律并描述趋势", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "not-applicable", "overlap": 0.0, "verbatimCoverage": 0.16, "facts": []}}
{"id": "ca_nCRdhiKP", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "数与代数", "dimension": "直观想象", "statement": "能根据 k 的正负，画出反比例函数 y=k/x 的大致图象，并指出其所在象限", "verb": "画出并指出", "object": "反比例函数的大致图象及所在象限", "type": "REPRESENTATIONAL", "literacy": ["直观想象"], "cognitive": "理解", "stageHint": {"min": "G7", "max": "G9"}, "courseType": null, "evidence": ["学生在纸上画出 k>0 时，图象位于第一、三象限的大致形状。", "学生在纸上画出 k<0 时，图象位于第二、四象限的大致形状。"], "assessment": "{{name}}，你能根据 k 的正负，画出反比例函数 y=k/x 的大致图象，并说出它在哪两个象限吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["patterns", "scale-proportion"], "practice": ["modeling", "math-computational"], "provenance": {"derivedFrom": "ca_o3F0sWDT", "method": "capability-rewrite", "why": "这条能力要求学生将关于图象特征的知识，转化为可观察的绘图和描述行为，旁观者可以通过检查其画出的图象和指出的象限来判定其是否掌握。", "srcSubject": "数学", "srcPage": 68, "srcText": "知道当 k>0 和 k<0 时反比例函数 y=k/x (k≠0) 图象的整体特征", "crosscuttingWhy": "识别k正负的规律，用数学建模画图", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "suspect", "overlap": 0.412, "verbatimCoverage": 0.348, "facts": ["反比例函数 y=k/x (k≠0) 的图象在 k>0 时具有整体特征", "反比例函数 y=k/x (k≠0) 的图象在 k<0 时具有整体特征"]}, "fieldIssues": ["independent-check-suspect"]}
{"id": "ca_wpQJXaLk", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "图形与几何", "dimension": "数学建模", "statement": "能从给定的现实问题中，识别并写出对应的方程或不等式", "verb": "识别并写出", "object": "现实问题对应的方程或不等式", "type": "PROCEDURAL", "literacy": ["数学建模"], "cognitive": "应用", "stageHint": {"min": "G7", "max": "G9"}, "courseType": null, "evidence": ["学生能从‘小明买了3支笔，付了20元，找回2元’的问题中，写出方程 3x + 2 = 20", "学生能从‘某商品原价100元，打折后不低于80元’的问题中，写出不等式 0.8x ≥ 80"], "assessment": "{{name}}能从‘小明买了3支笔，付了20元，找回2元’这样的问题里，写出对应的方程吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["patterns"], "practice": ["modeling", "analyzing-data"], "provenance": {"derivedFrom": "ca_6Q1EwgXX", "method": "capability-rewrite", "why": "这条能力要求学生将现实问题中的等量或不等关系，转化为数学表达式（方程或不等式），这是一个可观察、可判定的操作过程。", "srcSubject": "数学", "srcPage": 69, "srcText": "知道方程或不等式是现实问题中含有未知数的等量关系或不等关系的数学表达", "crosscuttingWhy": "识别模式并建模为数学表达式", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "suspect", "overlap": 0.5, "verbatimCoverage": 0.522, "facts": ["方程是现实问题中含有未知数的等量关系的数学表达", "不等式是现实问题中含有未知数的不等关系的数学表达"]}, "fieldIssues": ["independent-check-suspect"]}
{"id": "ca_curGQJ5b", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "图形与几何", "dimension": "逻辑推理", "statement": "能根据给定条件（如三个角相等或一个角为60°的等腰三角形）判定一个三角形是否为等边三角形，并说明理由", "verb": "判定并说明理由", "object": "一个三角形是否为等边三角形", "type": "PROCEDURAL", "literacy": ["逻辑推理"], "cognitive": "应用", "stageHint": {"min": "G7", "max": "G9"}, "courseType": null, "evidence": ["学生能正确判断一个三个角都相等的三角形是等边三角形，并写出判定依据。", "学生能正确判断一个有一个角是60°的等腰三角形是等边三角形，并写出判定依据。"], "assessment": "{{name}}能根据三个角相等或者一个角是60°的等腰三角形，判断它是不是等边三角形并说明理由吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["patterns", "structure-function"], "practice": ["explaining-designing"], "provenance": {"derivedFrom": "ca_iu287a38", "method": "capability-rewrite", "why": "这条能力要求学生将判定定理的知识应用于具体问题，通过观察条件、执行判定步骤并陈述理由来展示其掌握程度，这是一个可观察、可判定的程序性操作。", "srcSubject": "数学", "srcPage": 72, "srcText": "探索等边三角形的判定定理：三个角都相等的三角形（或有一个角是60°的等腰三角形）是等边三角形。", "crosscuttingWhy": "识别几何规律并基于结构特征进行推理说明", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "suspect", "overlap": 0.278, "verbatimCoverage": 0.536, "facts": ["三个角都相等的三角形是等边三角形", "有一个角是60°的等腰三角形是等边三角形"]}, "fieldIssues": ["independent-check-suspect"]}
{"id": "ca_MuNguAY3", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "图形与几何", "dimension": "逻辑推理", "statement": "能通过计算两个锐角的和是否为90度，判定一个三角形是否为直角三角形", "verb": "判定", "object": "一个三角形是否为直角三角形", "type": "PROCEDURAL", "literacy": ["逻辑推理"], "cognitive": "应用", "stageHint": {"min": "G7", "max": "G9"}, "courseType": null, "evidence": ["学生根据给定两个角的度数，正确计算其和并判断是否为直角三角形", "学生能识别出含两个已知角且互余的三角形是直角三角形，并指出直角顶点"], "assessment": "{{name}}能根据两个角的度数，算出它们的和是不是90度，来判断这个三角形是不是直角三角形吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["patterns", "structure-function"], "practice": ["math-computational"], "provenance": {"derivedFrom": "ca_G6ppUEiz", "method": "capability-rewrite", "why": "这条能力要求学生应用‘两个角互余的三角形是直角三角形’这一知识，通过具体计算来执行一个判定操作，其过程和结果（正确或错误）是旁观者可以直接观察和判定的。", "srcSubject": "数学", "srcPage": 73, "srcText": "掌握有两个角互余的三角形是直角三角形", "crosscuttingWhy": "运用数学计算，识别角度关系与三角形类型", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "suspect", "overlap": 0.308, "verbatimCoverage": 0.381, "facts": ["有两个角互余的三角形是直角三角形"]}, "fieldIssues": ["independent-check-suspect"]}
{"id": "ca_MYtgfxW4", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "图形与几何", "dimension": "几何直观", "statement": "能指出矩形中任意一个角并说明它是直角", "verb": "指出并说明", "object": "矩形中的一个角及其度数", "type": "CONCEPTUAL", "literacy": ["几何直观"], "cognitive": "理解", "stageHint": {"min": "G7", "max": "G9"}, "courseType": null, "evidence": ["在给出的矩形图形中，用手指或笔尖明确指向一个角", "口头或书面说明该角是直角（90度）"], "assessment": "{{name}}能指着矩形的一个角说它是直角吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["structure-function"], "practice": ["explaining-designing"], "provenance": {"derivedFrom": "ca_HBtrliy3", "method": "capability-rewrite", "why": "这条能力要求学生将「矩形的四个角都是直角」这一性质，应用于具体图形中的特定角，并做出可观察的判定行为。", "srcSubject": "数学", "srcPage": 73, "srcText": "探索并证明矩形、菱形的性质定理：矩形的四个角都是直角", "crosscuttingWhy": "识别形状特征并解释其属性", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "suspect", "overlap": 0.364, "verbatimCoverage": 0.471, "facts": ["矩形的四个角都是直角"]}, "fieldIssues": ["independent-check-suspect"]}
{"id": "ca_Vbi4kGKF", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "图形与几何", "dimension": "几何直观", "statement": "能指出给定圆中直径所对的圆周角并说明其度数", "verb": "指出并说明", "object": "直径所对的圆周角及其度数", "type": "CONCEPTUAL", "literacy": ["几何直观"], "cognitive": "理解", "stageHint": {"min": "G7", "max": "G9"}, "courseType": null, "evidence": ["在几何图形中正确标注出直径所对的圆周角", "说明该角的度数为90度或直角"], "assessment": "{{name}}能指出圆里直径所对的圆周角，并说明它是90度吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["structure-function", "patterns"], "practice": ["explaining-designing"], "provenance": {"derivedFrom": "ca_xaJFEOfI", "method": "capability-rewrite", "why": "这条能力要求学生应用“直径所对的圆周角是直角”这一知识，在具体情境中识别并描述该角，是可观察和判定的行为。", "srcSubject": "数学", "srcPage": 74, "srcText": "直径所对的圆周角是直角", "crosscuttingWhy": "识别几何结构特征并解释其性质", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "suspect", "overlap": 0.385, "verbatimCoverage": 0.4, "facts": ["直径所对的圆周角是直角"]}, "fieldIssues": ["composite", "independent-check-suspect"], "composite": true}
{"id": "ca_2mKMEG42", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "图形与几何", "dimension": "几何直观", "statement": "能在几何图形中识别出90°圆周角所对的弦，并判断该弦是否为直径", "verb": "识别并判断", "object": "90°圆周角所对的弦及其与直径的关系", "type": "CONCEPTUAL", "literacy": ["几何直观"], "cognitive": "理解", "stageHint": {"min": "G7", "max": "G9"}, "courseType": null, "evidence": ["在给定的圆中，准确画出或指出一个90°圆周角及其所对的弦", "根据弦的位置或长度，正确判断这条弦是否是圆的直径"], "assessment": "{{name}}能在圆里找到90度圆周角所对的弦，并判断它是不是直径吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["structure-function", "patterns"], "practice": ["analyzing-data"], "provenance": {"derivedFrom": "ca_pgXiycdV", "method": "capability-rewrite", "why": "这条能力要求学生将「90°的圆周角所对的弦是直径」这一陈述性知识，转化为在具体图形情境中进行识别和判断的操作性能力。", "srcSubject": "数学", "srcPage": 74, "srcText": "90°的圆周角所对的弦是直径", "crosscuttingWhy": "识别图形特征并判断关系", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "suspect", "overlap": 0.353, "verbatimCoverage": 0.385, "facts": ["90°的圆周角所对的弦是直径"]}, "fieldIssues": ["independent-check-suspect"]}
{"id": "ca_yNQm93sv", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "统计与概率", "dimension": "几何直观", "statement": "能举例说明平面直角坐标系如何将一个几何图形（如三角形）的顶点位置用坐标表示出来", "verb": "举例说明", "object": "平面直角坐标系如何将几何图形的顶点位置用坐标表示", "type": "REPRESENTATIONAL", "literacy": ["几何直观"], "cognitive": "理解", "stageHint": {"min": "G7", "max": "G9"}, "courseType": null, "evidence": ["学生能画出一个三角形，并写出其三个顶点的坐标", "学生能根据给定的三个坐标，在坐标系中画出对应的三角形"], "assessment": "{{name}}能画出一个三角形，并写出它的三个顶点坐标吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["structure-function", "systems"], "practice": ["modeling", "explaining-designing"], "provenance": {"derivedFrom": "ca_yU983c3b", "method": "capability-rewrite", "why": "这条能力要求学生将「沟通几何与代数」这一抽象概念，转化为具体的操作：用坐标表示几何点，或根据坐标画出几何图形。这是一个可观察、可判定的技能。", "srcSubject": "数学", "srcPage": 80, "srcText": "平面直角坐标系是数轴的拓展，是沟通几何与代数的桥梁", "crosscuttingWhy": "用坐标系建模表示几何图形", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "suspect", "overlap": 0.346, "verbatimCoverage": 0.323, "facts": ["平面直角坐标系是数轴的拓展", "平面直角坐标系是沟通几何与代数的桥梁"]}, "fieldIssues": ["independent-check-suspect"]}
{"id": "ca_L5zx25rS", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "统计与概率", "dimension": "数据意识", "statement": "能举出两个例子，说明其中发生的可能性大小不同，并用概率数值或语言描述其大小", "verb": "举出", "object": "两个概率不同的随机事件实例", "type": "CONCEPTUAL", "literacy": ["数据意识"], "cognitive": "理解", "stageHint": {"min": "G7", "max": "G9"}, "courseType": null, "evidence": ["举例说出掷一枚均匀硬币正面朝上与掷一枚骰子出现6点这两个事件，并比较其可能性大小", "用‘很可能’、‘不太可能’等语言或具体分数、百分数描述两个不同事件的发生概率"], "assessment": "{{name}}能举出两个例子，比如掷硬币和掷骰子，说明它们发生的可能性大小不同吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["patterns", "scale-proportion"], "practice": ["analyzing-data", "math-computational"], "provenance": {"derivedFrom": "ca_HoNtLGQO", "method": "capability-rewrite", "why": "这条能力要求学生将概率概念应用于具体实例，通过举例和描述行为来外化其对‘可能性大小度量’的理解。", "srcSubject": "数学", "srcPage": 83, "srcText": "理解概率是对随机事件发生可能性大小的度量", "crosscuttingWhy": "识别概率模式并量化比较大小", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "suspect", "overlap": 0.304, "verbatimCoverage": 0.323, "facts": ["概率是对随机事件发生可能性大小的度量"]}, "fieldIssues": ["composite", "independent-check-suspect"], "composite": true}
{"id": "ca_ae9wCC9P", "discipline": "数学", "track": "MATRIX", "strand": "学科内容", "topic": "综合与实践", "dimension": "数据意识", "statement": "能列举一个简单随机事件，并说明其所有可能结果的个数是有限的且每个结果发生的概率相等", "verb": "列举并说明", "object": "一个简单随机事件及其结果的有限性与等概率性", "type": "CONCEPTUAL", "literacy": ["数据意识"], "cognitive": "理解", "stageHint": {"min": "G7", "max": "G9"}, "courseType": null, "evidence": ["学生能正确说出掷一枚均匀骰子有6种可能结果，且每种结果出现的概率都是1/6", "学生能正确指出从一副洗匀的扑克牌中抽一张，有54种可能结果，且每张牌被抽到的概率相等"], "assessment": "{{name}}能说出掷一枚均匀骰子有几种可能结果，每种结果出现的概率是多少吗？", "evidenceSource": "capability-rewrite", "reviewStatus": "ai-reviewed", "reviewedBy": [], "deprecated": false, "supersededBy": null, "crosscutting": ["patterns", "scale-proportion"], "practice": ["analyzing-data"], "provenance": {"derivedFrom": "ca_r5pwkeWJ", "method": "capability-rewrite", "why": "这条能力要求学生将关于简单随机事件的知识（结果有限、概率相等）应用于一个具体实例，并能清晰地表述出来，这是一个可观察、可判定的行为。", "srcSubject": "数学", "srcPage": 84, "srcText": "类简单的随机事件，其所有可能发生结果的个数是有限的，每个可能结果发生的概率是相等的", "crosscuttingWhy": "识别等可能事件的规律与概率量级", "srcPageFrom": "extract-intermediate"}, "schemaVersion": "0.1.0", "topicFrom": "curriculum-page-index", "independentCheck": {"method": "模型只读原文（看不到本断言）自行抽事实，再机械比对实词覆盖", "verdict": "passed", "overlap": 0.8, "verbatimCoverage": 0.781, "facts": ["类简单的随机事件的所有可能发生结果的个数是有限的", "类简单的随机事件的每个可能结果发生的概率是相等的"]}}