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{"anchorId": "ca_4mJFqABe", "prerequisiteId": "ca_QqCETh82", "strength": "hard", "reason": "不先会列举简单随机现象中所有可能发生的结果，就无法用列表或树状图系统求解。", "evidence": [{"kind": "llm", "detail": "候选池 40 选 16，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G5 → G7"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "在画树状图时，他无法确定第一层该画几个分支，因为不知道简单随机现象的所有可能结果有哪些，导致树状图分支数量错误或遗漏。", "inInferenceGraph": true, "retagHash": "58d1224388e59033"}
{"anchorId": "ca_hsZ8jz4C", "prerequisiteId": "ca_PyRD5Ghx", "strength": "hard", "reason": "读写多位数需要理解不同数位上的数值意义", "evidence": [{"kind": "llm", "detail": "候选池 40 选 2，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "看到2537读作两千五百三十七时，他只会按顺序念出数字，无法解释哪个是千位、百位。", "inInferenceGraph": true, "retagHash": "dc1c5d950d0312b7"}
{"anchorId": "ca_tUKZPC5e", "prerequisiteId": "ca_YK9SqQvF", "strength": "hard", "reason": "不先会用数表示个数或顺序，就无法理解符号表示数的大小关系。", "evidence": [{"kind": "llm", "detail": "候选池 40 选 1，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 semantic"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "semantic", "failureSignature": "看到 3 和 5，他不知道哪个数更大，只能乱猜一个符号填上去。", "inInferenceGraph": true, "retagHash": "1533cd1013ae49dd"}
{"anchorId": "ca_tUKZPC5e", "prerequisiteId": "ca_hsZ8jz4C", "strength": "hard", "reason": "不先会认读写数，就无法用符号比较这些数的大小。", "evidence": [{"kind": "llm", "detail": "候选池 40 选 2，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "看到 305 和 350，会把 350 写成 35，然后判断 305 > 35", "inInferenceGraph": true, "retagHash": "3083e7d8cf0ee137"}
{"anchorId": "ca_9VNasAem", "prerequisiteId": "ca_YK9SqQvF", "strength": "soft", "reason": "用数表示物体个数或顺序是理解四则运算含义的基础，否则无法将运算与具体数量对应。", "evidence": [{"kind": "llm", "detail": "候选池 40 选 1，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 convention"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "convention", "failureSignature": "无可观测影响", "inInferenceGraph": false, "retagHash": "85dabf74f6220113"}
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{"anchorId": "ca_F9rkKeDv", "prerequisiteId": "ca_mvps8H7y", "strength": "soft", "reason": "不先掌握百以内加减法就无法熟练口算20以内加减法", "evidence": [{"kind": "llm", "detail": "候选池 40 选 6，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 instrument"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "instrument", "failureSignature": "做 15-8 时，他掰手指数数，数到 8 根手指不够用，就停下来发呆。", "inInferenceGraph": true, "retagHash": "57a54e0417f182bf"}
{"anchorId": "ca_mvps8H7y", "prerequisiteId": "ca_PyRD5Ghx", "strength": "hard", "reason": "不理解数位上数的数值，就无法正确进行百以内的进退位口算", "evidence": [{"kind": "llm", "detail": "候选池 40 选 3，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "计算 34+27 时，会竖式对齐写成 34+72，得出 106", "inInferenceGraph": true, "retagHash": "fd6050b8aa557b9c"}
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{"anchorId": "ca_2cp77aYv", "prerequisiteId": "ca_mvps8H7y", "strength": "hard", "reason": "不先掌握百以内加减法就无法处理更大数位的加减运算", "evidence": [{"kind": "llm", "detail": "候选池 40 选 7，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "列竖式计算 52-38 时，个位 2 减 8 不够减，他会直接用 8-2=6 写在个位，十位再用 5-3=2，得出结果 26。", "inInferenceGraph": true, "retagHash": "9367f74d4148ef17"}
{"anchorId": "ca_E4RKmfQR", "prerequisiteId": "ca_9VNasAem", "strength": "hard", "reason": "不先理解四则运算含义，就无法在情境中进行数的运算和解决问题。", "evidence": [{"kind": "llm", "detail": "候选池 40 选 5，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "他读完题后，会在草稿纸上反复画圈，却写不出一个表示加减的算式，只会用手指在题目文字上一个一个点数。", "inInferenceGraph": true, "retagHash": "aa2f9b221f5d5b5b"}
{"anchorId": "ca_E4RKmfQR", "prerequisiteId": "ca_YK9SqQvF", "strength": "hard", "reason": "不先能用数表示数量，就无法在生活情境中表达和运用数量关系。", "evidence": [{"kind": "llm", "detail": "候选池 40 选 1，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "老师问'一共有多少个苹果'，学生数出左边3个、右边5个，但不知道该把3和5写成算式3+5=8，只会用手指一个一个数完所有苹果。", "inInferenceGraph": true, "retagHash": "4099ac0d78983b14"}
{"anchorId": "ca_YdfHR7Pc", "prerequisiteId": "ca_b6a7ihBd", "strength": "soft", "reason": "不先会认读写万以上的数，就无法结合实例解释其含义", "evidence": [{"kind": "llm", "detail": "候选池 40 选 1，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "读出三十万零五百时，学生在万位上写3，百位上写5，中间的零全跳过不写。", "inInferenceGraph": true, "retagHash": "64c51028f681ee17"}
{"anchorId": "ca_YdfHR7Pc", "prerequisiteId": "ca_PvagbcfZ", "strength": "soft", "reason": "不先知道各数位名称，就无法解释万以上数的组成含义", "evidence": [{"kind": "llm", "detail": "候选池 40 选 3，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 instrument"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "instrument", "failureSignature": "指着数位表问'这个位置叫什么'时答不上来，但解释'34500大约是3万'时却能用'三万多'来描述", "inInferenceGraph": true, "retagHash": "ca5154d81f8f12b8"}
{"anchorId": "ca_b6a7ihBd", "prerequisiteId": "ca_PvagbcfZ", "strength": "hard", "reason": "不认识各数位的名称，就无法理解万以上数的位值和读写。", "evidence": [{"kind": "llm", "detail": "候选池 40 选 3，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "读数时按个级的读法直接读，把 30500 读成「三万零五百」，中间的两个零只读一个，而正确应读「三万零五百」。", "inInferenceGraph": true, "retagHash": "603b37d0376446e8"}
{"anchorId": "ca_5jt43pUh", "prerequisiteId": "ca_b6a7ihBd", "strength": "hard", "reason": "不先会认读写万以上的数，就无法用万、亿为单位表示大数", "evidence": [{"kind": "llm", "detail": "候选池 40 选 2，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "他指着数字 3050000000 的亿位，却说成是千万位，因为不会读数所以无法正确对应数位顺序表。", "inInferenceGraph": true, "retagHash": "fe11ae7e51641204"}
{"anchorId": "ca_5jt43pUh", "prerequisiteId": "ca_PvagbcfZ", "strength": "hard", "reason": "不先知道各数位的名称，就无法理解万、亿作为单位的含义", "evidence": [{"kind": "llm", "detail": "候选池 40 选 3，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "他指万位说这是五位数，指着亿位说这是九位数，但他说不清具体数值，因为他不知道每个数位上的计数单位是多少", "inInferenceGraph": true, "retagHash": "c853f70e66caaa2d"}
{"anchorId": "ca_cXxQKniy", "prerequisiteId": "ca_9hbKt4Gx", "strength": "hard", "reason": "比例尺是比的应用，需要先理解具体情境中两个量的比。", "evidence": [{"kind": "llm", "detail": "候选池 40 选 30，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "在写比例尺1:500时，把图上距离量得3厘米直接当3米去算实际距离，列成3×500=1500米，没有统一单位。", "inInferenceGraph": true, "retagHash": "afa0a1dd3f7fbcee"}
{"anchorId": "ca_26TqD3kA", "prerequisiteId": "ca_wBxFcaY6", "strength": "hard", "reason": "两位数乘除三位数属于整数四则混合运算，需要先掌握混合运算规则和括号使用。", "evidence": [{"kind": "llm", "detail": "候选池 40 选 13，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "列竖式计算三位数除以两位数时，试商后忘记用商乘除数再做减法，而是直接把被除数抄下来继续除。", "inInferenceGraph": true, "retagHash": "20d900125b6ab16a"}
{"anchorId": "ca_Xj7HBSx3", "prerequisiteId": "ca_qaCBdY9k", "strength": "soft", "reason": "不先会比较小数和分数的大小，就无法直观描述其特征和关系", "evidence": [{"kind": "llm", "detail": "候选池 40 选 11，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 convention"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "convention", "failureSignature": "无可观测影响", "inInferenceGraph": false, "retagHash": "1cf219c6e995f2d9"}
{"anchorId": "ca_yyMBrshz", "prerequisiteId": "ca_Rb3WmrqW", "strength": "hard", "reason": "不先理解加法和乘法的运算律，就无法从数学结构上描述其与减法和除法的关系", "evidence": [{"kind": "llm", "detail": "候选池 40 选 14，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "看到‘3-5’时写成‘5-3=2’，并回答‘没有负数’或‘不够减就不减了’", "inInferenceGraph": true, "retagHash": "9edc8b1241299ea8"}
{"anchorId": "ca_nM8mQ6t7", "prerequisiteId": "ca_Rb3WmrqW", "strength": "soft", "reason": "不先理解运算律的含义和字母表示，就无法运用运算律进行简便运算。", "evidence": [{"kind": "llm", "detail": "候选池 40 选 15，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 instrument"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "instrument", "failureSignature": "看到 25×17×4 时，会按顺序从左往右算 25×17=425，再算 425×4=1700，而不是先算 25×4=100 再算 100×17=1700。", "inInferenceGraph": true, "retagHash": "69bf25a3eaeeab30"}
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{"anchorId": "ca_mPeNYzFW", "prerequisiteId": "ca_idAkeFJq", "strength": "hard", "reason": "不先会用科学记数法表示数，就无法在计算器上正确处理和显示大数或小数。", "evidence": [{"kind": "llm", "detail": "候选池 40 选 14，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "他会失败在读取计算器显示结果时，看到屏幕显示“1.23E+05”这样的科学记数法，直接写成1.23而不是123000，或者完全不知道如何将计算器输出的科学记数法结果转换成普通数值。", "inInferenceGraph": true, "retagHash": "5dd2386cd40e4388"}
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{"anchorId": "ca_cugDS6rc", "prerequisiteId": "ca_Q6Yi7Lbr", "strength": "soft", "reason": "不先掌握对角线互相平分的判定，就无法理解两组对边分别相等的判定。", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 15，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "note": "端点断言已按课标原文动词修正，先修判断需重看", "type": "component", "failureSignature": "在证明两组对边分别相等的四边形是平行四边形时，他无法构造出对角线，或者画出对角线后，不知道如何利用“边边边”证明三角形全等，从而无法推出对角线互相平分或对边平行。", "inInferenceGraph": true, "retagHash": "960bbe6c75195034", "strengthCappedBy": "matrix-track"}
{"anchorId": "ca_Q6Yi7Lbr", "prerequisiteId": "ca_Zu1DWddH", "strength": "soft", "reason": "不先掌握等腰三角形的判定与性质，就无法通过三角形全等推导出对角线互相平分的判定", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 9，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "note": "端点断言已按课标原文动词修正，先修判断需重看", "type": "component", "failureSignature": "在证明时画出对角线交点后，无法识别出由此产生的两对全等三角形（如△AOB和△COD），导致无法得出边相等或角相等的结论，转而在证明过程中反复画出新的线段或标注无关的角，始终无法建立平行四边形判定所需的条件。", "inInferenceGraph": true, "retagHash": "3a02de3adec0a0e8", "strengthCappedBy": "matrix-track"}
{"anchorId": "ca_HBtrliy3", "prerequisiteId": "ca_ON3Zt8MJ", "strength": "soft", "reason": "矩形定义为三个角是直角的四边形，这是直接前置知识。", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 17，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "note": "端点断言已按课标原文动词修正，先修判断需重看", "type": "component", "failureSignature": "教师提问'矩形的四个角有什么特点'时，学生只能看着课本上的定义读'四个角都是直角'，但当教师追问'你怎么知道的'或要求画一个矩形时，学生无法指出图中的角是直角，或者画出的图形四条边是直角但角不是直角。", "inInferenceGraph": true, "retagHash": "a163940bc6fba1d0", "strengthCappedBy": "matrix-track"}
{"anchorId": "ca_m49djdHc", "prerequisiteId": "ca_OuWqaIiJ", "strength": "soft", "reason": "不先掌握平行四边形的判定，就无法理解其对角线性质并推导矩形判定。", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 14，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "note": "端点断言已按课标原文动词修正，先修判断需重看", "type": "component", "failureSignature": "在证明对角线相等的平行四边形是矩形时，他无法从平行四边形的性质（如对角线互相平分）出发，推导出三角形全等或等腰三角形，从而无法证明有一个角是直角。", "inInferenceGraph": true, "retagHash": "9017d18359816cae", "strengthCappedBy": "matrix-track"}
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{"anchorId": "ca_8tCroIx2", "prerequisiteId": "ca_HBtrliy3", "strength": "soft", "reason": "不先会矩形的四个角都是直角，就无法理解正方形作为特殊矩形的角属性", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 17，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "他指着正方形说这是菱形，但说不出它也是矩形，因为说不出矩形的角都是直角", "inInferenceGraph": true, "retagHash": "1772223998aa1ea3", "strengthCappedBy": "matrix-track"}
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{"anchorId": "ca_qSCFVPLu", "prerequisiteId": "ca_b6a7ihBd", "strength": "hard", "reason": "不先能认、读、写万以上的数，就无法理解亿位数值所表示的具体大小", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 2，模型提议未复核；本轮已两段式重标"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "指着亿位上的数字说它代表这个数字本身，比如把3亿说成3", "inInferenceGraph": true, "retagHash": "635fdce582300760"}
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{"anchorId": "ca_26TqD3kA", "prerequisiteId": "ca_2cp77aYv", "strength": "hard", "reason": "不先能计算两三位数加减法，就无法掌握多位数乘除法中的进退位处理。", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 8，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G1 → G3"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "列竖式计算 123×45 时，把 123 和 45 的个位对齐，而不是把 45 的个位和 123 的个位对齐，导致乘法计算错误。", "inInferenceGraph": true, "retagHash": "df1c124a19366a82"}
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{"anchorId": "ca_wBxFcaY6", "prerequisiteId": "ca_F9rkKeDv", "strength": "hard", "reason": "不先熟练口算基础运算就无法准确计算复杂算式", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 6，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G1 → G3"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "列竖式计算 15+8 时，用 5 减 8 得 3，写在个位上。", "inInferenceGraph": true, "retagHash": "a3def0024b5b2fc0"}
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{"anchorId": "ca_Frd9SZA4", "prerequisiteId": "ca_tUKZPC5e", "strength": "hard", "reason": "不先会用符号连接两个数表示大小关系，就无法比较分数和小数的大小", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 4，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G1 → G3"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "在数轴上标出0.5和1/2的位置时，他无法将1/2转化为0.5，而是将两个数标在数轴的不同位置，导致比较结果错误。", "inInferenceGraph": true, "retagHash": "5aae204990eb9b88"}
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{"anchorId": "ca_bEb3LYmT", "prerequisiteId": "ca_YK9SqQvF", "strength": "hard", "reason": "不先会用数表示数量或顺序，就无法理解分数作为数的概念", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 1，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G1 → G3"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "在数轴上找不到代表1/2的位置，因为不知道0到1之间该平均分成几份", "inInferenceGraph": true, "retagHash": "cf4bc82b2e5fac77"}
{"anchorId": "ca_nMYCawbc", "prerequisiteId": "ca_hsZ8jz4C", "strength": "hard", "reason": "不先会认读写万以内的数，就无法理解小数的表示和数轴上的位置", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 2，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G1 → G3"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "当要求在数轴上标出0.3时，学生会在0到1之间找不到第3个刻度，直接在0和1的中间位置画点并标记0.3，因为无法将1平均分成10份来确定0.1的位置。", "inInferenceGraph": true, "retagHash": "4788e654b90e9e1e"}
{"anchorId": "ca_nMYCawbc", "prerequisiteId": "ca_PyRD5Ghx", "strength": "hard", "reason": "不先会说出不同数位上的数值，就无法理解小数各数位的意义", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 3，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G1 → G3"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "在数轴上标0.3时，他把0到1之间平均分成3份而不是10份，标在第一个刻度处。", "inInferenceGraph": true, "retagHash": "ebd950f932b7ca96"}
{"anchorId": "ca_zDWZ5UXm", "prerequisiteId": "ca_hsZ8jz4C", "strength": "hard", "reason": "不先会认读写万以内的数，就无法比较这些数的大小", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 2，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G1 → G3"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 semantic"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "semantic", "failureSignature": "看到 305 和 350，会认为 305 更大，因为 305 有三个数字而 350 只有两个数字。", "inInferenceGraph": true, "retagHash": "1b8463da408b1ecf"}
{"anchorId": "ca_zDWZ5UXm", "prerequisiteId": "ca_PyRD5Ghx", "strength": "hard", "reason": "不先理解数位上的数值，就无法正确比较不同位数的数", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 3，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G1 → G3"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "比较 53 和 58 时，学生逐位比较，先比十位都是 5，再比个位时说 3 比 8 大，因为 3 在前 8 在后，所以 53 > 58。", "inInferenceGraph": true, "retagHash": "5806962717c67e05"}
{"anchorId": "ca_cem5VVVY", "prerequisiteId": "ca_rjapWFfz", "strength": "hard", "reason": "计算周长需要选择合适的长度单位进行计算", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 5，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G1 → G3"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "计算周长时，把长和宽的单位搞混，比如把 5 厘米和 3 米直接相加，得出 8 米或 8 厘米。", "inInferenceGraph": true, "retagHash": "5f4a61da50464f63"}
{"anchorId": "ca_cem5VVVY", "prerequisiteId": "ca_TmxSnW4W", "strength": "hard", "reason": "需要先能测量物体的长度才能进行周长计算", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 6，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G1 → G3"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "计算周长时列竖式25+25+15+15，他不知道25+15应该等于多少，直接把25和15的个位5和5相加得0，十位2和1相加得3，写成30。", "inInferenceGraph": true, "retagHash": "450ae612cfcf04a5"}
{"anchorId": "ca_khBk8JSQ", "prerequisiteId": "ca_rjapWFfz", "strength": "soft", "reason": "不先掌握长度单位，就无法理解面积单位和计算", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 5，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G1 → G3"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 convention"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "convention", "failureSignature": "无可观测影响", "inInferenceGraph": false, "retagHash": "fec71f069d498689"}
{"anchorId": "ca_khBk8JSQ", "prerequisiteId": "ca_F9rkKeDv", "strength": "hard", "reason": "不先掌握乘法口算，就无法进行面积乘法计算", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 13，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G1 → G3"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "他会在计算长乘宽时卡住，比如算 7×8，手指头数完不够用，最后写成 54 或 56，或者干脆空着不写。", "inInferenceGraph": true, "retagHash": "7629026f9b3aceb1"}
{"anchorId": "ca_DJE6yRRS", "prerequisiteId": "ca_rjapWFfz", "strength": "soft", "reason": "计算面积需要先掌握长度单位的概念和使用方法", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 5，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G1 → G3"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 convention"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "convention", "failureSignature": "无可观测影响", "inInferenceGraph": false, "retagHash": "2e87f17e2c3100a7"}
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{"anchorId": "ca_juXGkySv", "prerequisiteId": "ca_7VhGafE2", "strength": "hard", "reason": "计算平行四边形面积需要先掌握长方形、正方形的周长和面积计算基础。", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 22，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G3 → G5"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "他会直接用底乘邻边，得出 5×3=15，而不会用底乘高。", "inInferenceGraph": true, "retagHash": "531c1bd3338b75a1"}
{"anchorId": "ca_juXGkySv", "prerequisiteId": "ca_khBk8JSQ", "strength": "hard", "reason": "计算平行四边形面积通常需要转化为或理解与长方形面积的关系。", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 25，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G3 → G5"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "他会在画高这一步卡住，不知道该从平行四边形的一个顶点向对边画一条垂直线段，或者画出的线段不垂直于底边。", "inInferenceGraph": true, "retagHash": "8e97c22344a83d14"}
{"anchorId": "ca_juXGkySv", "prerequisiteId": "ca_qVvsKLFD", "strength": "hard", "reason": "认识平行线是理解平行四边形特征的前提。", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 10，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G3 → G5"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "他会在平行四边形的高上画一条与底边不垂直的线段，然后用这条斜线段的长度乘以底边来计算面积。", "inInferenceGraph": true, "retagHash": "6605c5335ae3db63"}
{"anchorId": "ca_hCGXjyva", "prerequisiteId": "ca_khBk8JSQ", "strength": "hard", "reason": "三角形面积计算通常基于长方形面积公式推导，需要先掌握长方形面积计算。", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 25，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G3 → G5"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "他会在计算三角形面积时，直接用底乘高，忘记除以2，得出错误答案。", "inInferenceGraph": true, "retagHash": "b4034e684dbc8212"}
{"anchorId": "ca_hCGXjyva", "prerequisiteId": "ca_7VhGafE2", "strength": "hard", "reason": "理解面积计算的通用方法和公式推导，需要先掌握长方形和正方形的面积计算。", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 22，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G3 → G5"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "他会拿三角形的三条边相加，再乘以底边，写成（边+边+边）×底", "inInferenceGraph": true, "retagHash": "7374eb0978f02107"}
{"anchorId": "ca_RVK4h7hv", "prerequisiteId": "ca_7VhGafE2", "strength": "soft", "reason": "梯形面积计算依赖于长方形或正方形面积计算公式推导的基础知识。", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 22，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G3 → G5"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 convention"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "convention", "failureSignature": "无可观测影响", "inInferenceGraph": false, "retagHash": "90fda4cc56a4a093"}
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{"anchorId": "ca_GfkKhKtA", "prerequisiteId": "ca_DJE6yRRS", "strength": "soft", "reason": "不先会计算正方形的面积，就无法理解体积和表面积的计算方法。", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 27，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G3 → G5"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 convention"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "convention", "failureSignature": "无可观测影响", "inInferenceGraph": false, "retagHash": "e18ce52b20fa937f"}
{"anchorId": "ca_GfkKhKtA", "prerequisiteId": "ca_7VhGafE2", "strength": "hard", "reason": "不先会计算长方形和正方形的周长与面积，就无法理解正方体表面积的计算。", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 22，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G3 → G5"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "计算表面积时，他列竖式 6×6=36，但把 36+36+36+36+36+36 算成 180，因为 6×6=36，他用 36×6 时，把 36 拆成 30+6，算 30×6=180，6×6=36，然后 180+36=216，但他只加了一次 36，得 180。", "inInferenceGraph": true, "retagHash": "39383d8698f2763a"}
{"anchorId": "ca_z5thZXiz", "prerequisiteId": "ca_7VhGafE2", "strength": "hard", "reason": "圆柱体积和表面积计算需要长方形面积和周长计算作为基础。", "crossDiscipline": null, "evidence": [{"kind": "llm", "detail": "候选池 40 选 22，模型提议未复核；本轮已两段式重标"}, {"kind": "standard-hierarchy", "detail": "课标学段序：G3 → G5"}, {"kind": "llm", "detail": "两段式重标：先写失败表现（不告知有分类任务），再独立调用分类为 component"}], "reviewStatus": "llm-proposed", "reviewedBy": [], "schemaVersion": "0.1.0", "type": "component", "failureSignature": "学生面对圆柱表面积公式时，会在计算两个圆的面积（πr²）这一步卡住，因为他不会计算正方形面积，不明白r²就是边长为r的正方形面积。", "inInferenceGraph": true, "retagHash": "b64186a8e67625bd"}
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