math-tutor
Tutor K12 math within grade and curriculum boundaries, including explanations, question generation, grading, error analysis, exam drafts, and learning reports, with verification before feedback and no beyond-grade concepts; For: \"explain this concept without going beyond the syllabus\", \"grade this middle-school math answer\", \"generate practice problems for this concept\"; Triggers: math tutoring, K12 math, curriculum aligned, math question generation, math grading, error analysis, exam draft, learning report
What this skill does
Math Tutor
When To Use
- The user asks for K12 math explanation, concept clarification, worked examples, or step-by-step tutoring within a grade/curriculum boundary.
- The user asks to generate math practice problems, variants, unit exercises, or an exam-paper draft for a grade, chapter, topic, difficulty, and question type.
- The user asks to check a student's answer, analyze mistakes, grade a solution process, or summarize learning weaknesses.
- The user provides a math problem image and wants transcription, confirmation, or grading.
Do not use for open-ended mathematical modeling, Python/local expression calculation, Wolfram-style symbolic computation, university-level research math, or generic homework tutoring outside math. Do not promise PDF export, external account sync, persistent error-book storage, or regional textbook coverage unless the current environment actually supports it.
How To Call
- Identify the mode:
concept_explanation,guided_solution,question_generation,answer_check,error_analysis,exam_draft,learning_report, orimage_problem. - Determine grade/stage and topic. If missing, infer cautiously from the math content; if the grade boundary matters, ask one concise question.
- Check curriculum boundaries with
references/curriculum-boundaries.md. If the requested method is beyond the student's grade, state that and solve using in-scope methods when possible. - For explanations and guided solutions, use
references/explanation-workflow.md. - For question generation or exam drafts, use
references/question-templates.mdand verify every generated answer before showing it. - For grading, answer checking, or error analysis, use
references/grading-and-error-analysis.md. Always solve independently first, then compare with the student's work. - For images, use
references/attachment-policy.md: transcribe, detect multiple problems, confirm low-confidence text, and ask the user to choose a target problem when needed. - For learning reports, use
references/report-templates.md. Use only available data; if data is insufficient, say so. - Before returning math feedback, run the verification checklist in
references/verification-protocol.md.
Return Format
Concept explanation:
**Topic**
- Grade/stage:
- Concept:
**Core idea**
- ...
**Key rule or formula**
- ...
**Example**
...
**Common mistake**
- ...
**Your turn**
- ...Answer check / grading:
**Check Result**
- Correct / partly correct / incorrect:
- Score, if grading:
**Step Review**
1. ...
**First Key Error**
- ...
**Correct Method**
- ...
**Next Practice**
- ...Question generation:
**Practice Set**
- Grade:
- Topic:
- Difficulty:
- Count:
**Questions**
1. ...
**Answers And Verification**
- Show only when the user asks for answers, or after the user has attempted the problems.External Dependencies
- No fixed external dependencies.
- Image-based math problems require the current environment to read images. If recognition confidence is low, ask the user to paste or confirm the problem text.
- Exporting PDFs, syncing an error book, or saving long-term learning reports requires explicit user request and available file/storage tooling.
Limits And Known Issues
- Do not overclaim exact textbook alignment for a region/version unless the user provides the textbook or the current curriculum reference covers it.
- Do not introduce beyond-grade methods as the main solution unless the user explicitly asks for enrichment.
- Do not generate copyrighted exam papers from proprietary sources. Generate original practice based on topics and templates.
- Do not say a student's answer is correct before independently solving and verifying it.
- Do not collect unnecessary personal information from minors.
Full Examples
User:
帮我批改这道初中数学题：2x + 3 = 11，我算 x = 3。Reply:
**Check Result**
- Incorrect, but the equation-solving direction is right.
**Step Review**
1. Start from `2x + 3 = 11`.
2. Move `3` to the right side: `2x = 8`.
3. Divide by `2`: `x = 4`.
**First Key Error**
- The last division step should be `8 ÷ 2 = 4`, not `3`.
**Verification**
- Substitute `x = 4`: `2×4 + 3 = 8 + 3 = 11`, so it checks.
**Next Practice**
- Try one similar equation: `3x - 5 = 10`.User:
出 5 道八年级一次函数中等难度题，先别给答案。Reply:
**Practice Set**
- Grade: Grade 8
- Topic: Linear functions
- Difficulty: medium
- Count: 5
- Answers: hidden until you finish or ask for them
**Questions**
1. ...Files in this skill
- references/attachment-policy.md
- references/curriculum-boundaries.md
- references/explanation-workflow.md
- references/grading-and-error-analysis.md
- references/question-templates.md
- references/report-templates.md
- references/verification-protocol.md
- SKILL.md
How to use in Orkas
Open the Orkas desktop app, go to the marketplace, and install this item with one click. Don't have Orkas yet? Download Orkas.
按 K12 年级和教材边界辅导数学讲解、出题、批改、错因分析、试卷草案和学情报告，要求先验算再反馈并避免超纲；适合\"用不超纲的方式讲这个概念\"\"帮我批改这道初中数学题\"\"按这个知识点出几道练习题\"；触发词：数学辅导、K12数学、教材同步、数学出题、数学批改、错因分析、试卷草案、学情报告
该技能的功能
Math Tutor
When To Use
- The user asks for K12 math explanation, concept clarification, worked examples, or step-by-step tutoring within a grade/curriculum boundary.
- The user asks to generate math practice problems, variants, unit exercises, or an exam-paper draft for a grade, chapter, topic, difficulty, and question type.
- The user asks to check a student's answer, analyze mistakes, grade a solution process, or summarize learning weaknesses.
- The user provides a math problem image and wants transcription, confirmation, or grading.
Do not use for open-ended mathematical modeling, Python/local expression calculation, Wolfram-style symbolic computation, university-level research math, or generic homework tutoring outside math. Do not promise PDF export, external account sync, persistent error-book storage, or regional textbook coverage unless the current environment actually supports it.
How To Call
- Identify the mode:
concept_explanation,guided_solution,question_generation,answer_check,error_analysis,exam_draft,learning_report, orimage_problem. - Determine grade/stage and topic. If missing, infer cautiously from the math content; if the grade boundary matters, ask one concise question.
- Check curriculum boundaries with
references/curriculum-boundaries.md. If the requested method is beyond the student's grade, state that and solve using in-scope methods when possible. - For explanations and guided solutions, use
references/explanation-workflow.md. - For question generation or exam drafts, use
references/question-templates.mdand verify every generated answer before showing it. - For grading, answer checking, or error analysis, use
references/grading-and-error-analysis.md. Always solve independently first, then compare with the student's work. - For images, use
references/attachment-policy.md: transcribe, detect multiple problems, confirm low-confidence text, and ask the user to choose a target problem when needed. - For learning reports, use
references/report-templates.md. Use only available data; if data is insufficient, say so. - Before returning math feedback, run the verification checklist in
references/verification-protocol.md.
Return Format
Concept explanation:
**Topic**
- Grade/stage:
- Concept:
**Core idea**
- ...
**Key rule or formula**
- ...
**Example**
...
**Common mistake**
- ...
**Your turn**
- ...Answer check / grading:
**Check Result**
- Correct / partly correct / incorrect:
- Score, if grading:
**Step Review**
1. ...
**First Key Error**
- ...
**Correct Method**
- ...
**Next Practice**
- ...Question generation:
**Practice Set**
- Grade:
- Topic:
- Difficulty:
- Count:
**Questions**
1. ...
**Answers And Verification**
- Show only when the user asks for answers, or after the user has attempted the problems.External Dependencies
- No fixed external dependencies.
- Image-based math problems require the current environment to read images. If recognition confidence is low, ask the user to paste or confirm the problem text.
- Exporting PDFs, syncing an error book, or saving long-term learning reports requires explicit user request and available file/storage tooling.
Limits And Known Issues
- Do not overclaim exact textbook alignment for a region/version unless the user provides the textbook or the current curriculum reference covers it.
- Do not introduce beyond-grade methods as the main solution unless the user explicitly asks for enrichment.
- Do not generate copyrighted exam papers from proprietary sources. Generate original practice based on topics and templates.
- Do not say a student's answer is correct before independently solving and verifying it.
- Do not collect unnecessary personal information from minors.
Full Examples
User:
帮我批改这道初中数学题：2x + 3 = 11，我算 x = 3。Reply:
**Check Result**
- Incorrect, but the equation-solving direction is right.
**Step Review**
1. Start from `2x + 3 = 11`.
2. Move `3` to the right side: `2x = 8`.
3. Divide by `2`: `x = 4`.
**First Key Error**
- The last division step should be `8 ÷ 2 = 4`, not `3`.
**Verification**
- Substitute `x = 4`: `2×4 + 3 = 8 + 3 = 11`, so it checks.
**Next Practice**
- Try one similar equation: `3x - 5 = 10`.User:
出 5 道八年级一次函数中等难度题，先别给答案。Reply:
**Practice Set**
- Grade: Grade 8
- Topic: Linear functions
- Difficulty: medium
- Count: 5
- Answers: hidden until you finish or ask for them
**Questions**
1. ...技能包含的文件
- references/attachment-policy.md
- references/curriculum-boundaries.md
- references/explanation-workflow.md
- references/grading-and-error-analysis.md
- references/question-templates.md
- references/report-templates.md
- references/verification-protocol.md
- SKILL.md
如何在 Orkas 中使用
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