Math Worksheet Generator#

Generate a student worksheet PDF + full step-by-step answer key PDF for any K-12 math topic. Compiles LaTeX with tectonic (no TeX installation required — it auto-downloads packages).

Model Selection (Automatic)#

This skill auto-detects the best available reasoning model and uses it for problem generation. Reasoning models (o1, o3, DeepSeek R1, Gemini DeepThink) work through math step-by-step and make significantly fewer errors than standard models.

Model rankings are kept fresh via a three-layer fallback:

1. Hosted JSON (fetched from GitHub, 7-day cache) — updated by maintainers as models ship
2. Bundled JSON ( references/model-rankings.json) — updated with each skill release on ClawhHub
3. Hardcoded defaults in the script — last-resort, never stale enough to cause failures

To update rankings without waiting for a skill release: edit the hosted JSON at the GitHub URL in references/model-rankings.md. The skill picks it up within 7 days.

Step 0 — run model detection before anything else:

bash

SKILL_DIR="$(dirname "$0")"
result=$(bash "$SKILL_DIR/scripts/check_reasoning_model.sh")
status=$(echo "$result" | awk '{print $1}')   # FOUND, FALLBACK, or NONE
model_alias=$(echo "$result" | awk '{print $2}')
model_full=$(echo "$result" | awk '{print $3}')

Then branch on the status:

FOUND_REASONING (o3, o1, DeepThink, DeepSeek R1) — best case, use for problem generation:

text

sessions_spawn(task="<problem generation prompt>", model=model_alias)

No warning needed. Sub-agent writes the .tex files + verify script, announces completion.

FOUND_STRONG (Claude Opus) — excellent quality, use it without alarming the user:

text

sessions_spawn(task="<generation prompt>", model=model_alias)

Optionally add a quiet note: "Using Opus — solid math accuracy and excellent LaTeX. For the hardest Algebra 2 problems, a reasoning model (DeepThink/o1) would be marginally better."

NONE — standard model only; proceed but surface a clear recommendation:

text

⚠️ No reasoning model or Opus detected. Worksheet generated with [current model].
For best accuracy, especially on multi-step problems, configure one of:
  • Gemini 2.5 Pro DeepThink  — google.generativeai.com (free tier available)
  • o1 / o3                   — platform.openai.com
  • DeepSeek R1               — platform.deepseek.com (very affordable)
  • Claude Opus               — console.anthropic.com
SymPy verification will catch most errors regardless.

StatusModel examplesActionFOUND_REASONINGDeepThink, o1, o3, R1Spawn silently, no warningFOUND_STRONGClaude Opus 4.xSpawn silently, optional quiet noteNONESonnet, Flash, GPT-4oUse current model + show recommendation

Prerequisites#

bash

brew install tectonic   # macOS/Linux — downloads packages on demand

Output directory (create if needed): ~/Documents/Worksheets/

Workflow#

1. Gather requirements#

Ask (or infer from context):

• Student: name, grade, course (e.g. "8th grade, Pre-Algebra")
• Topic: e.g. "factoring trinomials", "solving two-step equations"
• Problem count: default 10 if not specified
• Format preference: timed quiz, homework practice, mixed difficulty, or topic drill

Photo input shortcut: If the user sends a photo of homework or a textbook page, use the image tool to extract problem types, format, and difficulty — then mirror that style exactly.

2. Design problems#

Design problems appropriate to the student's level. Increase difficulty gradually across the set. Every problem must be mathematically correct — verify your own solutions.

See references/problem-library.md for topic-specific problem type menus.

3. Write LaTeX source#

Write three .tex files to /tmp/:

• ws_TOPIC_DATE.tex — student worksheet (blank work areas)
• ak_TOPIC_DATE.tex — answer key (full step-by-step solutions)
• ss_TOPIC_DATE.tex — skills summary / study guide (cheat sheet)

The skills summary is a 1–2 page reference card the student can use while working through the worksheet or when studying. It contains:

• One section per distinct skill tested (2–5 sections typical)
• A formula/rule box (blue) per skill — the key facts and formulas
• A mini worked example (green) per skill — brief pattern demonstration, simpler than worksheet problems
• An optional watch-out box (orange) — common mistakes worth flagging
• Optional key vocabulary section at the bottom

See references/latex-templates.md → "Skills Summary / Study Guide Template" for the full shell and box macros.

See references/latex-templates.md for document templates, coordinate planes, tables, geometric figures, and answer key patterns.

Required packages (include in every document):

latex

\usepackage[margin=1in, top=0.75in, bottom=0.75in]{geometry}
\usepackage{amsmath, amssymb}
\usepackage{tikz, pgfplots}
\usepackage{enumitem, fancyhdr, multicol, array, booktabs}
\pgfplotsset{compat=1.18}

Work space defaults: \vspace{5cm} per problem; 8cm for multi-step; 10cm+ for graphs.

4. Write and run the verification file#

Before compiling, write /tmp/verify_TOPIC_DATE.json — a structured data file describing each problem and its expected answer. The bundled scripts/verify.py evaluates this using SymPy. No generated code is ever executed.

bash

bash "$SKILL_DIR/scripts/run_verify.sh" /tmp/verify_TOPIC_DATE.json

JSON format:

json

{
  "topic": "graphing polynomials",
  "problems": [
    {"id": 1, "type": "solve",  "expr": "x**2 - 5*x + 6",      "expected": [2, 3]},
    {"id": 2, "type": "factor", "expr": "x**2 - 7*x + 12",     "expected": "(x-3)*(x-4)"},
    {"id": 3, "type": "eval",   "expr": "(x-1)*(x+2)", "at": {"x": 0}, "expected": -2},
    {"id": 4, "type": "zeros",  "expr": "x*(x-3)**2",           "expected": [0, 3]},
    {"id": 5, "type": "expand", "expr": "(x+2)**2",             "expected": "x**2 + 4*x + 4"},
    {"id": 6, "type": "manual", "desc": "Graph sketch — verify visually"}
  ]
}

Type reference:

TypeVerifiable?What it checkssolve✅Roots of expr=0 match expected listfactor✅Factored form matches expectedexpand✅Expanded form matches expectedeval✅expr evaluated at given values matches expectedzeros✅Zeros of expr match expected listmanual👁Flagged for human review — never fails automatically

Use manual for: graph sketches, sign charts, word problem setups, proofs.

If verification fails (exit 1): fix the LaTeX answer key and re-run. Do not compile until the answer key is correct.

5. Compile#

bash

SKILL_DIR="$(dirname "$0")"
bash "$SKILL_DIR/scripts/compile.sh" /tmp/ws_TOPIC_DATE.tex ~/Documents/Worksheets/
bash "$SKILL_DIR/scripts/compile.sh" /tmp/ak_TOPIC_DATE.tex ~/Documents/Worksheets/
bash "$SKILL_DIR/scripts/compile.sh" /tmp/ss_TOPIC_DATE.tex ~/Documents/Worksheets/

5. Deliver#

Send all three PDFs via the same channel the request came from:

• Telegram → message tool with filePath (copy to ~/.openclaw/media/outbound/ first)
• iMessage/SMS → imsg skill
• Email → gog skill (send all three as attachments)

Suggested send order: skills summary first (study guide), then worksheet, then answer key.

Printing: Do NOT print unless explicitly asked. If asked, print worksheet + skills summary (not answer key, unless requested). Use lpr -P <printer_name>.

Quality Checklist#

Before compiling, verify each problem:

• Mathematically correct (you checked the solution)
• Unambiguous problem statement
• Appropriate difficulty for the student's level
• Sufficient work space
• Diagrams/graphs/tables included where needed
• Problems vary across the set (not all the same sub-type)

File Naming#

text

ws_algebra2_factoring_2026-02-22.pdf   ← worksheet
ak_algebra2_factoring_2026-02-22.pdf   ← answer key
ss_algebra2_factoring_2026-02-22.pdf   ← skills summary / study guide

Prefix with student name when known: leo_ws_..., leo_ak_..., leo_ss_...

Troubleshooting#

ProblemFixtectonic not foundbrew install tectonicSlow first compileDownloading packages from CTAN — wait 30–60s, faster afterLaTeX error on line NCheck paired $...$, matching \begin{}/\end{}pgfplots not renderingEnsure \pgfplotsset{compat=1.18} is in preamblePDF not createdRead full tectonic output for the specific error