math-word-problems-graded

1,300 synthetic, graded math word problems spanning elementary through college level, with step-by-step solutions and structured metadata. Built for training and benchmarking mathematical reasoning in language models.

Dataset Summary

Split	Examples
train	1,040
validation	130
test	130
Total	1,300

Schema

Field	Type	Description
id	string	Unique MD5-based identifier (mwp-xxxxxxxxxx)
problem	string	The word problem text in natural language
solution	string	Step-by-step solution showing work
answer	string	Final answer (number, expression, or labeled value)
difficulty	string	easy / medium / hard / expert
grade_level	string	elementary / middle_school / high_school / college
topic	string	arithmetic / algebra / geometry / probability / statistics / calculus
domain	string	everyday / finance / science / general

Distribution

By Difficulty

Difficulty	Count	%
easy	455	35.0%
medium	623	47.9%
hard	178	13.7%
expert	44	3.4%

By Grade Level

Grade Level	Count	%
elementary	387	29.8%
middle_school	644	49.5%
high_school	225	17.3%
college	44	3.4%

By Topic

Topic	Count	%
algebra	523	40.2%
arithmetic	357	27.5%
geometry	204	15.7%
statistics	88	6.8%
probability	84	6.5%
calculus	44	3.4%

By Domain

Domain	Count	%
everyday	793	61.0%
finance	233	17.9%
science	129	9.9%
general	145	11.2%

Sample Examples

Easy — Arithmetic — Elementary

{
  "problem": "Alice has 43 apples and Bob has 67 apples. How many apples do they have together?",
  "solution": "Alice has 43 apples. Bob has 67 apples.\nTotal = 43 + 67 = 110 apples.",
  "answer": "110",
  "difficulty": "easy",
  "grade_level": "elementary",
  "topic": "arithmetic",
  "domain": "everyday"
}

Medium — Algebra — Middle School

{
  "problem": "A store buys gadgets at $120 each and sells them at $180 each. If they sell 40 units, what is their total profit?",
  "solution": "Revenue = 40 × $180 = $7200.\nTotal cost = 40 × $120 = $4800.\nProfit = $7200 - $4800 = $2400.",
  "answer": "$2400",
  "difficulty": "medium",
  "grade_level": "middle_school",
  "topic": "algebra",
  "domain": "finance"
}

Hard — Algebra — High School

{
  "problem": "Solve the system:\n  3x + 2y = 17\n  2x + 5y = 28",
  "solution": "Multiply eq1 by 5 and eq2 by 2:\n  15x + 10y = 85\n  4x + 10y = 56\nSubtract: 11x = 29\nx = ...",
  "answer": "x = 3, y = 4",
  "difficulty": "hard",
  "grade_level": "high_school",
  "topic": "algebra",
  "domain": "general"
}

Expert — Calculus — College

{
  "problem": "A spherical balloon's radius increases at 2 cm/s. How fast is the volume increasing when the radius is 10 cm?",
  "solution": "V = (4/3)πr³\ndV/dt = 4πr² × dr/dt = 4π × 100 × 2 ≈ 2513.27 cm³/s.",
  "answer": "≈ 2513.27 cm³/s",
  "difficulty": "expert",
  "grade_level": "college",
  "topic": "calculus",
  "domain": "science"
}

Generation Methodology

All problems are procedurally generated using parametric templates with randomized values:

• Arithmetic: addition, subtraction, multiplication, division, money/change, fractions, time
• Algebra: linear equations, age problems, rate/distance, mixture, work rate, percent, simple/compound interest, systems of equations, sequences, exponential/logarithm
• Geometry: area (rectangle, triangle, circle), circumference, volume (box, cylinder), Pythagorean theorem, surface area, perimeter
• Probability: coin/dice, marbles, compound events, combinatorics (permutations, combinations)
• Statistics: mean, median, standard deviation
• Calculus: derivatives, indefinite integrals, optimization, limits, related rates

Values are randomly seeded (seed=42) to ensure reproducibility. Deduplication applied via MD5 hash of problem + answer.

Intended Uses

• Fine-tuning language models for math reasoning (GSM8K-style)
• Benchmarking multi-step arithmetic and algebraic reasoning
• Curriculum learning experiments across difficulty grades
• Educational question generation research
• Few-shot prompting with graded difficulty levels

Limitations

• Problems are template-generated; real-world exams may feature more creative phrasing
• Calculus and college-level coverage is intentionally limited (44 examples); supplement with dedicated datasets for advanced use
• Domain diversity is weighted toward "everyday" scenarios

License

Apache 2.0 — free for commercial and research use with attribution.

Citation

@dataset{salutefaceaac2026mathwp,
  title        = {math-word-problems-graded},
  author       = {SalutefaceAAC},
  year         = {2026},
  publisher    = {Hugging Face},
  url          = {https://huggingface.co/datasets/SalutefaceAAC/math-word-problems-graded},
  license      = {Apache-2.0}
}