areebuzair/psm500k

Primary School Maths-500k Dataset

This repository contains a synthetic dataset of arithmetic expressions designed for fifth-grade level practice. The dataset is formatted in JSON and includes both the step-by-step intermediate results and the final rounded answer.

---

Dataset Overview

• Purpose: Provide a collection of basic arithmetic problems (addition, subtraction, multiplication, and division) that any fifth grader could solve.
• Data Type: JSON file containing a list of problem instances.
• Split: 90% training, 10% testing.

---

Data Format

Each entry in the JSON list has the following structure:

{
  "question": "<expression>",
  "steps": [
    "<intermediate step 1>",
    "<intermediate step 2>",
    ...
  ],
  "answer": <float or null>
}

• question: A string containing the arithmetic expression, using Python syntax. Only the operators +, -, *, and / are used. Nested operations follow standard precedence rules, and chained division x/y/z is parsed as (x/y)/z.
• steps: A list of strings capturing each major intermediate calculation (up to five decimal places). If a division by zero occurs at any step, the final step records an error message (e.g., "Division by Zero is not possible").
• answer: The final result rounded to two decimal places, or null if the expression could not be evaluated (e.g., due to division by zero).

---

Numerical Precision

• Intermediate results are computed and recorded with five decimal digits of precision.
• Final answers are rounded to two decimal digits.
• All absolute answers satisfy 0.005 < |answer| < 100000.

---

Value Range

• All numeric values in the questions range from 1 to 100.
• The final answer for each valid expression lies outside the interval [-0.005, 0.005] and within (-100000, 100000).

---

Train/Test Split

• The dataset is split into 90% training and 10% testing subsets.

• Filenames:

  • train.json — 90% of the data.
  • test.json — 10% of the data.

---

Examples

Valid expression:

{
  "question": "87*38",
  "steps": ["3306"],
  "answer": 3306
}

Expression with step-by-step precision:

{
  "question": "(61/48/90)/((17-38)+((83.34-14.71*41.33)-(10.36*1.72*36.11)-(56*53*98))+(23.72*49.97/77.8))+(43.88*30.28)",
  "steps": [
    "0.01412/(-21+(-524.6243-643.45131-290864)+15.23507)+1328.6864",
    "0.01412/(-21+-292032.07561+15.23507)+1328.6864",
    "0.01412/-292037.84054+1328.6864",
    "1328.6864"
  ],
  "answer": 1328.69
}

Division by zero:

{
  "question": "(36-27)/(98-98)",
  "steps": ["9/0" , "Division by Zero is not possible"],
  "answer": null
}

---

Licensing and Attribution

This dataset is released under the MIT license.

---