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docs/distribution_classes.md

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+# Balanced Student Section Distribution Plan
+
+## 1. Purpose
+
+This plan describes how already-promoted students will be distributed into sections for the next academic year.
+
+Promotion, deliberation, passing decisions, and student eligibility have already been completed and are outside the scope of this process.
+
+The distribution process must ensure that:
+
+* Students are divided as equally as possible among sections.
+* Each section contains a balanced number of students from every score range.
+* Section average scores are reasonably close.
+* User-defined minimum and maximum section sizes are respected.
+
+## 2. Required User Inputs
+
+Before starting the distribution, the user must enter:
+
+| Input                        | Description                                   |
+| ---------------------------- | --------------------------------------------- |
+| Number of Sections           | Number of sections to be created              |
+| Minimum Students per Section | Minimum permitted section size                |
+| Maximum Students per Section | Maximum permitted section size, if applicable |
+
+The student list must already include each student’s final score from the previous academic year.
+
+## 3. Score Range Classification
+
+Students must be classified using their previous-year final scores:
+
+| Score Group |  Score Range |
+| ----------- | -----------: |
+| Group 1     |       90–100 |
+| Group 2     |        80–89 |
+| Group 3     |        70–79 |
+| Group 4     | 69 and below |
+
+Each student must belong to exactly one score group.
+
+## 4. Validate the Number of Sections
+
+Let:
+
+* **N** = Total number of students to distribute.
+* **S** = Number of sections entered by the user.
+* **M** = Minimum number of students per section.
+* **X** = Maximum number of students per section.
+
+The requested section count is valid only when:
+
+**S × M ≤ N**
+
+When a maximum section size is used, the following condition must also be satisfied:
+
+**N ≤ S × X**
+
+Therefore, the complete validation rule is:
+
+**S × M ≤ N ≤ S × X**
+
+If no maximum section size is used, only the minimum condition applies.
+
+## 5. Validation Results
+
+The system should return one of the following results:
+
+### Insufficient Students
+
+The requested number of sections cannot be created because the total number of students is below the required minimum.
+
+### Capacity Exceeded
+
+The requested sections cannot contain all students without exceeding the maximum section size.
+
+### Valid Setup
+
+The entered number of sections and section-size limits are valid, and distribution may proceed.
+
+The system must not automatically change the number of sections entered by the user.
+
+## 6. Determine the Target Section Sizes
+
+Divide the total number of students by the number of sections.
+
+Each section should receive:
+
+**Base section size = N divided by S**
+
+Any remaining students should be assigned one at a time to different sections.
+
+The difference between the largest and smallest section should not exceed one student.
+
+Example:
+
+* Total students: 61
+* Number of sections: 2
+
+Result:
+
+* Section 1: 31 students
+* Section 2: 30 students
+
+## 7. Calculate the Score-Group Allocation
+
+For each score group:
+
+1. Count the number of students in that group.
+2. Divide the group total by the number of sections.
+3. Assign the base number to every section.
+4. Distribute any remaining students across different sections.
+
+For a score group containing **G** students:
+
+**Base allocation = G divided by S**
+
+**Remaining students = G modulo S**
+
+Example:
+
+* Students scoring 90–100: 11
+* Sections: 2
+
+Result:
+
+* Section 1: 6 students
+* Section 2: 5 students
+
+The difference between sections within the same score group should not exceed one student.
+
+## 8. Mathematical Limitation
+
+Exact equality is not always possible.
+
+For example, nine students from one score group cannot be divided equally between two sections. One section must receive five students and the other must receive four.
+
+Therefore, the required rule is:
+
+* Equal distribution when mathematically possible.
+* A maximum difference of one student when exact equality is impossible.
+
+## 9. Student Assignment Method
+
+Within each score group:
+
+1. Sort students from highest score to lowest score.
+2. Assign them using a snake-distribution method.
+3. Reverse the assignment direction after each round.
+
+For two sections, use:
+
+* First round: Section 1, Section 2
+* Second round: Section 2, Section 1
+* Third round: Section 1, Section 2
+
+For three sections, use:
+
+* First round: Section 1, Section 2, Section 3
+* Second round: Section 3, Section 2, Section 1
+
+This prevents one section from repeatedly receiving the highest-scoring students.
+
+## 10. Rotate Remaining Students
+
+Additional students caused by uneven division should not always be assigned to the first section.
+
+The section receiving the extra student should rotate between score groups.
+
+Example with two sections:
+
+| Score Range  | Section Receiving the Extra Student |
+| ------------ | ----------------------------------- |
+| 90–100       | Section 1                           |
+| 80–89        | Section 2                           |
+| 70–79        | Section 1                           |
+| 69 and below | Section 2                           |
+
+This helps maintain equal total section sizes.
+
+## 11. Balance the Average Scores
+
+After the initial distribution, calculate the average previous-year score for every section.
+
+The difference between the highest and lowest section averages should preferably not exceed one percentage point.
+
+If the difference is too large, students may be exchanged between sections when:
+
+* They belong to the same score range.
+* The exchange improves the average-score balance.
+* Section sizes remain valid.
+* Minimum and maximum limits are still satisfied.
+
+## 12. Additional Distribution Considerations
+
+After academic balancing, the distribution may also be reviewed for:
+
+* Gender balance, where applicable.
+* Special educational needs.
+* Language-support requirements.
+* Behavioral considerations.
+* Documented student-separation requirements.
+* Medical or accessibility needs.
+
+Any adjustment should preserve the score-range and section-size balance as much as possible.
+
+## 13. Final Distribution Summary
+
+The final result should include:
+
+| Section   | Total Students | 90–100 | 80–89 | 70–79 | 69 and Below | Average Score |
+| --------- | -------------: | -----: | ----: | ----: | -----------: | ------------: |
+| Section 1 |             30 |      5 |     8 |     9 |            8 |          78.4 |
+| Section 2 |             30 |      5 |     7 |     9 |            9 |          78.2 |
+
+## 14. Final Validation Checklist
+
+Before confirming the distribution, verify that:
+
+* The number of sections was entered by the user.
+* The minimum section size was entered by the user.
+* The maximum section size was entered, when applicable.
+* All students have been assigned exactly once.
+* No section is below the minimum size.
+* No section exceeds the maximum size.
+* Total section sizes differ by no more than one student.
+* Score-group counts differ by no more than one student.
+* Average scores are reasonably balanced.
+* No student is missing or duplicated.
+
+## 15. Final Rule
+
+The system distributes students only after promotion and deliberation are complete.
+
+The user determines the number of sections and the section-size limits.
+
+The system validates those values and creates the most balanced possible distribution based on:
+
+* Total student count.
+* Score-range counts.
+* Section-size limits.
+* Average section scores.