Proof scoring rubric

This page explains how FullProof scores students' solutions.

• A question's score starts at 100 and goes down for each of the mistakes listed below. In a question with several items, the deduction in each item is capped at that item's share of the question's score.
• How many points come off depends on the kind of mistake and on the weight of the step in the proof. A missing step based on a significant theorem costs more than a missing step based on a definition.
• Some questions are checked more strictly: a missing step based on a basic theorem costs 30 points instead of 20, a missing transitivity or algebra step costs 10 instead of 5, and a missing condition for congruence or similarity costs at least 10 points instead of 5.

Wrong statements

Mistake	Points
Wrong statement*	20
Statement that needs correcting, for example congruent instead of similar	10
Statement that needs a small correction, for example a missing degree sign	2

* For a wrong statement, the system usually ignores the wrong row and goes on checking the next rows. Statements based on the wrong one count as unsupported.

Deductions for statement corrections total at most 20 points. A wrong vertex order in congruence or similarity costs no points, but the system points it out.

Missing statements and reasons

Level *	Missing statement	Wrong/missing reason **	Close theorem and/or missing reason with correct supporting statements **
Significant theorem	30	10	5
Basic theorem	20	10	5
Significant definition	10	5	2
Transitivity and algebra	5	2 (wrong only)	2 (wrong only)
Basic definition	2	5 (wrong only)	2 (wrong only)
Trivial	0	2 (wrong only)	2 (wrong only)

* The theorems at each level are listed at the end of the page. ** Deductions for missing or wrong reasons total at most 25 points.

Incorrect use of a theorem

Theorems	Required steps	Points
Congruence theorems	3 conditions for congruence	at least 5 points per missing step, depending on the missing step's reason
Similarity theorems	2 conditions for similarity	at least 5 points per missing step, depending on the missing step's reason
Proportion theorems: Thales' theorem, the angle bisector theorem, the ratio of corresponding sides in similar triangles	writing the proportion explicitly	5

Mistakes in the proof's structure

Mistake	Points
Redundant step in the proof***	2 (max. 10 in total)
A statement based on what needs to be proved (on top of the usual deduction for missing steps)	10

*** The system doesn't look for redundant steps in a proof that has a wrong statement, or once the proof has already lost more than 60 points.

Levels of reasons, definitions and theorems

Level	Reasons
Reasons by a significant theorem	Every theorem except those listed below, including area formulas, the sum of the angles around a point, and the converse parallel-line theorems (lines parallel by alternate/corresponding/co-interior angles)
Reason by a basic theorem	In a triangle, equal sides face equal angles, and vice versa · adjacent/vertical angles · the angle sum in a triangle/quadrilateral · corresponding/alternate/co-interior angles between parallel lines
Reasons by a significant definition	Equilateral triangle · parallelogram / rhombus / rectangle / square · circle · midsegment
Basic definition	Median · adding/subtracting segments/angles/arcs
Transitivity and algebra	Transitivity · algebra · adding/subtracting areas
Trivial reasons	Definitions of: altitude · angle bisector · perimeter · midpoint · perpendicular lines · perpendicular bisector · parallel lines · isosceles triangle · right triangle · kite · trapezoid · isosceles trapezoid · right trapezoid
Close theorems	Swapping alternate/corresponding angles in the parallel-line theorems · swapping Thales and extended Thales · swaps within the parallelogram family - for example using the definition of a parallelogram instead of the theorem "in a rhombus, opposite sides are parallel"