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Criteria	Expert	Practioner	apprentice	novice
Mathematical Concepts	Explanation shows complete understanding of the mathematical concepts used to solve the problem.	Explanation shows substantial understanding of the mathematical concepts used to solve the problem.	Explanation shows some understanding of the mathematical concepts needed to solve the problem.	Explanation shows very limited understanding of the underlying concepts needed to solve the problem.
Mathematical Reasoning and creativity	Uses complex and refined mathematical reasoning. The finished products consistently show creativity through uniqueness, efficiency, or elaboration.	Uses effective mathematical reasoning. The finished products show frequent creativity through uniqueness, efficiency, or elaboration.	Some evidence of mathematical reasoning. The finished products sometimes show creativity through uniqueness, efficiency, or elaboration.	Little evidence of mathematical reasoning. The finished products rarely show creativity through uniqueness, efficiency, or elaboration.
Strategy/ Procedures	Typically, uses an efficient and effective strategy to solve the problem.	Typically, uses an effective strategy to solve the problem.	Sometimes uses an effective strategy to solve problems, but does not do it consistently.	Rarely uses an effective strategy was used to solve problems.
Mathematical Terminology and Notation	Correct terminology and notation are always used, making it easy to understand what was done.	Correct terminology and notation are usually used, making it fairly easy to understand what was done.	Correct terminology and notation are used, but it is sometimes not easy to understand what was done.	There is little use or a lot of inappropriate use, of terminology and notation.
PROGRESSION OF PRODUCTION	Student was engaged in work and listened to suggestions of others throughout the process. Student was resourceful and exhausted his/her resources available before referring to the teacher.	Student was engaged in the work, but had a little trouble listening to suggestions of others throughout the process. Student was frequently resourceful, but did not refer to one or two possible choices before referring to the teacher.	Student needed prompting to stay on-task and had much trouble listening to suggestions of others throughout the process. Student needed prompting to use available resources.	Student needed constant prompting to stay on task and did not accept the suggestions from others. Student needed constant prompting to use available resources.
Checking for accuracy	Two classmates have checked the work with the checklist and all appropriate corrections, detentions, or additions were made.	One classmate has checked the work with the checklist and all appropriate corrections, deletions, or additions were made.	One classmate has checked the work with the checklist, but some corrections, deletions, or additions were not made.	Work was not checked by a classmate OR no corrections, deletions, or additions were made based on feedback.