CATEGORY

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Mathematical Concepts

Explanation shows complete understanding of the mathematical concepts used to solve the problem(s).

Explanation shows substantial understanding of the mathematical concepts used to solve the problem(s).

Explanation shows some understanding of the mathematical concepts needed to solve the problem(s).

Explanation shows very limited understanding of the underlying concepts needed to solve the problem(s) OR is not written.

Mathematical Reasoning

Uses complex and refined mathematical reasoning.

Uses effective mathematical reasoning

Some evidence of mathematical reasoning.

Little evidence of mathematical reasoning.

Use of Manipulatives

Student always listens and follows directions and only uses manipulatives as instructed.

Student typically listens and follows directions and uses manipulatives as instructed most of the time.

Student sometimes listens and follows directions and uses manipulatives appropriately when reminded.

Student rarely listens and often "plays" with the manipulatives instead of using them as instructed.

Completion

All problems are completed.

All but one of the problems are completed.

All but two of the problems are completed.

Several of the problems are not completed.

Mathematical Errors

90-100% of the steps and solutions have no mathematical errors.

Almost all (85-89%) of the steps and solutions have no mathematical errors.

Most (75-84%) of the steps and solutions have no mathematical errors.

More than 75% of the steps and solutions have mathematical errors.

Strategy/Procedures

Typically, uses an efficient and effective strategy to solve the problem(s).

Typically, uses an effective strategy to solve the problem(s).

Sometimes uses an effective strategy to solve problems, but does not do it consistently.

Rarely uses an effective strategy to solve problems.