Assess Student #1’s work according to the following category:
Problem Solving
Reasoning & Proof
Communication
Connections
Representation
Overall Achievement Level
Novice

No strategy is chosen, or a strategy is chosen that will not lead to a solution.

Little or no evidence of engagement in the task present.

Apprentice

A partially correct strategy is chosen, or a correct strategy for only solving part of the task is chosen.

Evidence of drawing on some relevant previous knowledge is present, showing some relevant engagement in the task.

Practitioner

A correct strategy is chosen based on the mathematical situation in the task.

Planning or monitoring of strategy is evident.

Evidence of solidifying prior knowledge and applying it to the problem-solving situation is present.

Note: The Practitioner must achieve a correct answer.

Expert

An efficient strategy is chosen and progress towards a solution is evaluated.

Adjustments in strategy, if necessary, are made along the way, and/or alternative strategies are considered.

Evidence of analyzing the situation in mathematical terms and extending prior knowledge is present.

Note: The Expert must achieve a correct answer.

Novice

Arguments are made with no mathematical basis.

No correct reasoning nor justification for reasoning is present.

Apprentice

Arguments are made with some mathematical basis.

Some correct reasoning or justification for reasoning is present.

Practitioner

Arguments are constructed with adequate mathematical basis.

A systematic approach and/or justification of correct reasoning is present.

Expert

Deductive arguments are used to justify decisions and may result in formal proofs.

Evidence is used to justify and support decisions made and conclusions reached.

Novice

No awareness of audience or purpose is communicated.

No formal mathematical terms or symbolic notations are evident.

Apprentice

Some awareness of audience or purpose is communicated.

Some communication of an approach is evident through verbal/written accounts and explanations.

An attempt is made to use formal math language. One formal math term or symbolic notation is evident.

Practitioner

A sense of audience or purpose is communicated.

Communication of an approach is evident through a methodical, organized, coherent, sequenced and labeled response.

Formal math language is used to share and clarify ideas. At least two formal math terms or symbolic notations are evident, in any combination.

Expert

A sense of audience and purpose is communicated.

Communication of an approach is evident through a methodical, organize, coherent, sequenced and labeled response. Communication of an argument is supported by mathematical properties.

Formal math language and symbolic notation is used to consolidate math thinking and to communicate ideas. At least one of the two formal math terms or symbolic notations is beyond grade level.

Novice

No connections are made or connections are mathematically or contextually irrelevant.

Apprentice

A mathematical connection is attempted but is partially incorrect or lacks contextual relevance.

Practitioner

A mathematical connection is made. Proper contexts are identified that link both the mathematics and the situation in the task.

Some examples may include one or more of the following:

clarification of the mathematical or situational context of the task
exploration of mathematical phenomenon in the context of the broader topic in which the task is situated
noting patterns, structures and regularities

Expert

Mathematical connections are used to extend the solution to other mathematics or to a deeper understanding of the mathematics in the task.

Some examples may include one or more of the following:

testing and accepting or rejecting of a hypothesis or conjecture
explanation of phenomenon
generalizing and extending the solution to other cases