## Mathematics Brief Constructed Response

### Level 3

The response indicates **application** of a reasonable strategy that leads to a correct solution in the context of the problem. The **representations** are essentially correct. The **explanation** and/or **justification** is logically sound, clearly presented, fully developed, supports the solution, and does not contain significant mathematical errors. The response demonstrates a complete understanding and **analysis** of the problem.

### Level 2

The response indicates **application** of a reasonable strategy that may be incomplete or undeveloped. It may or may not lead to a correct solution. The **representations** are fundamentally correct. The **explanation** and/or **justification** supports the solution and is plausible, although it may not be well developed or complete. The response demonstrates a conceptual understanding and **analysis** of the problem.

### Level 1

The response indicates little or no attempt to **apply** a reasonable strategy or applies an inappropriate strategy. It may or may not have the correct answer. The **representations** are incomplete or missing. The **explanation** and/or **justification** reveals serious flaws in reasoning. The **explanation** and/or **justification** may be incomplete or missing. The response demonstrates a minimal understanding and **analysis** of the problem.

### Level 0

The response is completely incorrect or irrelevant. There may be no response, or the response may state, “I don't know.”

## Mathematics Extended Constructed Response

### Level 4

The response indicates **application** of a reasonable strategy that leads to a correct solution in the context of the problem. The **representations** are correct. The **explanation** and/or **justification** is logically sound, clearly presented, fully developed, supports the solution, and does not contain significant mathematical errors. The response demonstrates a complete understanding and **analysis** of the problem.

### Level 3

The response indicates **application** of a reasonable strategy that may or may not lead to a correct solution. The **representations** are essentially correct. The **explanation** and/or **justification** is generally well developed, feasible, and supports the solution. The response demonstrates a clear understanding and **analysis** of the problem.

### Level 2

The response indicates an incomplete **application** of a reasonable strategy that may or may not lead to a correct solution. The **representations** are fundamentally correct. The **explanation** and/or **justification** supports the solution and is plausible, although it may not be well developed or complete. The response demonstrates a conceptual understanding and **analysis** of the problem.

### Level 1

The response indicates little or no **application** of a reasonable strategy. It may or may not have the correct answer. The **representations** are incomplete or missing. The **explanation** and/or **justification** reveals serious flaws in reasoning. The explanation and/or justification may be incomplete or missing. The response demonstrates a minimal understanding and **analysis** of the problem.

### Level 0

The response is completely incorrect or irrelevant. There may be no response, or the response may state, “I don't know.”

**Explanation** refers to the student using the language of mathematics to communicate how the student arrived at the solution.

**Justification** refers to the student using mathematical principles to support the reasoning used to solve the problem or to demonstrate that the solution is correct. This could include the appropriate definitions, postulates and theorems.

**Essentially correct representations** may contain a few minor errors such as missing labels, reversed axes, or scales that are not uniform.

**Fundamentally correct representations** may contain several minor errors such as missing labels, reversed axes, or scales that are not uniform.

Last Revised 8/16/00