The following 8 Anchor Papers represent a range of score points and are used in conjunction with the rubrics to assess student responses.

Score for Anchor Paper #1: Rubric Score 1

Annotation: The response indicates little application of a reasonable strategy to prove BD bisects AC. The student has correctly identified from the diagram which two sides of the isosceles triangle are congruent: "AB=BC." Two statements "AD=DC" and "AC BD" can be proven, but the student does not justify them. The statements are neither part of the given information, nor are there steps to prove that they are correct statements. There is no justification present for any of the student's statements. The response demonstrates a minimal understanding and analysis of the problem.

Score for Anchor Paper #2: Rubric Score 1

Annotation: The response indicates no application of a reasonable strategy to prove BD bisects AC. The student has changed the given information of an isosceles triangle to "ABC is an equilateral triangle." The statement "D is the midpoint of AC" can be proven to be true, but it is an assumption made by the student without its justification. The statement is not part of the given information, nor are there steps to prove that it is a correct statement. The student marked angles A and C congruent, as well as BD congruent to itself. There is no justification present for any of the student's statements or congruent marks. The response demonstrates a minimal understanding and analysis of the problem.

Score for Anchor Paper #3: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The student has conveyed the conceptual idea that the bisector of the vertex angle of an isosceles triangle is also a median, but has not stated a theorem. The justification is incomplete and not well developed ("AB and CB are congruent, meaning AC is equally distanced from B on its endpoints…BD must be the same distance from AC's endpoints, because BD bisects B"). The response demonstrates a conceptual understanding and analysis of the problem.

Score for Anchor Paper #4: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The student recognizes that he/she could prove ΔABD ΔCBD in order to prove BD bisects AC. However, the student has committed several errors in his/her proof. The student appears to rely on, but has neglected to include, the statement "ABCB" and the justification for that statement (given). (It is a minor error to neglect stating the given information in the proof.) The student cites a non-existent theorem, SSA, to prove ΔABD ΔCBD. Another missing step in analysis is the statement ADCD and the justification, CPCTC (Corresponding parts of congruent triangles are congruent.) This response demonstrates evidence of a reasonable strategy because the student has given the statements and justification for two congruent parts of a triangle (A C, BD BD) that, if combined with the information ABDCBD, would have had the correct parts to prove the triangles congruent by a legitimate theorem of SAS. The response demonstrates a conceptual understanding and analysis of the problem.

Score for Anchor Paper #5: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy. The student clearly recognizes that he/she could prove ΔABD ΔCBD in order to prove BD bisects AC. All the steps are in a logical sequence. However, there are errors in the justification. A small error occurs when the student provides "given" as the justification for ABDCBD, when he/she should have more correctly stated "definition of angle bisector" and should have included BD bisects ABC in the Given. A more significant error is the incorrect theorem cited to justify ΔABD ΔCBD. The student should have stated SAS instead of ASA. The response demonstrates a clear understanding and analysis of the problem.

Score for Anchor Paper #6: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy. The student clearly recognizes that he/she could prove ΔABD ΔCBD in order to prove BD bisects AC. All the steps are in a logical sequence. However, the student neglects to state BD bisects ABC in his first step, and he/she does not include ΔABD ΔCBD with the correct SAS theorem as justification. The response demonstrates a clear understanding and analysis of the problem.

Score for Anchor Paper #7: Rubric Score 4

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The student clearly recognizes and proves that ΔABD ΔCBD by SAS in order to prove BD bisects AC. All the steps are in a logical sequence. The response demonstrates a complete understanding and analysis of the problem.

Score for Anchor Paper #8: Rubric Score 4

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The student clearly recognizes that he/she could prove ΔABD ΔCBD by ASA in order to prove BD bisects AC. The steps are in a logical sequence. The student has made one minor error of neglecting to state ABCB, which was given in the diagram. (It is a minor error to neglect stating the given information in the proof.) Overall, the response demonstrates a complete understanding and analysis of the problem.

Additional Scored Student Responses