The following 15 Sample Student Responses represent a range of score points.

Score for Sample Student Response #1: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy. The student clearly recognizes that he/she could prove ΔABD ΔCBD by ASA in order to prove BD bisects AC. All the steps are in a logical sequence. However, the student has made several small errors. The student has neglected to provide the statement ABD CBD, and the justification "definition of angle bisector." The justification for BAD BCD could be more fully developed by providing "the base angles of an isosceles triangle are congruent" rather than "in an isosceles triangle the angles across are congruent." The justification for the final step "BD bisects AC" should be "definition of segment bisector," not "definition of angle bisector." Because there are several small errors, the response demonstrates a clear rather than complete understanding and analysis of the problem. Compare to Anchor Paper #5.

Score for Sample Student Response #2: Rubric Score 1

Annotation: The response indicates no 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 and BC are the same length"). The statement "BD is directly in the center and bisects AC" can be proven to be true, but it is only an assumption made by the student unless justification is provided. The statement is not part of the given information, nor are there steps to prove that it is a correct statement. There is no justification present for the student's statement. The response demonstrates a minimal understanding and analysis of the problem. Compare to Anchor Paper #2.

Score for Sample Student Response #3: Rubric Score 4

Annotation: This response indicates application of a reasonable strategy. The student clearly recognizes the theorem that will prove BD bisects AC. "In an isosceles triangle, the bisector of the angle opposite the unequal side is the perpendicular bisector of that side" provides fully developed justification to support the solution. The response demonstrates a complete understanding and analysis of the problem.

Score for Sample Student Response #4: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The student states the conceptual idea that BD is the perpendicular bisector, but has not stated a theorem. The justification is incomplete and not well developed. "BAD BCD so that means there angles are equal making BD bisect it in half. So it would also split AC in half which is what a bisector does." The angles that should have been cited are ABD and CBD, not BAD and BCD. The response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #3.

Score for Sample Student Response #5: Rubric Score 1

Annotation: The response indicates no application of a reasonable strategy to prove BD bisects AC. The student has correctly identified from the given information which two angles ("BAD BCD") of the isosceles triangle are congruent. Two statements "BDC BDA" and "ADDC" can be proven to be true, but are only assumptions without justification made by the student. 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. Compare to Anchor Paper #1.

Score for Sample Student Response #6: 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. After stating the given information, the student attempts to prove congruent parts for the theorem HL. "ADB and CDB is 90°" will prove to be true, but is not justified by "Def. bisector". The student never states ΔABD ΔCBD. This response demonstrates evidence of a reasonable strategy because the student has given the statements and justification for two congruent parts of the triangles (AB BC, BD BD) that if combined with the information ΔABD ΔCBD, would have had the correct parts to prove the triangles congruent by the theorem SAS. The response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #4.

Score for Sample Student Response #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 ΔABD ΔCBD by ASA in order to prove BD bisects AC. The steps are in a logical sequence. The justification for each step is fully developed and supports the solution. The response demonstrates a complete understanding and analysis of the problem. Compare to Anchor Paper #8.

Score for Sample Student Response #8: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy. The student clearly recognizes that he/she could prove ΔABD ΔCBD by ASA in order to prove BD bisects AC. All the steps are in a logical sequence. However, the student has made several small errors. The student has neglected to provide the statement ABD CBD and its justification, "definition of angle bisector." The justification for A C should be "the base angles of an isosceles triangle are congruent," rather than merely "isos. Δ ." Because there are several small errors, the response demonstrates a clear, rather than complete, understanding and analysis of the problem. Compare to Anchor Paper #5.

Score for Sample Student Response #9: Rubric Score 2

Annotation: This response demonstrates an incomplete application of a reasonable strategy. The student recognizes that he/she must prove ΔABD ΔCBD in order to prove ADCD. It is unclear from his penmanship which congruence theorem he is using. The student's statement that "ADB CDB because it is a 90° ADB " is true, but it is not part of the given information and these angles are not appropriate angles to use. The other two parts necessary to prove the triangles congruent are not identified. The student recognizes that once the triangles are proven congruent, he can then state that "because all corresponding parts of a congrunt triangle are equal AD = DC. This means BD bisects AC". He/she does not give the justification for this last statement. Overall, this response demonstrates a conceptual understanding and analysis of the problem.

Score for Sample Student Response #10: 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 SAS in order to prove BD bisects AC. All the steps are in a logical sequence. The justification (CPCTC) is missing for the statement "AD and DC must also be congruent," but overall, the response demonstrates a complete understanding and analysis of the problem. Compare to Anchor Paper #7.

Score for Sample Student Response #11: Rubric Score 1

Annotation: The response indicates no application of a reasonable strategy to prove BD bisects AC. The student has correctly identified which two sides of the isosceles triangle are congruent from the diagram, but he/she tries to use that information to conclude that ADCD. The student assumes ΔABD ΔCBD to conclude "hence bisector BD." There is no justification present in the response. The response demonstrates a minimal understanding and analysis of the problem for correctly reading the congruent sides of the triangle from the diagram and showing statements that could be proven. Compare to Anchor Paper #1.

Score for Sample Student Response #12: Rubric Score 1

Annotation: This response demonstrates little application of a reasonable strategy. The student recognizes that proving the triangles congruent is a correct strategy, but this response has no supporting steps or justification. The response demonstrates minimal understanding and analysis of the problem.

Score for Sample Student Response #13: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy. The student clearly recognizes that he/she could prove ΔABD ΔCBD by SAS in order to prove BD bisects AC. All the steps are in a logical sequence. However, the student has neglected to state the given information of "BD is the angle bisector of ABC," a minor error. More significant is the incorrect justification "angle addition postulate" instead of "definition of angle bisector" for the statement ADB CDB. Because there are several small errors, the response demonstrates a clear, rather than complete, understanding and analysis of the problem. Compare to Anchor Paper #5.

Score for Sample Student Response #14: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The student has conveyed the conceptual idea that the altitude to the base of an isosceles triangle bisects both the vertex angle and the opposite segment. The student has made an assumption that BD forms two right angles with AC, which will prove to be true but there are no steps to prove that it is a correct statement. However, the student does recognize that "... AB and BC are congruent to each other. When you have a line that forms two congruent angles, as does BD, and the two other sides of the triangle are congruent, this means you have a perpendicular bisector. Therefore BD bisects line AC." The response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #3.

Score for Sample Student Response #15: 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 SAS in order to prove BD bisects AC. All the steps are in a logical sequence. The justification for one statement "the shared side BD" is not fully developed, with the student providing "it is congruent to itself" rather than citing the reflexive property. Overall, the response demonstrates a complete understanding and analysis of the problem.

Anchor Papers used in scoring