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: This response demonstrates a minimal understanding and analysis of the problem. Although the student attempts the proof, there is an incomplete strategy to prove similarity. The first step "BC=1200 ft/CD=40 ft/DE=20 ft" is unnecessary for the proof, a minor error. "BD" with the justification "right angles" is a correct step towards proving similarity because two pairs of angles need to be congruent in order to establish similarity, AA (angle-angle) theorem. A second pair of angles "CC" has the correct justification "vertical angles," but, since there is more than one angle at the point C, the angles are improperly named. "ABCEDC" is a true statement; however, the justification "SAS" (side-angle-side) is incorrect. The last statement "ΔABCΔEDC" by reason of "CPCTC" (corresponding parts of congruent triangles are congruent) is incorrect and reveals some confusion between similarity and congruence. No attempt is made to answer the second part of the problem. The student demonstrates little application of a reasonable strategy to solve the problem.

Score for Anchor Paper #2: Rubric Score 1

Annotation: This response demonstrates a minimal understanding and analysis of the problem. The student completely ignores the similarity proof, but does provide an answer for the second part of the problem. The correct cost of $4800 is clearly identified; however, there is little explanation of how the student derives this answer. "There would be 600 feet on either side of the bridge so I multiplied 600 by two and multiplied that by four" does not reveal the strategy employed to calculate the correct bridge length. There is little application of a reasonable strategy to solve the problem.

Score for Anchor Paper #3: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The student neglects the similarity proof altogether, but correctly answers the second part of the problem. Assuming similarity, the student applies an appropriate strategy, correctly setting up a ratio to solve for the length of the bridge. With the correct length of 600 feet, the student then calculates the correct cost ($4800) of railings for both sides of the bridge. Ignoring one part of the problem, but providing a full explanation of a correct strategy for the other part of the problem, indicates an incomplete application of a correct strategy to solve the problem.

Score for Anchor Paper #4: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The student uses an appropriate strategy (Angle-Angle-Angle) to prove similar triangles. The student correctly states and justifies BCADCE. The student does not state or justify ABCEDC by reason of "all right angles congruent." The student attempts to prove EA with the incorrect justification of "45, 45, 90 theorem," assuming a 45–45–90 triangle and naming a non-existent theorem. Although the student correctly calculates the length of both sides of the bridge, an incorrect cost ($2400) to put railings on both sides of the bridge is provided. The student also fails to provide a full explanation of an appropriate strategy to calculate the length of the bridge. The response indicates an incomplete application of a reasonable strategy to solve the problem.

Score for Anchor Paper #5: Rubric Score 3

Annotation: This response demonstrates a clear understanding and analysis of the problem. The student clearly conveys the understanding of proving two pairs of congruent angles to prove similar triangles. One pair of angles is correctly identified as vertical angles. However, the correct reason that ACB is congruent to ECD is the theorem, vertical angles are congruent. The correct angle-angle (AA) similarity theorem is cited. However, the student does not state that the given right triangles are congruent (the step needed to prove the second pair of congruent angles). The student provides unnecessary information (BC = 1200, CD = 40, DE = 20) in the similarity proof. The student sets up a proportion to calculate the correct bridge length and calculates the correct cost for railings on both sides of the bridge. Lacking a complete proof demonstrates a clear rather than a complete strategy for the entire problem.

Score for Anchor Paper #6: Rubric Score 3

Annotation: This response demonstrates a clear understanding and analysis of the problem. The student presents a proof with the steps and justification necessary to prove similarity by the AA (angle-angle) theorem. However, the step BD should have the justification of "all right angles are congruent." The information "BC=1200ft/CD=40ft/DE=20ft" is unnecessary for the proof. The correct cost of $4800 is clearly identified, but the response lacks a full explanation. "It is $4 a ft for railing and we need 1200 ft of it. So, 1200 • 4 = 4800" lacks explanation of the strategy employed to calculate the length of the bridge.

Score for Anchor Paper #7: Rubric Score 4

Annotation: This response demonstrates a complete understanding and analysis of the problem. The student clearly presents a logical proof, using the AA (angle-angle) theorem, to prove similarity. All the steps and justification are correct. The student uses an appropriate strategy of proportion to solve for the length of the bridge. Arriving at the correct length of 600 feet, the student calculates the correct $4800 cost to put railings on both sides of the bridge. The work provides a complete explanation for the strategy employed.

Score for Anchor Paper #8: Rubric Score 4

Annotation: This response demonstrates a complete understanding and analysis of the problem. The student clearly presents a logical proof, proving similarity by AAA (angle-angle-angle). The student's justification that ABCCDE because they are right angles rather than "all right angles are congruent" is a minor error. The steps and justification for the proof are correct. The student explains the appropriate strategy of finding the scale factor to solve for the length of the bridge. Calculating the correct 600-ft bridge length, the student arrives at the correct cost of $4800.

Additional Scored Student Responses