The following 9 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 shows little application of a reasonable strategy. The midpoint of AB is found by incorrectly substituting measurement for construction. The student uses that measurement of half of AB to form the other side of isosceles ΔABC, whereas the question required an equilateral triangle with all sides congruent to AB. The student constructs an isosceles right triangle, but does inscribe that triangle in a circle. Correct representations in the response are missing, except for a circle circumscribing the isosceles triangle. The explanation reveals serious flaws in reasoning and is based on measurement rather than construction. This response demonstrates a minimal understanding and analysis of the problem.

Score for Anchor Paper #2: Rubric Score 1

Annotation: There is no application of a reasonable strategy in this response. The student states that he/she "measured the base" and "drew the sides the same length as the whole base," which indicates measurement was used to draw the triangle. Although the response later indicates "I made the circle by using a compass," the circle's irregularity indicates it was hand-drawn. These two explanations reveal serious flaws in reasoning because measurement is used instead of construction. The correct representations are missing. Except for the faulty hand-drawn circle, the only representation is the triangle that was not constructed, but created by measurement. This response demonstrates minimal understanding and analysis of the problem because the student uses measurement throughout the response.

Score for Anchor Paper #3: Rubric Score 1

Annotation: This response provides a good explanation for how to draw an equilateral triangle with a given side AB using measurement; however, this strategy is inappropriate because the problem requires construction, not measurement. The explanation and representation are flawed because of the substitution of measurement for construction. There is no evidence of a construction of a circle circumscribing ΔABC, nor is there any construction for finding the center of the circle. There are some faint marks indicating that parts of a hand-drawn circle might have been attempted, but there is no explanation in words or arc marks. This response indicates minimal understanding and analysis of the problem.

Score for Anchor Paper #4: Rubric Score 2

Annotation: This student states, "I first measured the length of AB. Next I drew a perpendicular line through the center of AB." The response continues with other indications of measurement being substituted for the appropriate required strategy of construction. There is no evidence of arc marks to show construction was used, nor is there any explanation for the possibility of patty paper being used. The only mention of construction is "This gave me the radius for my circle. I then drew …using a compass." The explanation and representations are plausible for measurement, not construction. There is evidence of a good understanding of the mathematical principles throughout the response, but without the required construction, this response demonstrates only a conceptual understanding and analysis of the problem.

Score for Anchor Paper #5: Rubric Score 2

Annotation: This response indicates a conceptual understanding and analysis of the problem. The representation is incomplete. The constructed triangle is equilateral with arc marks to indicate a reasonable strategy. Multiple attempts at locating the center of the circle by trial and error are evident. The circle's center was found but not by construction techniques and does not reveal a good mathematical principle for finding the center, so the overall strategy employed is an incomplete correct strategy.

Score for Anchor Paper #6: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy, but has an error in the representation. The representation is essentially correct. The triangle and the circle, as well as the center point for the circle, were fully constructed. Arc marks serve as support for the correct strategy of construction. The written explanation also supports the correct strategy of construction techniques, although the student appears to have confused the terms protractor with compass, and perpendicular bisector with angle bisector. (We can assume the correct compass tool was used because "point" and "pencil" were mentioned.) However, an error, possibly in marking the length of AB, led to an isosceles triangle rather than an equilateral triangle. The correct strategy for finding the center of the triangle by finding the intersection of the angle bisectors was employed, but the incorrect triangle led to a circle that does not have all three points of the triangle located on the circle. This student has employed a completely correct strategy, fully explained, but has made an error in the application of that strategy. Overall, the response demonstrates a clear understanding and analysis of the problem.

Score for Anchor Paper #7: Rubric Score 3

Annotation: This response indicates an application of a reasonable strategy to construct a triangle. The representation is essentially correct. Clearly visible arc marks support the strategy of construction techniques used to construct the triangle, and the written explanation for the triangle confirms the use of construction techniques. However, there are no arc marks to support the strategy of constructing the perpendicular bisectors to find the center of the circle. Written explanation for the circle does not indicate another strategy for construction. The student conveys the mathematical principle that "where the perpendicular bisectors meet is the center of the circle," an acceptable strategy for this problem. Overall, the response demonstrates a clear 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 of the problem. The representation is correct, with all arc marks present to clearly explain and support the construction techniques used to construct the triangle, the center for the circle, and the circle. Written explanation provides confirmation of the correct strategy used to support the solution. The response demonstrates a complete understanding and analysis of the problem.

Score for Anchor Paper #9: Rubric Score 4

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution of the problem. The representations are correct, with all arc marks present to clearly explain and support the construction techniques used to construct the triangle, the center for the circle, and the circle. No written explanation is necessary, as having all arc marks present will fully support the correct solution. The response demonstrates a complete understanding and analysis of the problem.

Additional Scored Student Responses