The following 16 Sample Student Responses represent a range of score points.

Score for Sample Student Response #1: Rubric Score 1

Annotation: This response indicates little or no application of a reasonable strategy for construction. The representation has relevance, as we see an equilateral triangle inscribed in a circle. However, the representation reveals no indication of a reasonable strategy for construction, as there are no arc marks or explanation for the use of patty paper present to support the solution. The written explanation reveals that an inappropriate strategy of measuring was substituted for construction to draw the triangle. There is no written explanation or arc marks present to support the strategy used to find the center of the circle. This response demonstrates a minimal understanding and analysis of the problem. Compare to Anchor Paper #2.

Score for Sample Student Response #2: Rubric Score 2

Annotation: This response indicates the incomplete application of a reasonable strategy and demonstrates an overall conceptual understanding and analysis of the problem. There is a good understanding of the mathematical principles used to draw the equilateral triangle and to find the center of the circle. The student relies on knowledge that an equilateral triangle has three angles of sixty degrees and that the intersection of three angle bisectors will be the center of the circle. The representation is partially correct in that an equilateral triangle is inscribed in a circle, but there are no arc marks present to indicate a reasonable strategy for construction. The written explanation reveals that measuring (an inappropriate strategy for construction) was used to complete the problem. This response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #4.

Score for Sample Student Response #3: Rubric Score 4

Annotation: The representations in this response are accurate and demonstrate a reasonable strategy leading to a correct solution in the context of the problem. This student presents a logically sound explanation by doing the required construction and showing the arc marks. The symbols of the arc marks are used for both explanations. It is apparent from the arc marks at the top of the triangle that the student uses a compass to construct the equilateral triangle. In addition, the response shows constructed angle bisectors that were used to find the center of the triangle. This point is the center of the circle that properly circumscribes the triangle. This response indicates a complete understanding and analysis of the problem. Compare to Anchor Paper #9.

Score for Sample Student Response #4: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy and demonstrates a clear understanding and analysis of the problem. The representation is essentially correct. Clearly visible arc marks support the strategy of construction techniques used to construct the triangle. The written explanation confirms that construction techniques were used for the triangle. Written explanation for the circle does not indicate a strategy for construction, nor are there are any arc marks, but the student conveys the mathematical principle that the angle bisectors would give the circle's center. Compare to Anchor Paper #7.

Score for Sample Student Response #5: Rubric Score 2

Annotation: This response indicates the incomplete application of a reasonable strategy for construction. There is a good understanding of the mathematical principles used to draw the equilateral triangle and to find the center of the circle. The student relies on knowledge that an equilateral triangle has three angles of sixty degrees and that the intersection of three perpendicular bisectors will be the center of the circumscribed circle. The representation is partially correct in that an equilateral triangle is inscribed in a circle. However, the representation reveals no indication of a reasonable strategy for construction, as there are no arc marks or mention of patty paper present to support the solution. The written explanation reveals that measuring (an inappropriate strategy for construction) was used to complete the problem. This response demonstrates an overall conceptual understanding and analysis of the problem. Compare to Anchor Paper #4.

Score for Sample Student Response #6: 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. Compare to Anchor Paper #8.

Score for Sample Student Response #7: Rubric Score 3

Annotation: This response indicates an application of a reasonable strategy. The representation is fundamentally correct. There are no arc marks to support the strategy used to draw the triangle, but there are clearly visible arc marks that support the strategy of construction techniques used to find the center of the circle. The written explanation confirms that measurement (an inappropriate strategy for construction) was used for the triangle, but the student conveyed the mathematical principle of an equilateral triangle possessing three angles of sixty degrees. The student states in the written explanation for the circle that the center of the circle was found by constructing angle bisectors, but the arc marks indicate that the perpendicular bisector of each side was constructed. Construction of perpendicular bisectors is an acceptable strategy for this problem. This response demonstrates a clear understanding and analysis of the problem. Compare to Anchor Paper #6.

Score for Sample Student Response #8: Rubric Score 1

Annotation: This response indicates no application of a reasonable strategy. The representation is only partially correct. The representation of an equilateral triangle is relevant, but no arc marks or explanation for the use of patty paper is present to indicate an appropriate strategy. The written explanation indicates that the inappropriate strategy of measuring was employed. No indication of an attempt to inscribe the triangle in a circle is evident. This response demonstrates a minimal understanding and analysis of the problem. Compare to Anchor Paper #3.

Score for Sample Student Response #9: Rubric Score 2

Annotation: This response indicates incomplete application of a reasonable strategy. There is a good understanding of the mathematical principles used to draw the equilateral triangle and to find the center of the circle. The student relies on knowledge that an equilateral triangle has three sides of equal measure and that the intersection of its three medians will locate the center of the triangle. The representation is partially correct in that an equilateral triangle is inscribed in a circle. However, the representation reveals no indication of a reasonable strategy for construction, as there are no arc marks or explanation for the use of patty paper present to support the solution. The written explanation reveals that measuring (an inappropriate strategy for construction) was used to complete the problem. This response demonstrates an overall conceptual understanding and analysis of the problem. Compare to Anchor Paper #4.

Score for Sample Student Response #10: Rubric Score 4

Annotation: This response demonstrates a reasonable strategy that leads to a correct solution in the context of the problem. The two explanations are clearly sound and logically presented. To construct the equilateral triangle, the student states, "I extended the compass from A to b and made 2 arcs." This statement and observed arc marks support the explanation. Further arc marks are shown for the perpendicular bisectors of the sides "to find mid ," and the middle of the triangle is used to construct the required circle around ΔABC. These constructions all show correct representations. All of this demonstrates a complete understanding and analysis of the problem. Compare to Anchor Paper #8.

Score for Sample Student Response #11: Rubric Score 1

Annotation: This response indicates no application of a reasonable strategy. The representation is only partially correct. The representation of an equilateral triangle with an attempt to inscribe the triangle in a circle is relevant, but no arc marks are present to indicate an appropriate strategy. There is no written explanation to indicate the strategy employed. This response demonstrates a minimal understanding and analysis of the problem. Compare to Anchor Paper #2.

Score for Sample Student Response #12: Rubric Score 4

Annotation: This response demonstrates a reasonable strategy that leads to a correct solution in the context of the problem. The representation is correct. Clearly visible arc marks support the strategy for the construction of the triangle, the center for the circle, and the circle. The strategy for finding the center of the triangle by finding the intersection of the perpendicular bisectors is an acceptable strategy for this problem, and written explanation provides confirmation of the strategy used to support the solution. The response demonstrates a complete understanding and analysis of the problem. Compare to Anchor Paper #8.

Score for Sample Student Response #13: 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. Written explanation provides confirmation of the correct strategy used to support the solution. The response demonstrates a complete understanding and analysis of the problem. Compare to Anchor Paper #9.

Score for Sample Student Response #14: Rubric Score 2

Annotation: The overall strategy employed in this response is an incomplete correct strategy. The representation is fundamentally correct. The representation reveals that construction techniques were used to construct the triangle, because arc marks are evident, giving some explanation for correct strategy. However, we can also see multiple attempts at locating the center of the circle, probably by constructing the angle bisectors. This construction was not successfully done. There is a mark where the correct center of the circle is, but the student chose another point, resulting in a circle that does not intersect with all three vertices of the triangle. This response indicates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #5.

Score for Sample Student Response #15: Rubric Score 1

Annotation: There is little application of a reasonable strategy in this response. The student has drawn an equilateral triangle using measurement rather than construction. There is also no evidence of any construction for finding the center of the circle, but there is an incorrect attempt to construct a circle circumscribing ΔABC and to explain the process ("circle that was tangent to C"). This response demonstrates minimal understanding and analysis of the problem. Compare to Anchor Paper #2.

Score for Sample Student Response #16: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy, but has an error in the representation. The triangle and the circle, as well as the center point for the circle, were fully constructed. The arc marks and the written explanation serve as support for the correct strategies of construction. However, an error in marking the length of AB led to an isosceles triangle, rather than an equilateral triangle. The strategy for finding the center of the triangle by finding the intersection of the perpendicular bisectors is an acceptable strategy for the equilateral triangle of this problem. However, the student's incorrect isosceles triangle led to the construction of a faulty circle, one that does not have all three vertices of the triangle located on the circle. Thus, the representation is essentially, but not completely, correct. This student has employed a correct strategy that is fully explained, but he/she has made an error in the application of this strategy. Overall, the response demonstrates a clear understanding and analysis of the problem. Compare to Anchor Paper #6.

Anchor Papers used in scoring