The following 12 Sample Student Responses represent a range of score points.

Score for Sample Student Response #1: Rubric Score 2

Annotation: This response indicates application of a reasonable strategy that leads to a correct representation that conveys an overall conceptual understanding of the problem. The written explanation does not clearly justify dilation by scale factors greater than 1, and does not address dilation by scale factors between 0 and 1. "...with a scale factor of 3 you can just times everything by 3" seems to explain what he/she did in drawing the dilation image rather than to address the question of explaining dilation by a scale factor. This response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #3.

Score for Sample Student Response #2: Rubric Score 1

Annotation: This response indicates application of an inappropriate strategy. The representation is incorrect, but shows some understanding of scaling up in size, although not by the correct factor. The justification supports the solution "...double the amount usually when the scale factor is greater than one." The student does not address a dilation with a scale factor between 0 and 1. The response demonstrates minimal understanding and analysis of the problem.

Score for Sample Student Response #3: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy. The representation is correct. The justification is clearly presented, fully developed and supports the solution, revealing a correct strategy. The student explains the differences in dilation by scale factors between 0 and 1 and scale factors greater than 1 in terms of multiplying by the scale factor, giving specific examples. The student states, "...if the scale factor is 1/2 the coordinates would only be 1/2 of the original" and "If for example the Sf is >1, like it is in the problem above, the coordinates are multiplied by 3 and the figure will be bigger." The response demonstrates a complete understanding and analysis of the problem.

Score for Sample Student Response #4: Rubric Score 1

Annotation: This response indicates application of an inappropriate strategy. The representation is incorrect, but it has some relevance as the student has drawn a larger triangle. The justification, "With a dilation with scale factor between 0 and 1, the figure hardly moves and is basically the same. With a scale factor greater than 1, the figure's movements are very noticeable, and usually very big," has some relevance, but it is undeveloped and does not reveal a correct strategy for dilation. The response demonstrates a minimal understanding and analysis of the problem. Compare to Anchor Paper #2.

Score for Sample Student Response #5: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy. The representation is correct. The justification is clearly presented, fully developed and supports the solution, revealing a correct strategy. The student explains the differences in dilation by scale factors greater than 1 and scale factors between 0 and 1 in terms of multiplying by the scale factor, giving specific examples. ("The dilation of 3 made the triangle 3 times as big" and "… scale factor less then 1 decreases the size of a figure. dilation scale factor = .5 2 • .5=1.") The response demonstrates a complete understanding and analysis of the problem. Compare to Anchor Paper #6.

Score for Sample Student Response #6: Rubric Score 2

Annotation: This response indicates application of a reasonable strategy that leads to a correct representation that conveys an overall conceptual understanding of the problem. The student does not address a dilation with the required scale factor less than 1. Although the student explains, "1 is just a replica. More than 1 would be a larger shape that is proportionate," the student does not justify this statement. This response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #4.

Score for Sample Student Response #7: Rubric Score 2

Annotation: This response indicates application of a reasonable strategy that leads to a correct representation that conveys an overall conceptual understanding of the problem. The student does not address a dilation with the required scale factor less than or equal to 1. The student explains, "Since the larger triangle is 3 times as big as the smaller one, the scale factor and dilation is different (larger)." This response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #4.

Score for Sample Student Response #8: Rubric Score 1

Annotation: This response indicates application of an inappropriate strategy. The representation is incorrect, but has some relevance as the student has drawn a smaller triangle with a scale factor of 1/3. The justification "the bigger the scale factor the smaller the object is on scale" does not reveal a correct strategy for dilation, but this is consistent with the triangle drawn. The response demonstrates a minimal understanding and analysis of the problem.

Score for Sample Student Response #9: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy. The representation is correct. The justification is clearly presented, fully developed and supports the solution, revealing a correct strategy. The student explains the differences in dilation by scale factors between 0 and 1 and scale factors greater than 1 in terms of multiplying by the scale factor, giving specific examples. ("...a number being multiplied by .5, the number will be reduced in half." and "...if a number is multiplied by 2, then it will double.") The response demonstrates a complete understanding and analysis of the problem. Compare to Anchor Paper #6.

Score for Sample Student Response #10: Rubric Score 1

Annotation: This response indicates application of an inappropriate strategy. The representation is incorrect, but has some relevance as the student has drawn a larger triangle. The student adds three units to two legs of the triangle rather than multiplying by the scale factor of three--an inappropriate strategy. The student's justification, "The dilation of 3 makes it bigger by 3," is consistent with the representation. This response demonstrates a minimal understanding and analysis of the problem. Compare to Anchor Paper #2.

Score for Sample Student Response #11: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy. The representation is correct. The justification is clearly presented, fully developed and supports the solution, revealing a correct strategy. The student explains the differences in dilation by scale factors between 0 and 1 and scale factors greater than 1 in terms of multiplying by the scale factor, giving specific examples. ("...(0,6) becomes (0,3) and (4,0) becomes (2,0) with scale .5." "With scale 3, it became (0,18) and (12,0), calling for a figure 3 times as big." The response demonstrates a complete understanding and analysis of the problem. Compare to Anchor Paper #6.

Score for Sample Student Response #12: Rubric Score 2

Annotation: This response indicates application of a reasonable strategy that leads to a correct representation that conveys an overall conceptual understanding of the problem. The student does not address a dilation with the required scale factor less than or equal to 1. "To make the smaller triangle to grow by the scale factor of 3 is to multiply the numbers by 3. Then draw them on the scale and use a ruler to connect the dots" explains what he/she did in drawing the dilation image rather than clearly addressing the question of explaining dilation by scale factor. This response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #3.

Anchor Papers used in scoring