Figure ABCD is shown on the grid below. Use the answer box to complete the following. (You will also need to use graph paper to complete the answer satisfactorily.) On a grid, reflect ABCD across the y-axis. Label the image A'B'C'D'.   Use mathematics to explain how a reflection across the y-axis affects the coordinates of any point (x, y). Use words, symbols, or both in your explanation.   On the same grid, translate A'B'C'D' 6 units down. Label the image of this translation A"B"C"D".   Use mathematics to explain how a translation 6 units down affects the coordinates of any point (x, y). Use words, symbols, or both in your explanation.

The following 7 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 minimal understanding and analysis of the problem. Little understanding of the reflection is demonstrated. The student has reflected the original image, but over the line x=2 rather than the y-axis. The second transformation is correctly translated down 6 units from the student's reflection. Labeling demonstrates the correct orientation of the figures' vertices. The explanation ("making them negative") of the effect on the coordinates for a figure that is reflected over the y-axis is untrue for all the coordinates of the student's reflection. The explanation of the effect on the coordinates for a translation down 6 units is vague. "It changes them and make some coordinates all negatives" is untrue for all the coordinates of the student's translation.

Score for Anchor Paper #2: Rubric Score 1

Annotation: This response demonstrates a minimal understanding and analysis of the problem. The representations demonstrate little understanding of reflection, but some understanding of translation. The figures are not correctly labeled. The explanation of the effect on the coordinates of the reflection describes the incorrect process used. The explanation for the translation incorrectly states, "adds 6 to the coordinates," rather than, "subtracts 6 from the coordinates."

Score for Anchor Paper #3: Rubric Score 2

Annotation: This response demonstrates conceptual understanding and analysis of the problem. The representations are correct; both the reflection and translation were correctly executed and labeled. The explanations of the effects on the coordinates for both transformations describe the effects under the specific circumstances of the problem rather than a general rule. "Makes each x-coordinate a negative number" describes the effect of the reflection that was executed, but does not answer the item's general question of "how a reflection across the y-axis affects the coordinates of any point (x,y)." "Makes both coordinates negative numbers" describes the effect of the translation that was executed, but does not answer the item's general question of "how a translation 6 units down affects the coordinates of any point (x,y)."

Score for Anchor Paper #4: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The representations are fundamentally correct. The student has correctly performed the reflection, and the translation was executed correctly from the trapezoid's original position rather than the reflected image. Both figures are correctly labeled. The student has attempted to address how the coordinates are affected by each type of transformation, but the effects are specific rather than general with the student providing the coordinates after each translation.

Score for Anchor Paper #5: Rubric Score 2

Annotation: This response demonstrates conceptual understanding and analysis of the problem. The representations are fundamentally correct, demonstrating some understanding of both reflection and translation. The reflection has been executed over the x-axis rather than the y-axis as directed, and the translation 6 units down was performed on the original figure rather than the reflected image. Labeling is absent. The first explanation of the effect on the coordinates of a reflection over the y-axis, "Reflection y = T(x,-y)," actually describes when the figure is reflected over the x-axis, the transformation the student has performed. (The student has used the x-axis for the reflection instead of the y-axis). The explanation of the effect on the coordinates of a translation 6 units down correctly describes a reduction of the value of y by 6 units: "6 down = T(x,y-6)."

Score for Anchor Paper #6: Rubric Score 3

Annotation: This response demonstrates a complete understanding and analysis of the problem. The representations are correct; the student has correctly performed the two transformations of reflection and translation, and the figures are correctly labeled. The student provides two general descriptions of how the coordinates are affected after each transformation: "...the x changes to either positive or negative" and "...changes the y value, but not the x...just 6 units down."

Score for Anchor Paper #7: Rubric Score 3

Annotation: This response demonstrates complete understanding and analysis of the problem. The representations are correct; the student has correctly performed the transformations of reflection and translation correctly, and the figures are correctly labeled. The student has provided two general descriptions of the effects on the coordinates after each transformation: "all the x-coordinates are made opposite of what they originally were" and "the y-coordinate is just -6 of what it originally was."

Additional Scored Student Responses