The following two-part (drag and drop, multiple-choice) question, explained here in hopes of helping eighth-grade students and their parents in Maryland and Illinois prepare for the PARCC test near the end of this school year, appears on the released version of PARCC’s Spring 2016 test for grade eight math:
ΔPQR is transformed to the image ΔP′Q′R′.
Describe the single transformation that maps ΔPQR onto its image ΔP′Q′R′. Determine whether ΔPQR maintains its shape as a result of the transformation.
Drag and drop the correct words and phrases into the boxes.
The transformation is a __(blue)__ __(black)__.
ΔPQR is __(red)__ to the image ΔP′Q′R′.
The color-coded words and phrases:
- BLUE: dilation, rotation, reflection, translation
- BLACK: by a factor of ½, by a factor of 2, 90 degrees about vertex R, 180 degrees about vertex R, to the right, across the line, to the left
- RED: not congruent, congruent
A translation is performed on ΔP′Q′R′ to create image ΔP′′Q′′R′′. How does line segment P′′Q′′ compare to line segment P′Q′?
A. Line segment P′′Q′′ is longer than line segment P′Q′.
B. Line segment P′′Q′′ is shorter than line segment P′Q′.
C. Line segment P′′Q′′ is congruent to line segment P′Q′.
D. There is not enough information to compare the two line segments.
Analysis of this question and online accessibility
Translations, reflections, and rotations are examples of rigid motions, which are, intuitively, rules of moving points in the plane in such a way that preserves distance.
Some topics learned much earlier, including what students learned about angle and line measurements in fourth grade, is put to good use in the eighth-grade geometry standards now in the Common Core. And in some states, including Maryland, the ability to recognize and even perform any of the three rigid transformations was expected in third and fourth grade. The Common Core introduces these rigid transformations first in eighth grade under the umbrella of congruence of geometric figures.
The Common Core adds dilation, which results in a similar image. The dilated image will only be congruent to the original if the dilation factor is 1. As a result of the choice of dilation, a student’s answer in Part B is in jeopardy if he identifies the transformation incorrectly as a dilation by a factor of anything other than 1 (a factor of 1 is not one of the options).
As a result of the shift in the transformation skill to eighth grade, the question assesses students’ knowledge of the Common Core standard it purports to measure. Note that even many secondary school math teachers are reluctant to teach rigid transformations in geometry, according to a recent study conducted at the University of California, San Bernardino.
Multiple-choice questions like Part B can be delivered easily online and the drag and drop has an easy conversion to a multiple-choice format for paper-based tests, which makes this question accessible for students on any device they may use or on paper. Validity, reliability, and fairness measures should not differ significantly among the various delivery modes.
No special accommodation challenges can be identified with this question, so the question is considered fair.