About the task

CCSSM Alignment

Part a

Scoring

This single-part, machine-scorable task integrates standards from different domains with the reasoning called for in Standard for Mathematical Practice 2 and, because of the complexity of the problem, the precision demanded in Standard for Mathematical Practice 6—thus making it a “practice-forward” task. It also demonstrates a novel use of technology—interactive sliders that support student engagement.

According to the CCSSM, students in grade 6 should view equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and connect their understanding of multiplication and division with ratios and rates. This technology-enhanced task provides students with an opportunity to use a tool to visualize the relationship between inches and centimeters. Students interpret the ratio relationship between inches and centimeters and connect that relationship with several possible mathematical representations.

The multiple-answer, multiple-choice format allows for scoring of deeper thinking than is typically possible in a single-answer, multiple-choice format—students must consider each answer choice individually. The answer choices require that students translate among various representations of a proportional relationship, including ratio language and equations. To separate the correct answer choices from incorrect ones, students must engage in Standard for Mathematical Practice 2 (reason abstractly and quantitatively). Successful students demonstrate their habits of creating a coherent representation of the problem at hand, considering the units involved, and attending to the meaning of quantities.

The technology in this task has potential for future development by item development vendors. Students could use sliders to arrive at an answer to a question involving a proportional relationship and submit their answer electronically, thus eliminating the need for scoring by hand.

Note: A variation of this task is included on the PARCC website, based on an earlier version of the task.