About the task

CCSSM Alignment

Part a

Part b

Part c

Scoring

In the CCSSM, a key advance from grade 5 to grade 6 is that students extend their understanding of multiplication, division, and fractions to work with ratios, proportional relationships, and unit rates. Students also learn to apply properties of operations in their work with variables, expressions, and equations involving variables.

This three-part task involves the critical skill of using multiple representations. It requires that students represent and solve a problem, and then reason from those representations to make comparisons and draw conclusions. Because students solve a set of contextual word problems involving ratio and rate reasoning, this task targets Standard for Mathematical Practice 4: Model with mathematics, and is considered a “practice forward” task.

Part a provides an accessible entry point to the task with a straightforward table missing a few entries. In Part b, proportional information is presented a variety of representations. In Part c, even though only one question is asked, students must consider the information presented in each representation to sequence the cars in terms of their respective gas consumption.

This task is engaging both mathematically and contextually and allows for multiple possible solution strategies. It exemplifies three different machine-scorable formats: drag and drop, fill in the blank, and single-answer multiple choice.

Preliminary field-test data indicate that most students were challenged by this task and engaged with it for a reasonable length of time.