The following fill-in-the-number 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:
A right rectangular prism is shown:
To the nearest thousandth of an inch, what is the length of the diagonal, d?
Analysis of this question and online accessibility
New to eighth-grade math students under the Common Core is the ability to find diagonal distances on a coordinate plane using the Pythagorean Theorem, according to the North Carolina Department of Public Instruction.
- Khan Academy on the Pythagorean Theorem
- Purple Math on using the Pythagorean Theorem to find distances
Fill-in-the-number questions like this eliminate guessing as students can’t simply pick the option that looks best without doing the math. They can be delivered easily online and scored without human intervention.
On paper, these problems can be converted to a multiple-choice question, which can be scored without human intervention, or left in a fill-in-the-number presentation, which can’t. This makes the question accessible for students on any device they may use or on paper, although kids who learn information passively may have an easier time with a multiple-choice format. Fortunately that’s not too many students in our schools, and validity, reliability, and fairness measures should not differ significantly among the various delivery modes.
(A minor or irrelevant editorial error remains in the problem as published: The comma after the word diagonal should be omitted—the variable d restricts the meaning of the word “diagonal,” since there are two diagonals shown in the figure. For me, this is another example of either incompetence or sloppiness in the production of this test, for which the taxpayers of Illinois and Maryland have paid tens of millions of dollars.)
No special accommodation challenges can be identified with this question, so the question is considered fair.