The following multi-part constructed-response question, explained here in hopes of helping fourth-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 2015 “PBA” (performance-based assessment) test for fourth-grade math:
Jessica shades two grids that each equal one whole to represent and compare the fractions
From the choices, select the decimal that represents , and the decimal that represents . Then drag and drop each decimal into a box to create a true comparison.
_____ < _____
Jessica says that because 3 + 29 = 32 and there are 100 squares in each of the grids. Explain how you know Jessica is incorrect by using the grids or the decimal inequality you created. Then find the correct sum.
Resources for further study
Dan Johnson at Washington Elementary School in Wenatchee, Washington, has developed a compact tutorial about this particular set of skills and knowledge from the section of the Common Core. The page includes links, all the way down at the bottom, to other resources, including a practice test that serves as a little worksheet to let you practice on problems just like this.
Analysis of this question and online accessibility
The question measures knowledge of the Common Core math standard it purports to measure, in addition to assessing whether students are proficient in several math practices associated with the PARCC evidence statement.
The question can be delivered online and would yield performance statistics that are as valid as those obtained from paper-and-pencil test-takers. Note that some students who take the test online may encounter difficulties using the equation editor that is part of the online test-delivery system. We have written about this at great length and won’t belabor the point here, except to remind students that when you use the equation editor for a constructed-response problem like this, make sure you:
- Transfer all your work from scratch paper to the computer
- Include every step in your logic or explanation
No special accommodation challenges can be identified with this question, so the question is considered fair.
In a real classroom
Students can use graph paper and make grids of all sizes. The Common Core limits fourth-grade fractions to those with certain denominators, so that’s as far as testing can go, but give kids some graph paper and let them explore.