The purpose of this study was to examine students' understanding of and ability to interpret line graphs, using four tasks: two where students constructed a graph and two where students interpreted a given graph. The tasks were unique in that they did not simply involve the explanation of given data but included a language component that looked at students' cognitive processes and understanding while they were engaged in the tasks. The study is important because students are often able to define and even draw graphs yet perform poorly on graph interpretation items presented in high-stakes examinations. The sample for the study consisted of 91 fourth and fifth graders with and without learning disabilities (LD) from six schools in a major metropolitan area. Scoring rubrics were designed for each item. An analysis of variance by grade and group indicated no significant differences between fourth and fifth graders overall but revealed that typically achieving students performed at significantly higher levels than students with LD at both grade levels. Additional descriptive analyses looked at the patterns of errors evidenced and the nature of the students' constructions. These are discussed, and instructional implications are derived.