"Different representations often illuminate different aspects of a complex concept or relationship . . . In order to become deeply knowledgeable about fractions -- and many other concepts in school mathematics -- students will need a variety of representations that support their understanding." (NCTM, 2000, p. 69)

Ms. Minnie Dale, a teacher from Shelbyville, Kentucky, is introducing her students to a problem similar to the one you just worked on. In the following video segment (duration 6:02), you can watch her students working on using array representations to find fractional values of a whole number. Working in partners, students tackle this problem through the use of square tiles and grid paper.

Ms. Dale starts by explaining what an array is. Students work on making their own arrays to represent numbers, and then demonstrate their arrays to the whole class. Finally, they use the arrays they've created to find fractional values of numbers, such as 1/5 and 1/7 of 14.

As you watch, think about how the students are approaching the problem and how your own students would tackle this task. Consider what the students understand about the representations they use, and their general understanding of what is being represented.

Please watch the video excerpt now.

  Think about the classroom you just watched