This five-part task illustrates the important CCSSM shift to consider fractions not only as parts of a whole, but also as numbers that can be located on a number line. This latter meaning helps students develop an understanding of the structure of fractions within the number system and builds an important foundation for using number properties and developing operations with fractions.
The task includes components that focus on reasoning about fraction structure through identifying the location of fractions on a number line. Students also reason about the meaning of numerators and denominators and demonstrate understanding of equivalency as they construct viable arguments that precisely communicate their understanding of a fraction as a number (MP.7, MP.3, MP.6)—thus making it a “practice-forward” task.
Part a allows students an accessible entry point into the content, asking them to locate fractions on the number line as preparation for increasingly challenging material in the remainder of the task.
In Parts b and c, students demonstrate their understanding of the concept of comparing fractions with the same numerators or denominators, recognizing the roles of the numerator and denominator in a fraction (MP.7). Students have traditionally compared fractions by finding common denominators and then comparing the numerators. The CCSSM requires students to reason about fractions by considering how fraction size changes when only the numerators or only the denominators change. For example, when comparing and , students are asked to reason about the size of thirds and fourths to determine which fraction is greater, instead of finding equivalent fractions for each with the common denominator of 12ths.
Parts d and e represent a good example of asking students to use a concrete model to construct an argument (MP.3). Instead of just generating an equivalent fraction, students must construct an argument to prove that two given equivalent fractions are indeed equivalent. Area is connected to location on the number line as students progress from Part d to Part e. Students construct a viable argument to support their understanding of the structure in Part e (MP.3).
This task uses a variety of technology formats that allows students multiple ways of interacting with the content. The drag-and-drop and slider formats are engaging for students and provide multiple entry points by allowing them to test their conjectures before submitting their answer. In addition to the technology innovations, this task is novel because it calls for students to demonstrate their understanding of fractions at a deeper level than just applying or restating rules.
Use the navigation at the upper right of this page to access the task.