In the previous sections, you considered several different types of representation, reflected on how you as a teacher can expand students' use of representations, and explored your own use of representations as you solved a problem.

Now that you are familiar with the Standard and some of its aspects, we'd like you to apply it. Elementary school teacher Minnie Dale had her students work with several representations as they connected what they already knew about fractions to finding a fraction of a number. You may recognize "find a fraction of a number" as involving multiplying by a fraction, and wonder whether this is appropriate content for your grade level. Before you entertain such questions, use what you know about representation to work on this Interactive Activity.

As you work, pay close attention to the role representation plays in finding a fraction of a whole number without relying on standard computation methods. Also, pay attention to how certain representations may or may not be useful in particular situations, and think of alternative representations. Finally, view the video of the class and consider how you would help the students connect various forms of representation in order to further develop their understanding of fractions.

  Consider a problem