Can You Tell?

Suppose that a > 1, 0 < b < 1, and 0 < c < 2. Complete each sentence below by filling in the blank with <, =, >, or CT (can’t tell). Provide and justify your decision including a picture or model. Provide more than one example to justify any “can’t tell” responses: one that includes a solution to illustrate > and one that includes a solution to illustrate <.

(Reprinted with permission from Developing Number Sense in the Middle Grades, Addenda Series Grades 5-8, copyright 1991 by the National Council of Teachers of Mathematics. All rights reserved.)