Task# Sierpinski's Carpet

Illustrative MathematicsVaries

The purpose of this task is to help motivate the usefulness of exponential notation in a geometric context and to give students an opportunity to see that sometimes it is easier to write a number as a numeric expression rather than evaluating the expression, which is an important facet of MP7, Look for and make use of structure. The task assumes that students have seen and evaluated numeric expressions that involve whole-number exponents. Even so, students might not think to use exponential notation to represent the areas. If they haven't, part (d) will be very challenging.