Task# Scaling Up and Down

Illustrative MathematicsVaries

This task is structured so that a teacher can diagnose the depth of a student's understanding of what it means to multiply a number by a fraction, specifically in terms of scaling (as such it can be used formatively or summatively). Part A addresses whether or not a student understands basic fraction comparisons, and helps set them up to reason about the subsequent problems. Part B assesses whether students can recognize a context in which scaling is appropriate, and then assesses whether or not they can multiply a whole number by a fraction (both larger and smaller than 1). Part C looks at whether students can extend their knowledge of scaling to when both factors are fractions (the first situation has one number smaller and one number greater than 1, and in the second both are smaller than one).