A sample high school math problem from PARCC (The Partnership for Assessment and Readiness for College and Careers, a consortium of 23 states involved in developing Common Core tests):
PARCC's discussion of how this problem aligns with Common Core Standard MP.7:
A more challenging set of "seeing quadratic structure" problems from over a century ago (Wentworth's New School Algebra):
1. Are there other useful structures one could recognize the PARCC problem as having other than Q2 + 2Q = 0? For example, might recognizing it as having the form a*a = b*a be an alternative, non-brute-force way of seeing its solutions?
2. If "seeing structure in a quadratic equation" warrants a special Common Core standard (MP.7), why aren't students getting more challenging quadratic structure problems like those in Wentworth above?
3. Was "seeing structure in a quadratic equation" even more important a century ago, before we needed the Common Core authors to remind us of how important it is?