This approach is more inviting to them and leads them to reason about, look for, and
make use of structure.
Students receiving solid instruction focused strongly on mathematical practice # 7 (looking for and
making use of structure) are likely to be able to complete this problem more easily and efficiently than those who only learn to think about the problem as substituting each number individually and «checking if it works.»
The two most difficult practices to understand are Modeling with Mathematics (MP4) and Looking for and
Making Use of Structure (MP7).
A PPC is a perfect way to construct models, use appropriate tools strategically, and look for and
make use of structure, not to mention persevere.