2 — Reason Abstractly and Quantitatively
Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize to —abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved.
Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
These videos show a student solving a problem using an approach that reflects the knowledge and skill described in 4.OA.3 and another student both solving the same problem but using the knowledge and skill described in 8.EE.8. In both cases, the students move fluidly between the context and the mathematics and back again.