The classic Chickens and Pigs problem is considered to be an algebraic problem with two equations and two unknowns. In this article, the authors describe how third-grade teacher Maria is using it to develop a problem-based lesson because she is looking to her students' future needs. As Maria plans, she considers how a series of problems with the same mathematical structure can be used to help her students develop their problem-solving skills and strengthen their understanding of operations. Maria's goal is to help her students develop the processes of mathematics (problem solving, reasoning, communication, connections, and representation). In light of this goal, she considers the strategies, tools, and scaffolding her students will need to move their thinking ahead. Effective teachers of mathematics focus their instruction on "Principles and Standards for School Mathematics." The Standards are based on theories of cognition (how children process, learn, and retain information), constructivist theories (how children's mathematical understanding is built and develops over time), theories of language (how discourse supports learning), and social learning theories (how social and cultural contexts influence what and how children learn). Maria values the Standards and strives to make the mathematics applicable, interesting, and achievable for each child. However, in addition to the Standards and the cognitive, social, and emotional bases of learning, Maria also considers the biological basis of learning revealed in findings from neuroscience. Maria's classroom is student-centered, and her lessons encourage her students to construct their own understanding because she knows that this type of learning changes brains. Memory for mathematical concepts and procedures comes not from just moving through the motions and recording facts; mathematical memory is about problem solving, reasoning, communicating, connecting, and representing numbers. When lessons put multiple concepts together, children develop webs of connections that allow them to navigate mathematics more efficiently over time. Ideas that are associated evoke memories and become keepsakes of mathematical understanding. (Contains 2 figures.)