balanced math: concepts and computation

Mathematics at PCS 

manipulatives make learning visible for young mathematicians.

Through their math study, we want children to think deeply about mathematical relationships, develop strategies to solve problems, establish strong number sense, and apply math as a practical tool for discovering and understanding the world.

The mathematics program at PCS incorporates explicit whole-class instruction, daily small group work, independent skill practice, and inquiry based explorations woven through the thematic Integrated Unit to foster conceptual mathematical understanding and develop skill facility and fluency.

PCS uses a balanced mathematics framework to integrate conceptual understanding, traditional algorithms and computation, learner inquiry and project based learning. During structured math blocks, students engage with mathematical ideas across five strands of mathematics (counting and cardinality, number sense and base ten operations, algebraic thinking, measurement and data, and geometry), and formalize these concepts with skill and strategy practice utilizing games, numeracy routines, and problem solving. Incorporating tactile manipulatives (blocks, counters, dominos, cubes, base-ten units, and later, place value holders in computation) reinforces the connection between value and numeric representation for PCS’s younger mathematicians.

Mathematics work during the thematic Integrated Unit is focused on student-led projects and encourages logical reasoning and flexible mathematic thinking while providing meaningful context and opportunities for real-world application. Mathematicians in the Lower School may graph daily temperatures to know when to build turtle hibernation dens on campus; they may chart changes in white tailed deer populations across the US; or they may experiment with ratios and proportions to build a scale model Brooklyn Bridge; and mathematicians in the Middle School may use their knowledge of statistics to understand the allocation and distribution of Electoral College votes — all of these practices forge vital connections between abstract computations and the real values they represent and make math meaningful.

*PCS math curriculum aligns with Next Generation Learning Standards, and facilitators implement nationally recognized teaching tools and resources to support sequencing, lesson planning, and skill development. Resources vary from year to year, reflecting the needs of individual learners and current best practice.