Mathematics Curriculum Progression Map
In Pythagoras, our youngest students experience math through movement, games, stories, puzzles, manipulatives, and plenty of hands-on exploration. Each class includes a variety of short, engaging activities designed for young attention spans and gives children many different ways to play with numbers, shapes, patterns, and logic. At this age, just as important as what children learn is how they feel about math: our goal is to build curiosity and confidence and create positive early experiences that leave children excited to come back for more.
Euclid is designed for Kindergarten and 1st grade students who are ready to discover that math is about much more than addition and subtraction. Students explore patterns, shapes, number relationships, measurement, logic, and early problem solving through puzzles, games, and hands-on activities.
Children build, sort, compare, arrange, experiment, draw, and solve, using manipulatives and games to make abstract mathematical ideas concrete and visible. This gives them an opportunity to discover relationships for themselves before learning to express those ideas with words and symbols. Our goal at this age isn’t necessarily to race ahead, but to develop strong number sense, mathematical intuition, and a solid foundation for future learning. We don’t want our students to be intimidated by math; rather, we want them to see math as something they can play with, investigate, and figure out.
In Archimedes, our 1st–2nd graders take the next step from exploring mathematical ideas to using them to solve increasingly challenging problems. Students tackle logic puzzles, develop spatial reasoning, and begin working with more complex word problems, learning to decide how to approach a problem when the path to a solution isn’t immediately obvious. Hands-on activities remain an important part of the program, but the emphasis increasingly shifts toward reasoning: looking for patterns, testing ideas, trying different strategies, and persisting when the first attempt doesn’t work. Our goal is to develop confident, creative problem solvers with the mathematical reasoning and grit they’ll need as the material becomes more advanced.
In Gauss, our 2nd–3rd graders begin the transition from intuitive problem solving toward more formal mathematical thinking. Students learn to use precise mathematical language and definitions, particularly in geometry, while tackling increasingly complex, multi-step problems that require careful reasoning and persistence. Hands-on exploration remains an important part of the program, helping students investigate new ideas before expressing them more formally. Gauss builds the rigor and mathematical habits students will need for more advanced work while keeping curiosity, discovery, and the joy of figuring something out at the heart of the experience.
In Johnson, our 3rd–5th graders experience a significant jump in the level of challenge. Students tackle demanding competition-style problems and explore topics such as combinatorics, geometry, and number theory, while also encountering classic challenges like the Tower of Hanoi, river-crossing problems, and logic puzzles. At this level, success requires much more than applying a familiar procedure: students learn to experiment with different strategies, get stuck, rethink their approach, and try again. Johnson develops advanced mathematical thinking while building the creativity, strategy, and persistence needed to solve problems where the path to the answer is far from obvious.
In Lovelace, students move deeper into competition-style mathematics, tackling challenging problems in geometry, number theory, combinatorics, algebra, and other topics beyond the standard school curriculum. The focus increasingly shifts toward developing a toolkit of problem-solving strategies and learning to recognize when and how to use them. Students learn to break unfamiliar problems into manageable pieces, try different approaches, and persist when a solution isn’t immediately apparent, building the creativity and mathematical reasoning needed for more advanced competition math.
Groups Noether and Erdős are designed for early high school students aiming to excel in competitions like AMC 10, AIME, and the Lehigh Math Contest, as well as to explore advanced math topics. Special emphasis will be placed on perseverance and problem-solving strategies.
In addition to competition preparation, we’ll venture into advanced math topics that extend beyond the school curriculum. From exploring basic group theory to diving into the depths of modular arithmetic, our classes are designed to foster curiosity and a love for mathematics beyond the textbooks.
These groups are a good option for middle-school students with a strong interest in mathematics, whether their goal is to ace a competition or simply to expand their mathematical horizons.
In Kovalevskaya, students with a strong foundation in prealgebra tackle increasingly sophisticated competition-style problems in algebra, geometry, number theory, combinatorics, and other advanced topics. Students are expected to draw on a growing toolkit of strategies, combine concepts in unexpected ways, and develop efficient approaches to unfamiliar problems. A more substantial homework component provides the practice needed to build fluency and deepen these skills. Kovalevskaya requires greater mathematical maturity, independence, and persistence as students prepare for higher-level mathematics and increasingly challenging competitions.
