Algebra is introduced in seventh grade and students work with signed numbers, polynomials, the Golden Rule, and the “unwrapping” principle. Mathematics classes cover exponents and notation, metric measurement, the order of operations, signed numbers, factoring, graphic representation of data, and work with variables, expressions, and equations. Students also learn to evaluate algebraic expressions, to use formulas, to add and subtract like terms, and to write and solve equations. Problems of geometric measurement – perimeter, area, and volume – are solved through algebraic equations.
In geometry, seventh-grade students explore the pentagon and pentagram, the spiral, and the Golden Mean. The students see that these principles underlie natural forms such as the chambered nautilus and the pine cone as well as paintings and works of architecture. The class studies the Fibonacci series of numbers and the Pythagorean Theorem. Students also learn perspective drawing and create a portfolio of geometric drawings, carefully constructed using geometric instruments.
Eighth-grade math focuses first on algebra, including linear equations, manipulating polynomials, factoring monomials and binomials, and performing operations on negative and positive numbers. All previously introduced concepts are reviewed at a more advanced level. Students learn to solve linear equations graphically, to solve quadratic equations, and to work with rational and irrational numbers.
In geometry, students learn congruence of triangles, parallel and perpendicular segments, and the angles created by transversals. The five Platonic solids are introduced and students fashion three-dimensional models of them out of paper or clay. They learn to plot points, lines, and conic sections on a graph. Algebraic concepts begin to arise naturally as tools to solve word problems, and so, finally, algebra and geometry are integrated.