Middle School Overview
The mathematics program at Falk School is centered on inquiry and exploration. Through analysis of challenging mathematical questions that arise out of real life, students have the opportunity to develop deep understandings of important topics. As they develop their mathematical abilities, students are encouraged to find more abstract and useful ways to represent those understandings. They also gain perspective on the broad world of mathematics by working with different approaches to familiar topics such as alternative number systems, algebraic representations, and logical proofs. The emphasis at this level is on identifying, articulating and using understandings about the mathematical properties that govern the world around us.
Students are given assigned groupings in seventh and eighth grades in preparation for high school math tracks and course selections. Seventh grade students take either Pre-Algebra or Algebra and eighth grade students take either Algebra or Geometry.
Falk uses the MathScape series as the curricular text for the pre-algebra classes. MathScape was developed by the McGraw-Hill companies (http://www.glencoe.com/sec/math/mathscape/index.php/). In these classes, students work through multiple unit books in a school year spanning a variation of topics with inquiry-based activities and the use of manipulatives. Algebra classes use a traditional Prentice Hall textbook and geometry classes study from a traditional McDougal Littell text. These texts serve as a proper scope and sequencing of material, as well as practice problems, while our lessons maintain the spirit of inquiry with our students.
Pre-Algebra covers a wide variety of topics and focuses on bridging the gap between concrete and abstract reasoning with mathematics. Students work on fundamental computation skills such as fraction and integer arithmetic, statistics, and probability in generalized, algebraic formats. Mathematical logic and alternative number systems are also investigated and provide students with a deeper conceptual image how our decimal system works. Students study algebraic concepts in a variety of domains, both the abstract tasks of graphing and solving equations as well as more applied problems such as statistics, combinatorics, geometry, and trigonometry. Students develop deep understandings about how to create and solve mathematical models from real problems.
The Algebra 1 curriculum follows the rigor and content list of a traditional Algebra 1 course with additional content driven by students’ interests. Our students study variable expressions, solving equations, linear functions, systems of linear equations, precisely graphing and solving quadratic functions, factoring polynomials, exponential functions, exponent properties, and right triangles. Topics in this course are introduced in meaningful ways to our middle school children, such as throwing paper to study quadratic functions, or reading an excerpt from Lewis Carroll’s 1865 novel “Alice in Wonderland” to introduce exponential functions and properties.
The year in study always diverges from the traditional content and into other related or tangential topics, depending on the children’s interests. Latin root words, historical contexts of mathematicians and equations, cubic and quartic functions, are just a few of the many topics students inquire about and have become part of the curriculum.
The Geometry curriculum at Falk School differs from many other geometry classes by focusing heavily on the concepts of mathematical logic and proof. Students begin the year learning definitions and fundamental properties. Then, while most geometry textbooks provide theorems with little or no emphasis on the proofs of the theorems, our students work together throughout the year to formally prove a significant portion of planar Euclidean geometry. The course also contains several explorations of related topics such as computer logic, non-Euclidean geometries, and occasionally independent research projects. The class is designed to provide challenging rigor and exploration of logic in a way that is rarely available in traditional middle or high school level math curricula.