Academic Program
Middle School



The Math Department believes that persistence and ingenuity are essential to problem solving not just for school but for life. Our goals for our students are to experience the beauty of the discipline, master its essential content, and develop resilient, flexible, and efficient problem-solving skills all within an atmosphere of creative and open inquiry where mistakes are welcome.
Our students learn to experiment, notice patterns, generalize, look for counterexamples, construct convincing arguments, present their ideas orally and in writing, use precise language, consider the reasonableness of answers, and critique the arguments of others. Fluency of skills is critical for progress, and skills are learned and practiced in meaningful contexts so that each skill contributes to a coherent big-picture understanding. The program is problem-centered and allows students to connect their learning to real world situations.

In Grades 5 through 7, students complete their study of arithmetic operations and lay foundations for algebra and geometry. Primary texts for these courses are the Grade 6-8 books from Open-Up Resources. At the end of Grade 7 and for all of Grade 8, our high-school level sequence begins with a rigorous treatment of Algebra I using Phillips Exeter Academy’s Math 1 book.

Middle School Mathematics Curriculum

List of 4 items.

  • Math 5

    Grade 5 is a year of transitions. As students enter Middle School, they begin to extend their understanding of numbers into the abstract realm. They describe and graph patterns, represent and work with fractions, decimals, and percents, learn about primes as the building blocks of numbers, explore new geometric ideas, and interpret ratios and proportions. Students develop effective and accurate computation strategies while building a strong conceptual understanding of why these procedures work. Students learn that explaining one’s reasoning is just as important as getting the right answer. Through use of manipulatives, collaborative activities, and exploration with real life problems, students are encouraged to investigate the new concepts.
  • Math 6

    The Math 6 course focuses on the mastery and extension of whole numbers, fractions, decimals, percents, ratios, and proportions. Students are also introduced to thinking about and writing expressions and equations. Inductive reasoning and physical modeling serve to corroborate fundamental ideas and the effective organization of supporting work is emphasized. Students cement their understanding of these topics through collaborative class activities and projects. Estimation, approximation, and real-life problem-solving are integrated throughout the course. Basic algebraic ideas are introduced in order to generalize observations and in preparation for Pre-Algebra.
  • Math 7

    Grade 7 students use their robust skill set and number sense to delve into the more abstract elements of mathematics as they begin to explore the foundations of algebra. Understanding how to translate word problems and tables into algebraic equations and represent those relationships on the coordinate plane is at the heart of the curriculum. As the year progresses, the story problems and equations become more complex and students enhance their skill set working with linear equations, rational expressions, distributing and factoring, and eventually solve for a second variable in an equation or system of equations. The year culminates with an introduction to the opening pages of Phillips Exeter Academy’s Math 1 book.
  • Integrated Math I

    In this course, students develop facility in working with numbers, tables, equations, inequalities, and graphs. The focus is on careful reading, interpreting, and solving word problems. Hence, the building of algebra skills stems from the need to solve problems in context, rather than from drill and practice for its own sake. Students are given a lot of opportunities to collaborate with peers, and they work together to learn the skills of how to present their solutions to the class using precise language, appropriate mathematical terms, and convincing arguments. Topics covered in the course include equations and graphs that are linear and quadratic, distinguishing linear data from nonlinear data, inequalities, the basic rules of exponents, and other traditional Algebra I topics. Students also learn how to use the graphing calculator appropriately as an effective problem-solving tool.

Explore Our Curriculum

A K-12 independent school in New York city, The Spence School prepares a diverse community of girls and young women for the demands of academic excellence and responsible citizenship.


© 2023 Spence School