Curriculum Detail

SPL: Picker

Mathematics

In the universe of numbers, there are truths and falsehoods. Fundamentally, mathematics is the business of figuring out which is which. The goals for our students are to experience the beauty of the discipline, master its essential content, and most of all, develop resilient, flexible and efficient problem-solving skills. Real problems are those to which one doesn’t already know the answer, so solving them requires persistence and ingenuity. Our students learn to experiment, notice patterns, make conjectures and generalize, test with counterexamples, construct convincing arguments, present ideas orally and in writing, use precise structures and language, gauge the reasonableness of answers and critique the arguments of others. Fluency of skills is critical for progress, and skills are learned in meaningful contexts so that each new idea contributes to a coherent big-picture understanding.

In Grades 5 through 7, students complete their study of arithmetic relationships and lay foundations for algebra and geometry. Primary texts for these courses are from the Connected Math series designed at Michigan State University. Core topics include ratios, rates, fractions, decimals, percents, number theory, properties of operations and equality, integers, data analysis, probability, 2-D and 3-D geometric relationships, tessellations, area and volume, patterns and their generalizations, variable expressions, linear relationships and graphs and modeling real contexts with equations. Each unit is built around investigations that uncover key concepts; each investigation is followed by problem sets providing applications, reinforcement and challenging extensions.
 
In Grade 8, our high-school level sequence begins with a course comprising a rigorous treatment of Algebra I content, including linear, absolute-value
and quadratic functions. This is the first year of an integrated and problem-centered four-year program, using as primary texts Math 1 through Math 4 published by Phillips Exeter Academy. (See Upper School Mathematics for more detail.) In class, students present their solutions to problems and, with the teacher’s facilitation, identify key concepts and surprising connections between mathematical ideas as they emerge.

Middle School Mathematics Sequence
Grade 5 Math 5: Number and Space
Grade 6 Math 6: Patterns and Generalization
Grade 7 Math 7: Foundations of Algebra
Grade 8 Integrated Math 8: Algebra

  • Math 5: Number and Space

    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 and decimals, explore new geometric ideas, and learn to calculate and interpret experimental and theoretical probability. 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.

  • Math 6: Patterns and Generalization

    The core of the Grade 6 mathematics course is the mastery and extension of whole number, fraction and decimal concepts; ratio, proportion and percent; geometric relationships; and basic probability through the use of hands-on materials, visual representations, cooperative class activities and projects. Inductive reasoning and physical modeling serve to corroborate fundamental ideas and the effective organization of supporting work is emphasized. 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: Foundations of Algebra

    What is x? How do we solve 4x - 7 = 6 and what does it mean? Where do we use inequalities? These questions, among others, are explored while solidifying basic computational skills and number theory. Students learn how to communicate mathematically through exploratory projects and class work. Group work with individual responses is stressed. In this course, students build a foundation of linear equations and inequalities in preparation for Algebra I.

  • Integrated Math 8: Algebra

    Two crucial building blocks of all subsequent work are introduced this year: the idea of independent and dependent variables and the representation of their relationships using graphs. Methods are developed to analyze linear equations, systems of equations, inequalities, quadratic equations, rational expressions and radical expressions. Symbolic manipulation is emphasized, but the graphing calculator is also introduced as an exploratory tool.

Middle & Upper School

22 East 91st Street
New York, NY 10128

Lower School

56 East 93rd Street
New York, NY 10128

Athletic & Educational Facility

412 East 90th Street
New York, NY 10128
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.

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