Math Curriculum

The University of Chicago Laboratory Schools

Math Curriculum

Math Philosophy

The math program encourages students at the University of Chicago Laboratory Schools to enjoy mathematics and to master math skills they will need. Math teachers stress unifying ideas and connections between ideas; they see mathematics learning as a continuum rather than a sequence of separate, discrete blocks of material, and value the ability to formulate conjectures about mathematical principles, to verify those conjectures, and to apply previous knowledge to new situations.

The math faculty encourages students to develop confidence, independence, responsibility, and organizational and study skills. As they develop their mathematical skills, students are actively involved in presenting solutions to problems, participating in class discussion, utilizing technology that aids in problem solving, and exploring the relationships between concepts and applications of mathematical techniques in other academic areas. Students learn to write complete logical expositions of solutions and to present them to the class. Reading thoroughly and writing clearly are essential for success in math. Additionally, the math teams in middle school through high school support the math program by providing enrichment and challenge beyond the classroom.

Nursery/Kindergarten Math Program
The nursery and kindergarten math curriculum builds upon the young child's natural curiosity, enthusiasm, and intuitive mathematical thinking. Students are encouraged to exchange mathematical ideas with classmates and teachers in a variety of contexts involving everyday classroom routines and situations. Students' logical thinking is enhanced by problem solving that engages students in several mathematical areas: numbers and operations, algebra, geometry, measurement, data analysis and probability, reasoning, communication, connections and representations. Beginning in kindergarten, teachers use the Everyday Mathematics program of the UCSMP (The University of Chicago School Mathematics Project) to guide their curricular work.

First Grade through Fourth Grade Math Program
Building upon the foundation gained in nursery and kindergarten, students in first through fourth grade develop skills in math through many varied experiences with numbers and symbols. Students become mathematically literate and become skillful in the application of mathematical concepts to their daily lives. Basic arithmetic is introduced. Students become facile with many numerical representations of the same number (i.e. 6 = VI = 8-2). Students also learn to value mathematics through frequent math experiences that are related to other disciplines; for example, students may use graphing skills in social studies or encounter social studies issues in math class. In science class, students are introduced to graphing as a way to present the results of experiments in mathematical format. Finding multiple applications of the same math concepts, students measure time on clocks marked at five-minute intervals and they count money using nickels. They learn fact families to coordinate multiplication facts and division facts. Students begin to understand how to solve new problems as they encounter them in cooperative and individual settings. Students learn to use signs, symbols, and terminology in problem solving situations so the language of mathematics becomes natural and its logic clear. Finally students develop mathematical reasoning as they make conjectures, gather evidence, and build supporting arguments.

Middle School Math Program

Middle school students are a diverse group of learners; the math program in middle school offers varied levels of acceleration in order to provide organizational support, intellectual challenges, and solid mathematical foundations for the future. Middle school math courses use, review and strengthen basic arithmetic skills. As students encounter new skills, they apply and review them throughout the course and in subsequent courses. Students use games and puzzles in math as well as appropriate technological applications with calculators and math graphics programs. Critical reading of the text, small group work, substantial teacher support, and regular homework all provide opportunities for mastery of math skills. Exploration of open-ended questions gives students a taste of the rewards and challenges of real mathematics.

Fifth and Sixth Grade Math Program
Using the guiding principles of the middle school math program, teachers introduce, reinforce, and practice several important mathematical concepts. Fifth grade students encounter algorithms for multiplication and division, fractions and percentages, data analysis, basic geometric relationships, operations with positive and negative numbers, and mental math and estimation. The sixth grade pre-algebra course reviews the arithmetic of positive and negative integers, decimals, and fractions, while providing an introduction to algebra that provides students with systematic procedures for solving equations. Sixth grade math students also encounter basic geometry that includes symbolic notation, vocabulary, and properties of parallels, perpendiculars, angles, polygons and circles. In addition, sixth grade math students are introduced to probability and graphing.

Seventh and Eighth Grade Math Program
In order to address emerging developmental differences and needs of middle school students, the math department offers two math sequences beginning in seventh grade. At the end of 6th grade, math teachers, together with parents, use established criteria that address developmental needs and skills to agree upon placement of entering 7th grade students in either a one-year or two-year algebra program. All students, whether they enroll in the one-year or two-year algebra course, will learn the same algebraic mathematical principles and operations before entering high school.

The algebra course builds upon the sixth grade foundations, which provide a transition from arithmetic to algebra. Students in algebra are introduced to linear equations, coordinate geometry, systems of equations solved by both algebraic and graphical methods, second degree operations, and operations with polynomials, radicals, and exponents. Through the course students learn to apply what they have learned as they review and build upon skills. Students in geometry encounter the fundamental ideas of geometry through a process that balances inductive and deductive logic. Constructing figures by hand or using Geometer's Sketchpad software, students apply inductive reasoning to formulate conjectures about basic geometric principles. Then, they apply deductive reasoning to prove these conjectures, using both two column and paragraph format proofs. Students use proofs throughout the course as they study the following topics: triangles and their properties; congruence and similarity; properties of parallel and perpendicular lines; special quadrilaterals and polygons; Pythagorean Theorem, circles, and area; equation and slope of a line, distance formula, and algebraic proofs; geometry of three-dimensional space and surface area and volume of standard solids. Students also apply geometric concepts to art and computer projects.

High School Math Program

Our approach to describing the high school curriculum assumes that the foundational work done to this point prepares students to engage meaningfully in a wide variety of courses and topics in mathematics. Each course offered at U-High is rich and deep and more information about the details of the coursework can be found in the Program of Studies.

When students graduate from University High, we hope they will realize the beauty and joy of mathematics and appreciate the practical applications of mathematics. The math teachers believe in rigor, and they have high expectations; they also work to individualize and support each student's path through the math curriculum. In some courses, they provide opportunities for students to engage actively in problem solving by wrestling with long-term problems that engage students over a period of time, and that may involve the use of technology such as the Statistics software Fathom, geometry software such as Sketchpad, and graphing calculators. Ultimately, math students know math as a subject, not just as a sequence of skills to be mastered.

The high school math program meets the diverse needs of our students by allowing students to choose between a large number of courses and trajectories based upon sequential study that provide several mechanisms for reaching college level course work by senior year. The many possible courses and paths provide options that promote an experience of math that allows for investigation, contemplation, and enjoyment. Many students choose a course of study that leads to the completion of calculus by senior year; others complete pre-calculus by their senior year. Because teachers carefully plan with each student the appropriate pathway through the math curriculum students choose a course path that meets their needs, skill level, and ambition. The possible coursework includes Algebra, Advanced Algebra, Geometry, Trigonometry, Discrete Math, Statistics, Pre-Calculus, and Calculus.

Key components of the high school math program are class discussion, various problem-solving methods, group work, and the exploration and incorporation of technology. The rigorous and challenging math curriculum provides students with a solid foundation for college mathematics.