## Core-Plus Mathematics Curriculum Overview

The first three courses in the Contemporary Mathematics in Context series provide a common core of broadly useful mathematics for all students. These courses were developed to prepare students for success in college, in careers, and in daily life in contemporary society. Each of the three courses includes mathematics from four "strands" of mathematics.

 Algebra and Functions The algebra and functions strand develops student ability to recognize, represent, and solve problems involving relations among quantitative variables. Central to the development is the use of functions as mathematical models. The key algebraic models in the curriculum are linear, exponential, power, polynomial, logarithmic, rational, and periodic functions. Each algebraic model is investigated in four linked representations - verbal, graphic, numeric, and symbolic - with the aid of technology. Attention is also given to modeling with systems of equations, both linear and nonlinear, and to symbolic reasoning and manipulation. Geometry and Trigonometry The primary goal of the geometry and trigonometry strand is to develop visual thinking and student ability to construct, reason with, interpret, and apply mathematical models of patterns in visual and physical contexts. The focus is on describing patterns with regard to shape, size, and location; representing patterns with drawings, coordinates, or vectors; predicting changes and invariants in shapes under geometric transformations; and organizing geometric facts and relationships through deductive reasoning. Statistics and Probability The primary role of the statistics and probability strand is to develop student ability to analyze data intelligently, to recognize and measure variation, and to understand the patterns that underlie probabilistic situations. The ultimate goal is for students to understand how inferences can be made about a population by looking at a sample from that population. Graphical methods of data analysis, simulations, sampling, and experience with the collection and interpretation of real data are featured. Discrete Mathematics The discrete mathematics strand develops student ability to model and solve problems involving enumeration, sequential change, decision making in finite settings, and relationships among a finite number of elements. Topics include matrices, vertex-edge graphs, recursion, models of social decision making, and systematic counting methods. Key themes are discrete mathematical modeling, existence (Is there a solution?), optimization (What is the best solution?), and algorithmic problem solving (Can you efficiently construct a solution?).

(A Scope and Sequence (pdf - 548Kb) of mathematical topics typically taught in high school mathematics courses and their location in the CPMP four-year curriculum is available, as well as a chart indicating the Sequence of Units in Courses 1-4.)

Course 4 continues the preparation of students for college mathematics. In Course 4, formal and symbolic reasoning strategies, the hallmarks of advanced mathematics, are developed as complements to more intuitive arguments and numerical and graphical approaches to problems developed in Courses 1-3. The mathematical content and ten units in Course 4 allows considerable flexibility in tailoring a course to best prepare students for undergraduate programs. A sequence of units in Course 4 is recommended for students intending to pursue programs in the mathematical, physical, and biological sciences, or engineering (see the Sequence of Units chart) and a somewhat different sequence of units is recommended for students intending to pursue programs in the social, management, humanities, or some of the health sciences.

For students wishing to complete advanced placement courses such as AP Calculus and AP Statistics or complete International Baccalaureate Programs, it is recommended that they begin Course 1 as 8th graders. By beginning Course 1 in 8th grade, students can elect to enroll in AP Statistics as juniors and AP Calculus as seniors. Other options for acceleration are outlined in Preparing for College.