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.
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- 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.
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- 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.
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- 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?).
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(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.
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