CPMP Course 2 1st Edition Units

Unit 1  (sample material)
Matrix Models
Extends student ability to use matrices and matrix operations to represent and solve problems from a variety of real-world settings while connecting important mathematical ideas from several strands.
Topics include:
Matrix models in such areas as inventory control, social relations, archeology, recidivism, ecosystems, sports, tournament rankings, and Markov processes; matrix operations, including row sums, matrix addition, scalar multiplication, matrix multiplication, and matrix powers; properties of matrices; and matrix methods for solving systems of linear equations.
Unit 2
Patterns of Location, Shape, and Size
Develops student understanding of coordinate methods for representing and analyzing relations among geometric shapes, and for describing geometric change.
Topics include:
Modeling situations with coordinates, including computer-generated graphics; distance in the coordinate plane, midpoint of a segment, and slope; designing and programming algorithms; methods for solving systems of equations; coordinate and matrix models of isometric transformations (reflections, rotations, and translations) and of size transformations; and similarity.
Unit 3
Patterns of Association
Develops student understanding of the strength of association between two variables, how to measure the degree of the relation, and how to use this measure as a tool to create and interpret prediction lines for paired data.
Topics include:
Rank correlation, Pearson's correlation coefficient, cause and effect related to correlation, impact of outliers on correlation, least squares linear models, the relation of correlation to linear models, and variability in prediction.
Unit 4  (sample material)
Power Models
Develops student ability to recognize data patterns that involve direct or inverse power variation, to construct and analyze those models and combinations such as quadratic models, and to apply those models to a variety of problems.
Topics include:
Basic power models with rules of the form y = axb and combinations of power models with other simple models; analysis of quadratic models and equations from tabular, graphic, and symbolic viewpoints; square root and cube root relations, and fractional power and radical expressions.
Unit 5
Network Optimization
Extends student ability to use vertex-edge graphs to represent and analyze real-world situations involving network optimization, including optimal spanning networks and shortest routes.
Topics include:
Vertex-edge graph models, optimization, algorithmic problem solving, matrices, trees, minimal spanning trees, shortest paths, Hamiltonian circuits and paths, and Traveling Salesperson problems.
Unit 6  (sample material)
Geometric Form and Its Function
Develops student ability to model and analyze physical phenomena with triangles, quadrilaterals, and circles and to use these shapes to investigate trigonometric functions, angular velocity, and periodic change.
Topics include:
Parallelogram linkages, pantographs, similarity, triangular linkages (with one side that can change length); sine, cosine, and tangent ratios, indirect measurement; angular velocity, transmission factor, linear velocity; periodic change, radian measure, period, amplitude, and graphs of trigonometric models of the form y = A sin Bx or cos Bx.
Unit 7  (sample material)
Patterns in Chance
Develops student ability to understand and visualize situations involving chance by using simulation and mathematical analysis to construct probability distributions.
Topics include:
Probability distributions and their graphs, Multiplication Rule for Independent Events, waiting-time (or geometric) distributions, expected value, rare events, summation notation, and an introduction to the binomial distribution.
Capstone
Forests, the Environment, and Mathematics
A thematic, two-week, project-oriented activity that enables students to pull together and apply the important mathematical concepts and methods developed throughout the course.
 

Reference and Practice (RAP) (sample material)
The Course 2 Reference and Practice book provides Core-Plus students with summaries of previously learned concepts and methods; distributed practice to review and polish previously learned concepts and skills; and test-taking practice for standardized tests and for college admission tests.
Scope and Sequence (pdf - 548Kb) of topics across Courses 1-4

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