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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.
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- 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.
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| 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.
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- 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.
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| 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.
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- 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.
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| 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.
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- 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.
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| 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.
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- 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.
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| 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.
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- 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 y = A cos Bx.
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| 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.
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- 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.
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| 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.
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