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CPMP
Course 1 1st Edition Units
| Unit
1 (sample
material) |
- Patterns
in Data
- Develops student ability to make sense out of real-world data through use of graphical displays and summary statistics.
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- Topics
include:
- Distributions of data and their shapes, as displayed in number line plots, histograms, box plots, and stem-and-leaf plots; scatterplots and association; plots over time and trends; measures of center including mean, median, mode, and their properties; measures of variation including percentiles, interquartile range, mean absolute deviation, and their properties; transformations of data.
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| Unit
2 (sample
material) |
- Patterns
of Change
- Develops student ability to recognize important patterns of change among variables and to represent those patterns using tables of numerical data, coordinate graphs, verbal descriptions, and symbolic rules.
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- Topics
include:
- Coordinate graphs, tables, algebraic formulas (rules), relationships between variables, linear functions, nonlinear functions, and NOW-NEXT recurrence relations.
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| Unit
3 (sample
material) |
- Linear
Models
- Develops student confidence and skill in using linear functions to model and solve problems in situations that exhibit constant (or nearly constant) rate of change or slope.
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- Topics
include:
- Linear functions, slope of a line, rate of change, intercepts, the distributive property, linear equations (including y = a + bx and NOW-NEXT forms), solving linear equations and inequalities, using linear equations to model given data, and determining best-fit lines for scatterplot data.
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| Unit
4 (sample
material) |
- Graph
Models
- Develops student ability to use vertex-edge graphs to represent and analyze real-world situations involving relationships among a finite number of elements, including scheduling, managing conflicts, and finding efficient routes.
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- Topics
include:
- Vertex-edge graph models, optimization, algorithmic problem solving, Euler circuits and paths, matrix representation of graphs, graph coloring, chromatic number, digraphs, and critical path analysis.
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| Unit
5 (sample
material) |
- Patterns
in Space and Visualization
- Develops student visualization skills and an understanding of the properties of space-shapes including symmetry, area, and volume.
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- Topics
include:
- Two- and three-dimensional shapes, spatial visualization, perimeter, area, surface area, volume, the Pythagorean Theorem, polygons and their properties, symmetry, isometric transformations (reflections, rotations, translations, glide reflections), one-dimensional strip patterns, tilings of the plane, and the regular (Platonic) solids.
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| Unit
6 (sample
material) |
- Exponential
Models
- Develops student ability to use exponential functions to model and solve problems in situations that exhibit exponential growth or decay.
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- Topics
include:
- Exponential growth, exponential functions, fractals, exponential decay, recursion, half-life, compound growth, finding equations to fit exponential patterns in data, and properties of exponents.
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| Unit
7 (sample
material) |
- Simulation
Models
- Develops student confidence and skill in using simulation methods (particularly those involving the use of random numbers) to make sense of real-world situations involving chance.
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- Topics
include:
- Simulation, frequency tables and their histograms, random digit tables and random number generators, independent events, the Law of Large Numbers, and expected number of successes in a series of binomial trials.
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| Capstone |
- Planning
a Benefits Carnival
- 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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