Mathematics Competencies Tested on the CASA
The math test covers four major skill areas with each skill area addressing a number of sub-skills. An outline showing these skill areas and their major sub-skills is shown below.
Objective 0005: Number and Quantity
Demonstrate knowledge of number systems, number representations, number operations, and basic number theory, including:
- recognizing, converting among, and ordering various representations of rational numbers (e.g., integers, fractions, decimals, powers)
- representing rational and irrational numbers on number lines and coordinate axes
- computing fluently with rational numbers, including applying order of operations
- solving multistep problems and estimating solutions to problems using a variety of number representations
- finding common factors and multiples of multidigit numbers
- recognizing and representing ratio concepts (e.g., proportions, unit rates, percents)
- applying ratio concepts and proportional reasoning to solve mathematical and real-world problems
Objective 0006: Algebra and Functions
Demonstrate knowledge of mathematical expressions, basic algebraic techniques, and the use of equations and inequalities to model and solve problems, including:
- applying properties of arithmetic to algebraic expressions
- solving one-variable equations and inequalities
- evaluating algebraic expressions for a given value of a variable
- recognizing equivalent versions of algebraic expressions
- recognizing the difference between an independent and a dependent variable
- analyzing and solving linear equations and systems of equations
- using variables and algebraic expressions to model and solve real-world problems
Objective 0007: Measurement and Geometry
Demonstrate knowledge of the principles and procedures of measurement, basic properties of two- and three-dimensional figures, and reasoning in geometry, including:
- solving mathematical and real-world problems involving area, surface area, and volume of two- and three-dimensional figures
- recognizing and representing polygons on a coordinate plane
- solving problems involving scale drawings
- applying the formulas for the circumference and area of a circle
- using facts about complementary, supplementary, vertical, and adjacent angles to solve multistep problems
- applying the concepts of similarity and congruence
- applying the Pythagorean theorem
Objective 0008: Statistics and Probability
Demonstrate knowledge of the collection, presentation, and interpretation of data, and of the fundamental properties of probability, including:
- displaying and interpreting data presented in a variety of formats (e.g., dot plots, histograms, circle graphs)
- using and interpreting measures of center (e.g., mean, median, mode) and spread (e.g., standard deviation, interquartile range, outliers) in context
- using random sampling to draw inferences about populations
- making inferences about populations that are based on comparisons of center, variability, and visual overlap of distributions
- interpreting scatter plots and estimating lines of fit for data involving two variables
- applying fundamental properties of probability to estimate the outcomes of events
- determining probabilities using various representations (e.g., Venn diagrams, tree graphs)
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