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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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