Mathematics Competencies Tested on the CASA
The math test covers four major skill areas with each skill area addressing a number of subskills. An outline showing these skill areas and their major subskills 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 realworld 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 onevariable 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 realworld problems
Objective 0007: Measurement and Geometry
Demonstrate knowledge of the principles and procedures of measurement, basic properties of two and threedimensional figures, and reasoning in geometry, including:
 solving mathematical and realworld problems involving area, surface area, and volume of two and threedimensional 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)
