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CASA Mathematics Checklist Page 1 of 3 How do I use this document? This document contains a checklist for the content on the Mathematics test in the Core Academic Skills Assessment (CASA) teacher preparation exam. Be sure to familiarize yourself with how the test is organized. The blueprint a.k.a. the test map is broken down into 2 domains. Each domain has 2 standards and each standard has multiple parts. o Domain I – Numbers and Algebra Number and Quantity (Standard 9) Algebra and Functions (Standard 10) o Domain II – Geometry and Statistics Measurement and Geometry (Standard 11) Statistics and Probability (Standard 12) To get the most out of this document, review each of the questions and check off the line items you feel you’ve mastered. This document can be used as a guide to answer the question, “Am I ready to take the CASA Mathematics test?” If additional help is needed, be sure to consult a tutor in the CRC (ES-1125). CASA Mathematics Checklist Standard 9: Number and Quantity I can demonstrate knowledge of number systems, number representations, number operations, and basic number theory, including: I recognize, convert among, and order various representations of rational numbers (e.g., integers, fractions, decimals, powers). I know the different number types e.g. whole, integer, rational, irrational, real, etc. I can convert from a fraction to a decimal and vice versa. I represent rational and irrational numbers on number lines and coordinate axes. I can represent irrational and rational numbers on a number line I know how to represent irrational and rational numbers on a coordinate axes. I compute fluently with rational numbers, including applying order of operations. I know the order of operations. I can solve problems on order of operations. I can solve multistep problems and estimate solutions to problems using a variety of number representations. I know different ways that I can solve multi-step equations. I can use estimation to solve a problem. I can find common factors and multiples of multi-digit numbers. I know what a factor is. Given 2 or more numbers, I can calculate the least common denominator. I know what a multiple is. I recognize and represent ratio concepts (e.g., proportions, unit rates, percents). I know the definition of a ratio. I know the definition of a proportion. I can compare and contrast a ratio, proportion as well as a percent. I can apply ratio concepts and proportional reasoning to solve mathematical and real-word problems. I can solve word (story) problems about ratio concepts and proportional reasoning. I know different ways to solve word problems. CASA Mathematics Checklist Page 2 of 3 Standard 10: Algebra and Functions I demonstrate knowledge of mathematical expressions, basic algebraic techniques, and the use of equations and inequalities to model and solve problems, including: I can apply properties of arithmetic to algebraic expressions. I can combine like terms. I know how to simplify an algebraic expression. I know all of the algebraic properties e.g. commutative, associative, distributive, etc. I can solve one-variable equations and inequalities. I know different strategies for solving one variable equations and inequalities. I can evaluate algebraic expression or a given value of a variable. I can evaluate an algebraic expression. I recognize equivalent versions of algebraic expressions. I can evaluate an algebraic expression. I recognize the difference between an independent and dependent variable. I know what an independent variable is. I know the definition of a dependent variable. I can analyze and solve linear equations and systems of equations. I know the definition of a linear equation. I know the different equations of a line e.g. point-slope, slope-intercept, standard, etc. and can manipulate an equation into point-slope form, slope-intercept form, and/or standard form. I can solve a linear equation. I know at least the three different ways to solve a system of two equations presented below: Graphing Elimination Substitution I can use variables and algebraic expressions to model and solve real-world problems. I can solve word/story problems involving solving algebraic expressions. Domain II – Geometry and Statistics 0007 0008 Measurement and Geometry (Standard 11) Statistics and Probability (Standard 12) Standard 11: Measurement and Geometry: I am able to demonstrate knowledge of principles and procedures of measurement, basic properties of two- and three-dimensional figures, and reasoning in geometry, including: I can solve mathematical and real-world problems involving area, surface area, and volume of two- and threedimensional figures. I know how area is calculated. I know how to calculate surface area. I know how to calculate the volume of different shapes e.g. cube, sphere, cone, etc. I can recognize and represent polygons on a coordinate plane. I can draw a polygon on the coordinate plane. I can solve problems involving scale drawings. I know and can apply the formulas for the circumference and area of a circle. I know what a complementary, supplementary, vertical and adjacent angles are and can solve multistep problems involving each angle. CASA Mathematics Checklist Page 3 of 3 Standard 11: Measurement and Geometry: I am able to demonstrate knowledge of principles and procedures of measurement, basic properties of two- and three-dimensional figures, and reasoning in geometry, including: I know the different types of angles, what they look like and how to use that knowledge to solve word/story problems. I am able to apply the concepts of similarity and congruence. I know and understand the concept of similarity. I know and understand the concept of congruence. I can use similarity and congruence to solve word/story problems. I can apply the Pythagorean Theorem. I know what the Pythagorean Theorem is and the equation. I can solve problems using the Pythagorean Theorem. Standard 12: Statistics and Probability: I can demonstrate knowledge of collection, presentation, and interpretation of data, and of the fundamental properties of probability, including: I can display and interpret data presented in a variety of formats (e.g. dot plots, histograms, circle graphs). I know and understand different types of graphs. I can use and interpret measures of center (e.g. mean, median, mode) and spread (e.g. standard deviation, interquartile range, outliers) in context. I know what mean, median and mode and how to calculate each for a data set. I know how to calculate the mean, median and mode for a frequency distribution. I know what the standard deviation is, how to calculate it by hand, and what it represents. I know what an interquartile range is and how to calculate it. I know and understand the concept of an outlier and how an outlier would effect the mean, median, mode and standard deviation. I can use random sampling to draw inferences about populations. I know and understand the concept of sampling. I can make inferences about a population given a sample of the population. I can make inferences about populations that are based on comparisons of center, variability, and visual overlap of distributions. I can interpret scatter plots and estimate lines of fit for data involving two variables. I know the definition of scatter plot and how can it be used. I know and can determine lines of fit for data involving two variables. I can apply fundamental properties of probability to estimate the outcomes of events. I know and can apply the fundamental properties of probability. I can calculate the probability of an event occurring. I understand and can calculate conditional probability. I know how to calculate probability involving AND and OR. I can determine probabilities using various representations (e.g. Venn diagrams, tree graphs). I know what a Venn diagram is and how to use it to calculate probability. Given a Venn diagram, I can calculate the probability of an event occurring. I know how to construct a tree diagram/graph. Given a tree diagram, I can calculate the probability of an event occurring.
