| Originator: | Clifford, Laurel Status: Approved Department: MAT Mathematics | |
| Date Created: | 11/22/2013 Submitted: 11/22/2013 Completed: 12/10/2013 | |
| Effective Semester: | Fall | |
| Catalog Year: | 2014-15 | |
| Course Prefix: | MAT | |
| Course Number: | 142 | |
| Course Full Title: | College Mathematics | |
| Reason for Evaluation: | Competencies Change Prerequisite Change | |
| Current Credit: | 3 | |
| Lecture Hours: | 3 | |
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| SUN Course?: | No | |
| AGEC Course?: | Yes | |
| Articulated?: | Yes | |
| Transfer: | ASU NAU UA | |
| Prerequisite(s): | Grade of C or better in MAT 121 or MAT 099A or appropriate score on assessment test | |
| Corequisite(s): | none | |
| Catalog Course Description: | College Mathematics provides students a broad overview of mathematical topics, including Critical Thinking Skills, Geometry, Personal Finance, Probability, and Statistics. This course emphasizes the basic concepts, language and history of topics in mathematics that are not typically found in the traditional algebra sequence. This course satisfies the minimum competency requirement in mathematics and is recommended for those students majoring in the liberal arts, elementary education, and the social sciences whose major does not require College Algebra or Precalculus. | |
| Course Learning Outcomes: | 1. Draw parallels among historical milestones in mathematics and the development of mathematical thought
2. Integrate a variety of mathematical reasoning and critical thinking skills while exploring the diverse nature of mathematical expression 3. Devise mathematically sound pathways to solutions of contextual problems in personal finance, probability and statistics, geometry, number theory, and voting and apportionment 4. Make informed decisions in areas related to mathematics based upon mathematical models, reasoning, and problem solving experiences |
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| Course Competencies: | Competency 1 Construct mathematically sound pathways to viable solutions of contextual problems using critical thinking skills
Objective 1.1 Justify whether a given argument represents inductive or deductive reasoning Objective 1.2 Hypothesize generalizations of observed patterns utilizing inductive reasoning Objective 1.3 Create a counterexample to disprove generalizations Objective 1.4 Employ inductive and deductive reasoning to solve multi-step problems of varying complexity Objective 1.5 Construct solutions of contextual problems through the application of various problem solving techniques such as organized lists, diagrams, pictures, guess/check, proportional reasoning, dimensional analysis and algebraic equations Competency 2 Solve contextual problems related to personal finance with linear and exponential growth and decay Objective 2.1 Distinguish between linear and exponential growth and decay in a variety of representations and contexts including personal finance Objective 2.2 Solve applied problems involving ordinary interest, discount loans, and the United States Rule Objective 2.3 Solve investment problems involving compound interest, determine annual percentage yield, and find the present value of a future amount Objective 2.4 Solve problems involving present and future values of annuities Objective 2.5 Use the basic terminology associated with installment loans and mortgages Objective 2.6 Solve problems involving installment loans, amortization and mortgages Competency 3 Devise solutions to problems involving chance via the application of the concepts of probability Objective 3.1 Describe the contributions of personalities in the history of probability Objective 3.2 Distinguish between empirical and theoretical probability in context Objective 3.3 Determine the empirical probability of an event from given data Objective 3.4 Apply the law of large numbers in context Objective 3.5 Calculate theoretical probabilities of simple events for experiments having equally likely outcomes Objective 3.6 Determine the odds in favor and against and event Objective 3.7 Translate among the probability and the odds in favor of and against an event Objective 3.8 Calculate the expected value (mathematical expectation) of an experiment Objective 3.9 Judge whether a game is fair or not via its expected value Objective 3.10 Construct tree diagrams to determine the possible outcomes of an experiment and their probabilities Objective 3.11 Apply the counting principle to determine the number of possible outcomes of an experiment Objective 3.12 Apply principles of probability to solve "and" and "or" type problems Objective 3.13 Evaluate whether events in context are independent, dependent, and/or mutually exclusive Objective 3.14 Calculate conditional probability for simple dependent events Objective 3.15 Judge whether a combination or permutation is appropriate to calculate the number of outcomes for the sample space and the event Objective 3.16 Construct probabilities of complex events using permutations and combinations Objective 3.17 Apply the binomial theorem in solving probability problems where the method of solution is not given Competency 4 Integrate statistical reasoning concepts in the summarization and interpretation of data Objective 4.1 Distinguish among the various sampling techniques in context Objective 4.2 Evaluate given scenarios for common misuses of statistics Objective 4.3 Organize statistical data using frequency distributions Objective 4.4 Create graphical representations of statistical data using circle graphs, histograms, frequency polygons, and stem and leaf plots Objective 4.5 Judge which type of graphical representation is appropriate for representation of a given data set Objective 4.6 Hypothesize characteristics of populations from graphical representations of statistical data Objective 4.7 Calculate measures of central tendency and dispersion for data sets Objective 4.8 Interpret the contextual meaning of measures of central tendency and dispersion for a given data set Objective 4.9 Critique the appropriate use of measures of central tendency for a given data set Objective 4.10 Identify important characteristics of the normal distribution Objective 4.11 Calculate z-scores using data that is normally distributed Objective 4.12 Interpret the contextual meaning of z-scores for data that is normally distributed Objective 4.13 Calculate the percent of data set that falls within one (two, three) standard deviations of the mean Objective 4.14 Calculate the percent (or probability) of data below or above a particular z-score or between two z-scores using a standard normal distribution z-table Objective 4.15 Create scatterplots for bivariate data Objective 4.16 Hypothesize the type of correlation that exists in bivariate data from its scatterplot Objective 4.17 Make predictions about bivariate data in context through the application of linear regression Competency 5 Compare the properties of various number sets and patterns in problems of contextual and historical interest Objective 5.1 Identify the historical personages associated with number theory Objective 5.2 Apply the sieve of Erasthones Objective 5.3 Apply divisibility tests for 2, 3, 4, 5, 9, 10 in determining whether a number is prime or composite Objective 5.4 Calculate the greatest common divisor (GCD) and least common multiple (LCM) of two or more numbers via prime factorizations Objective 5.5 Judge whether a contextual problem involves the application of the GCD or the LCM Objective 5.6 Organize numbers into their appropriate set(s)in the progression through natural, whole, integer, rational, irrational, real, and imaginary numbers Objective 5.7 Convert terminating or repeating decimal numbers into their rational forms Objective 5.8 Create rational numbers between two given rational numbers through the application of the concept of density of rational numbers Objective 5.9 Discern between radical and transcendental numbers Objective 5.10 Judge which number sets are closed under various operations Objective 5.11 Apply the commutative, associative and distributive properties in numerical and verbal contexts Objective 5.12 Distinguish among arithmetic, geometric, and Fibonacci sequences in context Objective 5.13 Create the general formula (nth term) for arithmetic and geometric sequences Objective 5.14 Calculate the sum of finite arithmetic and geometric sequences in real-world contexts Objective 5.15 Identify the Fibonacci sequence and its relationship to the golden mean, nature, art and music Competency 6 Evaluate different methods for voting and apportionment for their flaws and benefits Objective 6.1 Evaluate the possible results of elections by applying different voting methods including plurality and plurality with elimination, Bourda count, and pairwise comparison Objective 6.2 Identify the majority, head-to-head, monotonicity and irrelevant alternatives criteria for a fair voting method, and which are satisfied by each of the methods above Objective 6.3 Apply apportionment methods such as Hamilton's, Jefferson's, Adam's and Webster's methods in context Objective 6.4 Identify the Alabama, Population, and New States paradoxes as flaws in apportionment methods Competency 7 Model geometric concepts during the problem solving process using Euclidean, Non-Euclidean and transformational geometry and their interrelationships Objective 7.1 Analyze the properties of various geometric figures such as points, lines, planes, segments, triangles, quadrilaterals and other polygons Objective 7.2 Calculate values for angles using angle relationships, parallel line relationships, and polygon properties Objective 7.3 Apply properties of similar figures in the solution of contextual problems involving indirect measurement Objective 7.4 Apply the concepts of area, perimeter, surface area and volume of various geometric figures Objective 7.5 Evaluate whether the concept of perimeter, area, surface area, or volume is appropriate while solving contextual problems Objective 7.6 Apply the Pythagorean Theorem in the solution of contextual problems involving indirect measurement Objective 7.7 Transform geometric figures using reflections, translations, rotations, and glide reflections Objective 7.8 Analyze a given figure for the symmetry it exhibits Objective 7.9 Contrast different interpretations of the parallel-line postulate and their relation to Euclidean and non-Euclidean geometries |
| Document | Document Name | File Type |
|---|---|---|
| Review Document | MAT142 Bloom's Taxonomy Worksheet - 2013-11-27 03:32:36 Etc/GMT | application/msword |
| Review Document | Response to MAT 142 Bloom's Taxonomy WS - 2013-12-03 07:07:45 Etc/GMT | application/msword |