## Mathematics Direct Enrollment (MDE)

### Introduction to Algebra - MDE 10

Effective: 2020-01-01

### Course Description

The course outline below was developed as part of a statewide standardization process.

### General Course Purpose

Prepares students for enrollment into MDE 60, MTH 101-133 or direct enrollment into MTH 154 or MTH 155 with co-requisite.

### Course Objectives

- Demonstrate comprehension of the major topics.
- Apply learned concepts and success skills toward continued progress in MDE 60, MTH 101-133 or direct enrollment in MTH 154 or MTH 155 with co-requisite.

### Major Topics to be Included

- Whole numbers (addition, subtraction, multiplication, division)
- Fractions (addition, subtraction, multiplication, division)
- Decimals (addition, subtraction, multiplication, division)
- Scientific notation
- Percentages (addition, subtraction, multiplication, division)
- Real Number Systems
- Basic Algebraic Equations (One-Step/Two-Step equations)
- Introduction to Graphing (without graphing calculators)

### Learning Support for Quantitative Reasoning - MDE 54

Effective: 2020-01-01

### Course Description

The course outline below was developed as part of a statewide standardization process.

### General Course Purpose

This course provides support to ensure student success with the MTH 154 objectives.

### Course Prerequisites/Corequisites

Corequisite: MTH 154

### Course Objectives

- Communication
- Interpret and communicate quantitative information and mathematical and statistical concepts using language appropriate to the context and intended audience.
- Use appropriate mathematical language in oral, written and graphical forms.
- Read and interpret real world advertisements, consumer information, government forms and news articles containing quantitative information.
- Use quantitative information from multiple sources to make or critique an argument.
- Problem Solving
- Share strategies to find solutions to life application problems to make sense of the mathematical content and persevere in solving them.
- Apply strategies for solving open-ended questions requiring analysis and synthesis of multiple calculations, data summaries, and/or models.
- Apply problem solving strategies to applications requiring multiple levels of engagement.
- Reasoning
- Reason, model, and draw conclusions or make decisions with quantitative information.
- Draw conclusions or make decisions in quantitatively based situations that are dependent upon multiple factors. Students will analyze how different situations would affect the decisions.
- Present written or verbal justifications of decisions that include appropriate discussion of the mathematics involved.
- Recognize when additional information is needed.
- Recognize the appropriate ways to simplify a problem or its assumptions.
- Evaluation
- Critique and evaluate quantitative arguments that utilize mathematical, statistical, and quantitative information.
- Evaluate the validity and possible biases in arguments presented in real world contexts based on multiple sources of quantitative information - for example; advertising, internet postings, consumer information, political arguments.
- Technology
- Use appropriate technology in a given context.
- Use a spreadsheet to organize quantitative information and make repeated calculations using simple formulas.
- Search for and apply internet-based tools appropriate for a given context - for example, an online tool to calculate credit card interest or a scheduling software package.
- Financial Literacy
- Simple Interest
- Define interest and its related terminology.
- Develop simple interest formula.
- Use simple interest formulas to analyze financial issues
- Compound Interest
- Compare and contrast compound interest and simple interest.
- Explore the mechanics of the compound interest formula addressing items such as why the exponent and (1+r/n) is used by building the concept of compounding interest through manual computation of a savings or credit account.
- Apply compound interest formulas to analyze financial issues
- Create a table or graph to show the difference between compound interest and simple interest.
- Borrowing
- Compute payments and charges associated with loans.
- Identify the true cost of a loan by computing APR
- Evaluate the costs of buying items on credit
- Compare total loan cost using varying lengths and interest rates.
- Investing
- Calculate the future value of an investment and analyze future value and present value of annuities (Take into consideration possible changes in rate, time, and money.)
- Compare two stocks and justify your desire to buy, sell, or hold stock investment.
- Explore different types of investment options and how choices may impact one's future such as in retirement.
- Perspective Matters - Number, Ratio, and Proportional Reasoning
- Real-life problems that include interpretation and comparison of summaries which extend beyond simple measures, such as weighted averages, indices, or ranking and evaluate claims based on them.
- Solve real-life problems requiring interpretation and comparison of various representations of ratios (i.e., fractions, decimals, rates, and percentages including part to part and part to whole, per capita data, growth and decay via absolute and relative change).
- Distinguish between proportional and non-proportional situations and, when appropriate, apply proportional reasoning leading to symbolic representation of the relationship. Recognize when proportional techniques do not apply.
- Solve real-life problems requiring conversion of units using dimensional analysis.
- Apply scale factors to perform indirect measurements (e.g., maps, blueprints, concentrations, dosages, and densities).
- Order real-life data written in scientific notation. The data should include different significant digits and different magnitudes.
- Modeling
- Obeservation
- Through an examination of examples, develop an ability to study physical systems in the real world by using abstract mathematical equations or computer programs
- Collect measurements of physical systems and relate them to the input values for functions or programs.
- Compare the predictions of a mathematical model with actual measurements obtained
- Quantitatively compare linear and exponential growth
- Explore behind the scenes of familiar models encountered in daily life (such as weather models, simple physical models, population models, etc.)
- Mathematical Modeling and Analysis
- Collect measurements and data gathered (possibly through surveys, internet, etc.) into tables, displays, charts, and simple graphs.
- Create graphs and charts that are well-labeled and convey the appropriate information based upon chart type.
- Explore interpolation and extrapolation of linear and non-linear data. Determine the appropriateness of interpolation and/or extrapolation.
- Identify and distinguish linear and non-linear data sets arrayed in graphs. Identifying when a linear or non-linear model or trend is reasonable for given data or context.
- Correctly associate a linear equation in two variables with its graph on a numerically accurate set of axes
- Numerically distinguish which one of a set of linear equations is modeled by a given set of (x,y) data points
- Identify a mathematical model's boundary values and limitations (and related values and regions where the model is undefined). Identify this as the domain of an algebraic model.
- Using measurements (or other data) gathered, and a computer program (spreadsheet or GDC) to create different regressions (linear and non-linear), determine the best model, and use the model to estimate future values.
- Application
- Starting with a verbally described requirement, generate an appropriate mathematical approach to creating a useful mathematical model for analysis
- Explore the graphical solutions to systems of simultaneous linear equations, and their real world applications
- Numerically analyze and mathematically critique the utility of specific mathematical models: instructor-provided, classmate generated, and self-generated
- Validity Studies
- Identify logical fallacies in popular culture: political speeches, advertisements, and other attempts to persuade
- Analyze arguments or statements from all forms of media to identify misleading information, biases, and statements of fact.
- Develop and apply a variety of strategies for verifying numerical and statistical information found through web searches.
- Apply the use of basic symbolic logic, truth values, and set theories to justify decisions made in real-life applications, such as if-then-else statements in spreadsheets, Venn Diagrams to organize options, truth values as related to spreadsheet and flow-chart output. (Students must have experience with both symbolic logic and basic truth tables to meet this standard.)

### Major Topics to be Included

- Arithmetic and order of operations
- Operations with fractions, percentages, and decimals
- Exponents
- Formulas
- Units and measurement
- Simplifying algebraic expressions and solving linear equations
- Using technology including calculators and spreadsheet software

### Learning Support for Statistical Reasoning - MDE 55

Effective: 2020-01-01

### Course Description

The course outline below was developed as part of a statewide standardization process.

### General Course Purpose

This course provides support to ensure student success with the MTH 155 objectives.

### Course Prerequisites/Corequisites

Corequisite: MTH 155

### Course Objectives

- Communication
- Interpret and communicate quantitative information and mathematical and statistical concepts using language appropriate to the context and intended audience
- Use appropriate statistical language in oral, written, and graphical terms.
- Read and interpret graphs and descriptive statistics.
- Problem Solving
- Make sense of problems, develop strategies to find solutions, and persevere in solving them.
- Understand what statistical question is being addressed, use appropriate strategies to answer the question of interest, and state conclusions using appropriate statistical language.
- Reasoning
- Reason, model, and draw conclusions or make decisions with quantitative information.
- Use probability, graphical, and numerical summaries of data, confidence intervals, and hypothesis testing methods to make decisions.
- Use probability, graphical, and numerical summaries of data, confidence intervals, and hypothesis testing methods to make decisions.
- Evaluation
- Critique and evaluate quantitative arguments that utilize mathematical, statistical, and quantitative information.
- Identify errors such as inappropriate sampling methods, sources of bias, and potentially confounding variables, in both observational and experimental studies.
- Identify mathematical or statistical errors, inconsistencies, or missing information in arguments.
- Technology
- Use appropriate technology in a given context.
- Use some form of spreadsheet application to organize information and make repeated calculations using simple formulas and statistical functions.
- Use technology to calculate descriptive statistics and test hypotheses.
- Graphical and Numerical Data Analysis
- Identify the difference between quantitative and qualitative data
- Identify the difference between discrete and continuous quantitative data
- Construct and interpret graphical displays of data, including (but not limited to) box plots, line charts, histograms, and bar charts
- Construct and interpret frequency tables
- Compute measures of center (mean, median, mode), measures of variation, (range, interquartile range, standard deviation), and measures of position (percentiles, quartiles, standard scores)
- Sampling and Experimental Design
- Recognize a representative sample and describe its importance
- Identify methods of sampling
- Explain the differences between observational studies and experiments
- Recognize and explain the key concepts in experiments, including the selection of treatment and control groups, the placebo effect, and blinding
- Probability Concepts
- Describe the difference between relative frequency and theoretical probabilities and use each method to calculate probabilities of events
- Calculate probabilities of composite events using the complement rule, the addition rule, and the multiplication rule.
- Use the normal distribution to calculate probabilities
- Identify when the use of the normal distribution is appropriate.
- Recognize or restate the Central Limit Theorem and use it as appropriate.
- Statistical Inference
- Explain the difference between point and interval estimates.
- Construct and interpret confidence intervals for population means and proportions.
- Interpret the confidence level associated with an interval estimate.
- Conduct hypothesis tests for population means and proportions.
- Interpret the meaning of both rejecting and failing to reject the null hypothesis.
- Use a p-value to reach a conclusion in a hypothesis test.
- Identify the difference between practical significance and statistical significance.
- Correlation and Regression
- Analyze scatterplots for patterns, linearity, and influential points
- Determine the equation of a least-squares regression line and interpret its slope and intercept.
- Calculate and interpret the correlation coefficient and the coefficient of determination.
- Categorical Data Analysis
- Conduct a chi-squared test for independence between rows and columns of a two-way contingency table.

### Major Topics to be Included

- Arithmetic and order of operations
- Operations with fractions, percentages, and decimals
- Exponents
- Formulas
- Units and measurement
- Simplifying algebraic expressions and solving linear equations
- Using technology including calculators and spreadsheet software

### Intermediate Algebra - MDE 60

Effective: 2020-01-01

### Course Description

The course outline below was developed as part of a statewide standardization process.

### General Course Purpose

Prepares students for enrollment into MTH 161 with co-requisite.

### Course Objectives

- Demonstrate comprehension of the major topics.
- Apply learned concepts and success skills toward continued progress in MTH 161 with co-requisite.

### Major Topics to be Included

- Properties of exponents
- Polynomials
- Factoring
- Solving quadratics and Pythagorean theorem
- Complex numbers
- Graphing (lines and quadratics)
- Linear equations and inequalities
- Linear systems
- Functions
- Rational expressions and equations
- Radical expressions and equations

### Learning Support for Pre-Calculus - MDE 61

Effective: 2020-01-01

### Course Description

The course outline below was developed as part of a statewide standardization process.

### General Course Purpose

This course provides support to ensure student success with the MTH 161 objectives.

### Course Prerequisites/Corequisites

Corequisite: MTH 161

### Course Objectives

- Relations and Functions
- Distinguish between relations and functions.
- Evaluate functions both numerically and algebraically.
- Determine the domain and range of functions in general, including root and rational functions.
- Perform arithmetic operations on functions, including the composition of functions and the difference quotient.
- Identify and graph linear, absolute value, quadratic, cubic, and square root functions and their transformations.
- Determine and verify inverses of one-to-one functions.
- Polynomial and Rational Functions
- Determine the general and standard forms of quadratic functions.
- Use formula and completing the square methods to determine the standard form of a quadratic function.
- Identify intercepts, vertex, and orientation of the parabola and use these to graph quadratic functions.
- Identify zeros (real-valued roots) and complex roots, and determine end behavior of higher order polynomials and graph the polynomial, and graph.
- Determine if a function demonstrates even or odd symmetry.
- Use the Fundamental Theorem of Algebra, Rational Root test, and Linear Factorization Theorem to factor polynomials and determine the zeros over the complex numbers.
- Identify intercepts, end behavior, and asymptotes of rational functions, and graph.
- Solve polynomial and rational inequalities.
- Interpret the algebraic and graphical meaning of equality of functions (f(x) = g(x)) and inequality of functions (f(x) > g(x))
- Decompose partial fractions of the form P(x)/Q(x) where Q(x) is a product of linear factors
- Exponential and Logarithmic Functions
- Identify and graph exponential and logarithmic functions and their transformations.
- Use properties of logarithms to simplify and expand logarithmic expressions.
- Convert between exponential and logarithmic forms and demonstrate an understanding of the relationship between the two forms.
- Solve exponential and logarithmic equations using one-to-one and inverse properties.
- Solve application problems involving exponential and logarithmic functions.
- Systems of Equations
- Solve three variable linear systems of equations using the Gaussian elimination method.

### Major Topics to be Included

- Factoring
- Simplifying algebraic expressions
- Solving higher order equations with real and complex roots
- Graphing
- Asymptotic behavior
- Power, polynomial, rational, exponential, and logarithmic functions
- Systems of equations and inequalities
- Inverse functions
- Difference quotient
- Gaussian elimination