MAT1043

Introduction to Mathematics

MAT 1043. Introduction to Mathematics. (3-0) 3 Credit Hours. (TCCN = MATH 1332)

Prerequisite: Satisfactory performance on a placement examination. This course is designed primarily for the liberal arts major to satisfy the Core Curriculum mathematics requirement. Topics may include logic; proofs; deductive and inductive reasoning; number theory; fundamentals of statistics; basic statistical graphs; causal connections; financial management; functions; linear graphs and modeling; exponential growth and decay; logarithms; fundamentals of probability; fundamentals of geometry; and basic ideas from trigonometry, calculus, and discrete mathematics. (Formerly MTC 1043. Credit cannot be earned for both MAT 1043 and MTC 1043.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: LRC1 $12; LRS1 $45; STSI $21.

Date	Sections	Topics	Prerequisite Skills	Student learning outcomes
Week 1	Lesson 1.A	Data	Understand what is a learning community	Collect data from daily life Work positively in a group to make a decision
Week 1	Lesson 1.B	Learning Community	Example	Seek and give help to one another inside and outside of class
Week 1	Lesson 1.C	First-degree equation involving percentages	Determine the original amount, given the percentage that a given number is of the original	Create a first-degree equation involving percentages and solve for the variable Apply and justify selection strategies to election results and decisions about other issues
Week 1	Lesson 1.D	Ranking methods	Example	Example
Week 1	Lesson 2.A	Graphical Display	Be able to read and interpret graphical displays Know the definition of mean Know the definition of median	Analyze a variety of graphical displays and interpret them in context Compute the mean of a set of data Construct a dot plot or histogram from data
Week 1	Lesson 2.C	Analyzing graphical displays	Compare side-by-side graphical displays	Be able to read and interpret graphical displays	Write a contextual analysis of a graphic display in a formal paper including appropriate mathematical language and explanations
Week 1	Lesson 3.A	Sampling	Students should know the symbols for pop. Mean, sample mean, pop. Standard deviation, sample standard deviation	Explain the difference between populations and samples Use the characteristics of a sample to describe the population Analyze the conclusions of a study and explain the limitations on inferences made
Week 1	Lesson 3.B	Mean and Central Limit Theorem	Students should know how to determine the mean of a data set	Graph sample means and use the central limit theorem to estimate the population mean
Example	Lesson 3.C	Standard Deviation	Students should be able to calculate the size of a portion given the size of the whole and a percentage	Use standard deviation to interpret the spread of a data set Calculate the percentage of data in a graph region
Example	Lesson 4.A	Probability	Students should be able to convert between fractions, decimals, and percentages	Calculate theoretical probability of two or more independent events Calculate AND and OR probabilities for independent events
Example	Lesson 4.B	Conditional Probability	Students should be able to determine a conditional probability	Calculate conditional probabilities for two or more dependent events
Example	Lesson 5.A	Conversions	Be able to calculate unit ratios Be able to use ratios to convert units Be able to perform dimensional analysis	Recognize when converting units is needed Use conversion to make comparisons
Example	Lesson 5.B	Index numbers	Be able to convert ratios to decimals and percentages, and divide Be able to describe types of averages	Perform calculations involving index numbers Make and justify decisions and evaluate claims using index numbers
Example	Lesson 5.C	Weighted averages	Should be able to calculate mean	Calculate weighted averages Use weighted averages to analyze data and draw conclusions about the data
Example	Lesson 5.D	Expected Value	Be able to calculate, percentages, means, and weighted averages be able to find the mean of a data set	Calculate expected value Make predictions about real world scenarios
Example	Lesson 6.A	Weighted moving average graphs	Weighted moving average Graph points Find the mean of a data set	Calculate and compare simple and weighted moving averages Analyze graphs of moving average data
Example	Lesson 6.B	Weighted moving average graphs continued	Weighted moving average Find the mean of a data set Ue a spreadsheet to do calculations and create graphs	Calculate and compare simple and weighted moving averages Write a contextual analysis of a graphical display Write a ratio or percentage and explain its meaning within a context
Example	Lesson 7.A	Ratios and percentages	Be able to write and simplify fractions, create a pie graph, convert fractions to percentages	Determine percentages based on part-to-whole ratios Write a ratio or percentage and explain in meaning within a context Read a budget, determine values of line items, and draw conclusions about the overall distributions of funds
Example	Lesson 7.B	Part-to-part ratios & Part-to-whole ratios	Example	Construct a pie graph based on ratios and percentages
Example	Lesson 7.C	Absolute change (additive reasoning) & Relative change (multiplicative reasoning)	Students should be able to create a line graph from data	Analyze data in a spreadsheet and graphs Develop reasonable hypothesis supported by evidence Create line graphs and describe patterns in graphs
Example	Lesson 7.D	Adjusting claims and hypothesis	Students should be able to create a line graph from data	Analyze data in a spreadsheet and graphs to compare changes in categories
Example	Lesson 7.E	Debt-to-income (DTI) ratios	Be able to write ratios and proportions, solve proportions, calculate percentages from ratios	Calculate a DTI ratio Draw conclusions from DTI about the appropriateness of the percentage of income spent on housing and debt
Example	Lesson 7.F	Proportional reasoning	Write rates, convert ratios to percentages	Interpret ratios and percentages as rates of change Compare ratios and percentages Interpret graphical displays Compare mathematical relationships using a variety of representations
Example	Lesson 8.A	Mathematical (Linear) relationships	Be able to plot ordered pairs, sketch graphs of linear equations, construct a linear equation given the slope and y intercept Write a linear equation based on a verbal description/or that passes through 2 points Solve a 2-step linear equation	Compare mathematical relationships using a variety of representations Write a linear equation given a slope and y intercept
Example	Lesson 8.B	Proportionality vs. Linearity	Determine when 2 quantities are proportional	Explain, compare, and contrast linear and proportional relationships
Example	Lesson 8.C	Simple and Compound Interest (Linear and Exponential Models)	Write a percentage as a decimal Perform calculations with percentages	Describe the difference between simple and compound interest in practical and mathematical terms Compare and contrast patterns in linear and exponential models
Example	Lesson 8.D	Regression	Read a scatterplot Interpret the slope of a line in context	Create a scatterplot and regression equation using technology and estimate the parameters of the line of best fit Interpret the parameters (slope, y-intercept, coefficient of determination) of a simple linear regression
Example	Lesson 8.E	Piecewise Linear Function	Use a percentage rate to calculate tax Use constant rates of change to write a linear equation Identify the slope of a linear function Solve a linear equation for a given output	Model a progressive income tax system algebraically and graphically Compare a progressive income tax system to a flat tax system and explain advantages and disadvantages of different income tax systems
Example	Lesson 9.A	Depreciation	Graph ordered pairs Identify the value of the output variable, given the input value, using a graphical and symbolic representation of the relationship between two variables	Interpolate and extrapolate using a graphical representation of the relationship between two variables Use a symbolic model to find the exact value of one variable, given the value of the other variable, and relate those values to the context of the problem
Example	Lesson 9.B	Geometric interpretation of interpolation	Graph data from a scenario Create proportions using the sides of similar triangles and solve them	Create a proportion between corresponding sides of similar triangles Use variables with subscripts
Example	Lesson 9.C	Univariate, Bivariate, Correlation and Causation	Calculate measures of central tendency Analyze data and visual displays of univariate and bivariate data and describe trends	Create a line graph for univariate data Determine, informally, the correlation between bivariate data Analyze data and related graphs and describe the trend of the data
Example	Lesson 9.D	Univariate, Bivariate, Correlation and Causation	Create and interpret a scatterplot	Explain why, even if there is a strong correlation, a change in one variable may not cause a change in the other
Example	Lesson 10.A	Time series model of exponential growth	Use formulas in spreadsheets	Develop a time series model for the Fibonacci problem Test whether data are exponential by comparing the rate of growth to the population size
Example	Lesson 10.B	Linear and Exponential Models	Create a table of values and scatterplot in a spreadsheet Calculate the average rate of growth for a period of time Calculate the first differences in a data set	Evaluate the mathematical appropriateness of a model give historical data Determine whether a data set suggests a linear or exponential relationship Use an appropriate model to predict a future outcome
Example	Lesson 11.A	Continuous Growth	Analyze the relationship of input and output values in a problem situation Determine whether numerical and graphical relationships are increasing at a constant rate, at an increasing rate or at a decreasing rate	Sketch a model for a population that increases at an increasing rate and a decreasing rate Identify behavior in a graph, draw conclusions about the behavior, and predict future outcomes
Example	Lesson 11.B	Carrying Capacity and Logistic Growth Rate	Calculate absolute and relative change Read delta notation for absolute change	Develop discrete models of natural phenomena and use the models to predict future values Calculate the carrying capacity and logistic growth rate of a real-world scenario
Example	Lesson 11.C	Logistic Growth Model	Determine the increasing and/or decreasing behavior of outputs in a table	Explore the changes of the values of the parameters of a logistic growth model and describe the effect of those changes on the model
Example	Lesson 11.D	Complex Population Growth and Decay Models	Find the constant of proportionality and express variables that are jointly proportional Determine how jointly proportional variables affect each other in an abstract model	Develop a parameterized time series model with more than two dependent variables in a spreadsheet
Example	Lesson 11.E	Analyzing Complex Population Growth and Decay Models	Extract data from an academic article and create models for the data	Determine parameters to match a model’s predictions against historical data Create a spreadsheet involving the formulas of the model to predict future behavior
Example	Lesson 12.A	Periodic Function	Plot points on coordinate axis Analyze the shape of a graph and find 12A coordinate values on a graph	Sketch a graph that depicts a periodic phenomenon Identify the period and amplitude of a periodic function Compare and contrast the graphs of different periodic models
Example	Lesson 12.B	The Sine Function	Plot points on a graph Understand that constants (Parameters) in an equation control the relationship between the dependent variable and independent variable	Describe the effect that changing one or more parameters has on the graph of a sine function Change the parameters of the sine curve to match given criteria