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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 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
  • Understand the difference between the terms plurality and majority in an election
  • 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
  • Multiple ranking methods can be employed to make decisions about other issues
  • Employ the "Instant Runoff" method to determine the winner of an election
Week 2 Lesson 1.D Ranking methods
  • Earning the most votes may not be sufficient to win an election
  • Employ the Borda Count method to determine the winner of an election
  • Apply and justify selection strategies to election results
Week 2 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 2 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 3 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 3 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
Week 3 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
Week 4 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
Week 4 Lesson 4.B Conditional Probability Students should be able to determine a conditional probability Calculate conditional probabilities for two or more dependent events
Week 5 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
Week 5 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
Week 5 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
Week 6 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
Week 6 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
  • Use simple and moving weighted averages to analyze data and draw conclusions about the data
Week 6 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
Week 6 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
Week 7 Lesson 7.B Part-to-part ratios & Part-to-whole ratios
  • Convert ratios to percentages
  • Sketch pie graphs using part-to-whole percentages
Construct a pie graph based on ratios and percentages
Week 7 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
  • Analyze and describe data using absolute (additive) comparison and relative (multiplicative) reasoning
Week 7 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
Week 8 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
Week 8 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
Week 8 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
Week 9 Lesson 8.B Proportionality vs. Linearity Determine when 2 quantities are proportional Explain, compare, and contrast linear and proportional relationships
Week 9 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
Week 10 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
Week 10 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
Week 10 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
Week 10 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
Week 11 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
Week 11 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
Week 11 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
Week 12 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
  • Identify and use an appropriate model to predict a future outcome
Week 12 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
Week 12 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
Week 13 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
Week 13 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
Week 14 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
Week 14 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
Week 15 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