ISE Math in Our World: A Quantitative Reasoning Approach

I was born and raised in Cleveland, and started college at Bowling Green State University in 1984 majoring in creative writing. Eleven years later, I walked across the graduation stage to receive a PhD in math, a strange journey indeed. After two years at Franklin and Marshall College in Pennsylvania, I came home to Ohio, accepting a tenure-track job at the Hamilton campus of Miami University. I’ve won a number of teaching awards in my career, and while maintaining an active teaching schedule, I now spend an inordinate amount of time writing textbooks and course materials. I’ve written or co-authored either seven or twelve textbooks, depending on how you count them, as well as several solutions manuals and interactive CD-ROMS. After many years as developmental math coordinator at Miami Hamilton, I share the frustration that goes along with low pass rates in the developmental math curriculum. Far too many students end up on the classic Jetson’s-style treadmill, with the abstract nature of the traditional algebra curriculum keeping them from reaching their goals. Like so many instructors across the country, I believe the time is right to move beyond the one-size-fits-all curriculum that treats students the same whether they hope to be an engineer or a pastry chef. “Because we’ve always done it that way” is NOT a good reason to maintain the status quo in our curriculum. Let’s work together to devise alternate pathways that help students to learn more and learn better while hastening their trip into credit-bearing math courses. Since my book (Math in Our World) is written for the Liberal Arts Math and Quantitative Literacy market, I think I’m in the right place at the right time to make a difference in the new and exciting pathways course. I’m in a very happy place right now: my love of teaching meshes perfectly with my childhood dream of writing. (Don’t tell my publisher this – they think I spend 20 hours a day working on textbooks – but I’m working on my first novel in the limited spare time that I have.) I’m also a former coordinator of Ohio Project NExT, as I believe very strongly in helping young college instructors focus on high-quality teaching as a primary career goal. I live in Fairfield, Ohio with my lovely wife Cat and fuzzy dogs Macleod and Tessa. When not teaching or writing, my passions include Ohio State football, Cleveland Indians baseball, heavy metal music, travel, golf, and home improvement. I can say without a doubt that I was made to be in a classroom. I followed the footsteps of my father, a 35-year middle school math teaching veteran, into this challenging yet rewarding career. My college experience began as a community college student at Lakeland College in Mattoon, Illinois. From there, I received a Bachelor of Science in Mathematics from Eastern Illinois University and a Master of Science in Mathematics from Southern Illinois University. I accepted a tenure-track faculty position at Parkland College, where I have taught developmental and college-level courses for 15 years. I had the opportunity to begin writing textbooks shortly after I started teaching at Parkland. My then department chair and mentor, James W. Hall, and I co-authored several textbooks in Beginning and Intermediate Algebra. In the fall of 2011, our department began discussing the idea of creating two tracks through our beginning and intermediate algebra courses. The idea stemmed from two issues. First, most of our beginning and intermediate algebra students were headed to either our Liberal Arts Math or our Introduction to Statistics course. Second, we wanted to beef up intermediate algebra to better prepare those students who were headed to college algebra. These were two competing ideas! Increasing the algebraic rigor of these courses seemed to “punish” students who were not heading to college algebra. With the two track system, we implemented a solution that best serves both groups of students. I have to admit that I was initially concerned that offering an alternate path through developmental mathematics for students not planning to take college algebra would lead to a lowering of standards. However, my participation in our committee investigating this idea led me to believe it was possible to offer a rigorous course that was exceedingly more appropriate for this group of students. Since there were no materials for the course, I began creating my own and was paired by McGraw Hill with Dave Sobecki. Together, we have created the material that I have been using for class testing. After a semester and a half of piloting these materials and seeing the level of enthusiasm and engagement in the mathematical conversations of my students, I am now convinced that this is an ideal course to refine and offer. As a trusted colleague told me, “this is just a long overdue idea.” Outside of the classroom and away from the computer, I am kept educated, entertained and ever-busy my wonderful wife, Nikki, and our two children, Charlotte, 6 and Jake, 5. I am an avid St. Louis Cardinals fan and enjoy playing recreational softball and golf in the summertime with colleagues and friends.

Unit 1: EVERYONE HAS PROBLEMS 




Lesson 1-1: Be Reasonable (Inductive and Deductive Reasoning) 

Objective 1: Explain the difference between inductive and deductive reasoning. 

Objective 2: Use inductive reasoning to make conjectures. 

Objective 3: Use deductive reasoning to prove or disprove a conjecture. 




Lesson 1-2: More or Less (Estimation and Interpreting Graphs)

Objective 1: Use rounding and mental arithmetic to estimate the answers to applied problems. 

Objective 2: Obtain and interpret information from bar graphs, pie charts, and time series graphs. 




Lesson 1-3: You Got a Problem? (Problem-Solving Strategies)

Objective 1: Identify the four steps in Polya’s problem-solving procedure. 

Objective 2: Apply Polya’s procedure to solving problems. 

Objective 3: Solve problems using different strategies: trial and error, drawing a diagram, using algebra, and comparing different outcomes. 




Unit 2: MANAGING YOUR MONEY 




Lesson 2-1: Giving 110 Percent (Review of Percents)

Objective 1: Perform conversions and calculations involving percents. 

Objective 2: Find percent increase or decrease. 

Objective 3: Solve problems using percents. 

Objective 4: Evaluate the legitimacy of claims based on percents. 




Lesson 2-2: Building It Is the Easy Part . . . (Budgeting)

Objective 1: Calculate take-home pay and monthly expenses. 

Objective 2: Identify necessary expenses and luxuries. 

Objective 3: Prepare a monthly budget. 

Objective 4: Prorate long-term expenses to save in advance for them.

 

Lesson 2-3: A Topic of Interest (Simple Interest) 

Objective 1: Define interest and understand related terminology. 

Objective 2: Develop simple interest formulas. 

Objective 3: Use simple interest formulas to analyze financial issues. 




Lesson 2-4: Like a Snowball Rolling Downhill (Compound Interest)

Objective 1: Describe how compound interest differs from simple interest. 

Objective 2: Develop compound interest formulas. 

Objective 3: Use compound interest formulas to analyze financial issues. 




Lesson 2-5: Buying Stuff Without Money (Installment Buying)

Objective 1: Compute payments and charges associated with installment loans. 

Objective 2: Identify the true cost of a loan by computing APR. 

Objective 3: Evaluate the costs of buying items on credit. 




Lesson 2-6: Investing in Yourself (Education and Home Loans)

Objective 1: Understand different student loan options. 

Objective 2: Compute interest and monthly payments on a student loan. 

Objective 3: Evaluate the effects of capitalizing interest. 

Objective 4: Analyze various aspects of a mortgage. 

Objective 5: Compare two mortgages of different lengths. 

Objective 6: Prepare an amortization schedule. 




Lesson 2-7: A Walk on Wall Street (Stocks and Bonds)

Objective 1: Read information from a stock listing. 

Objective 2: Calculate costs of buying stock, and profit or loss from selling. 

Objective 3: Study the price-to-earnings ratio, and use it to analyze the value of a stock. 

Objective 4: Calculate profit from a bond sale. 




Lesson 2-8: A Taxing Situation (Income Taxes)

Objective 1: Understand why we pay taxes. 

Objective 2: Explain the basic process of paying taxes. 

Objective 3: Determine the amount of tax due based on taxable income. 

Objective 4: Complete a 1040 form. 




Unit 3: PLACE YOUR BETS 




Lesson 3-1: So You’re Saying There’s a Chance . . . (Basic Probability)

Objective 1: Understand key terminology in the study of probability. 

Objective 2: Compute and interpret theoretical and empirical probabilities. 

Objective 3: Compare theoretical and empirical probability. 




Lesson 3-2: Make It Count (Sample Spaces and Counting Techniques)

Objective 1: Describe how counting techniques are useful in probability theory. 

Objective 2: Use tree diagrams and tables to determine sample spaces and compute probabilities. 

Objective 3: Develop and use the fundamental counting principle. 




Lesson 3-3: Combining Forces (Combinatorics)

Objective 1: Understand how combinatorics are useful in probability theory. 

Objective 2: Distinguish between permutations and combinations. 

Objective 3: Find the number of permutations and combinations of n objects. 

Objective 4: Find the number of permutations and combinations of n objects chosen r at a time. 




Lesson 3-4: Too Good to Be True? (Probability Using Counting Techniques)

Objective 1: Recognize probability problems where permutations are useful and where combinations are useful. 

Objective 2: Use permutations to calculate probabilities. 

Objective 3: Use combinations to calculate probabilities. 




Lesson 3-5: Odds and Ends (Odds and Expected Value)

Objective 1: Distinguish between odds and probability. 

Objective 2: Compute and interpret the odds in favor of and odds against an event. 

Objective 3: Compute odds from probability and vice versa. 

Objective 4: Develop a procedure for finding expected value. 

Objective 5: Compute and interpret expected values. 




Lesson 3-6: An Exclusive Club (Addition Rules for Probability)

Objective 1: Distinguish between events that are and are not mutually exclusive. 

Objective 2: Develop addition rules for finding probabilities of “or” events that are and are not mutually exclusive. 

Objective 3: Use the addition rules to calculate probabilities. 




Lesson 3-7: Independence Day (Multiplication Rules and Conditional Probability)

Objective 1: Distinguish between events that are and are not independent. 

Objective 2: Develop multiplication rules for finding probabilities of “and” events that are and are not independent. 

Objective 3: Use the multiplication rules to calculate probabilities. 

Objective 4: Define, compute, and interpret conditional probabilities. 




Lesson 3-8: Either/Or (Binomial Probabilities)

Objective 1: Identify binomial experiments. 

Objective 2: Compute and interpret probabilities of outcomes in a binomial experiment. 

Objective 3: C
ompute cumulative binomial probabilities.




Unit 4: STATISTICALLY SPEAKING 




Lesson 4-1: Crunching the Numbers (Gathering and Organizing Data)

Objective 1: Explain the difference between a population and a sample. 

Objective 2: Compare and contrast different sampling methods. 

Objective 3: Organize data with frequency distributions. 

Objective 4: Analyze data with stem and leaf plots. 




Lesson 4-2: Picture This (Representing Data Graphically) 

Objective 1: Draw and interpret bar graphs from frequency distributions. 

Objective 2: Draw and interpret pie charts from frequency distributions. 

Objective 3: Draw and interpret histograms and frequency polygons from frequency distributions. 

Objective 4: Draw and interpret time series graphs. 




Lesson 4-3: An Average Joe (Measures of Average)

Objective 1: Compute measures of average for given data. 

Objective 2: Interpret the story told by measures of average. 

Objective 3: Compute and interpret the mean for grouped data. 

Objective 4: Compute weighted grades. 

Objective 5: Use technology to compute measures of average. 




Lesson 4-4: Your Results May Vary (Measures of Variation)

Objective 1: Compute measures of variation for a given data set. 

Objective 2: Interpret standard deviation for a data set. 

Objective 3: Make meaningful comparisons of standard deviation for two data sets. 

Objective 4: Analyze the procedure for computing standard deviation. 




Lesson 4-5: Where Do You Rank? (Measures of Position in a Data Set)

Objective 1: Compute percentile ranks. 

Objective 2: Find data corresponding to a given percentile rank. 

Objective 3: Use percentiles to compare data from different sets. 

Objective 4: Compute quartiles and use them to analyze spread. 

Objective 5: Draw and interpret box plots. 




Lesson 4-6: Just a Normal Day (Normal Distributions and Z Scores)

Objective 1: Recognize characteristics of data that are normally distributed. 

Objective 2: Understand the connection between area under a normal curve, percentage, and probability. 

Objective 3: Make an educated guess about the empirical rule, then use the rule to calculate percentages and probabilities. 

Objective 4: Compare data values from different sets using Z scores. 




Lesson 4-7: The Way the Cookie Crumbles (Applications of the Normal Distribution)

Objective 1: Use normal distributions to find probabilities, percentages, and percentiles. 

Objective 2: Learn how normal distributions are used in manufacturing and packaging. 

Objective 3: Recognize data that are approximately normally distributed. 




Lesson 4-8: Making Connections (Correlation and Regression Analysis)

Objective 1: Draw and analyze scatter plots for two data sets. 

Objective 2: Define correlation coefficient, and decide if correlation coefficients are significant. 

Objective 3: Find regression lines and use them to make predictions. 

Objective 4: Recognize the difference between data sets being related and being linearly related. 




Lesson 4-9: Trust No One (Misuses of Statistics)

Objective 1: Identify misuses of sampling and evaluate their effect on statistical results. 

Objective 2: Recognize and describe common misuses of compiling and reporting statistics that make them meaningless or deceiving. 

Objective 3: Study ways that graphs can be manipulated to tell a desired story. 




Unit 5: BUILDING MODELS 




Lesson 5-1: Keeping Things in Proportion (Ratios and Proportions)

Objective 1: Compare two quantities using ratios. 

Objective 2: Describe the value of using ratios to compare quantities rather than differences. 

Objective 3: Solve proportions. 

Objective 4: Solve problems that involve proportional reasoning. 




Lesson 5-2: Making Some Extra Cash (The Basics of Graphing Functions)

Objective 1: Demonstrate an understanding of the significance of a rectangular coordinate system. 

Objective 2: Describe what the graph of an equation is. 

Objective 3: Use and interpret function notation. 

Objective 4: Graph and interpret linear functions. 

Objective 5: Graph and interpret quadratic functions. 




Lesson 5-3: A Slippery Slope (Modeling with Linear Functions)

Objective 1: Calculate slope and interpret as rate of change. 

Objective 2: Solve problems using linear modeling, both algebraically and using technology. 




Lesson 5-4: Ahead of the Curve (Modeling with Quadratic Functions)

Objective 1: Identify quantities that are and are not good candidates to be modeled with quadratic functions. 

Objective 2: Solve problems using quadratic modeling, both algebraically and using technology. 




Lesson 5-5: Progressing Regressively (Linear and Quadratic Regression)

Objective 1: Decide whether a linear or a quadratic model is most appropriate for a data set. 

Objective 2: Create a line or parabola of best fit from data. 




Lesson 5-6: Phone a Friend (Modeling with Exponential and Log Functions)

Objective 1: Identify quantities that are and are not good candidates to be modeled with exponential equations. 

Objective 2: Solve problems by exponential modeling, both algebraically and using technology. 

Objective 3: Define logarithms as inverses of exponentials. 

Objective 4: Solve problems by logarithmic modeling, both algebraically and using technology. 




Unit 6: THE JOY OF SETS 




Lesson 6-1: Setting Up (The Basics of Working with Sets)

Objective 1: Define sets and use different methods to represent them. 

Objective 2: Identify when sets are equivalent. 

Objective 3: Study cardinality for finite and infinite sets. 




Lesson 6-2: Busy Intersections, More Perfect Unions (Operations on Sets)

Objective 1: Find the complement and all subsets for a given set. 

Objective 2: Evaluate set statements involving subset notation. 

Objective 3: Perform and apply set operations: union, intersection, subtraction.

 

Lesson 6-3: Worlds Collide (Studying Sets with Two-Circle Venn Diagrams)

Objective 1: Illustrate sets with two-circle Venn diagrams. 

Objective 2: Develop and use De Morgan’s laws. 

Objective 3: Use Venn diagrams to decide if two sets are equal. 

Objective 4: Review
how Venn diagrams can be used in probability. 




Lesson 6-4: A Dollar for Your Thoughts (Using Sets to Solve Problems)

Objective 1: Illustrate sets with three-circle Venn diagrams. 

Objective 2: Decide if two sets are equal using three-circle Venn diagrams. 

Objective 3: Solve a variety of applied problems using Venn diagrams.




Unit 7: UNCOMMON SENSE 




Lesson 7-1: Opening Statements (Statements and Quantifiers)

Objective 1: Define and identify statements. 

Objective 2: Define the logical connectives and identify their use. 

Objective 3: Recognize and write negations of statements. 

Objective 4: Write statements symbolically, and translate symbolic statements back to verbal. 




Lesson 7-2: Finding the Truth (Truth Tables)

Objective 1: Build truth tables for negations, disjunctions, and conjunctions. 

Objective 2: Build truth tables for conditional and biconditional statements. 

Objective 3: Build truth tables for compound statements. 

Objective 4: Use the hierarchy of connectives, and compare it to order of operations. 




Lesson 7-3: To Be and Not to Be (Types of Statements in Logic)

Objective 1: Classify a statement as a tautology, a self-contradiction, or neither. 

Objective 2: Identify statements that are logically equivalent. 

Objective 3: Write and recognize negations of compound statements. 

Objective 4: Write and recognize the converse, inverse, and contrapositive of a statement. 

Objective 5: Evaluate logical connections between a statement and its converse, inverse, and contrapositive.

 

Lesson 7-4: Being Argumentative (Evaluating Logical Arguments)

Objective 1: Identify the difference between a valid argument and a fallacy. 

Objective 2: Use truth tables to evaluate the validity of arguments. 

Objective 3: Determine the validity of common argument forms. 

Objective 4: Use common argument forms to decide if arguments are valid. 




Unit 8: HOW DO YOU MEASURE UP? 




Lesson 8-1: Going to Great Lengths (Unit Conversion, Length, and the Metric System)

Objective 1: Understand the importance of units in measurement. 

Objective 2: Understand how dimensional analysis makes converting units easy. 

Objective 3: Identify the key components of the metric system. 

Objective 4: Convert between U.S. and metric units of length, and describe perspective on the size of these measurements. 




Lesson 8-2: New Dimensions (Measuring Area, Volume, and Capacity)

Objective 1: Understand the difference between unit conversions for length, and unit conversions for area and volume. 

Objective 2: Convert area and volume measurements within the U.S. system, and describe perspective on sizes of these measurements. 

Objective 3: Convert area and volume measurements between the U.S. and metric systems, and describe perspective on sizes of these measurements. 




Lesson 8-3: Weighty Matters (Units of Weight and Temperature)

Objective 1: Convert weight and temperature measurements within the U.S. and metric systems. 

Objective 2: Convert weight and temperature measurements between the U.S. and metric systems. 

Objective 3: Demonstrate an understanding of the sizes of measurements in these systems. 




Lesson 8-4: Stocking the Shelves (Evaluating Efficiency in Packaging)

Objective 1: Develop surface area and volume formulas for rectangular solids and cylinders. 

Objective 2: Study the volume-to-surface-area ratio for different product packages and identify its significance. 

Objective 3: Develop methods for deciding on optimal size and shape given certain goals. 




Units 9, 10, and 11 are available online. Though not included in this desk copy, they can be added to custom versions of the text built through Create or accessed in the Instructor Resources area of ALEKS.




Unit 9: UP FOR A VOTE 




Lesson 9-1: State Your Preference (Preference Tables and Plurality Voting)

Objective 1: Interpret the information in a preference table. 

Objective 2: Identify the winner of an election using the plurality method. 

Objective 3: Identify potential weaknesses of plurality voting. 




Lesson 9-2: We’re Number One! (Borda Count and Plurality with Elimination)

Objective 1: Determine the winners of elections using the Borda count method and the plurality-with-elimination method. 

Objective 2: Decide if elections violate the majority criterion or the monotonicity criterion. 




Lesson 9-3: It’s So Unfair! (Pairwise Comparison and Approval Voting)

Objective 1: Determine the winners of elections using the pairwise comparison method and approval voting. 

Objective 2: Decide if an election violates the irrelevant alternatives criterion. 

Objective 3: Describe Arrow’s impossibility theorem.

 

Lesson 9-4: Portion Control (Apportionment)

Objective 1: Describe what apportionment is and why it’s used. 

Objective 2: Compute standard divisors and quotas. 

Objective 3: Apportion items using a variety of methods. 




Unit 10: WARNING: GRAPHIC CONTENT 




Lesson 10-1: Color Your World (Basic Concepts of Graph Theory)

Objective 1: Define basic graph theory terms. 

Objective 2: Represent relationships with graphs. 

Objective 3: Decide if two graphs are equivalent. 

Objective 4: Recognize features of graphs. 

Objective 5: Apply graph coloring. 




Lesson 10-2: Efficiency Experts (Euler’s Theorem)

Objective 1: Define Euler path and Euler circuit. 

Objective 2: Use Euler’s theorem to decide if an Euler path or Euler circuit exists. 

Objective 3: Use Fleury’s algorithm to find an Euler path or Euler circuit. 

Objective 4: Solve practical problems using Euler paths or circuits. 




Lesson 10-3: Who Wants to Be a Zillionaire? (Hamilton Paths and Circuits)

Objective 1: Find Hamilton paths and Hamilton circuits on graphs. 

Objective 2: Solve a traveling salesperson problem using the brute force method. 

Objective 3: Find an approximate optimal solution using the nearest neighbor method. 

Objective 4: Draw a complete weighted graph based on provided information. 




Lesson 10-4: Tree Hugging (Trees)

Objective 1: Decide if a graph is a tree. 

Objective 2: Find a spanning tree for a graph. 

Objective 3: Find a minimum spanning tree for a weighted graph. 

Objective 4: Apply minimum spanning trees to problems in our world. 




Unit 11: DISCO
VERING NEW NUMBERS 




Lesson 11-1: History Lessons (Early and Modern Numeration Systems)

Objective 1: Use a tally system. 

Objective 2: Define and use simple grouping systems. 

Objective 3: Define and use multiplicative grouping systems. 

Objective 4: Define a positional system and identify place values. 




Lesson 11-2: Off Base (Base Number Systems) 

Objective 1: Convert between base 10 and other bases. 

Objective 2: Convert between binary, octal, and hexadecimal. 




Lesson 11-3: Working Out (Operations in Base Number Systems)

Objective 1: Add and subtract in bases other than 10. 

Objective 2: Multiply and divide in bases other than 10.