Pathways to Math Literacy, 2nd Edition

ISBN10: 1260404935 | ISBN13: 9781260404937

By David Sobecki and Brian Mercer

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Instructor Details

Table of Contents

Pathways to Math Literacy, 2nd EditionUnit 1: Organizing and Visualizing Numeric Data
Lesson 1-1: Where Does the Time Go? (Percentages, Pie Charts, and Bar Graphs)
Objective 1: Analyze personal time management for a week of activities.
Objective 2: Solve problems involving percentages.
Objective 3: Create and interpret pie charts.
Objective 4: Create and interpret bar graphs.
Lesson 1-2: Do You Have Anything To Add? (Using Addition and Subtraction Skills)
Objective 1: Identify circumstances where addition or subtraction is possible. Objective 2: Add or subtract quantities.
Lesson 1-3: It's About Accumulation (Using Multiplication and Division Skills)
Objective 1: Interpret multiplication as repeated addition.
Objective 2: Multiply or divide quantities.
Lesson 1-4: Avoiding Empty Pockets (Using Exponents and Order of Operation)
Objective 1: Distinguish between simple interest and compound interest.
Objective 2: Distinguish between linear and exponential growth.
Objective 3: Interpret exponents as repeated multiplication.
Objective 4: Simplify numeric expressions involving exponents and the order of operations.
Lesson 1-5: A Coordinated Effort (The Basics of Graphing) Objective 1: Use a rectangular coordinate system.
Objective 2: Connect data to graphs.
Objective 3: Interpret graphs.
Lesson 1-6: What are the Chances? (Basic Probability)
Objective 1: Compute and interpret basic probabilities.
Objective 2: Translate a probability to a percent chance.
Objective 3: Recognize the difference between theoretical and empirical probability.
Lesson 1-7: Debt: Bad, Chocolate: Good (Using Scientific Notation)
Objective 1: Convert numbers between decimal and scientific notation.
Objective 2: Describe the significance of writing numbers in scientific notation.
Lesson 1-8: What's Your Type? (Organizing Information with Venn Diagrams) Objective 1: Analyze how your personality type affects how you interact with others.
Objective 2: Create and interpret Venn diagrams.
Objective 3: Describe sets using appropriate terminology.
Lesson 1-9: News in the Data Age (Gathering and Organizing Data)
Objective 1: Explain the difference between a population and a sample.
Objective 2: Organize data with frequency distributions and histograms.
Objective 3: Analyze data with stem and leaf plots.
Unit 2: Making Sense of It All
Lesson 2-1: Did You Pass the Test? (Using Measures of Average)
Objective 1: Consider strategies for preparing for and taking math tests.
Objective 2: Understand the impact of a single question, or a single exam.
Objective 3: Calculate, interpret, and compare measures of average.
Lesson 2-2: Ins and Outs (Inputs, Outputs, and Interpreting Expressions)
Objective 1: Distinguish between inputs (independent variables) and outputs (dependent variables).
Objective 2: Evaluate expressions and formulas.
Objective 3: Write and interpret expressions.
Lesson 2-3: From Another Dimension (Working with Units and Formulas)
Objective 1: Determine units for area and volume calculations.
Objective 2: Use formulas to calculate areas and volumes.
Objective 3: Discuss important skills for college students to have.
Objective 4: Simplify expressions. Lesson 2-4: It Works like Magic (Dimensional Analysis)
Objective 1: Convert units using dimensional analysis.
Objective 2: Convert units within the metric system.
Objective 3: Convert rates of change.
Objective 4: Convert temperatures.
Lesson 2-5: Take a Guess! (Estimation and Number Sense)
Objective 1: Identify the steps in a systematic problem-solving procedure.
Objective 2: Make educated guesses.
Objective 3: Compare numbers using inequality symbols.
Lesson 2-6: It's All Relative (Interpreting Relative Change/Percent Error)
Objective 1: Compare change to relative change.
Objective 2: Apply percent error.
Lesson 2-7: Is that Normal? (Standard Deviation and Normal Distributions)
Objective 1: Identify the steps in computing standard deviation, and describe why they lead to a measure of variation.
Objective 2: Compute and interpret standard deviation.
Objective 3: Use a normal distribution to find probabilities.
Lesson 2-8: Meeting Expectations (Expected Value and Weighted Averages) Objective 1: Estimate expected value experimentally.
Objective 2: Compute expected value.
Objective 3: Compute weighted grades and GPA.
Unit 3: Thinking Linearly
Lesson 3-1: 88 Miles Per Hour! (Slope as a Rate of Change)
Objective 1: Interpret a rate of change.
Objective 2: Predict a future value from a rate of change.
Objective 3: Calculate a rate of change.
Objective 4: Find the intercepts of a line.
Objective 5: Interpret the meaning of the intercepts of a line.
Lesson 3-2: A Snow Job (Writing, Interpreting, and Evaluating Algebraic Expressions)
Objective 1: Write expressions based on given information.
Objective 2: Interpret algebraic expressions in context.
Objective 3: Evaluate and simplify expressions.
Lesson 3-3: All Things Being Equal (Solving Equations)
Objective 1: Explain what it means to solve an equation.
Objective 2: Demonstrate the procedures for solving a basic linear equation.
Objective 3: Solve a literal equation for a designated variable.
Lesson 3-4: All Quantities Are Not Created Equal (Solving Inequalities)
Objective 1: Demonstrate the procedures for solving a linear inequality.
Objective 2: Solve application problems that involve linear inequalities.
Lesson 3-5: What's Your Problem? (Solving Problems Numerically and Algebraically)
Objective 1: Solve application problems using numerical calculations.
Objective 2: Solve application problems using linear equations.
Lesson 3-6: Big Mac Exchange Rates (Direct Variation and Proportions)
Objective 1: Identify situations where direct variation occurs.
Objective 2: Write an appropriate direct variation equation for a situation.
Objective 3: Solve an application problem that involves direct variation.
Lesson 3-7: Big Mac Exchange Rates (Direct Variation and Proportions)
Objective 1: Write an equation of a line given a description of the relationship.
Objective 2: Write an equation of a line that models data from a table.
Objective 3: Write an equation of a line from a graph of the line.
Objective 4: Graph a line by plotting points.
Lesson 3-8: Party Planning (Point-Slope Form and Linear Modeling)
Objective 1: Find the y intercept and equation of a line given two points.
Objective 2: Find the equation of a line using point-slope form.
Objective 3: Convert between forms of a linear equation.
Lesson 3-9: The Great Tech Battle (Linear Relationships and Lines of Best Fit)
Objective 1: Determine whether two variables have a linear relationship.
Objective 2: Calculate the line of best fit for a set of data using a spreadsheet.
Objective 3: Calculate the line of best fir for a set of data using a calculator.
Objective 4: Interpret the correlation coefficient for a data set.
Lesson 3-10: All Systems Go (Solving Problems with Systems of Equations)
Objective 1: Solve an application problem involving a system of equations.
Objective 2: Illustrate the solution to a system of equations using a table.
Objective 3: Illustrate the solution to a system of equations using a graph.
Unit 4: Living in a Nonlinear World
Lesson 4-1: Oh Yeah? Prove It (Inductive and Deductive Reasoning)
Objective 1: Apply inductive reasoning to make a conjecture.
Objective 2: Disprove a conjecture by finding a counterexample.
Objective 3: Apply deductive reasoning to solve a problem.
Lesson 4-2: A Road Map to Success (The Pythagorean Theorem and Distance)
Objective 1: Solve application problems using the Pythagorean Theorem.
Objective 2: Solve application problems involving the distance formula.
Lesson 4-3: The Error of Your Ways (Polling and Margin of Error)
Objective 1: Determine the margin of error in a given poll.
Objective 2: Explain the meaning of the margin of error in a given poll.
Objective 3: Calculate the number of poll respondents needed for a given margin of error.
Lesson 4-4: Where's My Jetpack? (Inverse vs. Direct Variation)
Objective 1: Identify situations where inverse variation occurs.
Objective 2: Solve problems involving direct and inverse variation.
Lesson 4-5: Sit Back and Watch Your Money Grow (Exponential Growth Equations)
Objective 1: Define function and use function notation.
Objective 2: Identify the significance of a and b in an equation of the form y = ab^x
Objective 3: Find exponential models.
Objective 4: Compare exponential models using graphs, tables, and formulas.
Lesson 4-6: Follow the Bouncing Golf Ball (Exponential Curve Fitting)
Objective 1: Gather and organize data from an experiment.
Objective 2: Find an exponential equation of best fir for data.
Objective 3: Study the decay rate for exponential decay.
Lesson 4-7: Irate Ducks (Graphs of Quadratic Equations)
Objective 1: Identify a parabolic graph.
Objective 2: Solve problems using the graph of a quadratic equation.
Lesson 4-8: Minding Your Business (Add, Subtract, and Multiply Expressions)
Objective 1: Combine algebraic expressions using addition or subtraction.
Objective 2: Demonstrate the relationships between revenue, cost, and profit functions.
Objective 3: Combine algebraic expressions using multiplication.
Objective 4: Determine a revenue function from a demand function by multiplying algebraic expressions.
Lesson 4-9: The F Word (Factoring)
Objective 1: Explain why factoring is useful in algebra.
Objective 2: Explain the connection between zeros and x-intercepts.
Objective 3: Factor a trinomial.
Lesson 4-10: Going... Going... GONE! (The Quadratic Formula and Max/Min)
Objective 1: Solve a quadratic equation using the quadratic formula.
Objective 2: Find the vertex of a parabola using x = -b/2a.
Objective 3: Solve application problems using the quadratic formula.
Lesson 4-11: Down the Drain (Quadratic Curve Fitting)
Objective 1: Calculate the equation of best fit for a set of quadratic data using technology.
Objective 2: Solve application problems that involve a quadratic set of data.

Author Bios

About the Author

David Sobecki

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.

Brian Mercer

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.

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