LooseLeaf for Math in Our World: A Quantitative Reasoning Approach

Mathematics in Our World: A Quantitative Reasoning Approach, First Edition

Unit 1: EVERYONE HAS PROBLEMS

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

Objective 1: Review basic percents and rounding rules.

Objective 2: Use rounding and mental arithmetic to estimate the answers to applied problems.

Objective 3: Use estimation to obtain and interpret information from various types of graphs.

Lesson 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 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: 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 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 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 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 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 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 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 1040EZ form.

Unit 3: PLACE YOUR BETS

Lesson 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 2: Making 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: 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 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 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 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 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 8: Either/Or (The Binomial Distribution)

Objective 1: Identify binomial experiments.

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

Objective 3: Compute cumulative binomial probabilities.

Unit 4: STATISTICALLY SPEAKING

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

Objective 1: Use normal distribution 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 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 predicitons.

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

Lesson 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 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 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 3: A Slippery Slope (Modeling with Linear and Quadratic Functions)

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

Objective 2: Identify quantities that are and are not good candidates to be modeled with linear or quadratic functions.

Objective 3: Solve problems using linear and quadratic modeling, both algebraically and using technology.

Lesson 4: 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 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 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 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 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 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 negotiations of statements.

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

Lesson 2: Finding the Truth (Truth Tables)

Objective 1: Build truth tables for negotiations, 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 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 is converse, inverse, and contrapositive.

Lesson 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 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 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 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 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 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 ratio for different product packages and identify its significance.

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

Prep Skills Answers

Index

What does quantitative reasoning really mean? Is it just liberal arts math with a new name on the cover of the book? We say that it is not. It is about students productively struggling with context-based problems. It is not just learning how to do math problems, but more importantly learning how quantitative thinking is applied throughout the curriculum, and throughout a lifetime.