# LooseLeaf for Math in Our World: A Quantitative Reasoning Approach, 1st Edition

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* The estimated amount of time this product will be on the market is based on a number of factors, including faculty input to instructional design and the prior revision cycle and updates to academic research-which typically results in a revision cycle ranging from every two to four years for this product. Pricing subject to change at any time.

## Additional Product Information:

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.

# 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

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