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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’s about students productively struggling with context-based problems. It’s 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 Literacy Approach, First Edition
Unit 1: THE IMPORTANCE OF BEING NUMERATE
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: Where does the Time Go? (Using Percentages and Pie Charts)
Objective 1: Complete and analyze a weekly time chart.
Objective 2: Review a variety of calculations that invoice percentages.
Objective 3: Create and interpret pie charts by hand.
Objective 4: Use a spreadsheet to create a pie chart.
Lesson 3: It's All About Style (Interpreting and Drawing Bar Graphs)
Objective 1: Identify and understand your learning style.
Objective 2: Create and interpret bar graphs using a spreadsheet and by hand.
Objective 3: Decide whether a bar graph or a pie chart is more appropriate for a given situation.
Lesson 4: Take a Guess! (Estimation and Number Sense)
Objective 1: Make educated guesses in a variety of settings.
Objective 2: Estimate locations on a number line.
Objective 3: Compare numbers using inequality symbols.
Objective 4: Approximate square roots.
Lesson 5: Of Planes, Boats, Doll Houses, and Dr. Evil (Dimensional Analysis)
Objective 1: Understand the meaning of scale in models and maps.
Objective 2: Convert units using dimensional analysis.
Objective 3: View percentages in terms of scale.
Lesson 6: Relatively Speaking (Interpreting Relative Difference/Relative Error)
Objective 1: Compare difference and relative difference, and understand why relative difference is often a more meaningful comparison.
Objective 2: Apply relative error.
Objective 3: Find conversion factors for square and cubic units.
Lesson 7: Attraction and Melted Chocolate (Scientific Notation)
Objective 1: Write large and small numbers in scientificnotation.
Objective 2: Describe the significance of writing numbers in scientific notation.
Objective 3: Study Newton’s law of gravitation.
Objective 4: Compute the speed of light experimentally.
Lesson 8: 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 2: CONTENDING WITH CHANGE
Lesson 1: Follow the Pattern (Comparing Linear and Exponential Growth)
Objective 1: Recognize patterns and use them to make predictions.
Objective 2: Distinguish between linear and exponential growth.
Lesson 2: 88 Miles Per Hour (Rates of Change)
Objective 1: Compute rates of change and compare to ratios and conversion factors.
Objective 2: Interpret and use rates of change.
Objective 3: Convert units involving rates.
Lesson 3: Warning: Graphic Content (Graphing, Slope, and Rate of Change)
Objective 1: Understand and use a rectangular coordinate system.
Objective 2: Connect data to graphs and interpret graphs.
Objective 3: Define slope as a constant rate of change.
Objective 4: Define and interpret the y intercept of a line.
Objective 5: Write an equation of a line that models data from a description, table, or graph.
Lesson 4: The Great Tech Battle (Linear Relationships and Lines of Best Fit)
Objective 1: Decide if two data sets are linearly related.
Objective 2: Find lines of best fit for data using spreadsheets and calculators.
Objective 3: Use lines of best fit to analyze data.
Objective 4: Interpret correlation coefficients.
Lesson 5: Sit Back and Watch Your Money Grow (Exponential Growth Equations)
Objective 1: Illustrate exponential growth with a graph.
Objective 2: Solve problems using graphs representing exponential growth and decay.
Objective 3: Identify the significance of the parameters in an exponential equation.
Objective 4: Find exponential models.
Lesson 6: Follow the Bouncing Golf Ball (Exponential Curve Fitting)
Objective 1: Gather and organize data from an experiment.
Objective 2: Find an exponential curve of best fit for a real data set.
Objective 3: Study the rate of decay for an exponential equation.
Lesson 7: Keeping Current (Modeling Current Data with Linear or Exponential Equations)
Objective 1: Decide on an appropriate type of model for a given data set.
Objective 2: Model data with a linear or exponential equation.
Objective 3: Research current data to compare to values predicted by a model.
Unit 3: MANAGING YOUR MONEY
Lesson 1: 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: 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 3: 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 4: 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 5: 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 6: 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 4: STATISTICALLY SPEAKING
Lesson 1: A Likely Story (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: 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: 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 4: 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 5: 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 6: 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 7: 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 8: The Error of Your Ways (Polling and Margin of Error)
Objective 1: Identify margin of error in a poll.
Objective 2: Calculate and interpret the meaning of margin of error.
Objective 3: Calculate the number of respondents needed for a given margin of error.
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.
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