MyLab Math for Quantitative Reasoning -- Student Access Kit

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This course is ideal for accelerating students as an alternative to the traditional developmental math sequence and preparing them for a college-level statistics, liberal arts math, or STEM-prep course.

MyMathLab for Quantitative Reasoning is part of a series of MyMathLab courses built to support the New Mathways Project developed by the Charles A. Dana Center. The New Mathways Project embodies the Dana Center’s vision for a systemic approach to improving student success and completion through implementation of processes, strategies, and structures built around three mathematics pathways and a supporting student success course. Quantitative Reasoning develops quantitative literacy skills that will be meaningful in students’ professional, civic, and personal lives. This course emphasizes using data to make good decisions, and its goal is for students to gain the mental habit of seeking patterns and order when confronted with unfamiliar contexts. The MyMathLab course designed for use with Quantitative Reasoning provides:

• Interactive content to help prepare students for active classroom time
• In-Class Interactive Lessons to support students through an active classroom experience, accompanied by notebook PDFs.
• Homework assignments designed to assess conceptual understanding of important skills and concepts.
• Additional resources for instructors to help facilitate an interactive and engaging classroom

Built in MyMathLab

Content developed by the Charles A. Dana Center at The University of Texas at Austin will be delivered through MyMathLab. MyMathLab is an online homework, tutorial, and assessment program that engages students and improves results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

MyMathLab for Foundations for Mathematical Reasoning was developed by the Charles A. Dana Center at The University of Texas—Austin. The Dana Center brings together experienced faculty from two- and four-year institutions to author, review, field-test, and revise the New Mathways Project curricular materials.

The Dana Center develops and scales effective math and science innovations to support educators, administrators, and policy makers in creating seamless transitions throughout the K14 system for all students. Their work, based on research and two decades of experience, focuses on K—16 mathematics and science education with an emphasis on strategies for improving student engagement, motivation, persistence, and achievement. They develop innovative curricula, tools, protocols, and instructional supports and deliver powerful instructional and leadership development.

Lesson 1 Complex Numerical Summaries; Graphical Displays

Part 1A:  Data for Life

• Collect data from your daily life
• Work positively in a group to make a decision

Part 1B:  Our Learning Community

• Seek and give help to one another inside and outside of class.

Part 1C:  Instant Runoff

• Create a first-degree equation involving percentages and solve for the variable.
• Employ the “Instant Runoff” method to determine the winner of an election.
• Apply and justify the selection strategies to election results and decisions about other issues.

Part 1D:  Borda Count

• Employ the Borda Count method to determine the winner of an election.
• Apply and justify selection strategies to election results.

Lesson 2 Complex Numerical Summaries; Graphical Displays

Part 2A:  Graphical Displays

• Analyze a variety of graphical displays and interpret them in context.
• Compute the mean of a set of data.
• Construct a dotplot or histogram from data

Part 2B:  Forming Effective Study Groups

• Describe how to form and conduct an effective study group.
• Identify key characteristics of effective study groups.
• Form a study group and become an active member of the group.

Part 2C:  Mini-Project:  Graphical Displays

• Research additional related data and look for trends in the data (optional).
• Write a contextual analysis of a graphical display in a formal paper of at least two paragraphs long, including appropriate mathematical language and explanations.

Lesson 3 Complex Numerical summaries; Graphing Displays

Part 3A: Who is the Population?

• Explain the difference between a population and a sample.
• Use the characteristics of a study sample to describe the population.
• Analyze the conclusions of a study and explain the limitations on any inferences made about the population.

Part 3B: How Much Water Do I Drink?

• Determine the mean of a data set.
• Graph sample means and use the Central Limit Theorem to estimate the population mean.

Part 3C: How much Water Does Our Class Drink? (Optional)

• Use standard deviation to interpret the spread of a data set.
• Calculate the percentage of data in a graph region.

Lesson 5 Complex Numerical Summaries; Graphical Displays

Part 5A: Cost of Living Comparisons

• Recognize when converting units is needed.
• Use conversions to make comparisons.

Part 5B: Index Numbers

• Perform calculations involving index numbers.
• Make and justify decisions and evaluate claims using index numbers.

Part 5C: Polls, Polls, Polls!

• Calculate weighted averages.
• Use weighted averages to analyze data and draw conclusions about the data.

Part 5D: Average Income

• Calculate expected value.
• Make predictions about real-world scenarios based on your knowledge of averages, weighted averages, and expected values.

Lesson 6 Complex Numerical Summaries; Graphical Displays

Part 6A: How Can We Smooth the Data? (Optional)

• Calculate simple and weighted moving averages.
• Analyze graphs of moving average data.

Part 6B: Mini-Project: Income Disparities (Optional)

• Calculate and compare simple and weighted moving averages.
• Write a contextual analysis of a graphical display of weighted average data in a formal paper (at least two paragraphs long), including appropriate mathematical language and explanations.3

Lesson 7 Complex Numerical Summaries; Graphical Displays

Part 7A: the U.S. Budget Priorities

• Determine percentages based on part-to-whole ratios.
• Write a ratio or percentage and explain its meaning within a context.
• Read a budget, determine values of line items, and draw conclusions about the overall distribution of funds.

Part 7B: Understanding U.S. Budget Priorities

• Use part-to-part ratios, part-to-whole ratios, and percentages to calculate ratios and compare line items in budgets.
• Use ratios and percentages to construct a pie graph.
• Examine and interpret ratios, percentages, and pie graphs.

Part 7C: Changes to U.S. Budget Priorities

• Analyze data in a spreadsheet and graphs, using additive (absolute) comparison and multiplicative (relative) reasoning.
• Develop a reasonable hypothesis supported by evidence.
• Use spreadsheets to create a line graph and describe the pattern of the graph.

Part 7D: Percent of Total U.S. Budget

• Analyze data in spreadsheets and graphs to compare changes in categories.
• Revise a claim or hypothesis based on new evidence.

Part 7E: What’s My Credit Score?

• Calculate a DTI ratio.
• Draw a conclusion from the DTI about the appropriateness of the percentage of income spent on housing and debt.

Part 7F: U.S. Incarceration Rates

• Interpret ratios and percentages as rates of change.
• Compare two or more ratios and percentages.
• Read and interpret graphical displays.

Lesson 8 Mathematical Modeling

Part 8A: More Water, Please!

• Investigate and compare mathematical relationships using a variety of representations.
• Create representations to describe mathematical relationships.
• Write a linear equation given a slope and y-intercept.

Part 8B: What’s My Car Worth?

• Explain the difference between proportional and linear relationships.
• Explain why the proportionality of changes in two quantities is equivalent to one quantity having a constant rate of change.
• Compare and contrast linear and proportional relationships.

Part 8C: How Money Makes Money

• Describe the difference between simple and compound interest in practical and mathematical terms.
• Compare and contrast patterns in linear and exponential models.

Part 8D: Have My Choices Affected My Learning?

• Use technology to create a scatterplot and estimate the parameters of the line of best fit.
• Interpret the parameters (slope, y-intercept, correlation of determination) of a simple linear regression.

Part 8E: Mini-Project:  Progressive and Flat Income Tax Systems (Optional)

• Model a progressive income tax system algebraically and graphically.
• Compare a progressive income tax system to a flat tax system and identify different outcomes.
• Explain advantages and disadvantages of different income tax systems.

Part 8F: Mini-Project:  Estimating the Number of People in a Crowd (Optional)

• Use proportions to reason and make estimates.
• Communicate results with supportive documentation.

Lesson 9 Mathematical Modeling

Part 9A: Depreciation

• Interpolate and extrapolate using a graphical representation of the relationship between two variables.
• Use a symbolic model to find the exact value of one variable, given the value of the other variable, and relate those values to the context of the problem.

Part 9B: Appreciating Depreciation

• Create a proportion between corresponding sides of similar triangles.
• Use variables with subscripts.
• Use the formula for interpolation to find unknown values in a linear relationship.

Part 9C: How Much Should I Be Paid?

• Create a line graph for univariate data.
• Determine, informally, the correlation between bivariate data.
• Analyze data and related graphs and describe the trend of the data.

Part 9D:  Why Are You Wearing the Same Old Socks?

• Explain why, even if there is a strong correlation, a change in one variable may not cause a change in the other.

Lesson 10 Mathematical Modeling

Part 10A: Fibonacci’s Rabbits

• Develop a time series model for the Fibonacci problem.
• Test whether data are exponential by comparing the rate of growth to the population size.

Part 10B:  Is It Getting Crowded?

• Evaluate the mathematical appropriateness of a model given historical data.
• Determine whether a data set suggests a linear or exponential relationship.
• Use an appropriate model to predict a future outcome.

Lesson 11 Mathematical Modeling

Part 11A:  Oh, Deer!

• Sketch a model for a population that increases at an increasing rate.
• Sketch a model for a population that increases at a decreasing rate.
• Identify behavior in a graph, draw conclusions about the behavior, and predict future outcomes.

Part 11B:  Population Growth

• Develop discrete models of natural phenomena and use the models to predict future values.
• Calculate the carrying capacity and logistic growth rate of a real-world scenario.

Part 11C:  Can You Hear Me Now?

• Explore the changes in the values of the parameters of a logistic growth model and describe the effect of those changes on the model.

Part 11D:  Hares and Lynxes

• Identify the constant of proportionality in a real-world scenario.
• Develop a parameterized time series model with more than two dependent variables in a spreadsheet.

Part 11E:  Reindeer and Lichens

• Determine parameters to match a model’s predictions against historical data.
• Create a spreadsheet involving the formulas of the model to predict future behavior.
• Adjust models based on rounding to account for rounding.

Lesson 12 Mathematical Modeling (Optional)

Part 12A:  How Long Is the Longest Day?

• Sketch a graph that depicts a periodic phenomenon.
• Identify the period and amplitude of a periodic function.
• Compare and contrast the graphs of different periodic models.

Part 12B:  What’s My Sine?

• Describe the effect that changing one or more parameters has on the graph of a sine function.
• Change the parameters of the sine curve to match given criteria.

Part 12C:  SIR Disease

• Calculate the transmission and recovery rates in a SIR model.
• Determine whether the compartments of a SIR model are increasing or decreasing.
• Create a time series SIR model using a spreadsheet.

Part 12D:  SIR (Continued)

• Create a time series SIR model using a spreadsheet.

Lesson 13 Statistical Studies

Part 13A:  Mind the Gap in Income Inequality

• Describe how a statistical study uses sample data to make inferences about a population.
• Describe how to gather a representative sample used in a statistical study.
• Describe the most appropriate statistics to compute in a statistical study.
• Distinguish between explanatory and response variables, and between quantitative and categorical variables.

Part 13B:  When in Rome . . .

• Determine whether a statistical study is observational or experimental.
• Make appropriate conclusions from observational and experimental studies.

Part 13C:  A Lesson Worth Weighting For

• Identify the principles that would generate a representative sample.
• Implement a sampling process for generating a representative sample.

Part 13D:  Weight . . . There’s More!

• Create and implement a stratified sampling process for generating a representative sample.

Lesson 14 Statistical Studies

Part 14A:  Blood Pressure and Bias

• Determine when a sampling process can yield non-sampling errors due to bias.

Part 14B:  Taking Aim at Bias

• Identify methods of data gathering where bias is likely to occur.
• Distinguish the various types of bias in real situations.

Part 14C:  Conclusions in Observational Studies

• Identify elements of a research design that may introduce bias.
• Suggest corrections to a research design that can minimize bias.
• Identify inappropriate conclusions in an observational study.
• Make appropriate conclusions from observational studies.

Lesson 15 Statistical Studies

Part 15A:  The Video Game Diet

• Determine when a study design allows a conclusion to be made about cause and effect.
• Design an experimental study.

Part 15B:  All Things in Moderation

• Analyze a statistical study and identify possible confounding variables.
• Decide when confounding variables restrict conclusions about cause and effect.
• Design an experiment that allows conclusions about cause and effect.

Part 15C:  The Power of the Pill

• Decide when an experiment should introduce a placebo to control confounding.
• Design a double-blind study that uses a placebo to control confounding.

Part 15D:  Designing an Experiment

• Design a double-blind experiment with blocking.
• Make a conclusion that is appropriate to the results of an experimental study.

Part 15E:  In Conclusion

• Make appropriate conclusions from observational studies and from experimental studies.
• Identify problems in studies that prevent researchers from making inferences to populations or treatments.

Lesson 16 Complex Quantitative Information and Graphical Displays 

Part 16A:  Education Pays

• Determine information from a stacked column graph.
• Analyze data in a stacked column graph and write a brief summary of the information.

Part 16B:  Looking for Links

• Analyze data given in a stacked column graph and write a brief summary of the information.

Part 16C:  It’s About Time!

• Use a spreadsheet to sort specific information for analysis and graphing.
• Use a spreadsheet to build a stacked column graph.
• Analyze data and the related stacked column graph and make conclusions about the pattern of the data.

Part 16D:  Connecting the Dots

• Identify different variables in a graph with several variables.
• Analyze motion bubble charts to identify trends and patterns.

Part 16E:  Big Data (GIS)

• Convert from degrees, minutes, and seconds to a decimal equivalent.
• Choose the appropriate logic and write a query to identify a subset of a population.

Part 16F:  Big Brother–They’re Watching!

• Analyze and draw appropriate conclusions from heat maps.
• Answer questions using density information from a heat map.

Lesson 17 Complex Quantitative Information and Graphical Displays

Part 17A:  Decisions, Decisions

• Use quantitative and qualitative information to make financial decisions.
• Weigh pros and cons of situations and use that information to make a decision.

Part 17B:  The Write Approach to Data

• Identify necessary calculations to perform on data and incorporate resulting quantitative information into a summary or analysis.
• Write brief analyses of data presented in text, table, or graphical form, focusing on key patterns, essential information, and logical conclusions.

Part 17C:  Numbers Never Lie

• Find distortions or biases in graphical representations of data.
• Identify misleading aspects of graphs and mathematical errors in graphs. 
• Write an accurate critical analysis of data, summarize criticisms of data and graphs, and identify potentially misleading information.

Part 17D: Can You Feel the Heat?

• Analyze a regression line and use an R and/or R ² value to determine overall patterns and connections between variables.
• Make decisions and conclusions based on data, separately from anecdotes or individual experiences.

Lesson 18 Complex Quantitative Information and Graphical Displays

Part 18A:  Mini-Project:  Tornado Climatology

• Use proportions to reason and make interpretations.
• Choose appropriate ways to represent data and information in an effort to represent the complete and accurate story.
• Write an informative, objective report that is appropriate for the audience.

Part 18B:  The Making of a Model

• Develop, test, and justify a model for a physical phenomenon.

Part 18C:  What a Wonderful World!

• Employ the steps of the Modeling Cycle and determine the model that best fits the data.

Part 18D:  Mathematical Models

• Choose and create an appropriate algebraic model and make a reasonable forecast of the population of a city.

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