## Table of Contents

**Lesson 1 Complex Numerical Summaries; Graphical Displays**

**Part 1A: Data for Life**

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- 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**

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**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.

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**Lesson 3 Complex Numerical summaries; Graphing Displays**

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**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**

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**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.

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**Lesson 6 Complex Numerical Summaries; Graphical Displays**

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

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

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**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**

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**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.

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**Lesson 8 Mathematical Modeling**

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**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.

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**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.

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**Lesson 9 Mathematical Modeling**

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**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.

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**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.

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**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**

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**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**

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**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.

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**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.

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**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.

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**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.

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**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.

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**Lesson 12 Mathematical Modeling (Optional)**

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**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**

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**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.

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**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**

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**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**

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**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.

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**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.

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**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.

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**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.