# An Introduction to Income Inequality in America: Economics, History, Law

## Income Inequality Control

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## Implementing District Standards

The Common Core State Standards addressed in this unit are listed below.

CCSS.MATH.CONTENT.HSS.ID.B.6 Represent data on two quantitative variables on a scatterplot, and describe how the variables are related.

In this unit, students will learn to draw a scatterplot by hand and using the TI-84 Plus graphing calculator. Their scatterplots will depict the relationship between the Gini coefficient of a location and another measurable variable of interest. The scatterplots will allow them to visualize the extent to which the points in their data set form a linear pattern. Finally, the scatterplots will alert them to outliers, points that deviate from the overall pattern of the data.

CCSS.MATH.CONTENT.HSS.ID.B.6.A Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

CCSS.MATH.CONTENT.HSS.ID.B.6.C Fit a linear function for a scatterplot that suggests a linear association.

CCSS.MATH.CONTENT.HSS.ID.C.7 Interpret the slope and the intercept of a linear model in the context of the data.

Students will meet the above three standards with the help of technology. They will use the TI-84 Plus to produce a linear regression function that describes the relationship between the Gini coefficient and their variable of interest. They will utilize their linear regression function to make predictions. Furthermore, they will use the slope of their regression model to find out what happens to their variable of interest when the Gini coefficient increases or decreases.

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CCSS.MATH.CONTENT.HSS.ID.B.6.B
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Informally assess the fit of a function by plotting and analyzing residuals.

Students will learn to create a residual plot to assess whether a linear model appropriately describes the relationship between the Gini coefficient of a location and their variable of interest. By examining how the points of their residual plot are dispersed, students can judge how well a linear model fits their data.

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CCSS.MATH.CONTENT.HSS.ID.C.8
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Compute (using technology) and interpret the correlation coefficient of a linear fit.

Students will use the TI-84 Plus to determine the correlation coefficient for the relationship between the Gini index and a measurable variable of interest. They will use the correlation coefficient to assess whether a linear model is appropriate for their data and describe the strength of the linear relationship between their independent and dependent variable. The correlation will tell them whether their independent and dependent variables are positively associated, negatively associated, or neither.

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CCSS.MATH.CONTENT.HSS.ID.C.9
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Distinguish between correlation and causation.

This unit will enable students to understand that although a correlation coefficient may indicate a linear relationship between the Gini coefficient and their variable of interest, this does not imply that one variable is responsible for the other. For example, we cannot conclude that lack of mathematics education causes a nation to have a high level of income inequality, even if a correlation coefficient suggests a strong linear relationship between the Gini coefficient and the average years of math education in a country. There might be other factors that contribute to income inequality.