ALEX Lesson Plans
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Title: Adding Up Stats
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In groups, students will conduct surveys and collect the data from their surveys. Then they will analyze the data and create various methods of displaying the collected data.
Standard(s): [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6]
Subject: Mathematics (9  12), or Technology Education (6  8)
Title: Adding Up Stats
Description: In groups, students will conduct surveys and collect the data from their surveys. Then they will analyze the data and create various methods of displaying the collected data.
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Title: The Composition of Seawater
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This lesson develops student understanding of ocean water as a true solution. It demonstrates the differences of salinity and "salt" water. This lesson prepares the student to be able to apply the concepts of temperature, density, and layering of the oceans before conducting a lab dealing with these variables.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1]
Subject: Mathematics (9  12), or Science (9  12)
Title: The Composition of Seawater
Description: This lesson develops student understanding of ocean water as a true solution. It demonstrates the differences of salinity and "salt" water. This lesson prepares the student to be able to apply the concepts of temperature, density, and layering of the oceans before conducting a lab dealing with these variables.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Statistically Thinking
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The object of this project is for students to learn how to find univariate and bivariate statistics for sets of data. Also, the students will be able to determine if two sets of data are linearly correlated and to what degree. The students will use Microsoft PowerPoint and Excel to find, organize, and present their projects to the class.
Standard(s): [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama)
Subject: Mathematics (7  12)
Title: Statistically Thinking
Description: The object of this project is for students to learn how to find univariate and bivariate statistics for sets of data. Also, the students will be able to determine if two sets of data are linearly correlated and to what degree. The students will use Microsoft PowerPoint and Excel to find, organize, and present their projects to the class.
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Title: Math is Functional
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This lesson is a technologybased activity in which students extend graphing of linear functions to the use of spreadsheet software. After students have become proficient in constructing a table of values, students are able to efficiently graph equations with more extensive computational requirements. Furthermore, inquiry and discovery about slope and yintercept will help students conceptualize material normally presented in Algebra I textbooks.
Standard(s): [MA2013] AL1 (912) 13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2]
Subject: Mathematics (9  12), or Technology Education (9  12)
Title: Math is Functional
Description: This lesson is a technologybased activity in which students extend graphing of linear functions to the use of spreadsheet software. After students have become proficient in constructing a table of values, students are able to efficiently graph equations with more extensive computational requirements. Furthermore, inquiry and discovery about slope and yintercept will help students conceptualize material normally presented in Algebra I textbooks.
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Title: Ballistic Statistics!
Description:
Students will collect examples of various statistical instruments and form an electronic scrapbook. These materials will be gathered from electronic sources in addition to periodicals and other print resources.
Standard(s): [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama)
Subject: Mathematics (9  12), or Technology Education (9  12)
Title: Ballistic Statistics!
Description: Students will collect examples of various statistical instruments and form an electronic scrapbook. These materials will be gathered from electronic sources in addition to periodicals and other print resources.
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Title: Swimming Pool Math
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Students will use a swimming pool example to practice finding perimeter and area of different rectangles.
Standard(s): [MA2013] (8) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve realworld and mathematical problems. [8G9]
Subject: Mathematics (6  12)
Title: Swimming Pool Math
Description: Students will use a swimming pool example to practice finding perimeter and area of different rectangles.
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Title: The National Debt and Wars: Suggested Solutions
Description:
These reproducible graphs, from an Illuminations lesson, feature possible solutions to a student activity sheet in which students collect information about the national debt, plot the data by decade and determine whether an exponential curve is a good fit for the data.
Standard(s): [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama)
Subject: Mathematics,Social Studies Title: The National Debt and Wars: Suggested Solutions
Description: These reproducible graphs, from an Illuminations lesson, feature possible solutions to a student activity sheet in which students collect information about the national debt, plot the data by decade and determine whether an exponential curve is a good fit for the data. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Numerical Analysis
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In this lesson, one of a multipart unit from Illuminations, students use iteration, recursion, and algebra to model and analyze a changing fish population. They use an interactive spreadsheet application to investigate their models.
Standard(s): [MA2013] DM1 (912) 3: Use the recursive process and difference equations to create fractals, population growth models, sequences, series, and compound interest models. (Alabama)
Subject: Mathematics,Science Title: Numerical Analysis
Description: In this lesson, one of a multipart unit from Illuminations, students use iteration, recursion, and algebra to model and analyze a changing fish population. They use an interactive spreadsheet application to investigate their models. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Automobile Mileage: Year vs. Mileage
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In this lesson, one of a multipart unit from Illuminations, students plot data about automobile mileage and interpret the meaning of the slope and yintercept in the resulting equation for the least squares regression line. By examining the graphical representation of the data, students analyze the meaning of the slope and yintercept of the line and interpret them in the context of the reallife application. Students also make decisions about the age and mileage of automobiles based on the equation of the least squares regression line. This lesson incorporates an interactive regression line applet.
Standard(s): [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama)
Subject: Mathematics Title: Automobile Mileage: Year vs. Mileage
Description: In this lesson, one of a multipart unit from Illuminations, students plot data about automobile mileage and interpret the meaning of the slope and yintercept in the resulting equation for the least squares regression line. By examining the graphical representation of the data, students analyze the meaning of the slope and yintercept of the line and interpret them in the context of the reallife application. Students also make decisions about the age and mileage of automobiles based on the equation of the least squares regression line. This lesson incorporates an interactive regression line applet. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Exact Ratio
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This reproducible activity sheet, from an Illuminations lesson, features a series of questions pertaining to exact ratios and geometric sequences. In the lesson, students measure lengths on stringed musical instruments and discuss how the placement of frets on a fretted instrument is determined by a geometric sequence.
Standard(s): [MA2013] AL1 (912) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [FBF2]
Subject: Mathematics Title: Exact Ratio
Description: This reproducible activity sheet, from an Illuminations lesson, features a series of questions pertaining to exact ratios and geometric sequences. In the lesson, students measure lengths on stringed musical instruments and discuss how the placement of frets on a fretted instrument is determined by a geometric sequence. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Make a Conjecture
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In this lesson, one of a multipart unit from Illuminations, students explore rates of change and accumulation in context. They are asked to think about the mathematics involved in determining the amount of blood being pumped by a heart.
Standard(s): [MA2013] AL1 (912) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [FBF2]
Subject: Health,Mathematics Title: Make a Conjecture
Description: In this lesson, one of a multipart unit from Illuminations, students explore rates of change and accumulation in context. They are asked to think about the mathematics involved in determining the amount of blood being pumped by a heart. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: The Regression Line
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This lesson, one of a multipart unit from Illuminations, provides students with the opportunity to investigate the relationship between a set of data points and a curve used to fit the data points, using a computerbased interactive tool. Using the Regression Line Applet, students investigate the straight line, which is the graph of a linear function.
Standard(s): [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama)
Subject: Mathematics Title: The Regression Line
Description: This lesson, one of a multipart unit from Illuminations, provides students with the opportunity to investigate the relationship between a set of data points and a curve used to fit the data points, using a computerbased interactive tool. Using the Regression Line Applet, students investigate the straight line, which is the graph of a linear function. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: The Regression Line and Correlation
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This fourlesson unit, from Illuminations, provides students with the opportunity to investigate the relationship between a set of data points and a curve used to fit the data points, using a computerbased interactive tool. Using the Regression Line Applet, students investigate the properties of regression lines and correlation.
Standard(s): [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama)
Subject: Mathematics Title: The Regression Line and Correlation
Description: This fourlesson unit, from Illuminations, provides students with the opportunity to investigate the relationship between a set of data points and a curve used to fit the data points, using a computerbased interactive tool. Using the Regression Line Applet, students investigate the properties of regression lines and correlation. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Think of a Graph
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This reproducible transparency, from an Illuminations lesson, asks students to sketch a graph in which the side length of a square is graphed on the horizontal axis and the perimeter of the square is graphed on the vertical axis.
Standard(s): [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama)
Subject: Mathematics Title: Think of a Graph
Description: This reproducible transparency, from an Illuminations lesson, asks students to sketch a graph in which the side length of a square is graphed on the horizontal axis and the perimeter of the square is graphed on the vertical axis. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Shrinking Candles, Running Water, Folding Boxes
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This lesson, from Illuminations, allows students to look for functions within a given set of data. After analyzing the data, the students should be able to determine the type of function that represents the data.
Standard(s): [MA2013] PRE (912) 25: Compare effects of parameter changes on graphs of transcendental functions. (Alabama)
Subject: Mathematics Title: Shrinking Candles, Running Water, Folding Boxes
Description: This lesson, from Illuminations, allows students to look for functions within a given set of data. After analyzing the data, the students should be able to determine the type of function that represents the data. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Automobile Mileage: Comparing and Contrasting
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In this lesson, one of a multipart unit from Illuminations, students compare and contrast their findings from previous lessons of the unit. This lesson allows students the time they need to think about and discuss what they have done in the previous lessons. This lesson provides the teacher with another opportunity to listen to student discourse and assess student understanding.
Standard(s): [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1]
Subject: Mathematics Title: Automobile Mileage: Comparing and Contrasting
Description: In this lesson, one of a multipart unit from Illuminations, students compare and contrast their findings from previous lessons of the unit. This lesson allows students the time they need to think about and discuss what they have done in the previous lessons. This lesson provides the teacher with another opportunity to listen to student discourse and assess student understanding. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Bathtub Water Levels
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In this lesson, one of a multipart unit from Illuminations, students examine reallife data that illustrates a negative slope. Students interpret the meaning of the negative slope and yintercept of the graph of the reallife data. By examining the graphical representation of the data, students relate the slope and yintercept of the least squares regression line to the reallife data. They also interpret the correlation coefficient of the least squares regression line. This lesson incorporates an interactive regression line applet.
Standard(s): [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1]
Subject: Mathematics Title: Bathtub Water Levels
Description: In this lesson, one of a multipart unit from Illuminations, students examine reallife data that illustrates a negative slope. Students interpret the meaning of the negative slope and yintercept of the graph of the reallife data. By examining the graphical representation of the data, students relate the slope and yintercept of the least squares regression line to the reallife data. They also interpret the correlation coefficient of the least squares regression line. This lesson incorporates an interactive regression line applet. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Exploring Linear Data
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In this lesson, from Illuminations, students model linear data in a variety of settings. Students can work alone or in small groups to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit.
Standard(s): [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1]
Subject: Mathematics Title: Exploring Linear Data
Description: In this lesson, from Illuminations, students model linear data in a variety of settings. Students can work alone or in small groups to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
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Title: Gallery Walk
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In this lesson, one of a multipart unit from Illuminations, students view the work of other students in the class and explain their own work. Students move from graph to graph during this time and, without any talking, view the work of their classmates. While on their Gallery Walk, the students think about the data their classmates plotted and whether or not the information accompanying each graph seems appropriate. Each pair of students then stands next to their own work and explains one of the graphs.
Standard(s): [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1]
Subject: Mathematics Title: Gallery Walk
Description: In this lesson, one of a multipart unit from Illuminations, students view the work of other students in the class and explain their own work. Students move from graph to graph during this time and, without any talking, view the work of their classmates. While on their Gallery Walk, the students think about the data their classmates plotted and whether or not the information accompanying each graph seems appropriate. Each pair of students then stands next to their own work and explains one of the graphs. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Gather Data
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In this lesson, one of a multipart unit from Illuminations, students explore rates of change and accumulation in context by modeling cardiac output. They use an interactive Java applet to create a graph of the data they collect.
Standard(s): [MA2013] ALT (912) 37: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. [SID4]
Subject: Health,Mathematics Title: Gather Data
Description: In this lesson, one of a multipart unit from Illuminations, students explore rates of change and accumulation in context by modeling cardiac output. They use an interactive Java applet to create a graph of the data they collect. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Least Squares Regression
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In this ninelesson unit, from Illuminations, students interpret the slope and yintercept of least squares regression lines in the context of reallife data. Students use an interactive applet to plot the data and calculate the correlation coefficient and equation of the least squares regression line. These lessons develop skills in connecting, communicating, reasoning, and problem solving as well as representing fundamental ideas about data.
Standard(s): [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1]
Subject: Mathematics Title: Least Squares Regression
Description: In this ninelesson unit, from Illuminations, students interpret the slope and yintercept of least squares regression lines in the context of reallife data. Students use an interactive applet to plot the data and calculate the correlation coefficient and equation of the least squares regression line. These lessons develop skills in connecting, communicating, reasoning, and problem solving as well as representing fundamental ideas about data. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: The Effects of Outliers
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This lesson, one of a multipart unit from Illuminations, provides students with the opportunity to investigate the relationship between a set of data points and a curve used to fit the data points, using a computerbased interactive tool. Using the Regression Line Applet, students investigate the effect of outliers on a regression line and easily see their significance.
Standard(s): [MA2013] PRE (912) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [SIC1]
Subject: Mathematics Title: The Effects of Outliers
Description: This lesson, one of a multipart unit from Illuminations, provides students with the opportunity to investigate the relationship between a set of data points and a curve used to fit the data points, using a computerbased interactive tool. Using the Regression Line Applet, students investigate the effect of outliers on a regression line and easily see their significance. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Traveling Distances
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In this lesson, one of a multipart unit from Illuminations, students interpret the meaning of the slope and yintercept of a graph of reallife data. By examining the graphical representation of the data, students relate the slope and yintercept of the least squares regression line to the reallife data. They also interpret the correlation coefficient of the resulting least squares regression line. This lesson incorporates an interactive regression line applet.
Standard(s): [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1]
Subject: Mathematics Title: Traveling Distances
Description: In this lesson, one of a multipart unit from Illuminations, students interpret the meaning of the slope and yintercept of a graph of reallife data. By examining the graphical representation of the data, students relate the slope and yintercept of the least squares regression line to the reallife data. They also interpret the correlation coefficient of the resulting least squares regression line. This lesson incorporates an interactive regression line applet. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Road Rage
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In this Illuminations lesson, students use remotecontrolled cars to create a system of equations. The solution of the system corresponds to the cars crashing. Multiple representations are woven together throughout the lesson, using graphs, scatter plots, equations, tables, and technological tools. Students calculate the time and place of the crash mathematically, and then test the results by crashing the cars into each other.
Standard(s): [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama)
Subject: Mathematics Title: Road Rage
Description: In this Illuminations lesson, students use remotecontrolled cars to create a system of equations. The solution of the system corresponds to the cars crashing. Multiple representations are woven together throughout the lesson, using graphs, scatter plots, equations, tables, and technological tools. Students calculate the time and place of the crash mathematically, and then test the results by crashing the cars into each other. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: On Top of the World
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If you were standing on the top of Mount Everest, how far would you be able to see to the horizon? In this lesson, students will consider two different strategies for finding an answer to this question. The first strategy is algebraicstudents use data about the distance to the horizon from various heights to generate a rule. The second strategy is geometricstudents use the radius of the Earth and right triangle relationships to construct a formula. Then, students compare the two different rules based on ease of use as well as accuracy.
Standard(s): [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama)
Subject: Mathematics Title: On Top of the World
Description: If you were standing on the top of Mount Everest, how far would you be able to see to the horizon? In this lesson, students will consider two different strategies for finding an answer to this question. The first strategy is algebraicstudents use data about the distance to the horizon from various heights to generate a rule. The second strategy is geometricstudents use the radius of the Earth and right triangle relationships to construct a formula. Then, students compare the two different rules based on ease of use as well as accuracy. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Determining Functions Using Regression
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Students will determine the function of best fit for a set of data and recognize which category of function bests fit the data and know how to use technology to obtain a function. This lesson teaches these skills and prepares students for the subsequent lesson(s), in which they will collect their own data.
Standard(s): [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama)
Determining Functions Using Regression
http://illuminations...
Students will determine the function of best fit for a set of data and recognize which category of function bests fit the data and know how to use technology to obtain a function. This lesson teaches these skills and prepares students for the subsequent lesson(s), in which they will collect their own data.
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Title: Understanding the Least Squares Regression Line with a Visual Model: Measuring Error in a Linear Model
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This example from Illuminations allows students to explore three methods for measuring how well a linear model fits a set of data points. In this example, two of the methods use residuals and the third uses the shortest distance between a data point and the line given by the model. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The eexamples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath investigations.
Standard(s): [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama)
Subject: Mathematics Title: Understanding the Least Squares Regression Line with a Visual Model: Measuring Error in a Linear Model
Description: This example from Illuminations allows students to explore three methods for measuring how well a linear model fits a set of data points. In this example, two of the methods use residuals and the third uses the shortest distance between a data point and the line given by the model. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The eexamples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath investigations. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Thinkfinity Learning Activities
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Title: Line of Best Fit
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This student interactive, from Illuminations, allows the user to enter a set of data, plot the data on a coordinate grid, and determine the equation for a line of best fit. Students can choose to display a line of best fit based on their visual approximation as well as a computergenerated leastsquares regression line.
Standard(s): [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama)
Subject: Mathematics Title: Line of Best Fit
Description: This student interactive, from Illuminations, allows the user to enter a set of data, plot the data on a coordinate grid, and determine the equation for a line of best fit. Students can choose to display a line of best fit based on their visual approximation as well as a computergenerated leastsquares regression line. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
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Title: Flowing Through Mathematics
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This student interactive, from Illuminations, simulates water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time.
Standard(s): [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama)
Subject: Mathematics Title: Flowing Through Mathematics
Description: This student interactive, from Illuminations, simulates water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12

