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Title: Predict the Future?
Description:
Students will use data collected and a "bestfit line" to make predictions for the future. The example the students will be working on for this lesson will demonstrate an exponential regression.
Standard(s): [MA2013] PRE (912) 16: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. (Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Determine odd, even, neither.)* [FIF4] (Alabama)
Subject: Mathematics (9  12), or Technology Education (9  12)
Title: Predict the Future?
Description: Students will use data collected and a "bestfit line" to make predictions for the future. The example the students will be working on for this lesson will demonstrate an exponential regression.
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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: Exponential Growth and Decay
Description:
This lesson on exponential growth and decay involves a variety of teaching resources. There are a variety of websites used to teach and reinforce how to identify exponential growth or decay and how to solve problems relating to growth and decay. There is a lab provided that will help model these concepts being taught and computer based practice on these concepts. Videos are provided that give a picture image of how exponential growth and decay works. 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] PRE (912) 25: Compare effects of parameter changes on graphs of transcendental functions. (Alabama)
Subject: Mathematics (9  12)
Title: Exponential Growth and Decay
Description: This lesson on exponential growth and decay involves a variety of teaching resources. There are a variety of websites used to teach and reinforce how to identify exponential growth or decay and how to solve problems relating to growth and decay. There is a lab provided that will help model these concepts being taught and computer based practice on these concepts. Videos are provided that give a picture image of how exponential growth and decay works. 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: Density
Description:
Density is the ratio of mass to volume. Density will be introduced to students by a demonstration of coke verses diet coke. The teacher will then solve density problems for the students on the board. The class will then complete a lab on the density of plastics. After lab the students will compare results. Each group will present a Powerpoint presentation of their results.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] GEO (912) 40: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, British Thermal Units (BTUs) per cubic foot).* [GMG2]
Subject: Mathematics (9  12), or Science (8  12)
Title: Density
Description: Density is the ratio of mass to volume. Density will be introduced to students by a demonstration of coke verses diet coke. The teacher will then solve density problems for the students on the board. The class will then complete a lab on the density of plastics. After lab the students will compare results. Each group will present a Powerpoint presentation of their results.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: What is the slope of the stairs in front of the school?
Description:
The purpose of this lesson is to help students apply the mathematical definition of slope to a concrete example. The students will learn to make the appropriate measurements and apply the formula to calculate the slope of the stairs experimentally.
Standard(s): [MA2013] GEO (912) 31: Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [GGPE5]
Subject: Mathematics (8  12)
Title: What is the slope of the stairs in front of the school?
Description: The purpose of this lesson is to help students apply the mathematical definition of slope to a concrete example. The students will learn to make the appropriate measurements and apply the formula to calculate the slope of the stairs experimentally.
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Title: Finding the Slope of a Line
Description:
This lesson will use a slide presentation to facilitate teaching students how to find the slope of a line when given the graph of the line or two points. Students will interact with the presentation in two ways: first, by taking notes and practicing examples, and second, by linking to a slope activity on the Internet. This lesson may be done in one ninetyminute block or broken up over two fiftyminute periods. This lesson would be incorporated in a unit on graphing linear equations.
Standard(s): [MA2013] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8EE5]
Subject: Mathematics (8  12)
Title: Finding the Slope of a Line
Description: This lesson will use a slide presentation to facilitate teaching students how to find the slope of a line when given the graph of the line or two points. Students will interact with the presentation in two ways: first, by taking notes and practicing examples, and second, by linking to a slope activity on the Internet. This lesson may be done in one ninetyminute block or broken up over two fiftyminute periods. This lesson would be incorporated in a unit on graphing linear equations.
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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: 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: Linear Alignment
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In this Illuminations lesson, students explore linear equations and the effects of changing the slope and yintercept on a line. It gives students exposure to y = mx + b, and can be used as an introduction to the topic. Using graphing calculators, students are challenged to overlap lines onto the sides of polygons. To achieve this goal, students change slopes and yintercepts of lines, noting observations about behavior as they work. As students change the yintercept of a line, they see it raise or lower the line. As students change the slope, they see it affect the steepness of the line.
Standard(s): [MA2013] AL1 (912) 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [SID7]
Subject: Mathematics Title: Linear Alignment
Description: In this Illuminations lesson, students explore linear equations and the effects of changing the slope and yintercept on a line. It gives students exposure to y = mx + b, and can be used as an introduction to the topic. Using graphing calculators, students are challenged to overlap lines onto the sides of polygons. To achieve this goal, students change slopes and yintercepts of lines, noting observations about behavior as they work. As students change the yintercept of a line, they see it raise or lower the line. As students change the slope, they see it affect the steepness of the line. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
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Title: Graph Chart
Description:
This reproducible transparency, from an Illuminations lesson, contains the answers to the similarly named student activity in which students identify the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs.
Standard(s): [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1]
Subject: Mathematics Title: Graph Chart
Description: This reproducible transparency, from an Illuminations lesson, contains the answers to the similarly named student activity in which students identify the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Graphing What
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This reproducible activity sheet, from an Illuminations lesson, is used by students to record independent and dependent variables as well as the function and symbolic function rule for a set of graphs.
Standard(s): [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1]
Subject: Mathematics Title: Graphing What
Description: This reproducible activity sheet, from an Illuminations lesson, is used by students to record independent and dependent variables as well as the function and symbolic function rule for a set of graphs. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Apple Pie Recording Chart
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This reproducible activity sheet, from an Illuminations lesson, prompts students to use strings and rulers to measure and record the distance around several round objects, as well as the distance across the middle of those objects.
Standard(s): [MA2013] AL1 (912) 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [SID7]
Subject: Mathematics Title: Apple Pie Recording Chart
Description: This reproducible activity sheet, from an Illuminations lesson, prompts students to use strings and rulers to measure and record the distance around several round objects, as well as the distance across the middle of those objects. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Automobile Mileage: Age 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 of 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 put those meanings in the context of the reallife application. This lesson incorporates an interactive regression line applet.
Standard(s):
Subject: Mathematics Title: Automobile Mileage: Age 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 of 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 put those meanings in the context of the reallife application. This lesson incorporates an interactive regression line applet. 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: 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.
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 Centroid and 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 centroid of a data set and its significance for the line fitted to the data.
Standard(s):
Subject: Mathematics Title: The Centroid and 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 centroid of a data set and its significance for the line fitted to the 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: Building Bridges
Description:
In this lesson, from Illuminations, students attempt to make a transition from arithmetical to algebraic thinking by extending from problems that have singlesolution responses. Values organized into tables and graphs are used to move toward symbolic representations. Problem situations involving linear, quadratic, and exponential models are employed.
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,Professional Development Title: Building Bridges
Description: In this lesson, from Illuminations, students attempt to make a transition from arithmetical to algebraic thinking by extending from problems that have singlesolution responses. Values organized into tables and graphs are used to move toward symbolic representations. Problem situations involving linear, quadratic, and exponential models are employed. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Web Resources
Lesson Plans
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Title: Drug Filtering (Exponential Decay)
Description:
In this lesson, students observe a model of exponential decay, and how kidneys filter their blood. They will calculate the amount of a drug in the body over a period of time. Then, they will make and analyze the graphical representation of this exponential function.
Standard(s): [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1]
Drug Filtering (Exponential Decay)
http://illuminations...
In this lesson, students observe a model of exponential decay, and how kidneys filter their blood. They will calculate the amount of a drug in the body over a period of time. Then, they will make and analyze the graphical representation of this exponential function.
Interactives/Games
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Title: Graphing Exponential Functions
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This interactive graph lets students explore the different aspects of exponential graphs.
Standard(s): [MA2013] ALT (912) 27: Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [AREI11]
Graphing Exponential Functions
http://www.softschoo...
This interactive graph lets students explore the different aspects of exponential graphs.
Learning Activities
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Title: Graphing Exponential Functions
Description:
This interactive graph lets students explore the different aspects of exponential graphs.
Standard(s): [MA2013] ALT (912) 27: Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [AREI11]
Graphing Exponential Functions
http://www.softschoo...
This interactive graph lets students explore the different aspects of exponential graphs.
Thinkfinity Learning Activities
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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
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Title: Tube Viewer Simulation
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This student interactive, from Illuminations, simulates the effect of viewing an image through a tube. As students move the location of the person or change the length of the tube, the image and measurements also change.
Standard(s): [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1]
Subject: Mathematics Title: Tube Viewer Simulation
Description: This student interactive, from Illuminations, simulates the effect of viewing an image through a tube. As students move the location of the person or change the length of the tube, the image and measurements also change. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12

