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Title: It's All in the Family
Description:
Students will be motivated to learn how to build new linear functions from existing linear functions. Students will bring pictures of themselves and their parents from home to personally involve them in the lesson. Students will learn to use the patterns inherent in functions to quickly and accurately graph linear functions. This lesson will only deal with vertical shifts and the steepness of the line. Horizontal shifts will be dealt with in future lessons. In addtion, in future lessons students will transfer this knowledge to also graph exponential, quadratic, and absolute value functions.
This is a College and CareerReady Standards showcase lesson plan.
Standard(s): [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1]
Subject: Mathematics (9  12)
Title: It's All in the Family
Description: Students will be motivated to learn how to build new linear functions from existing linear functions. Students will bring pictures of themselves and their parents from home to personally involve them in the lesson. Students will learn to use the patterns inherent in functions to quickly and accurately graph linear functions. This lesson will only deal with vertical shifts and the steepness of the line. Horizontal shifts will be dealt with in future lessons. In addtion, in future lessons students will transfer this knowledge to also graph exponential, quadratic, and absolute value functions.
This is a College and CareerReady Standards showcase lesson plan.
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Title: Writing equations for parallel lines
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Students will complete a cooperative group assignment to discover that parallel lines have the same slope. They will view a PowerPoint presentation illustrating how to write an equation of a line parallel to a given line through a given point. Additional practice will be provided by means of a worksheet.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] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [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: Writing equations for parallel lines
Description: Students will complete a cooperative group assignment to discover that parallel lines have the same slope. They will view a PowerPoint presentation illustrating how to write an equation of a line parallel to a given line through a given point. Additional practice will be provided by means of a worksheet.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] AL1 (912) 7: Interpret expressions that represent a quantity in terms of its context.* [ASSE1] [MA2013] AL1 (912) 9: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* [ASSE3] [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 32: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 36: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [FBF3] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 39: Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. [FLE3] [MA2013] AL2 (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL2 (912) 34: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
[FBF3] [MA2013] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) [MA2013] ALT (912) 12: Interpret expressions that represent a quantity in terms of its context.* [ASSE1] [MA2013] ALT (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [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) [MA2013] ALT (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] ALT (912) 34: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
[FBF3] [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): [S1] (8) 1: Identify steps within the scientific process. [S1] CHE (912) 1: Differentiate among pure substances, mixtures, elements, and compounds. [S1] ENV (912) 1: Identify the influence of human population, technology, and cultural and industrial changes on the environment. [MA2013] AL1 (912) 4: Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. [NQ1] [MA2013] AL1 (912) 5: Define appropriate quantities for the purpose of descriptive modeling. [NQ2] [MA2013] AL1 (912) 6: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. [NQ3] [MA2013] AL1 (912) 15: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [ACED4] [MA2013] AL1 (912) 17: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [AREI3] [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] ALC (912) 1: Create algebraic models for applicationbased problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) [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: Cosmic Measurements
Description:
In this lesson, students will use hands on inquiry in cooperative learning groups to understand, develop and analyze common measurements used by astronomers. Students will use common objects such as straws, twizzlers, or toothpicks to measure the distance from a fixed object or central location to other objects. The students will then use this information to develop a unit of measurement like the astronomical unit. The students will measure the speed of an object such as a remote control car and use this to develop a unit similar to the lightyear. 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): [S1] E&S (912) 8: Explain the terms astronomical unit and light year. [MA2013] AL1 (912) 4: Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. [NQ1] [MA2013] AL1 (912) 5: Define appropriate quantities for the purpose of descriptive modeling. [NQ2] [MA2013] AL1 (912) 6: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. [NQ3] [MA2013] AL1 (912) 12: Create equations and inequalities in one variable, and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [MA2013] AL1 (912) 15: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [ACED4] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] ALC (912) 1: Create algebraic models for applicationbased problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) [MA2013] ALC (912) 10: Critique measurements in terms of precision, accuracy, and approximate error. (Alabama)
Subject: Mathematics (9  12), or Science (9  12)
Title: Cosmic Measurements
Description: In this lesson, students will use hands on inquiry in cooperative learning groups to understand, develop and analyze common measurements used by astronomers. Students will use common objects such as straws, twizzlers, or toothpicks to measure the distance from a fixed object or central location to other objects. The students will then use this information to develop a unit of measurement like the astronomical unit. The students will measure the speed of an object such as a remote control car and use this to develop a unit similar to the lightyear. 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: Creating a Payroll Spreadsheet
Description:
Spreadsheet software allows you to calculate numbers arranged in rows and columns for specific financial tasks. This activity allows students to create an "Employee Work/Pay Schedule" spreadsheet to reinforce spreadsheet skills. Students will practice spreadsheet skills by entering data, creating formulas, and using formatting commands.
Standard(s): [MA2013] ALC (912) 7: Use analytical, numerical, and graphical methods to make financial and economic decisions, including those involving banking and investments, insurance, personal budgets, credit purchases, recreation, and deceptive and fraudulent pricing and advertising. (Alabama) [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] ALC (912) 1: Create algebraic models for applicationbased problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 12: Create equations and inequalities in one variable, and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [TC2] CA2 (912) 5: Utilize advanced features of spreadsheet software, including creating charts and graphs,
sorting and filtering data, creating formulas, and applying functions.
Subject: Mathematics (9  12), or Technology Education (9  12)
Title: Creating a Payroll Spreadsheet
Description: Spreadsheet software allows you to calculate numbers arranged in rows and columns for specific financial tasks. This activity allows students to create an "Employee Work/Pay Schedule" spreadsheet to reinforce spreadsheet skills. Students will practice spreadsheet skills by entering data, creating formulas, and using formatting commands.
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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] GEO (912) 39: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [GMG1] [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) [MA2013] ALC (912) 1: Create algebraic models for applicationbased problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 14: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities and interpret solutions as viable or nonviable options in a modeling context. [ACED3] [MA2013] AL1 (912) 12: Create equations and inequalities in one variable, and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [MA2013] AL1 (912) 4: Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. [NQ1] [MA2013] GEO (912) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. [GCO12] [MA2013] ALC (912) 11: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama) [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [MA2013] AL1 (912) 28: 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.* [FIF4] [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] [MA2013] AL1 (912) 5: Define appropriate quantities for the purpose of descriptive modeling. [NQ2] [MA2013] GEO (912) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [GMG3] [MA2013] (6) 21: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. [6G1] [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: Finding Our Top Speed
Description:
This Illuminations lesson sets the stage for a discussion of travel in the solar system. By considering a realworld, handson activity, students develop their understanding of time and distance. The mathematics necessary for the lesson relate to measuring time and distance as well as graphing to portray the data collected.
Standard(s): [S1] (6) 11: Describe units used to measure distance in space, including astronomical units and light years. [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] [MA2013] (8) 13: Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. [8F3] [MA2013] (8) 14: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8F4] [MA2013] (8) 15: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [8F5] [MA2013] (8) 25: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [8SP1] [MA2013] (8) 26: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [8SP2] [MA2013] AL1 (912) 4: Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. [NQ1] [MA2013] AL1 (912) 5: Define appropriate quantities for the purpose of descriptive modeling. [NQ2] [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] [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 40: Interpret the parameters in a linear or exponential function in terms of a context. [FLE5] [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [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,Science Title: Finding Our Top Speed
Description: This Illuminations lesson sets the stage for a discussion of travel in the solar system. By considering a realworld, handson activity, students develop their understanding of time and distance. The mathematics necessary for the lesson relate to measuring time and distance as well as graphing to portray the data collected. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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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.
Standard(s): [MA2013] (6) 1: Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. [6RP1] [MA2013] (7) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4] [MA2013] (7) 17: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [7SP1] [MA2013] (7) 20: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. [7SP4] [MA2013] (8) 25: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [8SP1] [MA2013] (8) 26: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [8SP2] [MA2013] (8) 27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8SP3] [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] [MA2013] AL1 (912) 22: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). [AREI10] [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 40: Interpret the parameters in a linear or exponential function in terms of a context. [FLE5] [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: 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] (8) 14: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8F4] [MA2013] (8) 15: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [8F5] [MA2013] (8) 25: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [8SP1] [MA2013] (8) 28: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. [8SP4] [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 39: Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. [FLE3] [MA2013] AL1 (912) 40: Interpret the parameters in a linear or exponential function in terms of a context. [FLE5] [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
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Title: Inclined Plane
Description:
In this multipleday activity, from Illuminations, students time balls rolling down inclines of varying lengths and heights. They then try to make inferences about the relationships among the variables involved.
Standard(s): [S1] (8) 8: Identify Newton's three laws of motion. [S1] (8) 10: Differentiate between potential and kinetic energy. [MA2013] (6) 1: Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. [6RP1] [MA2013] (6) 2: Understand the concept of a unit rate ^{a}/_{b} associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. [6RP2] [MA2013] (6) 3: Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. [6RP3] [MA2013] (6) 29: Summarize numerical data sets in relation to their context, such as by: [6SP5] [MA2013] (7) 1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. [7RP1] [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2] [MA2013] (7) 3: Use proportional relationships to solve multistep ratio and percent problems. [7RP3] [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] [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] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [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,Science Title: Inclined Plane
Description: In this multipleday activity, from Illuminations, students time balls rolling down inclines of varying lengths and heights. They then try to make inferences about the relationships among the variables involved. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Counting Embedded Figures
Description:
In this Illuminations lesson, students look for patterns in an embeddedsquare problem. After looking at the patterns, students form generalizations for the pattern. This activity sharpens students algebraic thinking and visualization skills.
Standard(s): [MA2013] (6) 17: Use variables to represent numbers, and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number or, depending on the purpose at hand, any number in a specified set. [6EE6] [MA2013] AL1 (912) 12: Create equations and inequalities in one variable, and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [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] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL2 (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] ALT (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [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: Counting Embedded Figures
Description: In this Illuminations lesson, students look for patterns in an embeddedsquare problem. After looking at the patterns, students form generalizations for the pattern. This activity sharpens students algebraic thinking and visualization skills. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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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.
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] [MA2013] (8) 11: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.) [8F1] [MA2013] (8) 12: Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [8F2] [MA2013] (8) 13: Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. [8F3] [MA2013] (8) 14: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8F4] [MA2013] (8) 15: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [8F5] [MA2013] (8) 25: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [8SP1] [MA2013] (8) 26: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [8SP2] [MA2013] (8) 27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8SP3] [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] [MA2013] AL1 (912) 22: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). [AREI10] [MA2013] AL1 (912) 25: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [FIF1] [MA2013] AL1 (912) 26: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [FIF2] [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 40: Interpret the parameters in a linear or exponential function in terms of a context. [FLE5] [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] [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) [MA2013] AL2 (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL2 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] ALT (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [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) [MA2013] ALT (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] PRE (912) 17: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [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: 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): [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] [MA2013] (8) 12: Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [8F2] [MA2013] (8) 14: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8F4] [MA2013] (8) 25: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [8SP1] [MA2013] (8) 26: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [8SP2] [MA2013] (8) 27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8SP3] [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] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 32: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 40: Interpret the parameters in a linear or exponential function in terms of a context. [FLE5] [MA2013] AL1 (912) 41: Represent data with plots on the real number line (dot plots, histograms, and box plots). [SID1] [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [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] [MA2013] PRE (912) 42: Compute (using technology) and interpret the correlation coefficient of a linear fit. [SID8]
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: 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.
Standard(s): [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 40: Interpret the parameters in a linear or exponential function in terms of a context. [FLE5] [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) [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] PRE (912) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [SIC1] [MA2013] PRE (912) 48: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. [SIC5] [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: Smokey Bear Takes Algebra
Description:
In this lesson, from Illuminations, students learn about the many factors that play a role in creating a forestfire danger rating index. They work with the Angstrom and Nesterov Indexes, explain the relationship between relative humidity and fire danger, and use graphing calculators to model the relationship between the slope of the land versus the rate of fire spread.
Standard(s): [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [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] [MA2013] PRE (912) 17: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [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,Science Title: Smokey Bear Takes Algebra
Description: In this lesson, from Illuminations, students learn about the many factors that play a role in creating a forestfire danger rating index. They work with the Angstrom and Nesterov Indexes, explain the relationship between relative humidity and fire danger, and use graphing calculators to model the relationship between the slope of the land versus the rate of fire spread. 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): [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 40: Interpret the parameters in a linear or exponential function in terms of a context. [FLE5] [MA2013] AL1 (912) 44: Summarize categorical data for two categories in twoway frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. [SID5] [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [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] [MA2013] PRE (912) 42: Compute (using technology) and interpret the correlation coefficient of a linear fit. [SID8] [MA2013] AL2 (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL2 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5]
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: Armstrong Numbers
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In this Illuminations lesson, students explore Armstrong numbers, identify all Armstrong numbers less than 1000, and investigate a recursive sequence that uses a similar process. Throughout the lesson, students use spreadsheets or other technology. There are also links to online activities and other related resources.
Standard(s): [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [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 Title: Armstrong Numbers
Description: In this Illuminations lesson, students explore Armstrong numbers, identify all Armstrong numbers less than 1000, and investigate a recursive sequence that uses a similar process. Throughout the lesson, students use spreadsheets or other technology. There are also links to online activities and other related resources. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
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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.
Standard(s): [MA2013] (6) 17: Use variables to represent numbers, and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number or, depending on the purpose at hand, any number in a specified set. [6EE6] [MA2013] (6) 20: Use variables to represent two quantities in a realworld problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. [6EE9] [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4] [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] [MA2013] (8) 11: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.) [8F1] [MA2013] (8) 13: Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. [8F3] [MA2013] (8) 14: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8F4] [MA2013] (8) 15: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [8F5] [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] [MA2013] AL1 (912) 25: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [FIF1] [MA2013] AL1 (912) 26: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [FIF2] [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 39: Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. [FLE3] [MA2013] AL2 (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL2 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL2 (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] ALT (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [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) [MA2013] ALT (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] ALT (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [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: 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] (8) 14: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8F4] [MA2013] (8) 25: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [8SP1] [MA2013] (8) 26: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [8SP2] [MA2013] (8) 27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8SP3] [MA2013] (8) 28: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. [8SP4] [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] [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [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] [MA2013] PRE (912) 42: Compute (using technology) and interpret the correlation coefficient of a linear fit. [SID8] [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) [MA2013] AL2 (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL2 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] ALT (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] ALT (912) 22: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [ACED3] [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) [MA2013] ALT (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] PRE (912) 17: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [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: 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] (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] [MA2013] (8) 14: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8F4] [MA2013] (8) 25: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [8SP1] [MA2013] (8) 26: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [8SP2] [MA2013] (8) 27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8SP3] [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] [MA2013] AL1 (912) 14: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities and interpret solutions as viable or nonviable options in a modeling context. [ACED3] [MA2013] AL1 (912) 22: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). [AREI10] [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [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] [MA2013] ALC (912) 1: Create algebraic models for applicationbased problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) [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: Graph Chart
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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] (6) 20: Use variables to represent two quantities in a realworld problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. [6EE9] [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2] [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] [MA2013] (8) 11: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.) [8F1] [MA2013] (8) 12: Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [8F2] [MA2013] (8) 13: Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. [8F3] [MA2013] (8) 14: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8F4] [MA2013] (8) 26: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [8SP2] [MA2013] (8) 27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8SP3] [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] [MA2013] AL1 (912) 22: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). [AREI10] [MA2013] AL1 (912) 25: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [FIF1] [MA2013] AL1 (912) 26: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [FIF2] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 32: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 40: Interpret the parameters in a linear or exponential function in terms of a context. [FLE5] [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [MA2013] ALC (912) 1: Create algebraic models for applicationbased problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) [MA2013] AL2 (912) 12: Interpret expressions that represent a quantity in terms of its context.* [ASSE1] [MA2013] AL2 (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL2 (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] ALT (912) 12: Interpret expressions that represent a quantity in terms of its context.* [ASSE1] [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) [MA2013] PRE (912) 17: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] ALT (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [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: 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.
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] [MA2013] (8) 14: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8F4] [MA2013] (8) 25: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [8SP1] [MA2013] (8) 26: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [8SP2] [MA2013] (8) 27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8SP3] [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] [MA2013] AL1 (912) 22: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). [AREI10] [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 40: Interpret the parameters in a linear or exponential function in terms of a context. [FLE5] [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [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] [MA2013] PRE (912) 42: Compute (using technology) and interpret the correlation coefficient of a linear fit. [SID8] [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) [MA2013] AL2 (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL2 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] ALT (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [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) [MA2013] ALT (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] PRE (912) 17: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [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: 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.
Standard(s): [MA2013] (8) 25: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [8SP1] [MA2013] (8) 26: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [8SP2] [MA2013] (8) 28: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. [8SP4] [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] [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 40: Interpret the parameters in a linear or exponential function in terms of a context. [FLE5] [MA2013] AL1 (912) 43: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [SID3] [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [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] [MA2013] PRE (912) 42: Compute (using technology) and interpret the correlation coefficient of a linear fit. [SID8] [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) [MA2013] AL2 (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL2 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] ALT (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [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) [MA2013] ALT (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] PRE (912) 17: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [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: 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.
Standard(s): [S1] (8) 1: Identify steps within the scientific process. [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] [MA2013] (8) 12: Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [8F2] [MA2013] (8) 13: Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. [8F3] [MA2013] (8) 14: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8F4] [MA2013] (8) 15: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [8F5] [MA2013] (8) 25: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [8SP1] [MA2013] (8) 26: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [8SP2] [MA2013] (8) 27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8SP3] [MA2013] (8) 28: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. [8SP4] [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] [MA2013] AL1 (912) 14: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities and interpret solutions as viable or nonviable options in a modeling context. [ACED3] [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 40: Interpret the parameters in a linear or exponential function in terms of a context. [FLE5] [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] [MA2013] PRE (912) 42: Compute (using technology) and interpret the correlation coefficient of a linear fit. [SID8] [MA2013] ALC (912) 1: Create algebraic models for applicationbased problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) [MA2013] ALC (912) 7: Use analytical, numerical, and graphical methods to make financial and economic decisions, including those involving banking and investments, insurance, personal budgets, credit purchases, recreation, and deceptive and fraudulent pricing and advertising. (Alabama) [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) [MA2013] AL2 (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL2 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] ALT (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [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) [MA2013] ALT (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] PRE (912) 17: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [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: 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.
Standard(s): [MA2013] (8) 25: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [8SP1] [MA2013] (8) 26: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [8SP2] [MA2013] (8) 27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8SP3] [MA2013] (8) 28: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. [8SP4] [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] [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [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] [MA2013] PRE (912) 42: Compute (using technology) and interpret the correlation coefficient of a linear fit. [SID8] [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) [MA2013] AL2 (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL2 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] ALT (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [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) [MA2013] ALT (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] PRE (912) 17: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [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: 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.
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] [MA2013] (8) 14: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8F4] [MA2013] (8) 25: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [8SP1] [MA2013] (8) 26: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [8SP2] [MA2013] (8) 27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8SP3] [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] [MA2013] AL1 (912) 22: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). [AREI10] [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 40: Interpret the parameters in a linear or exponential function in terms of a context. [FLE5] [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [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] [MA2013] PRE (912) 42: Compute (using technology) and interpret the correlation coefficient of a linear fit. [SID8] [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) [MA2013] AL2 (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL2 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] ALT (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [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) [MA2013] ALT (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] PRE (912) 17: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [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: 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.
Standard(s): [MA2013] AL1 (912) 22: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). [AREI10] [MA2013] AL1 (912) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [FIF3] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [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) [MA2013] DM1 (912) 3: Use the recursive process and difference equations to create fractals, population growth models, sequences, series, and compound interest models. (Alabama) [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,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: 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.
Standard(s): [MA2013] AL1 (912) 4: Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. [NQ1] [MA2013] AL1 (912) 5: Define appropriate quantities for the purpose of descriptive modeling. [NQ2] [MA2013] AL1 (912) 6: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. [NQ3] [MA2013] AL1 (912) 12: Create equations and inequalities in one variable, and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [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] [MA2013] AL1 (912) 14: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities and interpret solutions as viable or nonviable options in a modeling context. [ACED3] [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 32: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 39: Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. [FLE3] [MA2013] AL1 (912) 40: Interpret the parameters in a linear or exponential function in terms of a context. [FLE5] [MA2013] AL1 (912) 41: Represent data with plots on the real number line (dot plots, histograms, and box plots). [SID1] [MA2013] AL1 (912) 42: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [SID2] [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [MA2013] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) [MA2013] ALC (912) 5: Determine approximate rates of change of nonlinear relationships from graphical and numerical data. (Alabama) [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) [MA2013] AL2 (912) 12: Interpret expressions that represent a quantity in terms of its context.* [ASSE1] [MA2013] AL2 (912) 20: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [MA2013] AL2 (912) 22: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [ACED3] [MA2013] AL2 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL2 (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL2 (912) 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] AL2 (912) 38: (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [SMD7] [MA2013] ALT (912) 12: Interpret expressions that represent a quantity in terms of its context.* [ASSE1] [MA2013] ALT (912) 20: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [MA2013] ALT (912) 22: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [ACED3] [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) [MA2013] ALT (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] PRE (912) 17: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] ALT (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [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] [MA2013] PRE (912) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [SIC1] [MA2013] PRE (912) 45: Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. [SIC2] [MA2013] PRE (912) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [SIC3] [MA2013] PRE (912) 49: Evaluate reports based on data. [SIC6] [MA2013] ALT (912) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] ALT (912) 42: (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [SMD7] [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: 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.
Standard(s): [MA2013] AL1 (912) 2: Rewrite expressions involving radicals and rational exponents using the properties of exponents. [NRN2] [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 32: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8] [MA2013] AL1 (912) 33: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [FIF9] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 39: Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. [FLE3] [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [MA2013] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) [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) [MA2013] AL2 (912) 12: Interpret expressions that represent a quantity in terms of its context.* [ASSE1] [MA2013] AL2 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL2 (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL2 (912) 34: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
[FBF3] [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) [MA2013] ALT (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [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: GraphIt!
Digital Tool:
TopNotes App Web Address URL:
https://itunes.apple.com/us/app/topnotestakenotes.../id548578836?mt=8 Standard(s):
[MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 33: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [FIF9] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 36: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [FBF3] Digital Tool Description: TopNotes is a powerful app for handwriting and organizing notes, sketches, diagrams, illusions and drawings.
Title: GraphIt! Digital Tool: TopNotes App Digital Tool Description: TopNotes is a powerful app for handwriting and organizing notes, sketches, diagrams, illusions and drawings.
Thinkfinity Interactive Games
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Title: Using Graphs, Equations, and Tables to Investigate the Elimination of Medicine from the Body: Modeling the Situation
Description:
This threepart eexample from Illuminations illustrates the use of iteration, recursion, and algebra to model and analyze the changing amount of medicine in an athlete's body. This example includes: (1) an interactive environment used to become familiar with the parameters involved and the range of results that can be obtained, (2) an interactive environment used to investigate how changing parameter values affects the stabilization level of medicine in the body, and (3) an interactive graphical analysis that provides a visual interpretation of the results. 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] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [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,Science Title: Using Graphs, Equations, and Tables to Investigate the Elimination of Medicine from the Body: Modeling the Situation
Description: This threepart eexample from Illuminations illustrates the use of iteration, recursion, and algebra to model and analyze the changing amount of medicine in an athlete's body. This example includes: (1) an interactive environment used to become familiar with the parameters involved and the range of results that can be obtained, (2) an interactive environment used to investigate how changing parameter values affects the stabilization level of medicine in the body, and (3) an interactive graphical analysis that provides a visual interpretation of the results. 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: Two Terrains
Description:
In this interactive from Illuminations, students learn about ratios while identifying the best path for a vehicle, depending on whether it has better on‑road or off‑road performance.
Standard(s): [MA2013] AL1 (912) 32: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1]
Subject: Mathematics Title: Two Terrains
Description: In this interactive from Illuminations, students learn about ratios while identifying the best path for a vehicle, depending on whether it has better on‑road or off‑road performance. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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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.
Standard(s): [MA2013] AL1 (912) 22: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). [AREI10] [MA2013] AL1 (912) 25: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [FIF1] [MA2013] AL1 (912) 26: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [FIF2] [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 40: Interpret the parameters in a linear or exponential function in terms of a context. [FLE5] [MA2013] AL1 (912) 41: Represent data with plots on the real number line (dot plots, histograms, and box plots). [SID1] [MA2013] AL2 (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL2 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL2 (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [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) [MA2013] ALT (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] ALT (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [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
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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.
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] [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 32: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] GEO (912) 36: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [GGMD3] [MA2013] GEO (912) 39: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [GMG1] [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] [MA2013] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) [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

