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Title: Penny Drop That Thang!
Description:
This lesson is designed to introduce and extend students' knowledge on slope and linear equations. Students will be able to differentiate finding the slope to creating a linear equation.
This is a College and CareerReady Standards showcase lesson plan.
Standard(s): [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] 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) 17: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [AREI3] [MA2013] AL1 (912) 20: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. [AREI6] [MA2013] AL1 (912) 23: Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [AREI11]
Subject: Mathematics (8  12)
Title: Penny Drop That Thang!
Description: This lesson is designed to introduce and extend students' knowledge on slope and linear equations. Students will be able to differentiate finding the slope to creating a linear equation.
This is a College and CareerReady Standards showcase lesson plan.
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Title: Exploring Slope
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The purpose of this lesson is to help students see the real world application of slope. The students will view a movie clip of slope, calculate the slope of stairs in the school building, and analyze results.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
Standard(s): [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) 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [SID7] [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]
Subject: Mathematics (8  12)
Title: Exploring Slope
Description: The purpose of this lesson is to help students see the real world application of slope. The students will view a movie clip of slope, calculate the slope of stairs in the school building, and analyze results.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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Title: Incline Plane and the Crashing Marble
Description:
Students will measure the effects of the height of an inclined plane on the force a marble produces to move a plastic, foam, or paper cup across a table. Students will discover that the higher the incline plane, the more force produced by the marble, which moves the cup a greater distance. Students will also learn how to graph data and discover the appropriate graph to use for comparison.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] (8) 8: Identify Newton's three laws of motion. [S1] (8) 9: Describe how mechanical advantages of simple machines reduce the amount of force needed for work. [S1] (8) 10: Differentiate between potential and kinetic energy. [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) 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] (8) 8: Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. [8EE6] [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]
Subject: Mathematics (6  8), or Science (8)
Title: Incline Plane and the Crashing Marble
Description: Students will measure the effects of the height of an inclined plane on the force a marble produces to move a plastic, foam, or paper cup across a table. Students will discover that the higher the incline plane, the more force produced by the marble, which moves the cup a greater distance. Students will also learn how to graph data and discover the appropriate graph to use for comparison.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: Graphing Stations
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This activity will be used to review all the forms of linear equations and to review graphing linear, their parallels and their perpendiculars. All the forms of linear equations will be reviewed for testing purposes. Students will participate in a round robin activity to help students master objectives before unit test.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) 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] (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]
Subject: Mathematics (8  12)
Title: Graphing Stations
Description: This activity will be used to review all the forms of linear equations and to review graphing linear, their parallels and their perpendiculars. All the forms of linear equations will be reviewed for testing purposes. Students will participate in a round robin activity to help students master objectives before unit test.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: Human slope
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Students will participate in this discovery activity intended for them to uncover the role each variable plays in the graph of a line in the form y = mx + b. Students will actually demonstrate lines in slope intercept form on a life size graph. They will compare different graphs to see what effect adding negative signs and coefficients to the variables have on the graph. They will also analysis what happens to the graph when a constant is added or subtracted from the variable.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] (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) 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) 8: Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. [8EE6] [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] (6) 11: Solve realworld and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. [6NS8] [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) 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) 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) 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]
Subject: Mathematics (6  12)
Title: Human slope
Description: Students will participate in this discovery activity intended for them to uncover the role each variable plays in the graph of a line in the form y = mx + b. Students will actually demonstrate lines in slope intercept form on a life size graph. They will compare different graphs to see what effect adding negative signs and coefficients to the variables have on the graph. They will also analysis what happens to the graph when a constant is added or subtracted from the variable.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: Investigating School Safety and Slope
Description:
Using a 'news report' approach, students investigate the slope of various stairways on the school campus and report on wheelchair accessibility and adherence to the Americans with Disabilities Act. (PowerPoint Included) An extension of this lesson includes the critique/design of existing/nonexistent ramps.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) 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) 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] 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] (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]
Subject: Mathematics (8  12)
Title: Investigating School Safety and Slope
Description: Using a 'news report' approach, students investigate the slope of various stairways on the school campus and report on wheelchair accessibility and adherence to the Americans with Disabilities Act. (PowerPoint Included) An extension of this lesson includes the critique/design of existing/nonexistent ramps.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: We Love to Graph!
Description:
The students will review plotting points on a Coordinate Plane through an interactive website. They will also practice changing the slope and yintercept on the website in order to see the effects. After this review, the students will work in groups to plot points and use slope to spell out letters of the alphabet. The students will then unscramble the letters to spell out "We Love to Graph!"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): [TC2] CA2 (912) 11: Critique digital content for validity, accuracy, bias, currency, and relevance. [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) 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]
Subject: Mathematics (8), or Technology Education (9  12)
Title: We Love to Graph!
Description: The students will review plotting points on a Coordinate Plane through an interactive website. They will also practice changing the slope and yintercept on the website in order to see the effects. After this review, the students will work in groups to plot points and use slope to spell out letters of the alphabet. The students will then unscramble the letters to spell out "We Love to Graph!"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: Heads Up!
Description:
The lesson is a handson project. Students will work in pairs to gather various measurements, organizing the data into a provided chart. The measurements will be used to review, reinforce, and introduce skills such as measures of central tendency, coordinate graphing, and various ways of representing data (i.e., stemandleaf plots, boxandwhisker plots, frequency tables, etc.).
Standard(s): [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] (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) 8: Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. [8EE6] [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]
Subject: Mathematics (7  8)
Title: Heads Up!
Description: The lesson is a handson project. Students will work in pairs to gather various measurements, organizing the data into a provided chart. The measurements will be used to review, reinforce, and introduce skills such as measures of central tendency, coordinate graphing, and various ways of representing data (i.e., stemandleaf plots, boxandwhisker plots, frequency tables, etc.).
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Title: What is the slope of the stairs in front of the school?
Description:
The purpose of this lesson is to help students apply the mathematical definition of slope to a concrete example. The students will learn to make the appropriate measurements and apply the formula to calculate the slope of the stairs experimentally.
Standard(s): [MA2013] (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) 8: Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. [8EE6] [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) 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) 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) 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] 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] GEO (912) 31: Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [GGPE5]
Subject: Mathematics (8  12)
Title: What is the slope of the stairs in front of the school?
Description: The purpose of this lesson is to help students apply the mathematical definition of slope to a concrete example. The students will learn to make the appropriate measurements and apply the formula to calculate the slope of the stairs experimentally.
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Title: Finding 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: Supreme Court Handshake
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In this lesson, one of a multipart unit from Illuminations, students explore the handshake problem, a classic problem in mathematics that asks, How many handshakes occur when n people shake hands with each other? Groups work to determine how many handshakes take place among the nine Supreme Court justices, and then generalize the problem to determine the number of handshakes in any size group. Students explore the problem using a verbal description, a table, a graph, a picture and an algebraic formula.
Standard(s): [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) 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]
Subject: Mathematics Title: Supreme Court Handshake
Description: In this lesson, one of a multipart unit from Illuminations, students explore the handshake problem, a classic problem in mathematics that asks, How many handshakes occur when n people shake hands with each other? Groups work to determine how many handshakes take place among the nine Supreme Court justices, and then generalize the problem to determine the number of handshakes in any size group. Students explore the problem using a verbal description, a table, a graph, a picture and an algebraic formula. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Beyond Handshakes
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In this lesson, one of a multipart unit from Illuminations, students explore triangular numbers. This exploration enhances students ability to generalize a pattern with variables.
Standard(s): [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) 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]
Subject: Mathematics Title: Beyond Handshakes
Description: In this lesson, one of a multipart unit from Illuminations, students explore triangular numbers. This exploration enhances students ability to generalize a pattern with variables. 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: 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: 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
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.
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
Description:
This reproducible transparency, from an Illuminations lesson, contains the answers to the similarly named student activity in which students identify the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs.
Standard(s): [MA2013] (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: 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: 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: What's the Function?
Digital Tool:
Answer Garden, an online brainstorming tool Web Address URL:
http://answergarden.ch/ Standard(s):
[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) 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] Digital Tool Description: Answer Garden is an online brainstorming tool that easily exports into other digital tools (wordle or tagxedo). It will also create a QR code which will facilitate easy access in a BYOD or 1:1 environment.
Title: What's the Function? Digital Tool: Answer Garden, an online brainstorming tool Digital Tool Description: Answer Garden is an online brainstorming tool that easily exports into other digital tools (wordle or tagxedo). It will also create a QR code which will facilitate easy access in a BYOD or 1:1 environment.
Web Resources
Lesson Plans
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Title: Growth Rate (Slope)
Description:
Given growth charts for the heights of girls and boys, students will use slope to approximate rates of change in the height of boys and girls at different ages. Students will use these approximations to plot graphs of the rate of change of height vs. age for boys and girls.
Standard(s): [MA2013] (8) 8: Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. [8EE6] [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] 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]
Growth Rate (Slope)
http://illuminations...
Given growth charts for the heights of girls and boys, students will use slope to approximate rates of change in the height of boys and girls at different ages. Students will use these approximations to plot graphs of the rate of change of height vs. age for boys and girls.
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Title: Talk or Text (Systems of Equations)
Description:
In this lesson, students compare different costs associated with two cell phone plans. They write equations with 2 variables and graph to find the solution of the system of equations. They then analyze the meaning of the graph and discuss other factors involved in choosing a cell phone plan.
Standard(s): [MA2013] (6) 14: Apply the properties of operations to generate equivalent expressions. [6EE3] [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) 8: Understand that rewriting an expression in different forms in a problem context can shed light on the problem, and how the quantities in it are related. [7EE2] [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]
Talk or Text (Systems of Equations)
http://illuminations...
In this lesson, students compare different costs associated with two cell phone plans. They write equations with 2 variables and graph to find the solution of the system of equations. They then analyze the meaning of the graph and discuss other factors involved in choosing a cell phone plan.
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Title: Pedal Power
Description:
In this lesson, students investigate slope as a rate of change. Students compare, contrast, and make conjectures based on distancetime graphs for three bicyclists climbing to the top of a mountain.
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) 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) 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [SID7]
Pedal Power
http://illuminations...
In this lesson, students investigate slope as a rate of change. Students compare, contrast, and make conjectures based on distancetime graphs for three bicyclists climbing to the top of a mountain.

