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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: Density
Description:
Density is the ratio of mass to volume. Density will be introduced to students by a demonstration of coke verses diet coke. The teacher will then solve density problems for the students on the board. The class will then complete a lab on the density of plastics. After lab the students will compare results. Each group will present a Powerpoint presentation of their results.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [S1] (8) 1: Identify steps within the scientific process. [S1] CHE (912) 1: Differentiate among pure substances, mixtures, elements, and compounds. [S1] ENV (912) 1: Identify the influence of human population, technology, and cultural and industrial changes on the environment. [MA2013] AL1 (912) 4: Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. [NQ1] [MA2013] AL1 (912) 5: Define appropriate quantities for the purpose of descriptive modeling. [NQ2] [MA2013] AL1 (912) 6: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. [NQ3] [MA2013] AL1 (912) 15: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [ACED4] [MA2013] AL1 (912) 17: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [AREI3] [MA2013] AL1 (912) 28: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* [FIF4] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] ALC (912) 1: Create algebraic models for applicationbased problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) [MA2013] GEO (912) 40: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, British Thermal Units (BTUs) per cubic foot).* [GMG2]
Subject: Mathematics (9  12), or Science (8  12)
Title: Density
Description: Density is the ratio of mass to volume. Density will be introduced to students by a demonstration of coke verses diet coke. The teacher will then solve density problems for the students on the board. The class will then complete a lab on the density of plastics. After lab the students will compare results. Each group will present a Powerpoint presentation of their results.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Cosmic Measurements
Description:
In this lesson, students will use hands on inquiry in cooperative learning groups to understand, develop and analyze common measurements used by astronomers. Students will use common objects such as straws, twizzlers, or toothpicks to measure the distance from a fixed object or central location to other objects. The students will then use this information to develop a unit of measurement like the astronomical unit. The students will measure the speed of an object such as a remote control car and use this to develop a unit similar to the lightyear. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [S1] E&S (912) 8: Explain the terms astronomical unit and light year. [MA2013] AL1 (912) 4: Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. [NQ1] [MA2013] AL1 (912) 5: Define appropriate quantities for the purpose of descriptive modeling. [NQ2] [MA2013] AL1 (912) 6: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. [NQ3] [MA2013] AL1 (912) 12: Create equations and inequalities in one variable, and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [MA2013] AL1 (912) 15: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [ACED4] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] ALC (912) 1: Create algebraic models for applicationbased problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) [MA2013] ALC (912) 10: Critique measurements in terms of precision, accuracy, and approximate error. (Alabama)
Subject: Mathematics (9  12), or Science (9  12)
Title: Cosmic Measurements
Description: In this lesson, students will use hands on inquiry in cooperative learning groups to understand, develop and analyze common measurements used by astronomers. Students will use common objects such as straws, twizzlers, or toothpicks to measure the distance from a fixed object or central location to other objects. The students will then use this information to develop a unit of measurement like the astronomical unit. The students will measure the speed of an object such as a remote control car and use this to develop a unit similar to the lightyear. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Writing Word Equations
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The students will learn to write word and formula equations. We will watch a web video about chemical equations. We will then complete the science in motion lab “The Color of Chemistry”. The students will also be required to write word and formula equations.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] PHS (912) 4: Use nomenclature and chemical formulas to write balanced chemical equations. [S1] CHE (912) 6: Solve stoichiometric problems involving relationships among the number of particles, moles, and masses of reactants and products in a chemical reaction. [S1] CHE (912) 6: Solve stoichiometric problems involving relationships among the number of particles, moles, and masses of reactants and products in a chemical reaction. [MA2013] AL1 (912) 2: Rewrite expressions involving radicals and rational exponents using the properties of exponents. [NRN2] [MA2013] AL2 (912) 2: Use the relation i^{2} = 1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. [NCN2] [MA2013] AL2 (912) 31: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8] [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] ALT (912) 2: Use the relation i^{2} = 1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. [NCN2] [MA2013] ALT (912) 31: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8]
Subject: Mathematics (9  12), or Science (9  12)
Title: Writing Word Equations
Description: The students will learn to write word and formula equations. We will watch a web video about chemical equations. We will then complete the science in motion lab “The Color of Chemistry”. The students will also be required to write word and formula equations.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: What is the slope of the stairs in front of the school?
Description:
The purpose of this lesson is to help students apply the mathematical definition of slope to a concrete example. The students will learn to make the appropriate measurements and apply the formula to calculate the slope of the stairs experimentally.
Standard(s): [MA2013] (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: Creating a Payroll Spreadsheet
Description:
Spreadsheet software allows you to calculate numbers arranged in rows and columns for specific financial tasks. This activity allows students to create an "Employee Work/Pay Schedule" spreadsheet to reinforce spreadsheet skills. Students will practice spreadsheet skills by entering data, creating formulas, and using formatting commands.
Standard(s): [MA2013] ALC (912) 7: Use analytical, numerical, and graphical methods to make financial and economic decisions, including those involving banking and investments, insurance, personal budgets, credit purchases, recreation, and deceptive and fraudulent pricing and advertising. (Alabama) [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [MA2013] AL1 (912) 28: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* [FIF4] [MA2013] ALC (912) 1: Create algebraic models for applicationbased problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 12: Create equations and inequalities in one variable, and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [TC2] CA2 (912) 5: Utilize advanced features of spreadsheet software, including creating charts and graphs,
sorting and filtering data, creating formulas, and applying functions.
Subject: Mathematics (9  12), or Technology Education (9  12)
Title: Creating a Payroll Spreadsheet
Description: Spreadsheet software allows you to calculate numbers arranged in rows and columns for specific financial tasks. This activity allows students to create an "Employee Work/Pay Schedule" spreadsheet to reinforce spreadsheet skills. Students will practice spreadsheet skills by entering data, creating formulas, and using formatting commands.
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Title: Swimming Pool Math
Description:
Students will use a swimming pool example to practice finding perimeter and area of different rectangles.
Standard(s): [MA2013] GEO (912) 39: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [GMG1] [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama) [MA2013] ALC (912) 1: Create algebraic models for applicationbased problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 14: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities and interpret solutions as viable or nonviable options in a modeling context. [ACED3] [MA2013] AL1 (912) 12: Create equations and inequalities in one variable, and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [MA2013] AL1 (912) 4: Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. [NQ1] [MA2013] GEO (912) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. [GCO12] [MA2013] ALC (912) 11: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama) [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [MA2013] AL1 (912) 28: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* [FIF4] [MA2013] AL1 (912) 13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL1 (912) 5: Define appropriate quantities for the purpose of descriptive modeling. [NQ2] [MA2013] GEO (912) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [GMG3] [MA2013] (6) 21: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. [6G1] [MA2013] (8) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve realworld and mathematical problems. [8G9]
Subject: Mathematics (6  12)
Title: Swimming Pool Math
Description: Students will use a swimming pool example to practice finding perimeter and area of different rectangles.
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Title: Rags to Riches or Riches to Rags?
Description:
In this lesson students will apply the interest formulas to make the best investment decision for our fictional character Algebrea Calculique. The students will be provided with a story explaining the situation that Algebrea faces and the investment choices that she has. To present their findings and conclusion, the students will write an expository essay. This lesson integrates mathematics into the writing process.
Standard(s): [ELA2013] (9) 21: Write informative or explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content. [W.910.2] [MA2013] ALT (912) 20: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [MA2013] ALT (912) 12: Interpret expressions that represent a quantity in terms of its context.* [ASSE1] [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) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) [MA2013] ALC (912) 1: Create algebraic models for applicationbased problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) [MA2013] AL2 (912) 20: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [MA2013] 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) 7: Interpret expressions that represent a quantity in terms of its context.* [ASSE1] [ELA2013] (10) 22: Write informative or explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content. [W.910.2] [ELA] (9) 7: Write in narrative, expository, and persuasive modes using figurative language and imagery, including simile and metaphor, when effective and appropriate. [ELA] (10) 7: Write in persuasive, expository, and narrative modes using an abbreviated writing process in timed and untimed situations.
Subject: English Language Arts (9  10), or English Language Arts (9  10), or Mathematics (9  12)
Title: Rags to Riches or Riches to Rags?
Description: In this lesson students will apply the interest formulas to make the best investment decision for our fictional character Algebrea Calculique. The students will be provided with a story explaining the situation that Algebrea faces and the investment choices that she has. To present their findings and conclusion, the students will write an expository essay. This lesson integrates mathematics into the writing process.
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Title: Percent Slope Tool
Description:
This reproducible activity, from an Illuminations lesson, provides a template by which students can create a tool for calculating the slope of realworld inclines.
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] GEO (912) 39: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [GMG1] [MA2013] ALC (912) 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) 2: Solve applicationbased problems by developing and solving systems of linear equations and inequalities. (Alabama)
Subject: Mathematics Title: Percent Slope Tool
Description: This reproducible activity, from an Illuminations lesson, provides a template by which students can create a tool for calculating the slope of realworld inclines. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Think of a Graph
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This reproducible transparency, from an Illuminations lesson, asks students to sketch a graph in which the side length of a square is graphed on the horizontal axis and the perimeter of the square is graphed on the vertical axis.
Standard(s): [MA2013] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8EE5] [MA2013] (8) 14: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8F4] [MA2013] (8) 25: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [8SP1] [MA2013] (8) 26: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [8SP2] [MA2013] (8) 27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8SP3] [MA2013] AL1 (912) 13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL1 (912) 14: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities and interpret solutions as viable or nonviable options in a modeling context. [ACED3] [MA2013] AL1 (912) 22: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). [AREI10] [MA2013] AL1 (912) 28: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* [FIF4] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [MA2013] AL1 (912) 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [SID7] [MA2013] ALC (912) 1: Create algebraic models for applicationbased problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama)
Subject: Mathematics Title: Think of a Graph
Description: This reproducible transparency, from an Illuminations lesson, asks students to sketch a graph in which the side length of a square is graphed on the horizontal axis and the perimeter of the square is graphed on the vertical axis. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Graph Chart
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: Do I Have to Mow the Whole Thing?
Description:
This lesson offers examples of inverse variation. Students collect data and generate graphs before finding specific equations for inverse variation relationships and examining their graphs and discuss the asymptotes.
Standard(s): [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)
Subject: Mathematics Title: Do I Have to Mow the Whole Thing?
Description: This lesson offers examples of inverse variation. Students collect data and generate graphs before finding specific equations for inverse variation relationships and examining their graphs and discuss the asymptotes. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Rates and Taxes
Description:
In this lesson, from Illuminations, students become familiar with percents and taxes. Students learn how to determine the amount of tax a family must pay based on a certain income.
Standard(s): [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] 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)
Subject: Mathematics,Social Studies Title: Rates and Taxes
Description: In this lesson, from Illuminations, students become familiar with percents and taxes. Students learn how to determine the amount of tax a family must pay based on a certain income. 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: Bean Counting
Description:
By using sampling from a large collection of beans, students get a sense of equivalent fractions, which leads to a better understanding of proportions. Equivalent fractions are used to develop an understanding of proportions. The numbersense of recognizing equivalent fractions is useful when students study slope and proportions.
Standard(s): [MA2013] (6) 1: Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. [6RP1] [MA2013] (6) 2: Understand the concept of a unit rate ^{a}/_{b} associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. [6RP2] [MA2013] (6) 3: Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. [6RP3] [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2] [MA2013] (7) 3: Use proportional relationships to solve multistep ratio and percent problems. [7RP3] [MA2013] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8EE5] [MA2013] 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)
Subject: Mathematics Title: Bean Counting
Description: By using sampling from a large collection of beans, students get a sense of equivalent fractions, which leads to a better understanding of proportions. Equivalent fractions are used to develop an understanding of proportions. The numbersense of recognizing equivalent fractions is useful when students study slope and proportions. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12

