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Title: Systems of Equations: What Method Do You Prefer?
Description:
The purpose of this lesson is to help students apply math concepts of solving systems of equations to real life situations. The students will use the three methods of graphing, substitution, and elimination to solve the system of 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): [MA2013] (8) 10: Analyze and solve pairs of simultaneous linear equations. [8EE8] [MA2013] AL1 (912) 19: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. [AREI5] [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] [MA2013] AL2 (912) 27: Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [AREI11] [MA2013] ALC (912) 2: Solve applicationbased problems by developing and solving systems of linear equations and inequalities. (Alabama) [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]
Subject: Mathematics (8  12)
Title: Systems of Equations: What Method Do You Prefer?
Description: The purpose of this lesson is to help students apply math concepts of solving systems of equations to real life situations. The students will use the three methods of graphing, substitution, and elimination to solve the system of 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: Make a Conjecture
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In this lesson, one of a multipart unit from Illuminations, students explore rates of change and accumulation in context. They are asked to think about the mathematics involved in determining the amount of blood being pumped by a heart.
Standard(s): [MA2013] AL1 (912) 4: Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. [NQ1] [MA2013] AL1 (912) 5: Define appropriate quantities for the purpose of descriptive modeling. [NQ2] [MA2013] AL1 (912) 6: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. [NQ3] [MA2013] AL1 (912) 12: Create equations and inequalities in one variable, and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [MA2013] AL1 (912) 13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL1 (912) 14: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities and interpret solutions as viable or nonviable options in a modeling context. [ACED3] [MA2013] AL1 (912) 28: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* [FIF4] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 32: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 39: Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. [FLE3] [MA2013] AL1 (912) 40: Interpret the parameters in a linear or exponential function in terms of a context. [FLE5] [MA2013] AL1 (912) 41: Represent data with plots on the real number line (dot plots, histograms, and box plots). [SID1] [MA2013] AL1 (912) 42: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [SID2] [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [MA2013] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) [MA2013] ALC (912) 5: Determine approximate rates of change of nonlinear relationships from graphical and numerical data. (Alabama) [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama) [MA2013] AL2 (912) 12: Interpret expressions that represent a quantity in terms of its context.* [ASSE1] [MA2013] AL2 (912) 20: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [MA2013] AL2 (912) 22: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [ACED3] [MA2013] AL2 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL2 (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL2 (912) 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] AL2 (912) 38: (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [SMD7] [MA2013] ALT (912) 12: Interpret expressions that represent a quantity in terms of its context.* [ASSE1] [MA2013] ALT (912) 20: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [MA2013] ALT (912) 22: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [ACED3] [MA2013] PRE (912) 16: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. (Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Determine odd, even, neither.)* [FIF4] (Alabama) [MA2013] ALT (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] PRE (912) 17: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] ALT (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] ALT (912) 37: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. [SID4] [MA2013] PRE (912) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [SIC1] [MA2013] PRE (912) 45: Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. [SIC2] [MA2013] PRE (912) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [SIC3] [MA2013] PRE (912) 49: Evaluate reports based on data. [SIC6] [MA2013] ALT (912) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] ALT (912) 42: (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [SMD7] [MA2013] AL1 (912) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [FBF2]
Subject: Health,Mathematics Title: Make a Conjecture
Description: In this lesson, one of a multipart unit from Illuminations, students explore rates of change and accumulation in context. They are asked to think about the mathematics involved in determining the amount of blood being pumped by a heart. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: WhelkCome to Mathematics
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In this fourlesson unit, from Illuminations, students make a conjecture, conduct an experiment, analyze data and work to a conclusion using rational functions to investigate the behavior of Northwestern Crows. Sea gulls and crows feed on various types of mollusks by lifting them into the air and dropping them onto a rock to break open their shells. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. Students investigate the relationship between the height of the drop and the number of drops.
Standard(s): [MA2013] AL2 (912) 22: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [ACED3] [MA2013] AL2 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL2 (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [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] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] PRE (912) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [SIC1] [MA2013] PRE (912) 45: Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. [SIC2] [MA2013] PRE (912) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [SIC3] [MA2013] PRE (912) 49: Evaluate reports based on data. [SIC6] [MA2013] PRE (912) 4: Determine numerically, algebraically, and graphically the limits of functions at specific values and at infinity. (Alabama) [MA2013] PRE (912) 18: c. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. [FIF7d] [MA2013] AM1 (912) 12: Calculate the limit of a sequence, of a function, and of an infinite series. (Alabama)
Subject: Mathematics,Science Title: WhelkCome to Mathematics
Description: In this fourlesson unit, from Illuminations, students make a conjecture, conduct an experiment, analyze data and work to a conclusion using rational functions to investigate the behavior of Northwestern Crows. Sea gulls and crows feed on various types of mollusks by lifting them into the air and dropping them onto a rock to break open their shells. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. Students investigate the relationship between the height of the drop and the number of drops. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Northwestern Crows
Description:
In this lesson, one of a multipart unit from Illuminations, students use rational functions to investigate the feeding behavior of Northwestern Crows. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. Students investigate the relationship between the height of the drop and the number of drops by viewing a video clip; then, they plan a classroom experiment to model the dropping of whelks in order to collect and analyze data.
Standard(s): [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) 33: Write a function that describes a relationship between two quantities.* [FBF1] [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] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] PRE (912) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [SIC1] [MA2013] PRE (912) 45: Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. [SIC2] [MA2013] PRE (912) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [SIC3] [MA2013] PRE (912) 49: Evaluate reports based on data. [SIC6] [MA2013] PRE (912) 4: Determine numerically, algebraically, and graphically the limits of functions at specific values and at infinity. (Alabama) [MA2013] PRE (912) 18: c. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. [FIF7d] [MA2013] PRE (912) 50: (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. [SMD1]
Subject: Mathematics,Science Title: Northwestern Crows
Description: In this lesson, one of a multipart unit from Illuminations, students use rational functions to investigate the feeding behavior of Northwestern Crows. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. Students investigate the relationship between the height of the drop and the number of drops by viewing a video clip; then, they plan a classroom experiment to model the dropping of whelks in order to collect and analyze data. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Road Trip!
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In this Illuminations lesson, students investigate the famous Traveling Salesman Problem by considering the shortest route between five northeastern cities. Three different algorithms for finding the shortest route are explored, and students are encouraged to look for others.
Standard(s): [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] AL2 (912) 46: (+) Use permutations and combinations to compute probabilities of compound events and solve problems. [SCP9] [MA2013] AL2 (912) 22: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [ACED3] [MA2013] 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]
Subject: Mathematics Title: Road Trip!
Description: In this Illuminations lesson, students investigate the famous Traveling Salesman Problem by considering the shortest route between five northeastern cities. Three different algorithms for finding the shortest route are explored, and students are encouraged to look for others. 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: Pick's Theorem as a System of Equations
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In this lesson, one of a multipart unit from Illuminations, students gather three examples from a geoboard or other representation to generate a system of equations. The solution provides the coefficients for Pick s Theorem.
Standard(s): [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) 19: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. [AREI5] [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] 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]
Subject: Mathematics Title: Pick's Theorem as a System of Equations
Description: In this lesson, one of a multipart unit from Illuminations, students gather three examples from a geoboard or other representation to generate a system of equations. The solution provides the coefficients for Pick s Theorem. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Isosceles Triangle Investigation
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This student interactive, from an Illuminations lesson, allows students to investigate the relationship between the area of the triangle and the length of its base.
Standard(s): [MA2013] GEO (912) 6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. [GCO6] [MA2013] GEO (912) 10: Prove theorems about triangles. Theorems include measures of interior angles of a triangle sum to 180^{o}, base angles of isosceles triangles are congruent, the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length, and the medians of a triangle meet at a point. [GCO10] [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] GEO (912) 17: Prove theorems about triangles. Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; and the Pythagorean Theorem proved using triangle similarity. [GSRT4] [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] 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] 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: Isosceles Triangle Investigation
Description: This student interactive, from an Illuminations lesson, allows students to investigate the relationship between the area of the triangle and the length of its base. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12

