ALEX Lesson Plans
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Title: Human Population Growth WebQuest
Description:
This is a technologybased lesson plan that integrates science and math to determine dynamics in population growth.
Standard(s): [MA2013] AL1 (912) 32: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8] [MA2013] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) [S1] BIO (912) 16: Identify densitydependent and densityindependent limiting factors that affect populations in an ecosystem.
Subject: Mathematics (9  12), or Science (9  12)
Title: Human Population Growth WebQuest
Description: This is a technologybased lesson plan that integrates science and math to determine dynamics in population growth.
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Title: Liquidity for Success
Description:
This lesson will input values to calculate financial ratios and intepret the information derived from the calculations. This is a Commerce and Information Technology lesson plan.
Standard(s): [FIN] FN2 (912) 8: Apply analysis ratios to evaluate solvency and earning power. [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) 6: Use the extreme value of a given quadratic function to solve applied problems. (Alabama) [MA2013] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama)
Subject: Finance (9  12), or Mathematics (9  12)
Title: Liquidity for Success
Description: This lesson will input values to calculate financial ratios and intepret the information derived from the calculations. This is a Commerce and Information Technology lesson plan.
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Title: Exponential Growth and Decay
Description:
This lesson on exponential growth and decay involves a variety of teaching resources. There are a variety of websites used to teach and reinforce how to identify exponential growth or decay and how to solve problems relating to growth and decay. There is a lab provided that will help model these concepts being taught and computer based practice on these concepts. Videos are provided that give a picture image of how exponential growth and decay works. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [MA2013] AL1 (912) 7: Interpret expressions that represent a quantity in terms of its context.* [ASSE1] [MA2013] AL1 (912) 9: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* [ASSE3] [MA2013] AL1 (912) 28: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* [FIF4] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 32: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 36: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [FBF3] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 39: Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. [FLE3] [MA2013] AL2 (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL2 (912) 34: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
[FBF3] [MA2013] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) [MA2013] ALT (912) 12: Interpret expressions that represent a quantity in terms of its context.* [ASSE1] [MA2013] ALT (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] PRE (912) 16: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. (Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Determine odd, even, neither.)* [FIF4] (Alabama) [MA2013] ALT (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] ALT (912) 34: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
[FBF3] [MA2013] PRE (912) 25: Compare effects of parameter changes on graphs of transcendental functions. (Alabama)
Subject: Mathematics (9  12)
Title: Exponential Growth and Decay
Description: This lesson on exponential growth and decay involves a variety of teaching resources. There are a variety of websites used to teach and reinforce how to identify exponential growth or decay and how to solve problems relating to growth and decay. There is a lab provided that will help model these concepts being taught and computer based practice on these concepts. Videos are provided that give a picture image of how exponential growth and decay works. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Discovering Earth's History
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This lesson introduces the basic principles that are used to interpret geologic time. It associates the relationships between the rock record and historical events that created the landforms on our planet. It explains how the rock record can be interpreted by geologists.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) 7: Explain techniques for determining the age and composition of Earth and the universe. [S1] E&S (912) 7: Explain techniques for determining the age and composition of Earth and the universe. [S1] E&S (912) 7: Explain techniques for determining the age and composition of Earth and the universe. [S1] E&S (912) 7: Explain techniques for determining the age and composition of Earth and the universe. [S1] E&S (912) 7: Explain techniques for determining the age and composition of Earth and the universe. [S1] E&S (912) 7: Explain techniques for determining the age and composition of Earth and the universe. [S1] AQU (912) 6: Describe adaptations that allow organisms to exist in specific aquatic environments. [S1] CHE (912) 3: Use the periodic table to identify periodic trends, including atomic radii, ionization energy, electronegativity, and energy levels. [S1] CHE (912) 8: Distinguish among endothermic and exothermic physical and chemical changes. [S1] CHE (912) 9: Distinguish between chemical and nuclear reactions. [S1] E&S (912) 7: Explain techniques for determining the age and composition of Earth and the universe. [S1] E&S (912) 10: Identify scientists and their findings relative to Earth and space, including Copernicus, Galileo, Kepler, Newton, and Einstein. [S1] ENV (912) 4: Identify the impact of pollutants on the atmosphere. [S1] ENV (912) 7: Identify reasons coastal waters serve as an important resource. [S1] FOR (912) 2: Explain ways to collect and preserve evidence from a crime scene. [S1] FOR (912) 6: Describe the decomposition process. [S1] FOR (912) 7: Identify the importance of skeletal remains in forensics. [S1] GEL (912) 2: Relate the concept of equilibrium to geological processes, including plate tectonics and stream flow. [S1] GEL (912) 3: Explain natural phenomena that shape the surface of Earth, including rock cycles, plate motions and interactions, erosion and deposition, volcanism, earthquakes, weathering, and tides. [S1] GEL (912) 4: Describe the topography of the sea floor and the continents. [S1] GEL (912) 6: Explain the concept of geological time within the framework of the geologic time scale. [S1] GEL (912) 7: Describe processes of rock formation. [S1] GEL (912) 11: Identify mass movements, including topples, slides, spreads, and flows. [S1] GEL (912) 15: Identify geological regions in Alabama and the southeastern United States. [S1] MAR (912) 1: Select appropriate equipment for scientific field investigations in marine environments. [S1] MAR (912) 3: Describe physical characteristics of oceans, including topography of the ocean floor, plate tectonics, wave motion, depth, and pressure. [S1] MAR (912) 6: Describe components of major marine ecosystems, including estuaries, coral reefs, benthic communities, and openocean communities. [S1] PHS (912) 1: Recognize periodic trends of elements, including the number of valence electrons, atomic size, and reactivity. [S1] PHS (912) 5: Describe physical and chemical changes in terms of endothermic and exothermic processes. [S1] PHS (912) 7: Relate velocity, acceleration, and kinetic energy to mass, distance, force, and time. [S1] PHS (912) 8: Relate the law of conservation of energy to transformations of potential energy, kinetic energy, and thermal energy. [S1] PHS (912) 10: Explain the relationship between electricity and magnetism. [S1] PHS (912) 11: Describe the nuclear composition of unstable isotopes and the resulting changes to their nuclear composition. [MA2013] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (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) 9: Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio. (Alabama) [MA2013] AL1 (912) 41: Represent data with plots on the real number line (dot plots, histograms, and box plots). [SID1]
Subject: Mathematics (9  12), or Science (9  12)
Title: Discovering Earth's History
Description: This lesson introduces the basic principles that are used to interpret geologic time. It associates the relationships between the rock record and historical events that created the landforms on our planet. It explains how the rock record can be interpreted by geologists.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: You Mean ANYTHING To The Zero Power Is One?
Description:
This lesson is a technologybased project to reinforce concepts related to the Exponential Function. It can be used in conjunction with any textbook practice set. Construction of computer models of several Exponential Functions will promote meaningful learning rather than memorization.
Standard(s): [TC2] CA2 (912) 5: Utilize advanced features of spreadsheet software, including creating charts and graphs,
sorting and filtering data, creating formulas, and applying functions. [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] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (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) 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) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [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) 2: Rewrite expressions involving radicals and rational exponents using the properties of exponents. [NRN2] [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] 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] 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] AL1 (912) 33: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [FIF9] [MA2013] 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] 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) 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) 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) 1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. [NRN1] [MA2013] AL1 (912) 9: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* [ASSE3]
Subject: Mathematics (9  12), or Technology Education (9  12)
Title: You Mean ANYTHING To The Zero Power Is One?
Description: This lesson is a technologybased project to reinforce concepts related to the Exponential Function. It can be used in conjunction with any textbook practice set. Construction of computer models of several Exponential Functions will promote meaningful learning rather than memorization.
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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]
Subject: 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: Predicting Your Financial Future
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In this Illuminations lesson, students use their knowledge of exponents to compute an investment s worth using a formula and a compound interest simulator. Students also use the simulator to analyze credit card payments and debt.
Standard(s): [MA2013] AL1 (912) 9: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* [ASSE3] [MA2013] AL1 (912) 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] 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) 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)
Subject: Mathematics Title: Predicting Your Financial Future
Description: In this Illuminations lesson, students use their knowledge of exponents to compute an investment s worth using a formula and a compound interest simulator. Students also use the simulator to analyze credit card payments and debt. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Exact Ratio
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This reproducible activity sheet, from an Illuminations lesson, features a series of questions pertaining to exact ratios and geometric sequences. In the lesson, students measure lengths on stringed musical instruments and discuss how the placement of frets on a fretted instrument is determined by a geometric sequence.
Standard(s): [MA2013] AL1 (912) 2: Rewrite expressions involving radicals and rational exponents using the properties of exponents. [NRN2] [MA2013] AL1 (912) 28: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* [FIF4] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 32: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8] [MA2013] AL1 (912) 33: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [FIF9] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 39: Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. [FLE3] [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [MA2013] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama) [MA2013] AL2 (912) 12: Interpret expressions that represent a quantity in terms of its context.* [ASSE1] [MA2013] AL2 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL2 (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL2 (912) 34: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
[FBF3] [MA2013] PRE (912) 16: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. (Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Determine odd, even, neither.)* [FIF4] (Alabama) [MA2013] ALT (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [FBF2]
Subject: Mathematics Title: Exact Ratio
Description: This reproducible activity sheet, from an Illuminations lesson, features a series of questions pertaining to exact ratios and geometric sequences. In the lesson, students measure lengths on stringed musical instruments and discuss how the placement of frets on a fretted instrument is determined by a geometric sequence. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Make a Conjecture
Description:
In this lesson, one of a multipart unit from Illuminations, students explore rates of change and accumulation in context. They are asked to think about the mathematics involved in determining the amount of blood being pumped by a heart.
Standard(s): [MA2013] AL1 (912) 4: Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. [NQ1] [MA2013] AL1 (912) 5: Define appropriate quantities for the purpose of descriptive modeling. [NQ2] [MA2013] AL1 (912) 6: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. [NQ3] [MA2013] AL1 (912) 12: Create equations and inequalities in one variable, and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [MA2013] AL1 (912) 13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL1 (912) 14: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities and interpret solutions as viable or nonviable options in a modeling context. [ACED3] [MA2013] AL1 (912) 28: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* [FIF4] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 32: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 39: Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. [FLE3] [MA2013] AL1 (912) 40: Interpret the parameters in a linear or exponential function in terms of a context. [FLE5] [MA2013] AL1 (912) 41: Represent data with plots on the real number line (dot plots, histograms, and box plots). [SID1] [MA2013] AL1 (912) 42: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [SID2] [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [MA2013] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) [MA2013] ALC (912) 5: Determine approximate rates of change of nonlinear relationships from graphical and numerical data. (Alabama) [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama) [MA2013] AL2 (912) 12: Interpret expressions that represent a quantity in terms of its context.* [ASSE1] [MA2013] AL2 (912) 20: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [MA2013] AL2 (912) 22: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [ACED3] [MA2013] AL2 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL2 (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL2 (912) 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] AL2 (912) 38: (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [SMD7] [MA2013] ALT (912) 12: Interpret expressions that represent a quantity in terms of its context.* [ASSE1] [MA2013] ALT (912) 20: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [MA2013] ALT (912) 22: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [ACED3] [MA2013] PRE (912) 16: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. (Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Determine odd, even, neither.)* [FIF4] (Alabama) [MA2013] ALT (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] PRE (912) 17: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] ALT (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] ALT (912) 37: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. [SID4] [MA2013] PRE (912) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [SIC1] [MA2013] PRE (912) 45: Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. [SIC2] [MA2013] PRE (912) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [SIC3] [MA2013] PRE (912) 49: Evaluate reports based on data. [SIC6] [MA2013] ALT (912) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] ALT (912) 42: (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [SMD7] [MA2013] AL1 (912) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [FBF2]
Subject: Health,Mathematics Title: Make a Conjecture
Description: In this lesson, one of a multipart unit from Illuminations, students explore rates of change and accumulation in context. They are asked to think about the mathematics involved in determining the amount of blood being pumped by a heart. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: The National Debt and Wars
Description:
This reproducible worksheet, from an Illuminations lesson, guides students as they collect information about the national debt, plot the data by decade and determine whether an exponential curve is a good fit for the data.
Standard(s): [MA2013] AL1 (912) 32: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8] [MA2013] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama)
Subject: Mathematics,Social Studies Title: The National Debt and Wars
Description: This reproducible worksheet, from an Illuminations lesson, guides students as they collect information about the national debt, plot the data by decade and determine whether an exponential curve is a good fit for the data. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Radioactive Decay: A Sweet Simulation of HalfLife
Description:
In this Science NetLinks lesson, the second lesson in a threepart series about isotopes, radioactive decay, and the nucleus, students are asked to simulate radioactive decay by pouring small candies and counting which candies fall with their manufacturer's mark down or up. The exercise they go through of predicting and successively counting the number of remaining '' markside up'' candies should help them understand that rates of decay of unstable nuclei can be measured, that the exact time that a certain nucleus will decay cannot be predicted, and that it takes a very large number of nuclei to find the rate of decay.
Standard(s): [S1] CHE (912) 3: Use the periodic table to identify periodic trends, including atomic radii, ionization energy, electronegativity, and energy levels. [S1] CHE (912) 9: Distinguish between chemical and nuclear reactions. [MA2013] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama)
Subject: Mathematics Title: Radioactive Decay: A Sweet Simulation of HalfLife
Description: In this Science NetLinks lesson, the second lesson in a threepart series about isotopes, radioactive decay, and the nucleus, students are asked to simulate radioactive decay by pouring small candies and counting which candies fall with their manufacturer's mark down or up. The exercise they go through of predicting and successively counting the number of remaining '' markside up'' candies should help them understand that rates of decay of unstable nuclei can be measured, that the exact time that a certain nucleus will decay cannot be predicted, and that it takes a very large number of nuclei to find the rate of decay. Thinkfinity Partner: Science NetLinks Grade Span: 9,10,11,12
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Title: Shedding the Light
Description:
In this fourlesson unit, from Illuminations, students investigate a mathematical model for the decay of light passing through water. The goal of this investigation is a rich exploration of exponential models in context. Students examine the way light changes as water depth increases, conduct experiments, explore related algebraic functions using an interactive Java applet and analyze the data collected.
Standard(s): [S1] PHS (912) 9: Compare methods of energy transfer by mechanical and electromagnetic waves. [S1] PHY (912) 6: Describe wave behavior in terms of reflection, refraction, diffraction, constructive and destructive wave interference, and the Doppler effect. [S1] PHY (912) 7: Describe properties of reflection, refraction, and diffraction. [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) 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] 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) 39: Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. [FLE3] [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [MA2013] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) [MA2013] DM1 (912) 3: Use the recursive process and difference equations to create fractals, population growth models, sequences, series, and compound interest models. (Alabama)
Subject: Mathematics,Science Title: Shedding the Light
Description: In this fourlesson unit, from Illuminations, students investigate a mathematical model for the decay of light passing through water. The goal of this investigation is a rich exploration of exponential models in context. Students examine the way light changes as water depth increases, conduct experiments, explore related algebraic functions using an interactive Java applet and analyze the data collected. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Frosty the Snowman Meets His Demise: An Analogy to Carbon Dating
Description:
The purpose of this Science NetLinks lesson is to develop the idea that carbon dating is based on gathering evidence in the present and extrapolating it to the past. Students use a simple graph to extrapolate data to its starting point.
Standard(s): [S1] CHE (912) 9: Distinguish between chemical and nuclear reactions. [MA2013] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama)
Subject: Mathematics, Science Title: Frosty the Snowman Meets His Demise: An Analogy to Carbon Dating
Description: The purpose of this Science NetLinks lesson is to develop the idea that carbon dating is based on gathering evidence in the present and extrapolating it to the past. Students use a simple graph to extrapolate data to its starting point. Thinkfinity Partner: Science NetLinks Grade Span: 9,10,11,12
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Title: Gather Data
Description:
In this lesson, one of a multipart unit from Illuminations, students explore the development of a mathematical model for the decay of light passing through water, in a rich exploration of exponential models in context. They conduct three experiments including a simulated ocean dive, using tinted Plexiglas to simulate water depth, and measuring light intensity within a column of water.
Standard(s): [S1] PHS (912) 9: Compare methods of energy transfer by mechanical and electromagnetic waves. [S1] PHY (912) 6: Describe wave behavior in terms of reflection, refraction, diffraction, constructive and destructive wave interference, and the Doppler effect. [S1] PHY (912) 7: Describe properties of reflection, refraction, and diffraction. [MA2013] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama)
Subject: Mathematics,Science Title: Gather Data
Description: In this lesson, one of a multipart unit from Illuminations, students explore the development of a mathematical model for the decay of light passing through water, in a rich exploration of exponential models in context. They conduct three experiments including a simulated ocean dive, using tinted Plexiglas to simulate water depth, and measuring light intensity within a column of water. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Web Resources
Interactives/Games
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Title: Compound Interest Simulator
Description:
This is an interactive tool that simulates and computes compounded interest on credit cards, savings accounts, and the stock market.
Standard(s): [MA2013] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama)
Compound Interest Simulator
http://illuminations...
This is an interactive tool that simulates and computes compounded interest on credit cards, savings accounts, and the stock market.
Thinkfinity Learning Activities
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Title: Flowing Through Mathematics
Description:
This student interactive, from Illuminations, simulates water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time.
Standard(s): [MA2013] AL1 (912) 13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL1 (912) 28: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* [FIF4] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 32: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] GEO (912) 36: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [GGMD3] [MA2013] GEO (912) 39: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [GMG1] [MA2013] GEO (912) 40: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, British Thermal Units (BTUs) per cubic foot).* [GMG2] [MA2013] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama)
Subject: Mathematics Title: Flowing Through Mathematics
Description: This student interactive, from Illuminations, simulates water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12

