Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures.
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G02.04: : Construct parallel lines, using only a compass and straight edge or a protractor and straight edge, and explain the strategy used.
Constructing Parallel and Perpendicular Lines
Construct parallel and perpendicular lines using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction.
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S01: : Students will be expected to demonstrate an understanding of normal distribution, including standard deviation and z-scores.
S01.01: : Explain, using examples, the meaning of standard deviation.
Real-Time Histogram
Try to click your mouse once every 2 seconds. The time interval between each click is recorded, as well as the error and percent error. Data can be displayed in a table, histogram, or scatter plot. Observe and measure the characteristics of the resulting distribution when large amounts of data are collected.
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Measure your reaction time by clicking your mouse as quickly as possible when visual or auditory stimuli are presented. The individual response times are recorded, as well as the mean and standard deviation for each test. A histogram of data shows overall trends in sight and sound response times. The type of test as well as the symbols and sounds used are chosen by the user.
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S02.02: : Calculate, using technology, the population standard deviation of a data set.
Real-Time Histogram
Try to click your mouse once every 2 seconds. The time interval between each click is recorded, as well as the error and percent error. Data can be displayed in a table, histogram, or scatter plot. Observe and measure the characteristics of the resulting distribution when large amounts of data are collected.
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S02.03: : Explain, using examples, the properties of a normal curve, including the mean, median, mode, standard deviation, symmetry, and area under the curve.
Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population.
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Try to click your mouse once every 2 seconds. The time interval between each click is recorded, as well as the error and percent error. Data can be displayed in a table, histogram, or scatter plot. Observe and measure the characteristics of the resulting distribution when large amounts of data are collected.
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Measure your reaction time by clicking your mouse as quickly as possible when visual or auditory stimuli are presented. The individual response times are recorded, as well as the mean and standard deviation for each test. A histogram of data shows overall trends in sight and sound response times. The type of test as well as the symbols and sounds used are chosen by the user.
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S02.04: : Determine if a data set approximates a normal distribution and explain the reasoning.
Sight vs. Sound Reactions
Measure your reaction time by clicking your mouse as quickly as possible when visual or auditory stimuli are presented. The individual response times are recorded, as well as the mean and standard deviation for each test. A histogram of data shows overall trends in sight and sound response times. The type of test as well as the symbols and sounds used are chosen by the user.
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S02.05: : Compare the properties of two or more normally distributed data sets.
Real-Time Histogram
Try to click your mouse once every 2 seconds. The time interval between each click is recorded, as well as the error and percent error. Data can be displayed in a table, histogram, or scatter plot. Observe and measure the characteristics of the resulting distribution when large amounts of data are collected.
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S02.07: : Solve a contextual problem that involves the interpretation of standard deviation.
Real-Time Histogram
Try to click your mouse once every 2 seconds. The time interval between each click is recorded, as well as the error and percent error. Data can be displayed in a table, histogram, or scatter plot. Observe and measure the characteristics of the resulting distribution when large amounts of data are collected.
5 Minute Preview
Measure your reaction time by clicking your mouse as quickly as possible when visual or auditory stimuli are presented. The individual response times are recorded, as well as the mean and standard deviation for each test. A histogram of data shows overall trends in sight and sound response times. The type of test as well as the symbols and sounds used are chosen by the user.
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S02.09: : Solve a contextual problem that involves normal distribution.
Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls.
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Try to click your mouse once every 2 seconds. The time interval between each click is recorded, as well as the error and percent error. Data can be displayed in a table, histogram, or scatter plot. Observe and measure the characteristics of the resulting distribution when large amounts of data are collected.
5 Minute Preview
Measure your reaction time by clicking your mouse as quickly as possible when visual or auditory stimuli are presented. The individual response times are recorded, as well as the mean and standard deviation for each test. A histogram of data shows overall trends in sight and sound response times. The type of test as well as the symbols and sounds used are chosen by the user.
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S02: : Students will be expected to interpret statistical data, using confidence intervals, confidence levels, and margin of error.
S02.01: : Explain, using examples, how confidence levels, margin of error, and confidence intervals may vary depending on the size of the random sample.
Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls.
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S02.02: : Explain, using examples, the significance of a confidence interval, margin of error, or confidence level.
Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls.
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RF01: : Students will be expected to model and solve problems that involve systems of linear inequalities in two variables.
RF01.01: : Model a problem using a system of linear inequalities in two variables.
Systems of Linear Inequalities (Slope-intercept form)
Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response.
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RF01.02: : Graph the boundary line between two half planes for each inequality in a system of linear inequalities, and justify the choice of solid or broken lines.
Systems of Linear Inequalities (Slope-intercept form)
Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response.
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RF01.03: : Determine and explain the solution region that satisfies a linear inequality, using a test point when given a boundary line.
Systems of Linear Inequalities (Slope-intercept form)
Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response.
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RF01.04: : Determine, graphically, the solution region for a system of linear inequalities, and verify the solution.
Systems of Linear Inequalities (Slope-intercept form)
Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response.
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RF01.05: : Explain, using examples, the significance of the shaded region in the graphical solution of a system of linear inequalities.
Systems of Linear Inequalities (Slope-intercept form)
Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response.
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RF01.06: : Solve an optimization problem using linear programming.
Linear Programming
Use the graph of the feasible region to find the maximum or minimum value of the objective function. Vary the coefficients of the objective function and vary the constraints. Explore how the graph of the feasible region changes in response.
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RF02: : Students will be expected to demonstrate an understanding of the characteristics of quadratic functions, including vertex, intercepts, domain and range, and axis of symmetry.
RF02.01: : Determine, with or without technology, the intercepts of the graph of a quadratic function.
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response.
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Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response.
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Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response.
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Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.
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RF02.02: : Determine, by factoring, the roots of a quadratic equation, and verify by substitution.
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response.
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Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response.
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RF02.03: : Determine, using the quadratic formula, the roots of a quadratic equation.
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.
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RF02.04: : Explain the relationships among the roots of an equation, the zeros of the corresponding function, and the x-intercepts of the graph of the function.
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response.
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Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response.
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Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.
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RF02.05: : Explain, using examples, why the graph of a quadratic function may have zero, one, or two x-intercepts.
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.
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RF02.06: : Express a quadratic equation in factored form, using the zeros of a corresponding function or the x-intercepts of its graph.
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response.
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RF02.07: : Determine, with or without technology, the coordinates of the vertex of the graph of a quadratic function.
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response.
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Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response.
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RF02.08: : Determine the equation of the axis of symmetry of the graph of a quadratic function, given x-intercepts of the graph.
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response.
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Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response.
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Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.
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RF02.09: : Determine the coordinates of the vertex of the graph of a quadratic function, given the equation of the function and the axis of symmetry, and determine if the y-coordinate of the vertex is a maximum or a minimum.
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response.
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Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response.
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RF02.11: : Sketch the graph of a quadratic function.
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response.
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Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response.
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RF02.12: : Solve a contextual problem that involves the characteristics of a quadratic function.
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response.
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Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.
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Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
