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RET: Aligning Research Projects with Standards and ExpectationsProject: Laser Pointing and Tracking with a DroneActivity in ProjectCurriculumStrandRelevant StandardExpectations Under StandardLearningOutcomesCalculate the angle the drone must move through to have the laser diode point at a particular spot in space that is different from the current spot it is pointing at.Create coordinates for current point and target point with respect to drone. Calculate angles of triangle based on: right triangle (for two points on a flat surface such as a wall), Direct measurement of one angle and calculation of others.Geometry: Two-Dimensional Shapes (G.2D)G.2D.1 Discover, evaluate and analyze the relationships between lines, angles, and polygons to solve real-world and mathematical problems; express proofs in a form that clearly justifies the reasoning, such as two-column proofs, paragraph proofs, flow charts, or illustrations.G.2D.1.1 Apply the properties of parallel and perpendicular lines, including properties of angles formed by a transversal, to solve real-world mathematical problems and determine if two lines are parallel, using algebraic reasoning and proofs. G.2D.1.2 Apply the properties of angles, including corresponding, exterior, interior, vertical, complementary, and supplementary angles to solve real-world and mathematical problems using algebraic reasoning and proofs.G.2D.1.5 Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints, and slopes of line segments.Students will be able to:Identify and use perpendicular lines to identify right angles, especially in trianglesUse the properties of corresponding, complementary, and supplementary angles to calculate the angle of rotation a drone needs to execute to perform a desired action.Calculate the length of a line segment from two coordinate pointsCalculate the lengths of the sides of a triangle from three coordinate points.Calculate the angle the drone must move through to point the laser diode at a particular spot in space that is different from the current spot it is pointing at.Frame the problem in terms of moving the drone through an arc of a circle, where the drone is at the center, the distance to the initial point is the radius, the line along the wall is the tangent, etc.Geometry: Circles (G.C)G.C.1 Solve real-world and mathematical problems using the properties of circles.G.C.1.2 Apply the properties of circles and relationships among angles, arcs, and distances in a circle among radii, chords, secants and tangents to solve problems using algebraic and logical reasoning.Students will be able to:Use the properties of circles to calculate the angle a drone must rotate through to move the laser pointer to a specific point, or to track a moving object.Frame the drone rotation and tracking problem using radius, arc or arc length, tangents, and/or secants.Calculate the angle the drone must move through to point the laser diode at a particular spot in space that is different from the current spot it is pointing at.Using measurements, in both 2D and 3D, calculate angles – both vertical and horizontal (attitude, pitch, roll) the drone must move through, for the purpose of programming movement, using the trigonometry of right triangles.Geometry: Right Triangle Geometry (G.RT)G.RT.1 Develop and verify mathematical relationships of right triangles and trigonometric ratios to solve real-world and mathematical problems.G.RT.1.1 Apply the distance formula and the Pythagoren Theorem and its converse to solve real-world and mathematical problems, as approximate and exact values, using algebraic and logical reasoning (include Pythagorean Triples).G.RT.1.3 Use the definition of the trigonometric functions to determine the sine, cosine, and tangent ratio of an acute angle in a right triangle. Apply the inverse trigonometric functions to find the measure of an acute angle in right triangles.Students will be able to:Calculate the angles in right triangles given measurements or calculations of the side lengths.Draw right triangles for the overall movement and for separate movements in the vertical and horizontal directions.Use right triangles and trigonometric functions to calculate separate angular measurements for the vertical and horizontal rotations of the drone, corresponding to the terms attitude, pitch, and roll.Solving geometrical formulas to find the angles, solving algebraic formulas to find the error between predicted and real, solving statistical formulas to find mean and standard deviation of multiple trials to assess accuracy.Algebraic Reasoning and Algebra (A)Algebra 1A1.A.1 Represent and solve mathematical and real-world problems using linear equations, absolute value equations, and systems of equations; interpret solutions in the original context.A1.A.1.1 Use knowledge of solving equations with rational values to represent and solve mathematical and real-world problems (e.g. angle measures, geometric formulas, science, or statistics) and interpret solutions in the original context.Students will be able to:Solve a set of equations based on geometry of right triangles and circles to find an angle or the side of a triangle.Write the error between the target location and the actual location of the laser pointer as an algebraic equation.Solve for the error for a number of different experimental trials using the algebraic equation for the error.Solving algebraic formulas for calculating the mean and standard deviation using the measured experimental data.Predicting the motion of an object based on equations or graphs of position vs. time, in order to tell the quadcopter where to point and when.Algebraic Reasoning and Algebra (A)Algebra 1A1.A.4 Analyze mathematical change involving linear equations in real-world and mathematical problemsA1.A.4.1 Calculate and interpret slope and the x- and y-intercepts of a line using a graph, an equation, two points, or a set of data points to solve real-world and mathematical problems.Students will be able to:Calculate the slope of the line describing the movement of an object, and connect the slope to the speed of object movement.Use the equation, and particularly the slope, of the line to predict where the object will be at a later time, so the drone can track the object correctly.Predicting the motion of an object based on equations or graphs of position vs. time, in order to tell the quadcopter where to point and when.Functions (F)Algebra 1A1.F.1 Understand functions as descriptions of covariation (how related quantities vary together) in real-world and mathematical problemsA1.F.1.3 Write linear functions, using function notation, to model real-world and mathematical situations.Students will be able to:Write a linear function of the movement of an object based on either measured or given data points describing the movementShow that the function describes how the object’s position varies together with variations in time.Predicting the motion of an object based on equations or graphs of position vs. time, in order to tell the quadcopter where to point and when.Functions (F)Algebra 1A1.F.3 Represent functions in multiple ways and use the representation to interpret real-world and mathematical problems.A1.F.3.1 Identify and generate equivalent representations of linear equations, graphs, tables, and real-world situations.A1.F.3.2 Evaluate a function at a given point in its domain and interpret the results in terms of real-world problems.Students will be able to:Use a table of measured points to generate an equivalent linear equation and/or graph of the object’s movement.Predict where the object will move next by evaluating the function at a future time and connecting the resulting number to a physical point in space.Measure, assess, and describe the statistical results of many trials when attempting to point the laser pointer at a target spot in space. Assess the ability of the drone to move accurately in a repeatable way.Data and Probability (D)Algebra 1A1.D.1 Display, describe, and compare data. For linear relationships, make predictions and assess the reliability of those predictions.A1.D.1.1 Describe a data set using data displays, describe and compare data sets using summary statistics, including measures of central tendency, location, and spread. Know how to use calculators, spreadsheets, or other appropriate technology to display data and calculate summary statistics. A1.D.1.2 Collect data and use scatter plots to analyze patterns and describe linear relationships between variables. Using graphing technology, determine regression lines and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions. .Students will be able to:Display the measured data using a graph or other data display, either through spreadsheets or other graphing technology.Calculate the mean, standard deviation (or average error or mean squared error) and location in space of each. Use the calculated mean and error data to describe the accuracy with which the drone points the laser pointer.Use the calculated data to describe the relationship between position accuracy and the angle of movement of the drone.Use regression lines and correlation coefficients to make predictions about the error observed for a larger or smaller rotation angle and then verify the prediction.Fitting of statistical data to normal or other distributions, evaluate the relationship between two variables (say angle moved and accuracy achieved, for example).Data and Probability (D)Algebra 2A2.D.1 Display, describe, and compare data. For linear and nonlinear relationships, make prediction and assess the reliability of those predictions.A2.D.1.1 Use the mean and standard deviation of a data set to fit it to a normal distribution (bell-shaped curve)A2.D.1.2 Collect data and use scatter plots to analyze patterns and describe linear, exponential or quadratic relationships between two variables. Using graphing calculators or other appropriate technology, determine regression equation and correlation coefficients; use regression equations to make predictions and correlation coefficients to assess the reliability of those predictions.Students will be able to:Display the measured data using a graph or other data display, either through spreadsheets or other graphing technology.Calculate the mean, standard deviation (or average error or mean squared error) and location in space of each. Use the calculated mean and error data to describe the accuracy with which the drone points the laser pointer.Use the calculated data to describe the relationship between position accuracy and the angle of movement of the drone.Use regression lines and correlation coefficients to make predictions about the error observed for a larger or smaller rotation angle and then verify the Use data analysis tools and algorithms to evaluate the statistical data and identify puter ScienceLevel 2Collection, Visualization and TransformationL2.DA.CVT.01 Use data analysis tools and techniques to identify patterns from complex real-world data.Students will be able to:Use analysis tools other than spreadsheets or graphing calculators to analyze the statistical properties of the collected data on pointing or tracking accuracy.Use analysis tools or develop programs to identify the relationship between angle size and level of accuracy, based on the collected or presented data.A laser diode circuit that sends codes (on-off codes such as binary, Morse code, or pulse-width modulation – latter for more advanced courses) could replace laser pointer. Students evaluate the effect of their system on the ability to communicate over distance. Students can discuss advantages of sending light over air and the free-space optical technology, depending on the level of the class.High School, Physical Science (HS-PS4)HP-PS4-2 Waves and their applications in technologies for information transfer.HP-PS4-5 Waves and their applications in technologies for information rmation can be digitized (e.g., a picture stored as the values of an array of pixels); in this form, it can be stored reliably in computer memory and sent over long distances as a series of wave pulses.Photoelectric materials emit electrons when they absorb light of a high-enough frequency.Multiple technologies based on the understanding of waves and their interactions with matter are part of every day experiences in the modern world (e.g., medical imaging, communications, scanners) and in scientific research. They are essential tools for producing, transmitting, and capturing signals and for storing and interpreting the information contained in them. Students will be able to:Discuss the different ways to encode signals on electromagnetic waves, including binary, Morse code, and pulse-width modulation.Discuss how optical waves transmit the variations of the encoding methods described above, and why you might transmit data in this way.Discuss and evaluate the operation of one or more photoelectric devices (detectors), such as measuring the responsivity (conversion factor) between optical power and electric current.Evaluate how the stability of the system impacts the accuracy or effectiveness of the communication system. Evaluate the effect of one variable (say distance) on the system stability. ................
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