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Rigor/Relevance Framework 6 5 C D Knowledge Assimilation Adaptation 4 3 2 A B Acquisition Application 1 Gold Seal Lesson Mrs. Farner—Tavares High School 1 2 3 4 5 Application Subject MATHEMATICS/ SCIENCE Grades 9-12 Science as Inquiry: Students demonstrate knowledge and skills necessary to perform scientific Instructional inquiry. Focus Math: Students use a variety of tools and techniques of measurement in a problem-solving situation. Students communicate the reasoning used in solving these problems. Algebraic Concepts and Relationships: Students use algebraic methods to investigate, model, and interpret patterns and functions involving numbers, shapes, data, and graphs in a problem-solving situation. Students evaluate and communicate the reasoning used in solving these problems. 1. Students will approximate initial velocity of a golf ball by calculating the velocity when someone Performance swings in only one direction. Since measuring the velocity of an object going straight up could be Task difficult, students are to measure in the horizontal direction. a. Start from your initial position (you can assume it to be the origin). b. You will make the “hole” at a set distance of 100 cm. Hit the ball with no vertical change (θ=0). Calculate your velocity 5 times; the average will be your initial velocity (V). You are going to swing your club at a (hopefully) constant rate. (See graph #1) Initial Velocity V = _________ 2. Measure out approximately 100 paces away from the “hole”. This will be your tee off point or your new origin. Measure exactly the distance from your origin to the hole using your measuring tape. This value will be your x value (horizontal distance). What would the y value be at this point? (______,______) 3. We are now going to hit the golf ball in parabolic trajectories. Would the center of the parabola act as a maximum or a minimum? Using your initial velocity calculated in Part 1 and the point of the hole in Part 2, you can calculate how long it should take the ball to reach the hole using the given parametric m equations and the constant g 9.81 . s2 How long would it take to make a hole in one if you putted the ball from your origin? x vx t 1 2 y vyt gt 2 vx V cos v y V sin 4. We are now going to try to make the hole with different angles on our shots. You will use the protractor and a piece of string to make the angle as close to exact as possible. You need to hit the ball with as close to the same velocity as possible. Calculate the time it should take to make it to the hole for each of the following angles. After you calculate the times, perform the experiment and record your observed times. x vx t 1 2 y vyt gt 2 vx V cos v y V sin (See graph #2) Are the calculated times the same as the observed times? Why do you think so? Would the time to the hole be the same (theoretically) if we hit the ball at 45° and 135°? 5. We are going to locate the vertex of parabolic trajectory with an initial angle measure of 45 degrees. We can easily solve for the x coordinate given the initial point (origin) and point of the “hole”. Where would the vertex of the parabola be located? In the center or could it be off to one side? How do you know? What does gravity have to do with location of the vertex? 6. Now that you have two points and the vertex (h,k) of your parabolic trajectory, you can solve for the equation. y a ( x h) 2 k 7. We have measured the physical parameters of projectile motion and then using that data analyzed them using various mathematical tools. Since the data was collected within the earth’s 7. We have measured the physical parameters of projectile motion and then using that data Performance analyzed them using various mathematical tools. Since the data was collected within the earth’s Task (cont.) gravitation g 9.81 m . How far would the golf ball travel if we did the experiment on other s2 planets? How high? How long would it be in flight? The data in table #3 can be used to calculate the answer to these questions: Scoring Guide Below Meets Exceeds TOTAL Outcomes with Criteria St'ds St'ds St'ds 1. Understanding of Physical Concepts Motion accurately represented in multiple formats (graphs, words, data, equations) 0-2 3-4 5-6 _____ showed accurate and complete 0-1 2 3 (out of calculations with units 12) 0-1 2 3 accurately described the motion of the golf ball using the language of physics 2. Experimentation used a trial and error method to effectively manipulate materials to 0-2 3-4 5-6 accomplish the proposed purpose data collection and reporting was accurate _____ and complete 0-1 2-3 4 (out of 17) interpretation and analysis of data was accurately and explicitly shown 0-1 2-3 4-5 proposed an appropriate and succinct 0 1 2 conclusion 3. Technology Usage submitted an attractively formatted, completely word-processed lab report 0-2 3-4 5-6 (including a data table organized in a row/column format) _____ successfully used Graphical Analysis to 0-1 2-3 4 __ plot and display data in report (out of generated a Sound 3.01 chart and included 0 2 4 16) it in report 0-1 2-3 2 electronically sized, copied, and pasted all graphs, charts, and diagrams into the word processed document. 4. Communication submitted a formal lab report containing all the customary sections, including data 1-2 3-4 5-6 in table form 1-2 3-4 5-6 presentation of data was organized and _____ easy to follow submitted a lab report _ which captures the essence of the experiment in an organized and (out of 1 2 3 15) informative manner; has style and is attractive followed rules of grammar, sentence construction, and punctuation; spelling errors were minimized Essential Science Sunshine State Standards Force and Motion Skills Standard 1: The student understands that types of motion may be described, measured, and predicted. (SC.C.1.4) 1. knows that all motion is relative to whatever frame of reference is chosen and that there is no absolute frame of reference from which to observe all motion. 2. knows that any change in velocity is an acceleration. Standard 2: The student understands that the types of force that act on an object and the effect of that force can be described, measured, and predicted. (SC.C.2.4) 1. knows that acceleration due to gravitational force is proportional to mass and inversely proportional to the square of the distance between the objects. 6. explains that all forces come in pairs commonly called action and reaction. The Nature of Science Standard 1: The student uses the scientific processes and habits of mind to solve problems. (SC.H.1.4) 1. knows that investigations are conducted to explore new phenomena, to check on previous results, to test how well a theory predicts, and to compare different theories. 7. understands the importance of a sense of responsibility, a commitment to peer review, truthful reporting of the methods and outcomes of investigations, and making the public aware of the findings. Standard 3: The student understands that science, technology, and society are interwoven and interdependent. (SC.H.3.4) 1.knows that performance testing is often conducted using small-scale models, computer simulations, or analogous systems to reduce the chance of system failure. 6. knows that scientific knowledge is used by those who engage in design and technology to solve practical problems, taking human values and limitations into account Mathematics Sunshine State Standards MA.A. 3.4.1 Understands and explains the affect of addition, subtraction, multiplication, and division on real numbers. MA.B. 1.4.2 Uses concrete and graphic models to derive formulas for finding rate, distance, time, angle measure, and arc lengths. MA.B.2.4.2 Solves real world problems involving rated measure (miles per hour, feet per second). MA.C.3.4.1 Using a rectangular coordinate system, applies and algebraically verifies properties of two- and three-dimensional figures MA.E. 1.4.1 Interprets data that has been collected, organized, and displayed in charts, tables, and plots. Pictures, Graph #1 Tables, d rt Graphs, Etc. Putt 1 Putt 2 Putt 3 Putt 4 Putt 5 Distance (cm) Time (s) Velocity (cm/s) Graph #2 Angle Time Calculated Time Observed 30° 45° 60° Graph #3 Planet Relative Surface Gravity Absolute Surface Gravity (m/sec2) Mercury 0.38 3.73 Venus 0.91 8.93 Earth 1.00 9.81 (sea level) Mars 0.38 3.73 Jupiter 2.34 22.96 Saturn 1.06 10.40 Uranus 0.92 9.03 Neptune 1.19 11.67 Pluto 0.06 0.59